Resources for Teaching Mathematics



Resources for Teaching Mathematics

| |Page |

|ABE Mathematics Verification Checklists |101 |

|Examples of Where Adults Use Mathematics |125 |

|Mathematics Sample Teaching Activities |147 |

|Mathematics Glossary |184 |

|Mathematics Internet Resources |195 |

ABE Mathematics Verification Checklist Level 1 – Grade Level 0.0 - 1.9

|Student |Instructor |Date Enrolled |

| | | |

|M.1.1 Number Sense and Operations |Date |Initials |

|M.1.1.1 Associate numbers and words for numbers | | |

|with quantities. | | |

|M.1.1.2 Demonstrate an understanding that if items | | |

|are rearranged, the numbers stay the same. | | |

|M.1.1.3 Read, write, order, and compare numbers | | |

|from 0 to 100. | | |

|M.1.1.4 Recognize and count numbers through 999. | | |

|M.1.1.5 Count by 2s, 5s, and 10s up to 100. | | |

|M.1.1.6 Identify even and odd numbers. | | |

|M.1.1.7 Add whole numbers up to three digits | | |

|(without carrying). | | |

|M.1.1.8 Demonstrate understanding of the concept of| | |

|subtraction, i.e., as in taking away or separating,| | |

|from numbers up to twenty. | | |

|M.1.1.9 Subtract whole numbers up to three digits | | |

|(without borrowing). | | |

|M.1.1.10 Demonstrate an understanding of the times | | |

|tables for the numbers 1, 2, 4, and 10. | | |

|M.1.1.11 Halve even numbers up to 10 and double | | |

|whole numbers up to 10. | | |

|M.1.1.12 Identify place value of ones, tens, and | | |

|hundreds. | | |

|M.1.1.13 Identify basic functions (+, -, x, (, =, | | |

|on/off) on the calculator and digits (0-9). | | |

|M.1.1.14 Identify fractional parts (1/4, 1/3, 1/2) | | |

|and whole. | | |

|M.1.1.15 Recognize currency (up to $20.00) and | | |

|coins; count and trade pennies, nickels, dimes, and| | |

|quarters to 100 cents. | | |

|M.1.1.16 Make and verify change. | | |

| | |

|M.2.1 Measurement |Date |Initials |

|M.2.1.1 Recognize and record time to the nearest | | |

|hour and half hour, from an analog and digital | | |

|clock, including understanding the meaning between | | |

|am and pm. | | |

|M.2.1.2 Interpret numeric representations of dates.| | |

|M.2.1.3 Understand use of standard US linear | | |

|measurements (inches, feet). | | |

|M.2.1.4 Understand use of standard US capacity | | |

|measurements (cups, pints, quarts, and gallons). | | |

|M.3.1 Geometry |Date |Initials |

|M.3.1.1 Model and use directional and positional | | |

|vocabulary appropriately. | | |

|M.3.1.2 Demonstrate an understanding of perimeter | | |

|being the measure around the outside edges of | | |

|squares and rectangles. | | |

|M.3.1.3 Identify and describe the properties of | | |

|common two-dimensional shapes (square, circle, | | |

|rectangle, triangle) using everyday language | | |

|(straight, curved, etc.). | | |

| | |

|M.4.1 Data Analysis and Probability |Date |Initials |

|M.4.1.1 Identify and name various simple visual | | |

|data (graphs, charts, tables) found in authentic | | |

|publications. | | |

|M.4.1.2 Interpret data organized in basic | | |

|categories and groupings. | | |

|M.4.1.3 Collect, label, and order numerical | | |

|information for a particular purpose (e.g., to | | |

|count and list stock). | | |

| | |

|M.5.1 Algebra |Date |Initials |

|M.5.1.1 Identify basic number patterns and | | |

|relationships inherent in addition and subtraction.| | |

|M.5.1.2 Sort up to 20 objects or lists by color, | | |

|shape, number, letter, or size. | | |

|M.5.1.3 Understand and complete simple number | | |

|sentences. | | |

ABE Mathematics Verification Checklist Level 2 – Grade Level 2.0 - 3.9 Page 1 of 2

|Student |Instructor |Date Enrolled |

| | | |

|M.1.2 Number Sense and Operations |Date |Initials |

|M.1.2.1 Read, write, order, and compare numbers in | | |

|the thousands including identifying place value. | | |

|M.1.2.2 Demonstrate understanding of the concept of | | |

|addition (i.e., as in adding on or combining), | | |

|including the role of place value. | | |

|M.1.2.3 Add whole numbers up to three digits using | | |

|carrying. | | |

|M.1.2.4 Subtract whole numbers up to three digits | | |

|using borrowing and checking. Demonstrate an | | |

|understanding of how addition and subtraction relate | | |

|to each other by checking answers using addition. | | |

|M.1.2.5 Demonstrate understanding of the concept of | | |

|multiplication, including the role of place value. | | |

|M.1.2.6 Demonstrate an understanding of multiplying | | |

|by 10 and 100. | | |

|M.1.2.7 Multiply whole numbers up to three digits by | | |

|one digit using carrying. | | |

|M.1.2.8 Demonstrate understanding of the concept of | | |

|division including the role of place value. | | |

|M.1.2.9 Divide whole numbers up to hundreds by one | | |

|digit. | | |

|M.1.2.10 Use rounding and estimation for tens and | | |

|hundreds. | | |

|M.1.2.11 Demonstrate an understanding that even | | |

|numbers can be paired and that odd numbers represent | | |

|amounts that when paired have one remaining. | | |

|M.1.2.12 Know all pairs of numbers with a total of | | |

|10. | | |

|M.1.2.13 Identify multiples of 2, 3, 4, 5, and 10 up | | |

|to x 10. | | |

|M.1.2.14 Demonstrate an understanding of the times | | |

|tables for the numbers 0 to 12. | | |

|M.1.2.15 Identify factoring of common numbers (e.g., | | |

|12 = 4x3 = 2x6 = 2x2x3). | | |

|M.1.2.16 Divide numbers by 10 and 100 and | | |

|back-multiply to check results of division. | | |

|M.1.2.17 Identify and demonstrate an understanding of| | |

|fractional parts including 1/8, 1/4, 1/3, 1/2, and | | |

|whole. | | |

|M.1.2.18 Demonstrate how fractions relate to | | |

|multiplication and division. | | |

|M.1.2.19 Add and subtract common fractions with like | | |

|denominators. | | |

|M.1.2.20 Identify improper fractions and mixed | | |

|numbers. | | |

|M.1.2.21 Identify and write amounts of money using | | |

|decimals, words, and symbols. | | |

|M.1.2.22 Demonstrate an understanding of decimal | | |

|notation and place value by reading, writing, | | |

|ordering, and comparing decimals to two decimal | | |

|places. | | |

|M.1.2.23 Convert and express simple common | | |

|fractions as decimals. | | |

|M.1.2.24 Show relationship between decimal system | | |

|and money. | | |

| | |

|M.2.2 Measurement |Date |Initials |

|M.2.2.1 Identify equivalent amounts of money using | | |

|different bills and coins. | | |

|M.2.2.2 Read, record, and use date concepts | | |

|(months, days of week) in common formats. | | |

|M.2.2.3 Read, record, and understand time of day. | | |

|M.2.2.4 Telling time to the nearest minute. | | |

|M.2.2.5 Identify halves and whole numbers on a | | |

|ruler (inches) and develop personal reference point| | |

|for one’s height. | | |

|M.2.2.6 Identify halves and whole numbers on weight| | |

|scales (pounds) and develop personal reference | | |

|point for one’s weight. | | |

|M.2.2.7 Identify and select appropriate measures | | |

|for capacity and weight. | | |

|M.2.2.8 Interpret temperature from Fahrenheit scale| | |

|in various situations, including negative | | |

|temperatures. | | |

|M.2.2.9 Read and record time of day in 24-hour | | |

|format. | | |

|M.2.2.10 Convert units of time: hours, minutes, and| | |

|seconds. | | |

|M.2.2.11 Identify customary US units of linear | | |

|measurement and equivalents: inches, feet, yards, | | |

|and miles. | | |

|M.2.2.12 Measure length, width, height, and | | |

|perimeter in inches, feet, and yards using a ruler | | |

|or tape measure. | | |

|M.2.2.13 Make rough-estimate approximations of | | |

|standard US measurements. | | |

|M.2.2.14 Read, interpret, and use map legends/keys.| | |

ABE Mathematics Verification Checklist Level 2 – Grade Level 2.0 - 3.9 Page 2 of 2

|Student |Instructor |Date Enrolled |

| | | |

|M.3.2 Geometry |Date |Initials |

|M.3.2.1 Demonstrate an understanding of the | | |

|concepts of sameness and halfness, i.e., identify | | |

|and show where line(s) of symmetry (i.e., the lines| | |

|that divide something into 2 equal parts) falls in | | |

|two-dimensional figures. | | |

|M.3.2.2 Use the four main compass directions (N, S,| | |

|E, W) for spatial orientation. | | |

|M.3.2.3 Define and correctly use the concept of | | |

|horizontal and vertical positions. | | |

|M.3.2.4 Follow a pattern or model to produce or | | |

|reproduce a shape or object. | | |

| | |

|M.4.2 Data Analysis and Probability |Date |Initials |

|M.4.2.1 Solve problems using simple graphs | | |

|(pictograph, bar, line, and circle), tables, or | | |

|distances on maps. | | |

|M.4.2.2 Identify, count, extract, and interpret | | |

|pertinent data organized in lists, tables, and | | |

|charts. | | |

|M.4.2.3 Reorient, reorganize, and reformat simple | | |

|data, i.e., create a table to record and present | | |

|numerical information. | | |

|M.4.2.4 Collect, label, and order numerical | | |

|information for a particular purpose (e.g., keep a | | |

|log, etc.). | | |

|M.4.2.5 Identify and interpret simple graphs, | | |

|tables, etc. | | |

|M.4.2.6 Read values on and make comparative | | |

|statements about relative values on a simple bar | | |

|graph. | | |

|M.4.2.7 Develop an understanding of events as | | |

|certain, impossible, likely, or unlikely to occur. | | |

|M.4.2.8 Determine the probability of simple events,| | |

|e.g., in the results of tossing a coin or rolling a| | |

|die, etc. | | |

|M.5.2 Algebra |Date |Initials |

|M.5.2.1 Recognize and create simple repeating | | |

|patterns using three or less items (e.g., color, | | |

|rhythmic, shape, number, and letter) and identify | | |

|the unit being repeated. | | |

|M.5.2.2 Identify basic number patterns and | | |

|relationships inherent in multiplication and | | |

|division (e.g., identify halves, doubles, and | | |

|triples of numbers). | | |

|M.5.2.3 Describe quantitative change, i.e., change | | |

|in the number of daylight hours or temperature over| | |

|time. | | |

|M.5.2.4 Interpret simple English word phrases, | | |

|i.e., mathematical expressions, equations, and | | |

|variables and write algebraic expressions. | | |

|M.5.2.5 Recognize, interpret, and use basic | | |

|mathematical symbols (+, -, =, ) and recognize | | |

|the different vocabulary used to represent each. | | |

|M.5.2.6 Translate simple mathematical expressions | | |

|involving +, -, . | | |

|M.5.2.7 Use a calculator to make basic calculations| | |

|and solve simple addition, subtraction, | | |

|multiplication, and division problems and check | | |

|solutions. | | |

|M.5.2.8 Solve single step, real-life word problems | | |

|involving addition, subtraction, multiplication, | | |

|and division using up to two digit whole numbers. | | |

|M.5.2.9 Determine and use appropriate rounding and | | |

|estimating techniques. Understand that the number | | |

|"5" rounds up. | | |

ABE Mathematics Verification Checklist Level 3 – Grade Level 4.0 - 5.9 Page 1 of 4

|Student |Instructor |Date Enrolled |

| | | |

|M.1.3 Number Sense and Operations |Date |Initials |

|M.1.3.1 Read, write, order, and compare large whole| | |

|numbers. | | |

|M.1.3.2 Identify place value in large whole numbers| | |

|and round off large whole numbers to nearest tens, | | |

|hundreds, thousands, ten-thousands, | | |

|hundred-thousands, million, etc. | | |

|M.1.3.3 Interpret the inverse relationship between | | |

|addition and subtraction and multiplication and | | |

|division. | | |

|M.1.3.4 Demonstrate an understanding of the | | |

|commutative and associative properties of addition | | |

|and multiplication. | | |

|M.1.3.5 Demonstrate an understanding of factors of | | |

|numbers up to 100. | | |

|M.1.3.6 Demonstrate an understanding of dividing by| | |

|multi-digit numbers and interpreting remainder and | | |

|expressing them as whole numbers, fractions, and | | |

|decimals. | | |

|M.1.3.7 Demonstrate an understanding of | | |

|back-multiplying to check results of division. | | |

|M.1.3.8 Demonstrate an understanding of prime | | |

|numbers and identify prime numbers up to 20. | | |

|M.1.3.9 Add and subtract whole numbers up to four | | |

|digits using efficient methods and checking | | |

|answers. | | |

|M.1.3.10 Multiply with two and three digit numbers | | |

|using efficient written methods including checking | | |

|answers. | | |

|M.1.3.11 Identify and calculate equivalent | | |

|fractions (fourths, thirds, halves, eighths, | | |

|fifths, and tenths) and simplify fractions to | | |

|lowest terms. | | |

|M.1.3.12 Convert improper fractions to mixed | | |

|numbers and mixed numbers to improper fractions. | | |

|M.1.3.13 Add and subtract fractions (fourths, | | |

|thirds, halves, eighths, fifths, and tenths) using | | |

|fractions that include like and unlike denominators| | |

|and whole and mixed numbers. | | |

|M.1.3.14 Multiply and divide by fractions (fourths,| | |

|thirds, halves, eighths, fifths, and tenths) using | | |

|fractions that include like and unlike denominators| | |

|and whole and mixed numbers. | | |

|M.1.3.15 Relate multiplication of fractions and | | |

|division. | | |

|M.1.3.16 Express a relationship between two | | |

|quantities as a fraction or fractional estimate. | | |

|M.1.3.17 Identify quantities that are proportional. | | |

|M.1.3.18 Interpret the meaning of ratio and express a | | |

|relationship between two quantities as a ratio. | | |

|M.1.3.19 Read, write, order, and compare decimals of | | |

|up to three decimal places. | | |

|M.1.3.20 Identify place value for decimals and round | | |

|decimals to one or two places or whole numbers. | | |

|M.1.3.21 Compute percentages when part and whole are | | |

|given using friendly numbers. | | |

|M.1.3.22 Convert decimals to fractions and percents, | | |

|fractions to decimals and percents, and percents to | | |

|fractions and decimals. | | |

|M.1.3.23 Add, subtract, multiply, and divide numbers | | |

|with decimals. | | |

|M.1.3.24 Read and write large numbers with decimals. | | |

|M.1.3.25 Determine a fraction or percent of a decimal.| | |

|M.1.3.26 Understand and interpret the meaning of | | |

|percent, i.e., percent represents a ratio of a part to| | |

|a whole where the whole is 100. | | |

|M.1.3.27 Read, write, order, and compare simple | | |

|percentages. | | |

|M.1.3.28 Find given percents of any given number. | | |

| |

|M.2.3 Measurement |Date |Initial|

| | |s |

|M.2.3.1 Calculate units of time using a clock (both 12| | |

|and 24 hour) and a calendar. | | |

|M.2.3.2 Identify and select appropriate metric | | |

|measurements. | | |

|M.2.3.3 Add, subtract, multiply, and divide sums of | | |

|money. | | |

|M.2.3.4 Demonstrate an understanding of the | | |

|interrelation of distance, time, and speed and make | | |

|simple calculations using distance, time, and speed | | |

|formula. | | |

|M.2.3.5 Read and interpret map scales, legends, and | | |

|mileage tables. | | |

|M.2.3.6 Measure with a standard ruler in inches and | | |

|feet to 1/16 inch accuracy and a metric ruler in cm | | |

|and mm. | | |

|M.2.3.7 Make informal comparisons between inches and | | |

|centimeters including estimating the number of | | |

|centimeters per inch. Create physical (bodily) | | |

|benchmarks for units. | | |

ABE Mathematics Verification Checklist Level 3 – Grade Level 4.0 - 5.9 Page 2 of 4

|Student |Instructor |Date Enrolled |

| | | |

|M.2.3 Measurement, cont. |Date |Initials |

|M.2.3.8 Convert and calculate with linear | | |

|measurements (inches, feet, yards, miles) and know | | |

|the relationship of familiar units and convert | | |

|units of measure in the same systems. | | |

|M.2.3.9 Use and apply concepts of weight and | | |

|capacity to solve problems. | | |

|M.2.3.10 Use, read, compare, and calculate with | | |

|positive and negative Fahrenheit temperatures, | | |

|i.e., know that temperature increases as it goes up| | |

|and decreases as it goes down and that the sign of | | |

|the temperature changes when crossing the zero | | |

|degree point. | | |

|M.2.3.11 Calculate times using the appropriate | | |

|value and convert between time formats (including | | |

|elapsed time), i.e., know equivalencies for hours, | | |

|seconds, minutes, days, weeks, months, decades, and| | |

|centuries. | | |

|M.2.3.12 Directly measure perimeter in linear units| | |

|and area in square units (sq. in., sq. ft., sq. | | |

|cm.). | | |

|M.2.3.13 Estimate, measure, and compare weights | | |

|(pounds, ounces) using simple instruments, | | |

|graduated in familiar units (ounces and pounds) and| | |

|know when to use appropriate measures. | | |

|M.2.3.14 Convert and calculate using standard US | | |

|units of weight: tons, pounds, ounces, etc. | | |

|M.2.3.15 Convert and calculate using standard US | | |

|units of capacity: ounces, quarts, and gallons. | | |

|M.2.3.16 Demonstrate an understanding of the | | |

|concept of two-dimensional measurements and square | | |

|units. | | |

|M.2.3.17 Read analog and digital scales on | | |

|measuring devices including meters, gauges, scales,| | |

|etc. using various types of units and calibrations.| | |

|M.3.3 Geometry |Date |Initials |

|M.3.3.1 Recognize, identify, and describe basic | | |

|geometric shapes (triangle, square, circle, | | |

|rectangle, hexagon, pentagon, and octagon). | | |

|M.3.3.2 Draw 2-D shapes of specific dimensions. | | |

|M.3.3.3 Use informal visual methods to describe and| | |

|compare shape, dimension, perimeter, area, angles, | | |

|and sides in 2-D and 3-D objects. | | |

|M.3.3.4 Identify properties, locations, and | | |

|functions of right angles, i.e., know that a right | | |

|angle is 90 degrees or a quarter turn, that two | | |

|right angles make a straight line, and four right | | |

|angles fill a space. | | |

|M.3.3.5 Use direction, distance, coordinates, | | |

|latitude, longitude, simple scales, labels, | | |

|symbols, and keys to read and use maps and plans. | | |

|M.3.3.6 Use graph paper to draw 2-D shapes in | | |

|different orientations on a grid. | | |

|M.3.3.7 Calculate the area of squares, rectangles, | | |

|and triangles and other common figures using given | | |

|formulas. | | |

|M.3.3.8 Recognize, identify, and describe the | | |

|properties of common 3-D shapes, i.e., cube, | | |

|cylinder, and sphere. | | |

|M.3.3.9 Identify triangles based on their | | |

|properties, i.e., right, isosceles, equilateral, | | |

|scalene, obtuse, and acute. | | |

|M.3.3.10 Identify common polygons of various | | |

|shapes, i.e., triangles, quadrilaterals, pentagons,| | |

|hexagons, and octagons. | | |

|M.3.3.11 Identify parallel, perpendicular, and | | |

|intersecting lines. | | |

|M.3.3.12 Describe characteristics of angles formed | | |

|by two intersecting lines, i.e., vertical, | | |

|supplementary, complementary, adjacent, and | | |

|corresponding/ congruent. | | |

|M.3.3.13 Identify angles of 90 and 45 degrees, | | |

|right, acute, and obtuse. | | |

|M.3.3.14 Use the secondary directions for spatial | | |

|orientation (e.g., NW, SW, NE, SE). | | |

|M.3.3.15 Use a map with a coordinate grid. | | |

|M.3.3.16 Create 3-D objects from 2-D | | |

|representations. | | |

ABE Mathematics Verification Checklist Level 3 – Grade Level 4.0 - 5.9 Page 3 of 4

|Student |Instructor |Date Enrolled |

| | | |

|M.4.3 Data Analysis and Probability |Date |Initials |

|M.4.3.1 Identify, describe, and compare how a | | |

|change in one variable relates to a change in a | | |

|second variable. | | |

|M.4.3.2 Demonstrate an understanding of the concept| | |

|of categories such as shape, size, color, or yes/no| | |

|responses and know how to count each category for | | |

|subtotals. | | |

|M.4.3.3 Represent information so that it makes | | |

|sense to others. | | |

|M.4.3.4 Demonstrate an understanding that when | | |

|objects or responses are divided into categories, | | |

|all data must be included in one and only one | | |

|category; therefore, categories must identify | | |

|distinct sets. | | |

|M.4.3.5 Demonstrate an understanding of scatter | | |

|plots, i.e., that each X in a line plot represents | | |

|one and only one item or response; therefore, it is| | |

|verifiable that the number of responses is equal to| | |

|the number of X’s. | | |

|M.4.3.6 Demonstrate an understanding that a graph | | |

|is a visual representation and a table arranges | | |

|information in rows and columns. | | |

|M.4.3.7 Sort graphs and tables by type. | | |

|M.4.3.8 Demonstrate an understanding that lists and| | |

|tables can be ordered in different ways such as | | |

|alphabetically, numerically, or randomly. | | |

|M.4.3.9 Compare relative values on a bar graph. | | |

|M.4.3.10 Determine whether or not a graph/table | | |

|connects to statements made in text using title, | | |

|data labels, and percent matches. | | |

|M.4.3.11 Support simple statements with data and | | |

|know if statements using “double” and “half” or | | |

|fifty percent are accurate. | | |

|M.4.3.12 Make observations, draw conclusions, | | |

|compare, and extract information from bar and | | |

|circle graphs. | | |

|M.4.3.13 Know that probability is the ratio of the | | |

|potential successful outcomes to total | | |

|possibilities and state probability as a ratio in | | |

|multiple forms (colon, words, and fractions) with | | |

|simple scenarios. | | |

|M.4.3.14 Determine the probability of basic events | | |

|and express the likelihood of an occurrence as a | | |

|ratio, fraction, or percent. | | |

|M.5.3 Algebra |Date |Initials |

|M.5.3.1 Identify relationships and complete number | | |

|sequences inherent in the addition and | | |

|multiplication tables. | | |

|M.5.3.2 Recognize and create repeating patterns and| | |

|identify the unit being repeated using four or more| | |

|items. | | |

|M.5.3.3 Demonstrate an understanding that a | | |

|horizontal number line moves from left to right | | |

|using lesser to greater values and that intervals | | |

|on a number line must follow a constant progression| | |

|by values including negative and positive numbers | | |

|and common fractions and decimals. | | |

|M.5.3.4 Read and understand positive and negative | | |

|numbers as showing direction and change on both | | |

|horizontal and vertical number lines, i.e., | | |

|demonstrate an understanding that a horizontal | | |

|number line moves from left to right using lesser | | |

|to greater values and that a vertical number line | | |

|moves from the bottom up using lesser to greater | | |

|values. | | |

|M.5.3.5 Recognize and understand the commutative | | |

|and associative properties of addition and | | |

|multiplication by using them to rewrite | | |

|expressions. | | |

|M.5.3.6 Read, write, and simplify word expressions | | |

|using algebraic notation for addition, subtraction,| | |

|multiplication, division, and parentheses. | | |

|M.5.3.7 Demonstrate an understanding that a | | |

|variable represents a missing value in addition and| | |

|subtraction expressions, e.g., substitute the value| | |

|for the variable in one-step expressions using | | |

|whole numbers when the value is given. | | |

|M.5.3.8 Solve simple one-step equations by | | |

|recognizing that addition and subtraction are | | |

|inverse operations and that multiplication and | | |

|division are inverse operations and knowing the | | |

|unknown of simple equations can be found by using | | |

|the inverse of the operation present. | | |

|M.5.3.9 Demonstrate an ability to use the symbols >| | |

|and < in number statements with larger numbers. | | |

|M.5.3.10 Understand and use exponents to represent | | |

|repeated multiplication. | | |

ABE Mathematics Verification Checklist Level 3 – Grade Level 4.0 - 5.9 Page 4 of 4

|Student |Instructor |Date Enrolled |

| | | |

|M.5.3 Algebra, cont. |Date |Initials |

|M.5.3.11 Read, write, and compute squares and cubes| | |

|of whole numbers, i.e., 4(4) = 42 = 16 and 2(2)(2) | | |

|= 23 = 8. | | |

|M.5.3.12 Interpret and solve simple (one or two | | |

|steps) real-life word problems involving addition, | | |

|subtraction, multiplication, and division. | | |

|M.5.3.13 Identify and apply simple formulas with | | |

|one or two arithmetical steps for real-life | | |

|contexts. | | |

|M.5.3.14 Write an equation representing verbal | | |

|situations with no more than two operations, i.e., | | |

|translate simple word problems involving unknown | | |

|quantities into simple equations. | | |

|M.5.3.15 Develop flexibility in solving problems by| | |

|selecting strategies, i.e., determine when and how | | |

|to split a problem into simpler parts to make | | |

|solving easier. | | |

|M.5.3.16 Compute using the correct order of | | |

|operations to solve problems including | | |

|multiplication, division, addition, and subtraction| | |

|(M, D, A, S). | | |

|M.5.3.17 Apply estimation strategies and mental | | |

|math to approximate solutions and then use a | | |

|calculator to calculate solutions to contextual | | |

|problems containing whole numbers and decimals to | | |

|two places. | | |

|M.5.3.18 Use the calculator to find squares, square| | |

|roots, and cubes of whole number quantities, i.e., | | |

|know the calculator keys that generate squares, | | |

|square roots, and cubes of numbers. | | |

ABE Mathematics Verification Checklist Level 4 – Grade Level 6.0 - 8.9 Page 1 of 3

|Student |Instructor |Date Enrolled |

| | | |

|M.1.4 Number Sense and Operations |Date |Initials |

|M.1.4.1 Carry out calculations using addition, | | |

|subtraction, multiplication, and division with | | |

|numbers of any size using efficient written methods| | |

|including ways to check answers, e.g., approximate | | |

|calculations, estimation, etc. | | |

|M.1.4.2 Identify the greatest common factor in a | | |

|given number set. | | |

|M.1.4.3 Identify prime numbers up to 100. | | |

|M.1.4.4 Read, write, order, and compare fractions | | |

|and mixed numbers. | | |

|M.1.4.5 Recognize and use equivalent forms of | | |

|common fractions (e.g., 1/2 = 5/10). | | |

|M.1.4.6 Demonstrate an understanding of simple | | |

|percent increase and decrease. | | |

|M.1.4.7 Round decimals in practical contexts and | | |

|verbal problems. | | |

|M.1.4.8 Multiply and divide with numbers involving | | |

|decimals, e.g., 2.5 x 3.6 and 3.2 ÷ .06 with pencil| | |

|and paper and using the calculator. | | |

|M.1.4.9 Use proportions to solve one-step real-life| | |

|problems, i.e., involving percents, dimensions, | | |

|scales, etc. | | |

|M.1.4.10 Recognize and use equivalencies between | | |

|common fractions, decimals, and percents to find | | |

|part of whole-number quantities, i.e., know common | | |

|fraction, decimal, and percent equivalents, e.g., | | |

|50% = 1/2 = .5, 25% = .25 = 1/4, .75 = 75% = 3/4. | | |

|M.1.4.11 Compute percents by finding the part, the | | |

|percent, and the whole. | | |

|M.1.4.12 Use a calculator to calculate efficiently | | |

|using whole numbers, fractions, decimals, and | | |

|percents. | | |

|M.2.4 Measurement |Date |Initials |

|M.2.4.1 Read, measure, estimate, calculate, and | | |

|compare with and between Fahrenheit and Celsius | | |

|temperatures using formulas provided. | | |

|M.2.4.2 Measure common three-dimensional shapes | | |

|(e.g., a room, window, box, etc.) and represent the| | |

|information as a scale drawing. | | |

|M.2.4.3 Use the language (meters to measure length,| | |

|grams to measure mass, liters to measure volume) | | |

|and prefixes (mili, centi, deci, deca, hecto, kilo)| | |

|of metric units to describe environment. | | |

|M.2.4.4 Make informal comparisons and estimations | | |

|between grams and ounces, kilograms and pounds, and| | |

|liters and quarts, i.e., 1 ounce is approximately | | |

|29 grams, a paper clip weighs about 1 gram, a | | |

|kilogram is about 2.2 pounds, and a liter is a | | |

|little larger than a quart (1.1 qts.). | | |

|M.2.4.5 Calculate volume and surface area of basic | | |

|cubes, cylinders, and rectangular containers using | | |

|formulas provided. | | |

|M.2.4.6 Calculate the perimeter and area of basic | | |

|irregular or composite shapes, i.e., shapes formed | | |

|by a combination of rectangles and triangles using | | |

|formulas provided. | | |

|M.2.4.7 Find equivalencies and solve problems using| | |

|conversions of units of weight, length/width, and | | |

|capacity. | | |

|M.2.4.8 Interpret, calculate, apply rates, and | | |

|estimate equivalencies involving time such as | | |

|velocity (mi/hr, ft/sec, m/sec), frequency | | |

|(calls/hr), consumption (cal/day, kw/hr), flow | | |

|(gal/min), change (degrees/min, inches/year), and | | |

|unit rates (cents/min, $/sq. ft., mi/gal). | | |

|M.2.4.9 Interpret and use scale drawings to solve | | |

|real-life problems. | | |

|M.2.4.10 Relate the measure of one object to | | |

|another (e.g., this is about 3 times as long, 6 of | | |

|these will fit in there) and plan linear spacing in| | |

|a design (e.g., how many lines of what size can fit| | |

|on a poster of a certain height?). | | |

ABE Mathematics Verification Checklist Level 4 – Grade Level 6.0 - 8.9 Page 2 of 3

|Student |Instructor |Date Enrolled |

| | | |

|M.3.4 Geometry |Date |Initials |

|M.3.4.1 Identify and compare elements of a circle | | |

|(center, radius, diameter, arc, circumference). | | |

|M.3.4.2 Calculate circumference of a circle using | | |

|formulas provided. | | |

|M.3.4.3 Understand the relationship of angles when | | |

|you have a system of parallel lines cut by a | | |

|transversal. | | |

|M.3.4.4 Show more than one line of symmetry in | | |

|complex shapes. | | |

|M.3.4.5 Interpret concepts of similarity and | | |

|identify figures that are similar or congruent. | | |

|M.3.4.6 Demonstrate understanding of the 360–degree| | |

|system of measuring angles and rotation. | | |

|M.3.4.7 Estimate the measure of an angle, | | |

|accurately measure an angle using a protractor, and| | |

|draw angles of specific measures using a protractor| | |

|and ruler. | | |

|M.3.4.8 Apply the Pythagorean Theorem using simple | | |

|numbers and basic right triangles. | | |

| |

|M.4.4 Data Analysis and Probability |Date |Initials |

|M.4.4.1 Develop and draw conclusions from tables | | |

|and graphs using instructor or student selected | | |

|information. | | |

|M.4.4.2 Gather data to answer a posed question and | | |

|analyze and present data visually. | | |

|M.4.4.3 Demonstrate that a table can display the | | |

|same data as a line or bar graph. | | |

|M.4.4.4 Find the average (mean), median, mode, and | | |

|range for a data set. Note: it is important for | | |

|students to recognize that mean and median numbers | | |

|are considered “averages” and that averages | | |

|represent numbers typical of the data that can | | |

|support an argument. | | |

|M.4.4.5 Identify the minimum, maximum, and spread | | |

|of a data set and describe the effect of spread on | | |

|mean and median, i.e., know the minimum or maximum | | |

|value can greatly affect the mean but will not | | |

|affect the median. | | |

|M.4.4 Data Analysis and Probability, |Date |Initials |

|cont. | | |

|M.4.4.6 Demonstrate an understanding of line | | |

|graphs, i.e., that lines going up mean increase, | | |

|lines tilting down mean decrease and that they can | | |

|vary over time, flat lines mean no change, and use | | |

|specific vocabulary to describe trends, i.e., sharp| | |

|increase, plummeted, etc. | | |

|M.4.4.7 Know when percent figures don’t add up to | | |

|100% and when numbers and percent figures (50%, | | |

|25%, 10%) don’t match up, i.e., understand that | | |

|circle graphs represent 100%. | | |

|M.4.4.8 Recognize that some visual representations | | |

|distort actual data (bar widths can provide | | |

|misleading information) or see where authors of | | |

|data reports can manipulate data to benefit | | |

|themselves or malign others in provided materials | | |

|and know how to recognize who produced a data | | |

|report and how their interests might affect the | | |

|report – conflict of interest. | | |

|M.4.4.9 Reorient, reorganize, restate, summarize, | | |

|or reformat report data (make graphs) for a | | |

|particular purpose and audience. | | |

|M.4.4.10 Determine and compare probabilities of | | |

|chance events (e.g., winning lottery prizes). | | |

|M.4.4.11 Calculate the possible combinations (a | | |

|selection of items where order doesn’t matter) of | | |

|up to five items in simple, practical situations | | |

|(e.g., I have 4 tickets and 5 potential guests). | | |

|M.4.4.12 Calculate the possible permutations (an | | |

|arrangement of items/data in a certain order) of up| | |

|to five elements in simple, practical situations | | |

|(e.g., ways to sequence titles of 4 different | | |

|colors in a pattern). | | |

ABE Mathematics Verification Checklist Level 4 – Grade Level 6.0 - 8.9 Page 3 of 3

|Student |Instructor |Date Enrolled |

| | | |

|M.5.4 Algebra |Date |Initials |

|M.5.4.1 Identify and use simple formulas from | | |

|tables with one or two arithmetical steps for | | |

|real-life contexts. | | |

|M.5.4.2 Use graphs to analyze the nature of changes| | |

|in quantities in linear relationships and use | | |

|vocabulary to describe linear change. | | |

|M.5.4.3 Recognize and describe patterns in given | | |

|sets of numbers in a functional relationship and | | |

|how changes in one quantity can affect another. | | |

|M.5.4.4 Demonstrate understanding of the Cartesian | | |

|coordinate system. | | |

|M.5.4.5 Use coordinate grid to identify and locate | | |

|specific points on the x- and y-axes. | | |

|M.5.4.6 Graph simple linear equations by generating| | |

|a table of values from an equation and plotting the| | |

|coordinates on a graph. | | |

|M.5.4.7 Determine the slope of a line when given | | |

|two points on the line or the equation of a line | | |

|and relate it to change. | | |

|M.5.4.8 Write the equation of a simple line when | | |

|given two points or slope and one point. | | |

|M.5.4.9 Demonstrate an understanding of like terms | | |

|by combining like terms in simple algebraic | | |

|expressions. | | |

|M.5.4.10 Demonstrate an understanding of the order | | |

|of operations and use the order of operations when | | |

|simplifying algebraic expressions. | | |

|M.5.4.11 Add and subtract integers, i.e., positive | | |

|and negative numbers. | | |

|M.5.4.12 Multiply and divide integers, i.e., | | |

|positive and negative numbers. | | |

|M.5.4.13 Calculate square roots of perfect squares,| | |

|estimate within range of square root value, and | | |

|demonstrate an understanding of how squaring and | | |

|taking the square root are related. | | |

|M.5.4.14 Evaluate, add, subtract, multiply, and | | |

|divide expressions involving exponents. | | |

|M.5.4.15 Demonstrate an understanding of scientific| | |

|notation, i.e., a shorter way to write large or | | |

|really small numbers. | | |

|M.5.4.16 Demonstrate an understanding of and solve | | |

|basic algebraic equations involving multiple steps.| | |

|M.5.4 Algebra, cont. |Date |Initials |

|M.5.4.17 Translate word phrases into algebraic | | |

|expressions and vice versa. | | |

|M.5.4.18 Demonstrate an understanding of | | |

|substituting values into simple formulas and | | |

|solving for the unknown value. | | |

|M.5.4.19 Demonstrate an understanding of the | | |

|distributive property, e.g., 75 x 12 = 75 x 10 + 75| | |

|x 2 and 2(a + 6) = 2a + 12 | | |

|M.5.4.20 Read, write, order, and compare positive | | |

|and negative numbers and identify positive and | | |

|negative numbers on a number line. | | |

|M.5.4.21 Solve real-life, multi-step word problems | | |

|involving money, measurement, and other contextual | | |

|situations using whole numbers, decimals, and | | |

|percents. For example, solve problems relating to | | |

|payroll deductions, computing and comparing unit | | |

|pricing, rebates, discounts, deficits, sales taxes,| | |

|shipping and handling fees, etc. | | |

|M.5.4.22 Recognize and eliminate extraneous | | |

|information in word problems. | | |

Level 1 – Grade Level 0-1.9 Page 1 of 2

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.1.1 Number Sense and Operations |Materials Used - Include specific activity, book, page |Mastery Level %|Date & Initials |

| |number, etc. | | |

|M.1.1.1 Associate numbers and words for numbers with | | | |

|quantities. | | | |

|M.1.1.2 Demonstrate an understanding that if items are | | | |

|rearranged, the numbers stay the same. | | | |

|M.1.1.3 Read, write, order, and compare numbers from 0 to| | | |

|100. | | | |

|M.1.1.4 Recognize and count numbers through 999. | | | |

|M.1.1.5 Count by 2s, 5s, and 10s up to 100. | | | |

|M.1.1.6 Identify even and odd numbers. | | | |

|M.1.1.7 Add whole numbers up to three digits (without | | | |

|carrying). | | | |

|M.1.1.8 Demonstrate understanding of the concept of | | | |

|subtraction, i.e., as in taking away or separating, from | | | |

|numbers up to twenty. | | | |

|M.1.1.9 Subtract whole numbers up to three digits | | | |

|(without borrowing). | | | |

|M.1.1.10 Demonstrate an understanding of the times tables| | | |

|for the numbers 1, 2, 4, and 10. | | | |

|M.1.1.11 Halve even numbers up to 10 and double whole | | | |

|numbers up to 10. | | | |

|M.1.1.12 Identify place value of ones, tens, and | | | |

|hundreds. | | | |

|M.1.1.13 Identify basic functions (+, -, x, (, =, on/off)| | | |

|on the calculator and digits (0-9). | | | |

|M.1.1.14 Identify fractional parts (1/4, 1/3, 1/2) and | | | |

|whole. | | | |

|M.1.1.15 Recognize currency (up to $20.00) and coins; | | | |

|count and trade pennies, nickels, dimes, and quarters to | | | |

|100 cents. | | | |

|M.1.1.16 Make and verify change. | | | |

Level 1 – Grade Level 0-1.9 Page 2 of 2

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.2.1 Measurement |Materials Used - Include specific activity, book, page |Mastery Level %|Date & Initials|

| |number, etc. | | |

|M.2.1.1 Recognize and record time to the nearest hour and | | | |

|half hour, from an analog and digital clock, including | | | |

|understanding the meaning between am and pm. | | | |

|M.2.1.2 Interpret numeric representations of dates. | | | |

|M.2.1.3 Understand use of standard US linear measurements | | | |

|(inches, feet). | | | |

|M.2.1.4 Understand use of standard US capacity | | | |

|measurements (cups, pints, quarts, and gallons). | | | |

| |

|M.3.1 Geometry |Materials Used - Include specific activity, book, page |Mastery Level %|Date & Initials|

| |number, etc. | | |

|M.3.1.1 Model and use directional and positional | | | |

|vocabulary appropriately. | | | |

|M.3.1.2 Demonstrate an understanding of perimeter being | | | |

|the measure around the outside edges of squares and | | | |

|rectangles. | | | |

|M.3.1.3 Identify and describe the properties of common | | | |

|two-dimensional shapes (square, circle, rectangle, | | | |

|triangle) using everyday language (straight, curved, | | | |

|etc.). | | | |

| |

|M.4.1 Data Analysis and Probability |Materials Used - Include specific activity, book, page |Mastery Level %|Date & Initials|

| |number, etc. | | |

|M.4.1.1 Identify and name various simple visual data | | | |

|(graphs, charts, tables) found in authentic publications. | | | |

|M.4.1.2 Interpret data organized in basic categories and | | | |

|groupings. | | | |

|M.4.1.3 Collect, label, and order numerical information | | | |

|for a particular purpose (e.g., to count and list stock). | | | |

| |

|M.5.1 Algebra |Materials Used - Include specific activity, book, page |Mastery Level %|Date & Initials|

| |number, etc. | | |

|M.5.1.1 Identify basic number patterns and relationships | | | |

|inherent in addition and subtraction. | | | |

|M.5.1.2 Sort up to 20 objects or lists by color, shape, | | | |

|number, letter, or size. | | | |

|M.5.1.3 Understand and complete simple number sentences. | | | |

Level 2 – Grade Level 2.0-3.9 Page 1 of 3

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.1.2 Number Sense and Operations |Materials Used - Include specific activity, book, page |Mastery Level %|Date & Initials|

| |number, etc. | | |

|M.1.2.1 Read, write, order, and compare numbers in the | | | |

|thousands including identifying place value. | | | |

|M.1.2.2 Demonstrate understanding of the concept of | | | |

|addition (i.e., as in adding on or combining), including | | | |

|the role of place value. | | | |

|M.1.2.3 Add whole numbers up to three digits using | | | |

|carrying. | | | |

|M.1.2.4 Subtract whole numbers up to three digits using | | | |

|borrowing and checking. Demonstrate an understanding of how| | | |

|addition and subtraction relate to each other by checking | | | |

|answers using addition. | | | |

|M.1.2.5 Demonstrate understanding of the concept of | | | |

|multiplication (i.e., as in repeated addition, multiple | | | |

|groups, rows, and columns), including the role of place | | | |

|value. | | | |

|M.1.2.6 Demonstrate an understanding of multiplying by 10 | | | |

|and 100. | | | |

|M.1.2.7 Multiply whole numbers up to three digits by one | | | |

|digit using carrying. | | | |

|M.1.2.8 Demonstrate understanding of the concept of | | | |

|division (i.e., as dividing a set into equal groups, or | | | |

|determining number of groups within a set), including the | | | |

|role of place value. | | | |

|M.1.2.9 Divide whole numbers up to hundreds by one digit. | | | |

|M.1.2.10 Use rounding and estimation for tens and hundreds.| | | |

|For example, estimate the sum of 406 and 798 (nearest | | | |

|hundred) or estimate the difference between 836 and 425 | | | |

|(nearest ten). | | | |

|M.1.2.11 Demonstrate an understanding that even numbers can| | | |

|be paired and that odd numbers represent amounts that when | | | |

|paired have one remaining. | | | |

|M.1.2.12 Know all pairs of numbers with a total of 10. | | | |

|M.1.2.13 Identify multiples of 2, 3, 4, 5, and 10 up to x | | | |

|10. | | | |

|M.1.2.14 Demonstrate an understanding of the times tables | | | |

|for the numbers 0 to 12. | | | |

|M.1.2.15 Identify factoring of common numbers (e.g., 12 = | | | |

|4x3 = 2x6 = 2x2x3). | | | |

|M.1.2.16 Divide numbers by 10 and 100 and back-multiply to | | | |

|check results of division. | | | |

|M.1.2.17 Identify and demonstrate an understanding of | | | |

|fractional parts including 1/8, 1/4, 1/3, 1/2, and whole. | | | |

Level 2 – Grade Level 2.0-3.9 Page 2 of 3 ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.1.2 Number Sense and Operations, cont. |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.1.2.18 Demonstrate how fractions relate to multiplication and| | | |

|division (e.g., divide these 12 into 3 parts; 1/3 of 12 is 4, | | | |

|2/3 is 8). | | | |

|M.1.2.19 Add and subtract common fractions with like | | | |

|denominators. | | | |

|M.1.2.20 Identify improper fractions and mixed numbers. | | | |

|M.1.2.21 Identify and write amounts of money using decimals, | | | |

|words, and symbols. | | | |

|M.1.2.22 Demonstrate an understanding of decimal notation and | | | |

|place value by reading, writing, ordering, and comparing | | | |

|decimals to two decimal places. | | | |

|M.1.2.23 Convert and express simple common fractions as | | | |

|decimals. | | | |

|M.1.2.24 Show relationship between decimal system and money. | | | |

| |

|M.2.2 Measurement |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.2.2.1 Identify equivalent amounts of money using different | | | |

|bills and coins. | | | |

|M.2.2.2 Read, record, and use date concepts (months, days of | | | |

|week) in common formats. | | | |

|M.2.2.3 Read, record, and understand time of day. | | | |

|M.2.2.4 Telling time to the nearest minute. | | | |

|M.2.2.5 Identify halves and whole numbers on a ruler (inches) | | | |

|and develop personal reference point for one’s height. | | | |

|M.2.2.6 Identify halves and whole numbers on weight scales | | | |

|(pounds) and develop personal reference point for one’s weight.| | | |

|M.2.2.7 Identify and select appropriate measures for capacity | | | |

|and weight. | | | |

|M.2.2.8 Interpret temperature from Fahrenheit scale in various | | | |

|situations, including negative temperatures. | | | |

|M.2.2.9 Read and record time of day in 24-hour format. | | | |

|M.2.2.10 Convert units of time: hours, minutes, and seconds. | | | |

|M.2.2.11 Identify customary US units of linear measurement and | | | |

|equivalents. | | | |

|M.2.2.12 Measure length, width, height, and perimeter using | | | |

|inches, feet, and yards using a ruler or tape measure. | | | |

|M.2.2.13 Make rough-estimate approximations of standard US | | | |

|measurements. | | | |

|M.2.2.14 Read, interpret, and use map legends/keys. | | | |

Level 2 – Grade Level 2.0-3.9 Page 3 of 3

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.3.2 Geometry |Materials Used - Include specific activity, book, |Mastery Level %|Date & |

| |page number, etc. | |Initials |

|M.3.2.1 Demonstrate an understanding of the concepts of sameness | | | |

|and halfness. | | | |

|M.3.2.2 Use the four main compass directions (N, S, E, W) for | | | |

|spatial orientation. | | | |

|M.3.2.3 Define and correctly use the concept of horizontal and | | | |

|vertical positions. | | | |

|M.3.2.4 Follow a pattern or model to produce or reproduce a shape| | | |

|or object. | | | |

| |

|M.4.2 Data Analysis and Probability |Materials Used - Include specific activity, book, |Mastery Level %|Date & |

| |page number, etc. | |Initials |

|M.4.2.1 Solve problems using simple graphs (pictograph, bar, | | | |

|line, and circle), tables, or distances on maps. | | | |

|M.4.2.2 Identify, count, extract, and interpret pertinent data | | | |

|organized in lists, tables, and charts. | | | |

|M.4.2.3 Reorient, reorganize, and reformat simple data. | | | |

|M.4.2.4 Collect, label, and order numerical information for a | | | |

|particular purpose. | | | |

|M.4.2.5 Identify and interpret simple graphs, tables, etc. | | | |

|M.4.2.6 Read values on and make comparative statements about | | | |

|relative values on a simple bar graph. | | | |

|M.4.2.7 Develop an understanding of events as certain, | | | |

|impossible, likely, or unlikely to occur. | | | |

|M.4.2.8 Determine the probability of simple events. | | | |

| |

|M.5.2 Algebra |Materials Used - Include specific activity, book, |Mastery Level %|Date & |

| |page number, etc. | |Initials |

|M.5.2.1 Recognize and create simple repeating patterns using 3 or| | | |

|less items and identify the unit being repeated. | | | |

|M.5.2.2 Identify basic number patterns and relationships inherent| | | |

|in multiplication and division. | | | |

|M.5.2.3 Describe quantitative change, i.e., change in the number | | | |

|of daylight hours or temperature over time. | | | |

|M.5.2.4 Interpret simple English word phrases, i.e., mathematical| | | |

|expressions, equations, and variables and write algebraic | | | |

|expressions. | | | |

|M.5.2.5 Recognize, interpret, and use basic mathematical symbols | | | |

|(+, -, =, ) and recognize the different vocabulary used to | | | |

|represent each. | | | |

|M.5.2.6 Translate simple mathematical expressions involving +, -,| | | |

|. | | | |

|M.5.2.7 Use a calculator to make basic calculations and solve | | | |

|simple addition, subtraction, multiplication, and division | | | |

|problems and check solutions. | | | |

|M.5.2.8 Solve single step, real-life word problems involving | | | |

|addition, subtraction, multiplication, and division using up to | | | |

|two digit whole numbers. | | | |

|M.5.2.9 Determine and use appropriate rounding and estimating | | | |

|techniques. | | | |

Level 3 – Grade Level 4.0-5.9 Page 1 of 6

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.1.3 Number Sense and Operations |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.1.3.1 Read, write, order, and compare large whole numbers. | | | |

|M.1.3.2 Identify place value in large whole numbers and round | | | |

|off large whole numbers to nearest tens, hundreds, thousands, | | | |

|ten-thousands, hundred-thousands, million, etc. | | | |

|M.1.3.3 Interpret the inverse relationship between addition and | | | |

|subtraction and multiplication and division. | | | |

|M.1.3.4 Demonstrate an understanding of the commutative and | | | |

|associative properties of addition and multiplication. | | | |

|M.1.3.5 Demonstrate an understanding of factors of numbers up to| | | |

|100. | | | |

|M.1.3.6 Demonstrate an understanding of dividing by multi-digit | | | |

|numbers and interpreting remainder and expressing them as whole | | | |

|numbers, fractions, and decimals. | | | |

|M.1.3.7 Demonstrate an understanding of back-multiplying to | | | |

|check results of division. | | | |

|M.1.3.8 Demonstrate an understanding of prime numbers and | | | |

|identify prime numbers up to 20. | | | |

|M.1.3.9 Add and subtract whole numbers up to four digits using | | | |

|efficient methods and checking answers. | | | |

|M.1.3.10 Multiply with two and three digit numbers using | | | |

|efficient written methods including checking answers. | | | |

|M.1.3.11 Identify and calculate equivalent fractions (fourths, | | | |

|thirds, halves, eighths, fifths, and tenths) and simplify | | | |

|fractions to lowest terms. | | | |

|M.1.3.12 Convert improper fractions to mixed numbers and mixed | | | |

|numbers to improper fractions. | | | |

|M.1.3.13 Add and subtract fractions (fourths, thirds, halves, | | | |

|eighths, fifths, and tenths) using fractions that include like | | | |

|and unlike denominators and whole and mixed numbers. | | | |

|M.1.3.14 Multiply and divide by fractions (fourths, thirds, | | | |

|halves, eighths, fifths, and tenths) using fractions that | | | |

|include like and unlike denominators and whole and mixed | | | |

|numbers. | | | |

|M.1.3.15 Relate multiplication of fractions and division. | | | |

|M.1.3.16 Express a relationship between two quantities as a | | | |

|fraction or fractional estimate. | | | |

|M.1.3.17 Identify quantities that are proportional. | | | |

|M.1.3.18 Interpret the meaning of ratio and express a | | | |

|relationship between two quantities as a ratio. | | | |

|M.1.3.19 Read, write, order, and compare decimals of up to three| | | |

|decimal places. | | | |

Level 3 – Grade Level 4.0-5.9 Page 2 of 6

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.1.3 Number Sense and Operations, cont. |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.1.3.20 Identify place value for decimals and round decimals | | | |

|to one or two places or whole numbers. | | | |

|M.1.3.21 Compute percentages when part and whole are given | | | |

|using friendly numbers. | | | |

|M.1.3.22 Convert decimals to fractions and percents, fractions| | | |

|to decimals and percents, and percents to fractions and | | | |

|decimals. | | | |

|M.1.3.23 Add, subtract, multiply, and divide numbers with | | | |

|decimals. | | | |

|M.1.3.24 Read and write large numbers with decimals. | | | |

|M.1.3.25 Determine a fraction or percent of a decimal. | | | |

|M.1.3.26 Understand and interpret the meaning of percent, | | | |

|i.e., percent represents a ratio of a part to a whole where | | | |

|the whole is 100. | | | |

|M.1.3.27 Read, write, order, and compare simple percentages. | | | |

|M.1.3.28 Find given percents of any given number. | | | |

| |

|M.2.3 Measurement |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.2.3.1 Calculate units of time using a clock (both 12 and 24 | | | |

|hour) and a calendar. | | | |

|M.2.3.2 Identify and select appropriate metric measurements. | | | |

|M.2.3.3 Add, subtract, multiply, and divide sums of money. | | | |

|M.2.3.4 Demonstrate an understanding of the interrelation of | | | |

|distance, time, and speed and make simple calculations using | | | |

|distance, time, and speed formula. | | | |

|M.2.3.5 Read and interpret map scales, legends, and mileage | | | |

|tables. | | | |

|M.2.3.6 Measure with a standard ruler in inches and feet to | | | |

|1/16 inch accuracy and a metric ruler in cm and mm. | | | |

|M.2.3.7 Make informal comparisons between inches and | | | |

|centimeters including estimating the number of centimeters per| | | |

|inch. Create physical (bodily) benchmarks for units. | | | |

|M.2.3.8 Convert and calculate with linear measurements | | | |

|(inches, feet, yards, miles) and know the relationship of | | | |

|familiar units and convert units of measure in the same | | | |

|systems. | | | |

|M.2.3.9 Use and apply concepts of weight and capacity to solve| | | |

|problems. | | | |

Level 3 – Grade Level 4.0-5.9 Page 3 of 6

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.2.3 Measurement, cont. |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.2.3.10 Use, read, compare, and calculate with positive and | | | |

|negative Fahrenheit temperatures, i.e., know that temperature | | | |

|increases as it goes up and decreases as it goes down and that| | | |

|the sign of the temperature changes when crossing the zero | | | |

|degree point. | | | |

|M.2.3.11 Calculate times using the appropriate value and | | | |

|convert between time formats (including elapsed time), i.e., | | | |

|know equivalencies for hours, seconds, minutes, days, weeks, | | | |

|months, decades, and centuries. | | | |

|M.2.3.12 Directly measure perimeter in linear units and area | | | |

|in square units (sq. in., sq. ft., sq. cm.). | | | |

|M.2.3.13 Estimate, measure, and compare weights (pounds, | | | |

|ounces) using simple instruments, graduated in familiar units | | | |

|(ounces and pounds) and know when to use appropriate measures.| | | |

|M.2.3.14 Convert and calculate using standard US units of | | | |

|weight: tons, pounds, ounces, etc. | | | |

|M.2.3.15 Convert and calculate using standard US units of | | | |

|capacity: ounces, quarts, and gallons. | | | |

|M.2.3.16 Demonstrate an understanding of the concept of | | | |

|two-dimensional measurements and square units. | | | |

|M.2.3.17 Read analog and digital scales on measuring devices | | | |

|including meters, gauges, scales, etc. using various types of | | | |

|units and calibrations. | | | |

| |

|M.3.3 Geometry |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.3.3.1 Recognize, identify, and describe basic geometric | | | |

|shapes (triangle, square, circle, rectangle, hexagon, | | | |

|pentagon, and octagon). | | | |

|M.3.3.2 Draw 2-D shapes of specific dimensions. | | | |

|M.3.3.3 Use informal visual methods to describe and compare | | | |

|shape, dimension, perimeter, area, angles, and sides in 2-D | | | |

|and 3-D objects. | | | |

|M.3.3.4 Identify properties, locations, and functions of right| | | |

|angles, i.e., know that a right angle is 90 degrees or a | | | |

|quarter turn, that two right angles make a straight line, and | | | |

|four right angles fill a space. | | | |

|M.3.3.5 Use direction, distance, coordinates, latitude, | | | |

|longitude, simple scales, labels, symbols, and keys to read | | | |

|and use maps and plans. | | | |

|M.3.3.6 Use graph paper to draw 2-D shapes in different | | | |

|orientations on a grid. | | | |

|M.3.3.7 Calculate the area of squares, rectangles, and | | | |

|triangles and other common figures using given formulas. | | | |

|M.3.3.8 Recognize, identify, and describe the properties of | | | |

|common 3-D shapes, i.e., cube, cylinder, and sphere. | | | |

Level 3 – Grade Level 4.0-5.9 Page 4 of 6

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.3.3 Geometry, cont. |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.3.3.9 Identify triangles based on their properties, i.e., | | | |

|right, isosceles, equilateral, scalene, obtuse, and acute. | | | |

|M.3.3.10 Identify common polygons of various shapes, i.e., | | | |

|triangles, quadrilaterals, pentagons, hexagons, and octagons. | | | |

|M.3.3.11 Identify parallel, perpendicular, and intersecting | | | |

|lines. | | | |

|M.3.3.12 Describe characteristics of angles formed by two | | | |

|intersecting lines, i.e., vertical, supplementary, | | | |

|complementary, adjacent, and corresponding/ congruent. | | | |

|M.3.3.13 Identify angles of 90 and 45 degrees, right, acute, | | | |

|and obtuse. | | | |

|M.3.3.14 Use the secondary directions for spatial orientation | | | |

|(e.g., NW, SW, NE, SE). | | | |

|M.3.3.15 Use a map with a coordinate grid. | | | |

|M.3.3.16 Create 3-D objects from 2-D representations. | | | |

| |

|M.4.3 Data Analysis and Probability |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.4.3.1 Identify, describe, and compare how a change in one | | | |

|variable relates to a change in a second variable. | | | |

|M.4.3.2 Demonstrate an understanding of the concept of | | | |

|categories such as shape, size, color, or yes/no responses and| | | |

|know how to count each category for subtotals. | | | |

|M.4.3.3 Represent information so that it makes sense to | | | |

|others. | | | |

|M.4.3.4 Demonstrate an understanding that when objects or | | | |

|responses are divided into categories, all data must be | | | |

|included in one and only one category; therefore, categories | | | |

|must identify distinct sets. | | | |

|M.4.3.5 Demonstrate an understanding of scatter plots, i.e., | | | |

|that each X in a line plot represents one and only one item or| | | |

|response; therefore, it is verifiable that the number of | | | |

|responses is equal to the number of X’s. | | | |

|M.4.3.6 Demonstrate an understanding that a graph is a visual | | | |

|representation and a table arranges information in rows and | | | |

|columns. | | | |

|M.4.3.7 Sort graphs and tables by type. | | | |

|M.4.3.8 Demonstrate an understanding that lists and tables can| | | |

|be ordered in different ways such as alphabetically, | | | |

|numerically, or randomly. | | | |

|M.4.3.9 Compare relative values on a bar graph. | | | |

Level 3 – Grade Level 4.0-5.9 Page 5 of 6

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.4.3 Data Analysis and Probability, cont. |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.4.3.10 Determine whether or not a graph/table connects to | | | |

|statements made in text using title, data labels, and percent | | | |

|matches. | | | |

|M.4.3.11 Support simple statements with data and know if | | | |

|statements using “double” and “half” or fifty percent are | | | |

|accurate. | | | |

|M.4.3.12 Make observations, draw conclusions, compare, and | | | |

|extract information from bar and circle graphs. | | | |

|M.4.3.13 Know that probability is the ratio of the potential | | | |

|successful outcomes to total possibilities and state | | | |

|probability as a ratio in multiple forms (colon, words, and | | | |

|fractions) with simple scenarios. | | | |

|M.4.3.14 Determine the probability of basic events and express| | | |

|the likelihood of an occurrence as a ratio, fraction, or | | | |

|percent. | | | |

| |

|M.5.3 Algebra |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.5.3.1 Identify relationships and complete number sequences | | | |

|inherent in the addition and multiplication tables. | | | |

|M.5.3.2 Recognize and create repeating patterns and identify | | | |

|the unit being repeated using four or more items. | | | |

|M.5.3.3 Demonstrate an understanding that a horizontal number | | | |

|line moves from left to right using lesser to greater values | | | |

|and that intervals on a number line must follow a constant | | | |

|progression by values including negative and positive numbers | | | |

|and common fractions and decimals. | | | |

|M.5.3.4 Read and understand positive and negative numbers as | | | |

|showing direction and change on both horizontal and vertical | | | |

|number lines, i.e., demonstrate an understanding that a | | | |

|horizontal number line moves from left to right using lesser | | | |

|to greater values and that a vertical number line moves from | | | |

|the bottom up using lesser to greater values. | | | |

|M.5.3.5 Recognize and understand the commutative and | | | |

|associative properties of addition and multiplication by using| | | |

|them to rewrite expressions. | | | |

|M.5.3.6 Read, write, and simplify word expressions using | | | |

|algebraic notation for addition, subtraction, multiplication, | | | |

|division, and parentheses. | | | |

|M.5.3.7 Demonstrate an understanding that a variable | | | |

|represents a missing value in addition and subtraction | | | |

|expressions, e.g., substitute the value for the variable in | | | |

|one-step expressions using whole numbers when the value is | | | |

|given. | | | |

Level 3 – Grade Level 4.0-5.9 Page 6 of 6

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.5.3 Algebra, cont. |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.5.3.8 Solve simple one-step equations by recognizing that | | | |

|addition and subtraction are inverse operations and that | | | |

|multiplication and division are inverse operations and knowing| | | |

|the unknown of simple equations can be found by using the | | | |

|inverse of the operation present. | | | |

|M.5.3.9 Demonstrate an ability to use the symbols > and < in | | | |

|number statements with larger numbers. | | | |

|M.5.3.10 Understand and use exponents to represent repeated | | | |

|multiplication. | | | |

|M.5.3.11 Read, write, and compute squares and cubes of whole | | | |

|numbers, i.e., 4(4) = 42 = 16 and 2(2)(2) = 23 = 8. | | | |

|M.5.3.12 Interpret and solve simple (one or two steps) | | | |

|real-life word problems involving addition, subtraction, | | | |

|multiplication, and division. | | | |

|M.5.3.13 Identify and apply simple formulas with one or two | | | |

|arithmetical steps for real-life contexts. | | | |

|M.5.3.14 Write an equation representing verbal situations with| | | |

|no more than two operations, i.e., translate simple word | | | |

|problems involving unknown quantities into simple equations. | | | |

|M.5.3.15 Develop flexibility in solving problems by selecting | | | |

|strategies, i.e., determine when and how to split a problem | | | |

|into simpler parts to make solving easier. | | | |

|M.5.3.16 Compute using the correct order of operations to | | | |

|solve problems including multiplication, division, addition, | | | |

|and subtraction (M, D, A, S). | | | |

|M.5.3.17 Apply estimation strategies and mental math to | | | |

|approximate solutions and then use a calculator to calculate | | | |

|solutions to contextual problems containing whole numbers and | | | |

|decimals to two places. | | | |

|M.5.3.18 Use the calculator to find squares, square roots, and| | | |

|cubes of whole number quantities, i.e., know the calculator | | | |

|keys that generate squares, square roots, and cubes of | | | |

|numbers. | | | |

Level 4 – Grade Level 6.0-8.9 Page 1 of 4

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.1.4 Number Sense and Operations |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.1.4.1 Carry out calculations using addition, subtraction, | | | |

|multiplication, and division with numbers of any size using | | | |

|efficient written methods including ways to check answers, | | | |

|e.g., approximate calculations, estimation, etc. | | | |

|M.1.4.2 Identify the greatest common factor in a given number | | | |

|set. | | | |

|M.1.4.3 Identify prime numbers up to 100. | | | |

|M.1.4.4 Read, write, order, and compare fractions and mixed | | | |

|numbers. | | | |

|M.1.4.5 Recognize and use equivalent forms of common fractions| | | |

|(e.g., 1/2 = 5/10). | | | |

|M.1.4.6 Demonstrate an understanding of simple percent | | | |

|increase and decrease. | | | |

|M.1.4.7 Round decimals in practical contexts and verbal | | | |

|problems. | | | |

|M.1.4.8 Multiply and divide with numbers involving decimals, | | | |

|e.g., 2.5 x 3.6 and 3.2 ÷ .06 with pencil and paper and using | | | |

|the calculator. | | | |

|M.1.4.9 Use proportions to solve one-step real-life problems, | | | |

|i.e., involving percents, dimensions, scales, etc. | | | |

|M.1.4.10 Recognize and use equivalencies between common | | | |

|fractions, decimals, and percents to find part of whole-number| | | |

|quantities, i.e., know common fraction, decimal, and percent | | | |

|equivalents. | | | |

|M.1.4.11 Compute percents by finding the part, the percent, | | | |

|and the whole. | | | |

|M.1.4.12 Use a calculator to calculate efficiently using whole| | | |

|numbers, fractions, decimals, and percents. | | | |

| |

|M.2.4 Measurement |Materials Used - Include specific activity, book, page |Mastery Level |Date & |

| |number, etc. |% |Initials |

|M.2.4.1 Read, measure, estimate, calculate, and compare with | | | |

|and between Fahrenheit and Celsius temperatures using formulas| | | |

|provided. | | | |

|M.2.4.2 Measure common 3-D shapes (e.g. a room, window, box, | | | |

|etc.) and represent the information as a scale drawing. | | | |

|M.2.4.3 Use the language (meters to measure length, grams to | | | |

|measure mass, liters to measure volume) and prefixes (mili, | | | |

|centi, deci, deca, hecto, kilo) of metric units to describe | | | |

|environment. | | | |

|M.2.4.4 Make informal comparisons and estimations between | | | |

|grams and ounces, kilograms and pounds, and liters and quarts.| | | |

Level 4 – Grade Level 6.0-8.9 Page 2 of 4

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.2.4 Measurement, cont. |Materials Used - Include specific activity, book, page |Mastery Level|Date & |

| |number, etc. |% |Initials |

|M.2.4.5 Calculate volume and surface area of basic cubes, | | | |

|cylinders, and rectangular containers using formulas provided. | | | |

|M.2.4.6 Calculate the perimeter and area of basic irregular or | | | |

|composite shapes, i.e., shapes formed by a combination of | | | |

|rectangles and triangles using formulas provided. | | | |

|M.2.4.7 Find equivalencies and solve problems using conversions | | | |

|of units of weight, length/width, and capacity. | | | |

|M.2.4.8 Interpret, calculate, apply rates, and estimate | | | |

|equivalencies involving time such as velocity (mi/hr, ft/sec, | | | |

|m/sec), frequency (calls/hr), consumption (cal/day, kw/hr), flow | | | |

|(gal/min), change (degrees/min, inches/year), and unit rates | | | |

|(cents/min, $/sq. ft., mi/gal). | | | |

|M.2.4.9 Interpret and use scale drawings to solve real-life | | | |

|problems. | | | |

|M.2.4.10 Relate the measure of one object to another (e.g., this | | | |

|is about 3 times as long, 6 of these will fit in there) and plan | | | |

|linear spacing in a design (e.g., how many lines of what size can| | | |

|fit on a poster of a certain height?). | | | |

| |

|M.3.4 Geometry |Materials Used - Include specific activity, book, page |Mastery Level % |Date & Initials|

| |number, etc. | | |

|M.3.4.1 Identify and compare elements of a circle (center, | | | |

|radius, diameter, arc, circumference). | | | |

|M.3.4.2 Calculate circumference of a circle using formulas | | | |

|provided. | | | |

|M.3.4.3 Understand the relationship of angles when you have | | | |

|a system of parallel lines cut by a transversal. | | | |

|M.3.4.4 Show more than one line of symmetry in complex | | | |

|shapes. | | | |

|M.3.4.5 Interpret concepts of similarity and identify | | | |

|figures that are similar or congruent. | | | |

|M.3.4.6 Demonstrate understanding of the 360–degree system | | | |

|of measuring angles and rotation. | | | |

|M.3.4.7 Estimate the measure of an angle, accurately measure| | | |

|an angle using a protractor, and draw angles of specific | | | |

|measures using a protractor and ruler. | | | |

|M.3.4.8 Apply the Pythagorean Theorem using simple numbers | | | |

|and basic right triangles. | | | |

Level 4 – Grade Level 6.0-8.9 Page 3 of 4

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.4.4 Data Analysis and Probability |Materials Used - Include specific activity, book, page |Mastery Level|Date & |

| |number, etc. |% |Initials |

|M.4.4.1 Develop and draw conclusions from tables and graphs | | | |

|using instructor or student selected information. | | | |

|M.4.4.2 Gather data to answer a posed question and analyze and | | | |

|present data visually. | | | |

|M.4.4.3 Demonstrate that a table can display the same data as a| | | |

|line or bar graph. | | | |

|M.4.4.4 Find the average (mean), median, mode, and range for a | | | |

|data set. Note: it is important for students to recognize that | | | |

|mean and median numbers are considered “averages” and that | | | |

|averages represent numbers typical of the data that can support| | | |

|an argument. | | | |

|M.4.4.5 Identify the minimum, maximum, and spread of a data set| | | |

|and describe the effect of spread on mean and median, i.e., | | | |

|know the minimum or maximum value can greatly affect the mean | | | |

|but will not affect the median. | | | |

|M.4.4.6 Demonstrate an understanding of line graphs, i.e., that| | | |

|lines going up mean increase, lines tilting down mean decrease | | | |

|and that they can vary over time, flat lines mean no change, | | | |

|and use specific vocabulary to describe trends, i.e., sharp | | | |

|increase, plummeted, etc. | | | |

|M.4.4.7 Know when percent figures don’t add up to 100% and when| | | |

|numbers and percent figures (50%, 25%, 10%) don’t match up, | | | |

|i.e., understand that circle graphs represent 100%. | | | |

|M.4.4.8 Recognize that some visual representations distort | | | |

|actual data (bar widths can provide misleading information) or | | | |

|see where authors of data reports can manipulate data to | | | |

|benefit themselves or malign others in provided materials and | | | |

|know how to recognize who produced a data report and how their | | | |

|interests might affect the report – conflict of interest. | | | |

|M.4.4.9 Reorient, reorganize, restate, summarize, or reformat | | | |

|report data (make graphs) for a particular purpose and | | | |

|audience. | | | |

|M.4.4.10 Determine and compare probabilities of chance events | | | |

|(e.g., winning lottery prizes). | | | |

|M.4.4.11 Calculate the possible combinations (a selection of | | | |

|items where order doesn’t matter) of up to five items in | | | |

|simple, practical situations (e.g., I have 4 tickets and 5 | | | |

|potential guests). | | | |

|M.4.4.12 Calculate the possible permutations (an arrangement of| | | |

|items/data in a certain order) of up to five elements in | | | |

|simple, practical situations (e.g., ways to sequence titles of | | | |

|4 different colors in a pattern). | | | |

Level 4 – Grade Level 6.0-8.9 Page 4 of 4

ABE Mathematics Verification Checklist with Materials Used and Mastery Level

|Student |Instructor |Date Enrolled |

| | | |

|M.5.4 Algebra |Materials Used - Include specific activity, book, |Mastery Level|Date & |

| |page number, etc. |% |Initials |

|M.5.4.1 Identify and use simple formulas from tables with one or two | | | |

|arithmetical steps for real-life contexts. | | | |

|M.5.4.2 Use graphs to analyze the nature of changes in quantities in | | | |

|linear relationships and use vocabulary to describe linear change. | | | |

|M.5.4.3 Recognize and describe patterns in given sets of numbers in a| | | |

|functional relationship and how changes in one quantity can affect | | | |

|another. | | | |

|M.5.4.4 Demonstrate understanding of the Cartesian coordinate system.| | | |

|M.5.4.5 Use coordinate grid to identify and locate specific points on| | | |

|the x- and y-axes. | | | |

|M.5.4.6 Graph simple linear equations by generating a table of values| | | |

|from an equation and plotting the coordinates on a graph. | | | |

|M.5.4.7 Determine the slope of a line when given two points on the | | | |

|line or the equation of a line and relate it to change. | | | |

|M.5.4.8 Write the equation of a simple line when given two points or | | | |

|slope and one point. | | | |

|M.5.4.9 Demonstrate an understanding of like terms by combining like | | | |

|terms in simple algebraic expressions. | | | |

|M.5.4.10 Demonstrate an understanding of the order of operations and | | | |

|use the order of operations when simplifying algebraic expressions. | | | |

|M.5.4.11 Add and subtract integers. | | | |

|M.5.4.12 Multiply and divide integers. | | | |

|M.5.4.13 Calculate square roots of perfect squares, estimate within | | | |

|range of square root value, and demonstrate an understanding of how | | | |

|squaring and taking the square root are related. | | | |

|M.5.4.14 Evaluate, add, subtract, multiply, and divide expressions | | | |

|involving exponents. | | | |

|M.5.4.15 Demonstrate an understanding of scientific notation. | | | |

|M.5.4.16 Demonstrate an understanding of and solve basic algebraic | | | |

|equations involving multiple steps. | | | |

|M.5.4.17 Translate word phrases into algebraic expressions and vice | | | |

|versa. | | | |

|M.5.4.18 Demonstrate an understanding of substituting values into | | | |

|simple formulas and solving for the unknown value. | | | |

|M.5.4.19 Demonstrate understanding of the distributive property. | | | |

|M.5.4.20 Read, write, order, and compare positive and negative | | | |

|numbers and identify positive and negative numbers on a number line. | | | |

|M.5.4.21 Solve real-life, multi-step word problems involving money, | | | |

|measurement, and other contextual situations using whole numbers, | | | |

|decimals, and percents. | | | |

|M.5.4.22 Recognize and eliminate extraneous information in word | | | |

|problems. | | | |

Examples of Where Adults Use Mathematics

Level 1 – Grade Level 0.0 – 1.9

|M.1.1 Number Sense and Operations: Students will develop and apply concepts of number sense and operations to explore, analyze, and solve a variety |

|of mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.1.1.1 Associate numbers and words for numbers with |Counting things one at a time, e.g., counting medicine tablets, how many to take at a|

|quantities, i.e., identify numbers (numerals and written words)|time |

|and match to quantities for numerals 1 through 20. |Buying produce |

| |Buy one, get one free sales |

|M.1.1.2 Demonstrate an understanding that if items are |Counting people in a group to make sure no one is missing |

|rearranged, the numbers stay the same. |Counting dollar bills to pay for a purchase |

| |Counting items at the grocery express lane |

| |Using the remote control for a TV |

| |Watching a digital timer on a microwave count down the time |

|M.1.1.3 Read, write, order, and compare numbers from 0 to 100. |Telling which address falls within a given block |

| |Writing a money order for a whole dollar amount (no change) |

|M.1.1.4 Recognize and count numbers through 999. |Finding a hospital or hotel room |

| |Recognizing when house numbers go up or down  |

| |Finding pages in a book |

|M.1.1.5 Count by 2s, 5s, and 10s up to 100. |Counting nickels and dimes |

| |Finding the amount of money in a small stack of $2, $5 or $10 bills  |

|M.1.1.6 Identify even and odd numbers. |Identifying which side of the street a house number would be on |

| |Identifying which side of the hall an even or odd numbered room would be on |

|M.1.1.7 Add whole numbers up to three digits (without |Finding total spent when buying two items |

|carrying). | |

|M.1.1.8 Demonstrate understanding of the concept of |Figuring how much money remains after shopping for small purchases less than $20 |

|subtraction, i.e., as in taking away or separating, from | |

|numbers up to twenty. | |

|M.1.1.9 Subtract whole numbers up to three digits (without |Finding approximate amounts left after making purchase |

|borrowing). | |

|M.1.1.10 Demonstrate an understanding of the times tables for |Computing earnings for hours worked, i.e., 8 hours worked at $10 per hour |

|the numbers 1, 2, 4, and 10. | |

|M.1.1.11 Halve even numbers up to 10 and double whole numbers |Dividing cookies among children, i.e., 8 cookies among 2 children |

|up to 10. |Computing earnings for two hours |

|M.1.1.12 Identify place value of ones, tens, and hundreds. |Reading pay stubs, money orders, and checks |

|M.1.1.13 Identify basic functions (+, -, x, (, =, on/off) on |Helping children who are learning to use a calculator |

|the calculator and digits (0-9). | |

|M.1.1.14 Identify fractional parts (1/4, 1/3, 1/2) and whole. |Cutting a cake in half |

| |Dividing a soda or candy among three children |

|M.1.1.15 Recognize currency (up to $20.00) and coins; count and|Paying bills, writing checks |

|trade pennies, nickels, dimes, and quarters to 100 cents. |Reading receipts for purchases |

|M.1.1.16 Make and verify change. |Checking amount of change when shopping, eating out, paying bills in cash, paying for|

| |services |

|M.2.1 Measurement: Students will develop and apply concepts of standard measurements and use measurement tools to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.2.1.1 Recognize and record time to the nearest hour and half |Reading appointment times |

|hour, from an analog and digital clock, including understanding|Reading schedules |

|the meaning between am and pm. |Beginning and ending time for children’s school and/or daycare |

| |Setting the alarm on a clock |

|M.2.1.2 Interpret numeric representations of dates. |Reading calendars |

| |Filling in dates on forms |

| |Reading and understanding dates on bills |

|M.2.1.3 Understand use of standard US linear measurements |Filling in forms asking for height |

|(inches, feet). | |

|M.2.1.4 Understand use of standard US capacity measurements | Reading a basic recipe |

|(cups, pints, quarts, and gallons). | |

|M.3.1 Geometry: Students will develop and apply concepts of geometric properties, relationships, and methods to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.3.1.1 Model and use directional and positional vocabulary |Assembling a piece of furniture from a diagram |

|appropriately. |Giving oral directions for getting from one place to another |

|M.3.1.2 Demonstrate an understanding of perimeter being the |Fencing a garden |

|measure around the outside edges of squares and rectangles. |Putting baseboard around a room |

|M.3.1.3 Identify and describe the properties of common |Understanding road signs |

|two-dimensional shapes (square, circle, rectangle, triangle) |Identifying things, e.g., a curved road, a straight highway, a rotary |

|using everyday language (straight, curved, etc.). |Passing drivers test or renewing driver’s license, e.g., recognizing the shape and |

| |meaning of a triangular yield sign |

| |Recognizing the shapes used in buildings and around the home (i.e., doors, cookware, |

| |etc.), and other everyday structures and items |

| |Reading directions |

|M.4.1 Data Analysis and Probability: Students will develop and apply concepts of data analysis and probability to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.4.1.1 Identify and name various simple visual data (graphs, |Reading visual data in an advertisement or poster |

|charts, tables) found in authentic publications. |Reading magazines and newspapers |

| |Looking up tax payments |

| |Finding current interest rates |

|M.4.1.2 Interpret data organized in basic categories and |Planning a neighborhood party |

|groupings. | |

|M.4.1.3 Collect, label, and order numerical information for a |Keeping track of who will or will not attend a party |

|particular purpose (e.g., to count and list stock). |Sorting stock by size |

|M.5.1 Algebra: Students will develop and apply concepts of basic algebra, patterns, relationships, and functions to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.5.1.1 Identify basic number patterns and relationships |Playing card games |

|inherent in addition and subtraction. | |

|M.5.1.2 Sort up to 20 objects or lists by color, shape, number,|Sorting laundry |

|letter, or size. |Sorting bottles for recycling |

| |Sorting telephone numbers by area code and figuring which are long distance calls |

| |Shelving stock in a store |

|M.5.1.3 Understand and complete simple number sentences. |Helping children with homework |

| |Test taking when seeking employment |

Examples of Where Adults Use Mathematics

|Level 2 – Grade Level 2.0 – 3.9 |

|M.1.2 Number Sense and Operations: Students will develop and apply concepts of number sense and operations to explore, analyze, and solve a variety |

|of mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.1.2.1 Read, write, order, and compare numbers in the |Telling which address falls within a given block |

|thousands including identifying place value. |Writing a money order or check for a whole dollar amount (no change)  |

|M.1.2.2 Demonstrate understanding of the concept of addition |Paying a seven dollar amount by using one five dollar bill and two ones or a |

|(i.e., as in adding on or combining), including the role of |thirteen dollar amount by using a ten dollar bill and three ones |

|place value. |Figuring hours of work or sleep |

|M.1.2.3 Add whole numbers up to three digits using carrying. |Adding up purchases before paying |

| |Checking charges on bills |

|M.1.2.4 Subtract whole numbers up to three digits using |Balancing a checkbook  |

|borrowing and checking. Demonstrate an understanding of how |Making change (e.g. for a $20 bill, by counting from the price to $20) |

|addition and subtraction relate to each other by checking | |

|answers using addition. | |

|M.1.2.5 Demonstrate understanding of the concept of |Reading a checkbook |

|multiplication (i.e., as in repeated addition, multiple groups,|Estimating population of people |

|rows, and columns), including the role of place value. |Reading food labels |

|M.1.2.6 Demonstrate an understanding of multiplying by 10 and |Changing dollar amounts to dimes and pennies and vice versa |

|100. |Changing meters to centimeters and vice versa |

|M.1.2.7 Multiply whole numbers up to three digits by one digit |Determining the cost of multiple items purchased at the same price |

|using carrying. | |

|M.1.2.8 Demonstrate understanding of the concept of division |Dividing recipes |

|(i.e., as dividing a set into equal groups, or determining |Reading food labels |

|number of groups within a set), including the role of place |Building projects |

|value. | |

|M.1.2.9 Divide whole numbers up to hundreds by one digit. |Calculating the cost of a single item when purchased in multiples, i.e. 3 items for |

| |$2 |

|M.1.2.10 Use rounding and estimation for tens and hundreds. For|Budgeting to pay bills |

|example, estimate the sum of 406 and 798 (nearest hundred) or |Estimating total cost of items to be purchased |

|estimate the difference between 836 and 425 (nearest ten). | |

|M.1.2.11 Demonstrate an understanding that even numbers can be |Identifying the number of possible couples at a dance or a dinner party |

|paired and that odd numbers represent amounts that when paired | |

|have one remaining. | |

|M.1.2.12 Know all pairs of numbers with a total of 10. |Adding using mental math |

|M.1.2.13 Identify multiples of 2, 3, 4, 5, and 10 up to x 10. |Increasing speed of daily calculations |

|M.1.2.14 Demonstrate an understanding of the times tables for |Increasing speed of daily calculations |

|the numbers 0 to 12. | |

|M.1.2.15 Identify factoring of common numbers (e.g., 12 = 4x3 =|Dealing with money, breaking down larger bills |

|2x6 = 2x2x3). | |

|M.1.2.16 Divide numbers by 10 and 100 and back-multiply to |Dividing money into $10 or $100 denominations |

|check results of division. | |

|M.1.2.17 Identify and demonstrate an understanding of |Following recipes |

|fractional parts including 1/8, 1/4, 1/3, 1/2, and whole. |Preparing/dividing portions of a meal among family members |

|M.1.2.18 Demonstrate how fractions relate to multiplication and|Dividing a board into equal parts |

|division (e.g., divide these 12 into 3 parts; 1/3 of 12 is 4, |Dividing a dozen Easter eggs among 3 children, 4 children, etc. |

|2/3 is 8). |Dividing a bag of candy among a specific number of people |

|M.1.2.19 Add and subtract common fractions with like |Combining ingredients in a recipe |

|denominators. |Calculating parts that are left over, i.e., cutting wood, fabric, pizza, etc. |

| |Using a 1/4 cup to measure 3/4 cup for a recipe |

|M.1.2.20 Identify improper fractions and mixed numbers. |Dividing using more than one whole, i.e., more than one pizza |

|M.1.2.21 Identify and write amounts of money using decimals, |Reading bank statements, checks, bills |

|words, and symbols. |Reading letters, forms, lease agreements, etc. involving money amounts  |

|M.1.2.22 Demonstrate an understanding of decimal notation and |Determining and comparing the weight of items by reading product labels |

|place value by reading, writing, ordering, and comparing | |

|decimals to two decimal places. | |

|M.1.2.23 Convert and express simple common fractions as |Realizing sales prices given in percents relate to fractional parts, i.e., 50% off |

|decimals. |is the same as 1/2 off. |

|M.1.2.24 Show relationship between decimal system and money, |Making purchases |

|i.e., show that 10¢ can be written as $.10, 25¢ can be written |Counting coins |

|as $.25, etc. | |

|M.2.2 Measurement: Students will develop and apply concepts of standard measurements and use measurement tools to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.2.2.1 Identify equivalent amounts of money using different |Getting out money to pay at the register |

|bills and coins. |Verifying change given at the store |

|M.2.2.2 Read, record, and use date concepts (months, days of |Completing forms (birth date, today’s date) |

|week) in common formats. |Recording appointment dates, i.e., Wednesday, July 16, 2008 |

|M.2.2.3 Read, record, and understand time of day. |Reading a bus schedule that uses am and pm |

|M.2.2.4 Telling time to the nearest minute. |Looking at a clock outside a bank and know if one is on time |

|M.2.2.5 Identify halves and whole numbers on a ruler (inches) |Measuring the length and width of a photo |

|and develop personal reference point for one’s height. |Giving one’s height on a medical form |

|M.2.2.6 Identify halves and whole numbers on weight scales |Buying fruit and vegetables by the pound |

|(pounds) and develop personal reference point for one’s weight.|Giving one’s weight on a medical form |

|M.2.2.7 Identify and select appropriate measures for capacity |Buying groceries |

|(cups, pints, quarts, and gallons) and weight (ounces, pounds, |Doubling a recipe |

|tons). |Determining the amount of weight to put on a truck |

|M.2.2.8 Interpret temperature from Fahrenheit scale in various |Reading a thermometer |

|situations, including negative temperatures. |Taking a person’s temperature |

|M.2.2.9 Read and record time of day in 24-hour format. |Determining time to complete a task |

| |Purchasing plane tickets and traveling to a foreign country |

| |Understanding military time |

|M.2.2.10 Convert units of time: hours, minutes, and seconds. |Cooking a turkey |

| |Calculating “piece work” |

| |Calculating time to travel to work |

|M.2.2.11 Identify customary US units of linear measurement and |Measuring a window using correct units |

|equivalents: inches, feet, yards, and miles. |Buying fabric for a costume |

|M.2.2.12 Measure length, width, height, and perimeter in |Purchasing window shades or coverings, weather stripping, lumber, rug, or fabric |

|inches, feet, and yards using a ruler or tape measure. |Describing a rectangular photo or frame |

| |Finding the length of fencing around a garden |

|M.2.2.13 Make rough-estimate approximations of standard US |Purchasing meats from a meat counter |

|measurements. |Planning a party |

|M.2.2.14 Read, interpret, and use map legends/keys. |Being able to read map legends/keys |

|M.3.2 Geometry: Students will develop and apply concepts of geometric properties, relationships, and methods to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.3.2.1 Demonstrate an understanding of the concepts of |Cutting cake in half or folding objects |

|sameness and halfness, i.e., identify and show where line(s) of|Designing and making a quilt |

|symmetry (i.e., the lines that divide something into 2 equal |Recognizing patterns, symmetry, and balance in landscaping, design, art, and |

|parts) falls in two-dimensional figures. |architecture |

|M.3.2.2 Use the four main compass directions (N, S, E, W) for |Reading a road sign or route sign which uses north, south, east or west |

|spatial orientation. |Making a simple map with cardinal directions |

| |Locating offices, apartments that are labeled with compass directions |

|M.3.2.3 Define and correctly use the concept of horizontal and |Reading a medical brochure |

|vertical positions. |Following assembly directions given in product manuals |

|M.3.2.4 Follow a pattern or model to produce or reproduce a |Sewing, quilting |

|shape or object. |Building, construction |

|M.4.2 Data Analysis and Probability: Students will develop and apply concepts of data analysis and probability to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.4.2.1 Solve problems using simple graphs (pictograph, bar, |Student attendance chart |

|line, and circle), tables, or distances on maps. |Children’s weekly chore chart |

| |Student demographic information |

|M.4.2.2 Identify, count, extract, and interpret pertinent data |Analyzing nutrition labels |

|organized in lists, tables, and charts. |Comparing electric usage from month to month |

| |Comparing minutes used on cell phone |

| |Grouping cents off coupons based on store layout |

|M.4.2.3 Reorient, reorganize, and reformat simple data, i.e., |Making a list of minutes used on cell phone for the past year |

|create a table to record and present numerical information. |Making list of electricity used and cost for each month for the past year |

| |Keeping a list of calories consumed for each meal over a period of time |

|M.4.2.4 Collect, label, and order numerical information for a |Keeping a log of temperature changes |

|particular purpose (e.g., keep a log, etc.). |Keeping track of a babies growth or weight |

|M.4.2.5 Identify and interpret simple graphs, tables, etc. |Reading a graph in an ad or poster |

| |Reading a chart or graph in a health pamphlet |

| |Checking items against a stock list |

|M.4.2.6 Read values on and make comparative statements about |Reading a nutrition graph in a health poster |

|relative values on a simple bar graph. |Conversing about information contained in newspapers and magazines |

|M.4.2.7 Develop an understanding of events as certain, |Making a call when flipping a coin |

|impossible, likely, or unlikely to occur. |Making decisions about how weather may affect outdoor plans |

| |Predicting the outcome of a sporting event |

| |Deciding to avoid or use certain products |

|M.4.2.8 Determine the probability of simple events, e.g., in |Gambling |

|the results of tossing a coin or rolling a die, etc. | |

 

|M.5.2 Algebra: Students will develop and apply concepts of basic algebra, patterns, relationships, and functions to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.5.2.1 Recognize and create simple repeating patterns using three or less|Counting beats in music |

|items (e.g., color, rhythmic, shape, number, and letter) and identify the |Designing a necklace and describing the assembly rule |

|unit being repeated. |Laying tile on a floor |

|M.5.2.2 Identify basic number patterns and relationships inherent in |Playing card games |

|multiplication and division (e.g., identify halves, doubles, and triples |Preparing for further study |

|of numbers). |Finding the cost of tickets for an amusement ride for three children |

| |Planning fare for round trip subway travel |

| |Sharing the cost of pizza between two friends |

|M.5.2.3 Describe quantitative change, i.e., change in the number of |Discussing weather patterns |

|daylight hours or temperature over time. |Describing seasons, daylight savings time |

| |Describing changes in the tide |

| |Discussing changes in gas and food prices |

|M.5.2.4 Interpret simple English word phrases, i.e., mathematical |Shopping |

|expressions, equations, and variables and write algebraic expressions. |Solving word problems |

|M.5.2.5 Recognize, interpret, and use basic mathematical symbols (+, -, =,|Using a calculator to find the total whole dollar amount of a grocery bill|

|) and recognize the different vocabulary used to represent each. |Using a calculator to find how much change you get from a $20 bill |

| |Helping children with homework |

|M.5.2.6 Translate simple mathematical expressions involving +, -, . |Taking tests when seeking employment |

|M.5.2.7 Use a calculator to make basic calculations and solve simple |Finding the total score for a card game |

|addition, subtraction, multiplication, and division problems and check |Finding the change for a purchase |

|solutions. |Going grocery shopping |

| |Calculating the total bills for a month or the total check written over a |

| |period of time |

| |Finding the price of 3 items ordered from a menu |

|M.5.2.8 Solve single step, real-life word problems involving addition, |Helping a child with homework |

|subtraction, multiplication, and division using up to two digit whole |Calculating distance traveling and miles left |

|numbers. |Shopping |

| |Calculating total and differences |

| |Working out the shortfall in numbers, e.g., eggs for a recipe, plants to |

| |fill a display tray, cups to serve visitors |

|M.5.2.9 Determine and use appropriate rounding and estimating techniques. |Estimating costs when shopping |

|Understand that the number "5" rounds up. |Budgeting, estimating total bills for a month |

Examples of Where Adults Use Mathematics

Level 3 – Grade Level 4.0 – 5.9

|M.1.3 Number Sense and Operations: Students will develop and apply concepts of number sense and operations to explore, analyze, and solve a variety |

|of mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.1.3.1 Read, write, order, and compare large whole numbers, |Filing papers in numerical order |

|i.e., thousands, millions, and billions. |Reading route numbers on delivery labels |

| |Purchasing large ticket items |

| |Budgeting |

| |Filling out income tax forms |

|M.1.3.2 Identify place value in large whole numbers and round off|Rounding numbers to make approximate calculations |

|large whole numbers to nearest tens, hundreds, thousands, | |

|ten-thousands, hundred-thousands, million, etc. | |

|M.1.3.3 Interpret the inverse relationship between addition and |Working “backwards” to find components with a large number |

|subtraction and multiplication and division. | |

|M.1.3.4 Demonstrate an understanding of the commutative and |Shopping for food and clothing |

|associative properties of addition and multiplication (e.g., 2 | |

|pounds of meat at $3/lb. costs the same as 3 pounds at $2/lb.). | |

|M.1.3.5 Demonstrate an understanding of factors of numbers up to |Dealing with money, breaking larger bills into smaller amounts |

|100. | |

|M.1.3.6 Demonstrate an understanding of dividing by multi-digit |Calculating cost of purchasing multiple items in bulk |

|numbers and interpreting remainder and expressing them as whole |Dividing money, food, or liquid items |

|numbers, fractions, and decimals. | |

|M.1.3.7 Demonstrate an understanding of back-multiplying to check|Shopping and tracking total cost |

|results of division. |Balancing checkbook |

|M.1.3.8 Demonstrate an understanding of prime numbers and |Finding common denominators and factoring |

|identify prime numbers up to 20. | |

|M.1.3.9 Add and subtract whole numbers up to four digits using |Calculating the production shortfall from a daily target |

|efficient methods and checking answers. |Performing mental addition |

| |Checking deposits in a checking account |

|M.1.3.10 Multiply with two and three digit numbers using |Finding the average number of hotdogs per person sold at an event |

|efficient written methods including checking answers. |Finding how many buses are needed to transport three classes of children for a field|

| |trip |

| |Calculating miles per gallon that a car attains |

| |Estimating travel time in hours based on distance and speed |

|M.1.3.11 Identify and calculate equivalent fractions (fourths, |Using a 1/4 cup measure to add 3/4 of a cup of flour to a recipe |

|thirds, halves, eighths, fifths, and tenths) and simplify |Reading fractions used in sale signs and special offers (e.g., 1/2 off)  |

|fractions to lowest terms. |Recognizing relationships in the context of measures, (e.g., that 2/8 inch = 1/4 |

| |inch) |

|M.1.3.12 Convert improper fractions to mixed numbers and mixed |Planning a meal, figuring quantities, doubling recipes |

|numbers to improper fractions. | |

|M.1.3.13 Add and subtract fractions (fourths, thirds, halves, |Determining the amount of fabric to buy for a sewing project |

|eighths, fifths, and tenths) using fractions that include like |Combining or reducing lengths for craft or construction projects |

|and unlike denominators and whole and mixed numbers. |Adding hours on a time sheet that includes fractions |

|M.1.3.14 Multiply and divide by fractions (fourths, thirds, |Finding time-and-a-half pay rate when working overtime |

|halves, eighths, fifths, and tenths) using fractions that include|Reducing the quantities in a recipe |

|like and unlike denominators and whole and mixed numbers. |Determining price when discount is given as a fraction off, i.e., 1/2 off or 1/4 off|

| | |

| |Canning and freezing foods (e.g., how many 3/4 quart jars are needed for 5 gallons |

| |of tomatoes?) |

| |Determining the length of a shelf (e.g., how long the shelf would need to be to hold|

| |20 1.5 inch binders?) |

|M.1.3.15 Relate multiplication of fractions and division, i.e., |Generating solutions using mental mathematics in situations involving common |

|multiplying by 1/4 is equivalent to dividing by 4 and dividing by|fractions |

|1/4 is equivalent to multiplying by 4. | |

|M.1.3.16 Express a relationship between two quantities as a |Calculating interest with time as a fraction of a year |

|fraction or fractional estimate, e.g., 54 of 352 graduates = | |

|54/352 or about 1/6. | |

|M.1.3.17 Identify quantities that are proportional. |Dividing sticks of butter, i.e., 1/2 stick = 1/4 cup |

| |Reading and interpreting scales on a map |

|M.1.3.18 Interpret the meaning of ratio and express a |Servings per container |

|relationship between two quantities as a ratio. |Reading map scales, reading recipes |

| |Reading game scores, i.e., wins/losses |

|M.1.3.19 Read, write, order, and compare decimals of up to three |Reading and comparing gas prices |

|decimal places. |Reading and comparing metric measurements |

| |Reading price tags |

| |Understanding prices on a menu |

|M.1.3.20 Identify place value for decimals (tenths, hundredths, |Reading price tags |

|and thousandths) and round decimals to one or two places or whole|Understanding monetary amounts |

|numbers. |Reading gas pump information  |

| |Estimating cost of groceries, restaurant bill, tips, etc. |

|M.1.3.21 Compute percentages when part and whole are given using |Calculating a percent increase in pay or demographics |

|friendly numbers, e.g., 10%, 25%, 50%, and 75%. |Analyzing issues such as budgets |

| |Interpreting newspaper articles |

|M.1.3.22 Convert decimals to fractions and percents, fractions to|Ordering a half pound at a deli that uses a digital scale |

|decimals and percents, and percents to fractions and decimals. |Recognizing 50% off and half-price as the same |

|M.1.3.23 Add, subtract, multiply, and divide numbers with |Working with money |

|decimals. |Paying bills |

| |Balancing checking account |

|M.1.3.24 Read and write large numbers with decimals (e.g., 12.6 |Understanding city, county, state, and national budgets and deficits |

|million = 12,600,000). | |

|M.1.3.25 Determine a fraction or percent of a decimal, e.g., .25 |Calculating tips |

|= 1/4 = 25%, 1.5 = 1 1/2 = 150%, etc. | |

|M.1.3.26 Understand and interpret the meaning of percent, i.e., |Figuring 7% sales tax on a one dollar item |

|percent represents a ratio of a part to a whole where the whole | |

|is 100. | |

|M.1.3.27 Read, write, order, and compare simple percentages. |Comparison shopping |

| |Understanding TV and radio advertisements using percents |

|M.1.3.28 Find given percents of any given number, i.e., what is |Determining savings on sale items |

|5% of 125?, what is 6.5% of 90?, etc. |Comparison shopping |

|M.2.3 Measurement: Students will develop and apply concepts of standard measurements and use measurement tools to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.2.3.1 Calculate units of time using a clock (both 12 and 24 |Matching 12 and 24 hour times |

|hour) and a calendar. |Understanding arrival and departure times for flights to other countries |

|M.2.3.2 Identify and select appropriate metric measurements |Reading medicine and nutritional labels |

|including meters, liters, and grams. |Buying products labeled in metric units |

|M.2.3.3 Add, subtract, multiply, and divide sums of money |Balancing a checkbook |

|including decimal notation. |Figuring one’s share of a restaurant bill being divided equally |

| |Finding cost of multiple units of an item |

|M.2.3.4 Demonstrate an understanding of the interrelation of |Estimating time of arrival with slower or faster speeds |

|distance, time, and speed and make simple calculations using |Estimating the time a trip will take from one place to another travelling at the |

|distance, time, and speed formula. |speed limit |

|M.2.3.5 Read and interpret map scales, legends, and mileage |Inferring distances on a road map |

|tables. |Reading a map to plan a hiking trip |

|  |Using mileage tables to find distance from one place to another |

| |Planning a vacation |

| |Analyzing bus routes |

|M.2.3.6 Measure with a standard ruler in inches and feet to |Knowing when precise measure is needed (e.g., cutting out quilt blocks or measuring |

|1/16 inch accuracy and a metric ruler in centimeters and |for a woodworking project) |

|milliliters. | |

|M.2.3.7 Make informal comparisons between inches and |Using a ruler with both inches and centimeter scales |

|centimeters including estimating the number of centimeters per |Selecting the appropriately sized wrench when working on a European-made car |

|inch. Create physical (bodily) benchmarks for units, e.g., |Mixing cleaning chemicals in the correct proportions by comparing metric to standard |

|fingernail = 1 cm; thumb joint = 1 inch. |liquid measure |

| |Measuring correct doses of medication |

|M.2.3.8 Convert and calculate with linear measurements (inches,|Substituting the use of foot rulers for a yardstick or a one cup measure for a quart |

|feet, yards, miles) and know the relationship of familiar |measure |

|units, e.g., 12 inches in a foot, 3 feet in a yard, 4 cups in a|Doing home repairs and carpentry projects |

|quart and convert units of measure in the same systems. | |

|M.2.3.9 Use and apply concepts of weight and capacity to solve |Loading a washing machine correctly to maintain balance throughout the cycle |

|problems, i.e., know the difference between weight and |Reading the capacity of a liquid to near exact measure |

|capacity. | |

|M.2.3.10 Use, read, compare, and calculate with positive and |Reading weather forecasts |

|negative Fahrenheit temperatures, i.e., know that temperature |Understanding wind chill factor |

|increases as it goes up and decreases as it goes down and that | |

|the sign of the temperature changes when crossing the zero | |

|degree point. | |

|M.2.3.11 Calculate times using the appropriate value and |Understanding that 2 centuries is 200 years to appreciate past events and their place|

|convert between time formats (including elapsed time), i.e., |in history |

|know equivalencies for hours, seconds, minutes, days, weeks, | |

|months, decades, and centuries. | |

|M.2.3.12 Directly measure perimeter in linear units and area in|Planning renovations or paint for a room |

|square units (sq. in., sq. ft., sq. cm.). |Making a cover for a countertop |

| |Sewing a chair cover |

|M.2.3.13 Estimate, measure, and compare weights (pounds, |Placing objects of various weights on shelves or hanging them on walls |

|ounces) using simple instruments, graduated in familiar units |Shopping for fresh vegetables in a market |

|(ounces and pounds) and know when to use appropriate measures. |Buying beverages for a large group |

|M.2.3.14 Convert and calculate using standard US units of |Weighing items at the grocery store |

|weight: tons, pounds, ounces, etc. | |

|M.2.3.15 Convert and calculate using standard US units of |Reading a recipe |

|capacity: ounces, quarts, and gallons. | |

|M.2.3.16 Demonstrate an understanding of the concept of |Painting a room |

|two-dimensional measurements and square units. |Planting a garden |

|M.2.3.17 Read analog and digital scales on measuring devices |Weighing yourself or other items on a scale |

|including meters, gauges, scales, etc. using various types of |Reading the dashboard of a car |

|units and calibrations. |Reading parking meters |

| |Checking the air pressure in tires |

|M.3.3 Geometry: Students will develop and apply concepts of geometric properties, relationships, and methods to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.3.3.1 Recognize, identify, and describe basic geometric |Reading road signs |

|shapes (triangle, square, circle, rectangle, hexagon, pentagon,|Passing driver’s license exam |

|and octagon). |Understanding shapes of buildings on maps |

|M.3.3.2 Draw two-dimensional (2-D) shapes of specific |Completing crafts, carpentry, and other projects |

|dimensions. | |

|M.3.3.3 Use informal visual methods to describe and compare |Organizing a closet |

|shape, dimension, perimeter, area, angles, and sides in |Packing a trunk |

|two-dimensional (2-D) and three-dimensional (3-D) objects. |Covering a package with paper  |

| |Tying string around a package |

|M.3.3.4 Identify properties, locations, and functions of right |Creating tiling or quilting patterns |

|angles, i.e., know that a right angle is 90 degrees or a |Framing a picture |

|quarter turn, that two right angles make a straight line, and | |

|four right angles fill a space. | |

|M.3.3.5 Use direction, distance, coordinates, latitude, |Planning an automobile trip |

|longitude, simple scales, labels, symbols, and keys to read and|Finding a city on a globe |

|use maps and plans. |Tracking a hurricane |

|M.3.3.6 Use graph paper to draw two- dimensional shapes in |Creating a pattern for a model plane |

|different orientations on a grid. |Reading floor plans |

|M.3.3.7 Calculate the area of squares, rectangles, and |Reading house plans, determining the size of rooms |

|triangles and other common figures using given formulas. |Calculating amount of carpet for a room |

| |Landscaping gardens of various shapes |

| |Wallpapering or painting |

|M.3.3.8 Recognize, identify, and describe the properties of |Pouring concrete |

|common three-dimensional shapes, i.e., cube, cylinder, and |Fitting items into storage |

|sphere. |Comparing capacities of containers |

| |Building a gingerbread house |

|M.3.3.9 Identify triangles based on their properties, i.e., |Laying flooring or tile |

|right, isosceles, equilateral, scalene, obtuse, and acute. |Quilting |

| |Landscaping |

|M.3.3.10 Identify common polygons of various shapes, i.e., |Quilting patterns |

|triangles, quadrilaterals, pentagons, hexagons, and octagons. |Highway signage |

| |Driver’s license sign test |

|M.3.3.11 Identify parallel, perpendicular, and intersecting |Scrapbooking |

|lines. |Reading city roadmaps |

| |Discussing city streets |

| |Landscaping |

|M.3.3.12 Describe characteristics of angles formed by two |Framing pictures |

|intersecting lines, i.e., vertical, supplementary, |Using a miter saw |

|complementary, adjacent, and corresponding/congruent. |Installing baseboard and crown molding |

|M.3.3.13 Identify angles of 90 and 45 degrees, right, acute, |Framing pictures |

|and obtuse. |Using borders for landscaping, wallpaper, quilts, scrapbooking |

| |Carpentry |

|M.3.3.14 Use the secondary directions for spatial orientation |Understanding a weather report |

|(e.g., NW, SW, NE, SE). |Tracking hurricane |

|M.3.3.15 Use a map with a coordinate grid. |Reading maps |

| |Finding locations on maps that are given using coordinates |

|M.3.3.16 Create three-dimensional objects from two-dimensional |Using diagram to build a birdhouse |

|representations. |Doing Origami |

| |Wrapping presents |

|M.4.3 Data Analysis and Probability: Students will develop and apply concepts of data analysis and probability to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.4.3.1 Identify, describe, and compare how a change in one |Tracking wages when paid an hourly rate on a variable work schedule |

|variable relates to a change in a second variable, i.e., |Following monthly bills (e.g., rent, heating, and telephone) in order to budget |

|situations with constant/fixed and varying/variable rates of | |

|change. | |

|M.4.3.2 Demonstrate an understanding of the concept of |Keeping track of who will or will not attend party  |

|categories such as shape, size, color, or yes/no responses and |Sorting stock by size |

|know how to count each category for subtotals. |Tracking gas usage and expenditure |

|M.4.3.3 Represent information so that it makes sense to others,|Reporting on responses to party or meeting |

|i.e., demonstrate an understanding that information can be |Keeping records for a club |

|represented in different ways (list, table, or diagram) and the|Reading labels when grocery shopping |

|importance of labeling information. |Designing and writing material for a report or publication |

|M.4.3.4 Demonstrate an understanding that when objects or |Checking monthly totals against weekly totals |

|responses are divided into categories, all data must be |Tracking utility or cell phone bills |

|included in one and only one category; therefore, categories | |

|must identify distinct sets, i.e., find a total from subtotaled| |

|categories to verify inclusion of all data. | |

|M.4.3.5 Demonstrate an understanding of scatter plots, i.e., |Keeping a visual tally of responses by category |

|that each X in a line plot represents one and only one item or |Further study in mathematics |

|response; therefore, it is verifiable that the number of | |

|responses is equal to the number of X’s. | |

|M.4.3.6 Demonstrate an understanding that a graph is a visual |Reading newspapers and magazines |

|representation and a table arranges information in rows and |Reading advertisements |

|columns. |Finding current interest rates |

|M.4.3.7 Sort graphs and tables by type, i.e., know that a bar |Participating in conversations about represented data |

|graph uses bars of various heights to display amount, line |Presenting information to children or co-workers |

|graphs use lines to display changes in amount, and circle or | |

|pie graphs represent the whole. | |

|M.4.3.8 Demonstrate an understanding that lists and tables can |Using the yellow pages |

|be ordered in different ways such as alphabetically, |Checking items against a stock list |

|numerically, or randomly. | |

|M.4.3.9 Compare relative values on a bar graph, i.e., |Conversing about information contained in newspapers and magazines |

|demonstrate an understanding that comparative statements such | |

|as greater than or less than can be made based on the height of| |

|the bars and relative numerical terms such as twice or half. | |

|M.4.3.10 Determine whether or not a graph/table connects to |Reading insurance documents to decide if what they state matches what they show in |

|statements made in text using title, data labels, and percent |tables and charts |

|matches, i.e., know how to locate data labels in tables and | |

|graphs to verify they match statements. | |

|M.4.3.11 Support simple statements with data and know if |Taking political actions to institute changes in the community |

|statements using “double” and “half” or fifty percent are |Discussing numbers with peers and co-workers |

|accurate. |Reading and/or responding to consumer materials |

|M.4.3.12 Make observations, draw conclusions, compare, and |Understanding investments and mutual funds |

|extract information from bar and circle graphs. | |

|M.4.3.13 Know that probability is the ratio of the potential |Determining the chances of winning a prize in a drawing |

|successful outcomes to total possibilities and state | |

|probability as a ratio in multiple forms (colon, words, and | |

|fractions) with simple scenarios. | |

|M.4.3.14 Determine the probability of basic events (e.g., in |Tossing a coin |

|the results of drawing cards from a deck of cards, chance of |Rolling dice |

|baby being born on a certain day of week, etc.) and express the|Planning attendance at a social event |

|likelihood of an occurrence as a ratio, fraction, or percent. |Selecting a car |

|M.5.3 Algebra: Students will develop and apply concepts of basic algebra, patterns, relationships, and functions to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.5.3.1 Identify relationships and complete number sequences |Using rate tables for postage |

|inherent in the addition and multiplication tables. |Creating sales tax tables |

|M.5.3.2 Recognize and create repeating patterns and identify |Using a table for increasing recipe amounts |

|the unit being repeated using four or more items. |Choosing proper drill bit |

| |Creating Sales Tax tables |

| |Using mental math strategies |

| |Using rate tables for prices |

|M.5.3.3 Demonstrate an understanding that a horizontal number |Reading and interpreting scales |

|line moves from left to right using lesser to greater values |  |

|and that intervals on a number line must follow a constant | |

|progression by values including negative and positive numbers | |

|and common fractions and decimals. | |

|M.5.3.4 Read and understand positive and negative numbers as |Viewing an automotive electrical gauge to determine if the battery is charging or |

|showing direction and change on both horizontal and vertical |discharging |

|number lines, i.e., demonstrate an understanding that a |Reading a thermometer to determine if fever is going up or coming down |

|horizontal number line moves from left to right using lesser to|  |

|greater values and that a vertical number line moves from the | |

|bottom up using lesser to greater values. | |

|M.5.3.5 Recognize and understand the commutative and |Preparing for further study |

|associative properties of addition and multiplication by using | |

|them to rewrite expressions. | |

|M.5.3.6 Read, write, and simplify word expressions using |Following convention in notation and order of operation |

|algebraic notation for addition, subtraction, multiplication, |Taking tests when seeking employment |

|division, and parentheses. |Billing procedures |

|M.5.3.7 Demonstrate an understanding that a variable represents|Preparing for further study |

|a missing value in addition and subtraction expressions, e.g., |Translating and solving word problems |

|substitute the value for the variable in one-step expressions | |

|using whole numbers when the value is given. | |

|M.5.3.8 Solve simple one-step equations by recognizing that |Preparing for further study |

|addition and subtraction are inverse operations and that | |

|multiplication and division are inverse operations and knowing | |

|the unknown of simple equations can be found by using the | |

|inverse of the operation present. | |

|M.5.3.9 Demonstrate an ability to use the symbols > and < in |Using mathematical language and symbols to compare and order numbers |

|number statements with larger numbers. | |

|M.5.3.10 Understand and use exponents to represent repeated |Computing with formulas on a standardized test |

|multiplication, i.e., recognize that exponents indicate the | |

|number of times that the base is written as a factor. | |

|M.5.3.11 Read, write, and compute squares and cubes of whole |Reading pollen count per cubic meter |

|numbers, i.e., 4(4) = 42 = 16 and 2(2)(2) = 23 = 8. | |

|M.5.3.12 Interpret and solve simple (one or two steps) |Taking a standardized or employment test |

|real-life word problems involving addition, subtraction, |Finding the total charge on a purchase |

|multiplication, and division. |Multiplying the monthly cable charge by twelve to find the annual charge |

| |Finding the area of a square room |

|M.5.3.13 Identify and apply simple formulas with one or two |Finding distance, rate, or time |

|arithmetical steps for real-life contexts. |Finding interest on a loan from a table |

|M.5.3.14 Write an equation representing verbal situations with |Entering an expression in a spreadsheet |

|no more than two operations, i.e., translate simple word |Increasing amounts in recipes |

|problems involving unknown quantities into simple equations. | |

|M.5.3.15 Develop flexibility in solving problems by selecting |Calculating individual restaurant bills when they have been combined into one total |

|strategies, i.e., determine when and how to split a problem |check |

|into simpler parts to make solving easier. | |

|M.5.3.16 Compute using the correct order of operations to solve|Planning a budget |

|problems including multiplication, division, addition, and |Estimating the cost of an event |

|subtraction (M, D, A, S). | |

|M.5.3.17 Apply estimation strategies and mental math to |Finding the total charge on a purchase |

|approximate solutions and then use a calculator to calculate |Multiplying the monthly cable charge by twelve to find the annual charge |

|solutions to contextual problems containing whole numbers and |Finding the area of a rectangular room |

|decimals to two places. |Determining a restaurant tip |

|M.5.3.18 Use the calculator to find squares, square roots, and |Finding the area of a square room |

|cubes of whole-number quantities, i.e., know the calculator |Finding the volume of a square box or cylinder |

|keys that generate squares, square roots, and cubes of numbers.|Using the Pythagorean Theorem |

Examples of Where Adults Use Mathematics

Level 4 – Grade Level 6.0 – 8.9

|M.1.4 Number Sense and Operations: Students will develop and apply concepts of number sense and operations to explore, analyze, and solve a variety |

|of mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.1.4.1 Carry out calculations using addition, subtraction, |Using mental and written methods of calculation to generate results when solving |

|multiplication, and division with numbers of any size using |problems using whole numbers of any size |

|efficient written methods including ways to check answers, e.g., | |

|approximate calculations, estimation, etc. | |

|M.1.4.2 Identify the greatest common factor in a given number |Preparing for higher level study |

|set. | |

|M.1.4.3 Identify prime numbers up to 100. |Preparing for higher level study |

|M.1.4.4 Read, write, order, and compare fractions and mixed |Reading fractions used in recipes |

|numbers. |Comparing interest rates (e.g., 1 1/4% versus 1 1/2%) |

|M.1.4.5 Recognize and use equivalent forms of common fractions |Calculating the size of a container required to hold a variety of portions |

|(e.g., 1/2 = 5/10). |Changing minutes to fractions of an hour on a time sheet |

| |Representing the outcome of observations as a fraction |

|M.1.4.6 Demonstrate an understanding of simple percent increase |Finding a price increase of 10% |

|and decrease. |Finding a cost-of-living salary increase |

|M.1.4.7 Round decimals in practical contexts and verbal problems.|Performing estimations of mathematical problems to check work |

|M.1.4.8 Multiply and divide with numbers involving decimals, |Finding cost of buying multiples of same item |

|e.g., 2.5 x 3.6 and 3.2 ÷ .06 with pencil and paper and using the|Finding unit cost of grocery items |

|calculator. | |

|M.1.4.9 Use proportions to solve one-step real-life problems, |Diluting a liquid in a given ratio (e.g., weed killer, paint) |

|i.e., involving percents, dimensions, scales, etc. |Recognizing when a problem can be solved using proportions |

| |Adjusting a recipe for a larger or smaller number of servings |

| |Converting measurements from one standard to another |

|M.1.4.10 Recognize and use equivalencies between common |Understanding how to read a digital scale |

|fractions, decimals, and percents to find part of whole-number |Computing discounts efficiently and flexibly using percent or fraction equivalencies|

|quantities, i.e., know common fraction, decimal, and percent |Estimating savings at a sale |

|equivalents, e.g., 50% = 1/2 = .5, 25% = .25 = 1/4, .75 = 75% = |Finding a tip using mental math |

|3/4. | |

|M.1.4.11 Compute percents by finding the part, the percent, and |Finding interest rates, mortgage rates, car loan interest |

|the whole. | |

|M.1.4.12 Use a calculator to calculate efficiently using whole |Doing any calculations at this level |

|numbers, fractions, decimals, and percents. | |

|M.2.4 Measurement: Students will develop and apply concepts of standard measurements and use measurement tools to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.2.4.1 Read, measure, estimate, calculate, and compare with and |Reading a thermometer |

|between Fahrenheit and Celsius temperatures using formulas |  |

|provided. | |

|M.2.4.2 Measure common three-dimensional shapes (e.g., a room, |Creating plans for building a model |

|window, box, etc.) and represent the information as a scale |Drawing plans for a carpentry project |

|drawing. |Creating a pattern for a sewing project |

|M.2.4.3 Use the language (meters to measure length, grams to |Traveling or communicating with people outside of the United States |

|measure mass, liters to measure volume) and prefixes (mili, | |

|centi, deci, deca, hecto, kilo) of metric units to describe | |

|environment. | |

|M.2.4.4 Make informal comparisons and estimations between grams |Measuring medications   |

|and ounces, kilograms and pounds, and liters and quarts, i.e., 1 |Replacing automotive fluids |

|ounce is approximately 29 grams, a paper clip weighs about 1 |Estimating number of pints of blood in the human body given the number of liters |

|gram, a kilogram is about 2.2 pounds, and a liter is a little | |

|larger than a quart (1.1 qts.). | |

|M.2.4.5 Calculate volume and surface area of basic cubes, |Filling a sand box or garden with mulch |

|cylinders, and rectangular containers using formulas provided. | |

|M.2.4.6 Calculate the perimeter and area of basic irregular or |Estimating amount of material required to cover a piece of furniture |

|composite shapes, i.e., shapes formed by a combination of | |

|rectangles and triangles using formulas provided. | |

|M.2.4.7 Find equivalencies and solve problems using conversions |Comparing the weights of different animals  |

|of units of weight, length/width, and capacity. | |

|M.2.4.8 Interpret, calculate, apply rates, and estimate |Calculating miles per gallon of gas, average miles per hour for a trip |

|equivalencies involving time such as velocity (mi/hr, ft/sec, |Estimating the amount of gas needed for a trip |

|m/sec), frequency (calls/hr), consumption (cal/day, kw/hr), flow |Determining how long it would take to fill a pool if you know the water flow per |

|(gal/min), change (degrees/min, inches/year), and unit rates |minute |

|(cents/min, $/sq. ft., mi/gal). | |

|M.2.4.9 Interpret and use scale drawings to solve real-life |Making quilt blocks from a scale drawing |

|problems. |Building projects using a scale drawing |

| |Reading house plans |

|M.2.4.10 Relate the measure of one object to another (e.g., this |Making posters and other visual presentations for school, college, work, or |

|is about 3 times as long, 6 of these will fit in there) and plan |community organization |

|linear spacing in a design (e.g., how many lines of what size can| |

|fit on a poster of a certain height?). | |

|M.3.4 Geometry: Students will develop and apply concepts of geometric properties, relationships, and methods to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.3.4.1 Identify and compare elements of a circle (center, |Measuring automobile tires   |

|radius, diameter, arc, circumference). |Designing circular gardens |

| |Making circle graphs |

|M.3.4.2 Calculate circumference of a circle using formulas |Determining the length of material needed to go around a circular table |

|provided. | |

|M.3.4.3 Understand the relationship of angles when you have a |Cutting molding at a correct angle so that both ends meet with no space in between |

|system of parallel lines cut by a transversal. | |

|M.3.4.4 Show more than one line of symmetry in complex shapes. |Cutting cake in half |

| |Folding objects, origami |

| |Creating a “snowflake” or hanging decoration using folded paper and scissors |

|M.3.4.5 Interpret concepts of similarity and identify figures |Cropping photographs |

|that are similar or congruent. |Assembling items bought unassembled (e.g., toys, exercise equipment, furniture) |

| |Enlarging or reducing the size of photographs |

| |Scrapbooking |

|M.3.4.6 Demonstrate understanding of the 360–degree system of |Making circle graphs for a budget |

|measuring angles and rotation. | |

|M.3.4.7 Estimate the measure of an angle, accurately measure an |Estimating where a line of symmetry would fall in a rectangular object |

|angle using a protractor, and draw angles of specific measures |Cutting molding for a corner |

|using a protractor and ruler. | |

|M.3.4.8 Apply the Pythagorean Theorem using simple numbers and |Building projects |

|basic right triangles. |Quilting and Scrapbooking |

|M.4.4 Data Analysis and Probability: Students will develop and apply concepts of data analysis and probability to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.4.4.1 Develop and draw conclusions from tables and graphs using|Understanding data presented in tables, charts, and graphs in reading material |

|instructor or student selected information. | |

|M.4.4.2 Gather data to answer a posed question and analyze and |Planning what kind of pizza or sandwiches to order for an employee luncheon |

|present data visually. |Conducting a survey for community planning |

| |Organizing findings in a chart or table |

|M.4.4.3 Demonstrate that a table can display the same data as a |Creating a graph to illustrate weight gain or loss |

|line or bar graph. |Creating a graph to illustrate temperatures over a one-week period |

|M.4.4.4 Find the average (mean), median, mode, and range for a |Estimating one’s daily expenses |

|data set. Note: it is important for students to recognize that |Explaining the median salary or median years worked in company statistics |

|mean and median numbers are considered “averages” and that |Debating proposed rent increases |

|averages represent numbers typical of the data that can support | |

|an argument. | |

|M.4.4.5 Identify the minimum, maximum, and spread of a data set |Interpreting statistical data accurately |

|and describe the effect of spread on mean and median, i.e., know |Reading temperature charts and population graphs |

|the minimum or maximum value can greatly affect the mean but will|Using a graph to illustrate the breakdown of household expenses while describing |

|not affect the median. |them orally |

|M.4.4.6 Demonstrate an understanding of line graphs, i.e., that |Looking at reports on stock market to see if they reflect the trends represented |

|lines going up mean increase, lines tilting down mean decrease |Using consumer reports to make decisions |

|and that they can vary over time, flat lines mean no change, and | |

|use specific vocabulary to describe trends, i.e., sharp increase,| |

|plummeted, etc. | |

|M.4.4.7 Know when percent figures don’t add up to 100% and when |Reading expenditure reports to determine if money spent is totally accounted for |

|numbers and percent figures (50%, 25%, 10%) don’t match up, i.e.,|Understanding and analyzing circle graphs found in reading materials |

|understand that circle graphs represent 100%. | |

|M.4.4.8 Recognize that some visual representations distort actual|Reading advertisements to make choices |

|data (bar widths can provide misleading information) or see where|Reading newspaper articles and deciding if what they state accurately matches what |

|authors of data reports can manipulate data to benefit themselves|they show |

|or malign others in provided materials and know how to recognize |Analyzing accident-related data |

|who produced a data report and how their interests might affect | |

|the report – conflict of interest. | |

|M.4.4.9 Reorient, reorganize, restate, summarize, or reformat |Summarizing data for a school report |

|report data (make graphs) for a particular purpose and audience. |Restating/explaining graph to children |

|M.4.4.10 Determine and compare probabilities of chance events |Understanding the chances of winning the lottery or other sweepstakes prizes |

|(e.g., winning lottery prizes). | |

|M.4.4.11 Calculate the possible combinations (a selection of |Buying clothes |

|items where order doesn’t matter) of up to five items in simple, |Selecting an outfit to wear |

|practical situations (e.g., I have 4 tickets and 5 potential |Dealing out playing cards |

|guests). | |

|M.4.4.12 Calculate the possible permutations (an arrangement of |Entering a security code |

|items/data in a certain order) of up to five elements in simple, |Opening a combination lock |

|practical situations (e.g., ways to sequence titles of 4 |Dialing numbers on a phone |

|different colors in a pattern). | |

|M.5.4 Algebra: Students will develop and apply concepts of basic algebra, patterns, relationships, and functions to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Examples of Where Adults Use It |

|M.5.4.1 Identify and use simple formulas from tables with one or |Converting temperature between Celsius and Fahrenheit |

|two arithmetical steps for real-life contexts. |Finding interest on a loan |

|M.5.4.2 Use graphs to analyze the nature of changes in quantities|Interpreting information presented in graphical form in newspapers or magazines |

|in linear relationships and use vocabulary to describe linear |Knowing changes in time and distance when speed changes on a trip |

|change (e.g., rises steadily, fall, gradually declines). | |

|M.5.4.3 Recognize and describe patterns in given sets of numbers |Using recipes to identify patterns, i.e., doubling or tripling ingredients |

|in a functional relationship and how changes in one quantity can | |

|affect another. | |

|M.5.4.4 Demonstrate understanding of the Cartesian coordinate |Making a graph to represent real-life data |

|system. | |

|M.5.4.5 Use coordinate grid to identify and locate specific |Organizing and displaying data to detect patterns and departures from patterns |

|points on the x- and y-axes. | |

|M.5.4.6 Graph simple linear equations by generating a table of |Locating information on a map using coordinates |

|values from an equation and plotting the coordinates on a graph. |Plotting data to create a graph for a real-life situation |

|M.5.4.7 Determine the slope of a line when given two points on |Reading charts and graphs in newspapers and magazines |

|the line or the equation of a line and relate it to change. | |

|M.5.4.8 Write the equation of a simple line when given two points|Understanding how lines are used to make graphs |

|or slope and one point. | |

|M.5.4.9 Demonstrate an understanding of like terms by combining |Preparing for further study |

|like terms in simple algebraic expressions. |Helping children with homework |

|M.5.4.10 Demonstrate an understanding of the order of operations |Solving algebraic equations containing multiple operations |

|and use the order of operations when simplifying algebraic |Helping children with homework |

|expressions. |Preparing for further study |

|M.5.4.11 Add and subtract integers, i.e., positive and negative |Reading wind-chill chart |

|numbers. |Reading a thermometer |

| |Balancing a checkbook |

| |Finding temperature change |

|M.5.4.12 Multiply and divide integers, i.e., positive and |Preparing for further study in algebra or higher math |

|negative numbers. | |

|M.5.4.13 Calculate square roots of perfect squares, estimate |Estimating the number of 12-inch tiles needed to cover a rectangular floor |

|within range of square root value, and demonstrate an | |

|understanding of how squaring and taking the square root are | |

|related. | |

|M.5.4.14 Evaluate, add, subtract, multiply, and divide |Ordering concrete (e.g., cubic yards) |

|expressions involving exponents. |Understanding exponential growth of bacteria or virus such as HIV |

|M.5.4.15 Demonstrate an understanding of scientific notation, |Computing lottery winnings |

|i.e., a shorter way to write large or really small numbers. |Expressing great distances |

|M.5.4.16 Demonstrate an understanding of and solve basic |Solving real-life word problems |

|algebraic equations involving multiple steps, e.g., 3x + 25 = |Preparing for further study in algebra or higher math  |

|100, 2x – 16 = 42, 3y+ 3 = 42, m/5 – 25 = 200. |Helping children with homework |

|M.5.4.17 Translate word phrases into algebraic expressions and |Entering an expression in a spreadsheet |

|vice versa. |Solving real-life word problems |

|M.5.4.18 Demonstrate an understanding of substituting values into|Preparing for further study |

|simple formulas and solving for the unknown value. |Using formulas to solve real-life problems |

|M.5.4.19 Demonstrate an understanding of the distributive |Knowing that taking two tablets four times a day is different than taking four |

|property, e.g., 75 x 12 = 75 x 10 + 75 x 2 and 2(a + 6) = 2a + 12|tablets twice a day |

|M.5.4.20 Read, write, order, and compare positive and negative |Using a “thermometer” to represent the progress of a fund-raiser |

|numbers and identify positive and negative numbers on a number |Preparing for further study in algebra or higher math  |

|line. | |

|M.5.4.21 Solve real-life, multi-step word problems involving |Understanding city, state, and federal budgets |

|money, measurement, and other contextual situations using whole |Understanding payroll deductions |

|numbers, decimals, and percents. For example, solve problems |Comparing price per item/weight when viewing traditional unit price tags at stores |

|relating to payroll deductions, computing and comparing unit |Reading unit price to determine best buy |

|pricing, rebates, discounts, deficits, sales taxes, shipping and |Ordering from a catalog or completing office supply requests |

|handling fees, etc. | |

|M.5.4.22 Recognize and eliminate extraneous information in word |Deciding when information given is not relevant for a decision |

|problems. |Choosing the information needed to made decisions |

Mathematics Sample Teaching Activities

Level 1 – Grade Level 0.0 – 1.9

|M.1.1 Number Sense and Operations: Students will develop and apply concepts of number sense and operations to explore, analyze, and solve a variety |

|of mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.1.1.1 Associate numbers and words for numbers with |Materials: Decks of flash cards with numerals on one side and names of those numbers on the |

|quantities, i.e., identify numbers (numerals and |other side, for all numbers 1 thru 20. Enough decks for each pair of students. Consider having |

|written words) and match to quantities for numerals 1|students make the sets of cards or see Template M.1.1.1 in Appendix C. |

|through 20. |Activity 1: One student in each pair calls out the name of the number as it is displayed to him.|

| |Reshuffle deck and then have students trade roles. |

| |Activity 2: Students in each pair write the number as the name is displayed to them. Reshuffle |

| |deck before students trade roles. Consider variations of this activity. |

|M.1.1.2 Demonstrate an understanding that if items |Materials: Decks of flash cards as identified in M.1.1.1, one deck per pair of students. |

|are rearranged, the total number of items stays the |Activity 1: One student arranges the cards from 1 to 20. Other student shuffles deck and lays |

|same. |the cards down in a row, which will not be in numerical order. Both count the cards. |

| |Materials: Penny, nickel, dime, quarter. |

| |Activity 2: Instructor projects coins in various orders, and each time asks how many coins are |

| |on the screen. |

|M.1.1.3 Read, write, order, and compare numbers from |Materials: Deck of 101 flash cards numbered from 0 to 100 with numbers on one side and written |

|0 to 100. |names on other side. Consider having students make the cards or see Template M.1.1.3 in Appendix|

| |C. |

| |Activity 1: After shuffling, deal each pair of students ten cards number side up. After one |

| |student states name of that number, other student checks back of card to see if name is correct.|

| |Then students switch roles. |

| |Activity 2: After shuffling, deal each pair of students ten cards word side up. Each student |

| |writes the number in a column as one card is moved from the top of the deck to reveal the next |

| |card. Then students compare columns and resolve discrepancies, as directed by instructor. |

| |Activity 3: After shuffling, deal each pair of students ten cards word side up. One student |

| |arranges them in order of lowest value to highest value, except for one intentional mistake. The|

| |other student then locates and corrects that mistake. |

| |Activity 4: Deal 2 cards to each student and have students tell class which number is lower and |

| |which is higher. Repeat after collecting and reshuffling cards. |

| |Materials: Spiral Board Game for each group of 2 to 4 students. See Appendix C Template M.1.1.3 |

| |Spiral Board Game. Enough dice for each student to have one die. Game piece for each student, |

| |for example, different color buttons. |

| |Activity 5: Students play a board game to help with counting to 100. See Appendix C Template |

| |M.1.1.3 for instructions. |

|M.1.1.4 Recognize and count numbers through 999. |Materials: One box of toothpicks per pair of students. Rubber bands of different colors. |

| |Activity 1: After instructor assigns a number, one student counts that number of toothpicks, |

| |then other student recounts. If pair members do not agree, they trade toothpicks with another |

| |pair and pairs check each other’s counts. |

| |Activity 2: Instructor puts several toothpicks in a bundle and wraps them with a rubber band, |

| |then gives a bundle of toothpicks to each pair of students. Pairs count toothpicks and record |

| |rubber band color and toothpick count, then trades with another pair and counts the toothpicks |

| |in the new bundle. After each pair has counted at least two bundles of toothpicks, instructor |

| |writes color on chalkboard, and then records all counts of how many toothpicks in that bundle. |

| |One option for dealing with count discrepancies is to have another pair of students count the |

| |toothpicks in that bundle. |

|M.1.1.5 Count by 2s, 5s, and 10s up to 100. |Materials: Shuffled deck of flash cards from M.1.1.1 for each pair of students. |

| |Activity 1: Students select the cards that would be used to count by 2s and arrange them in |

| |ascending order. |

| |Materials: Shuffled deck of # flash cards from M.1.1.3 for each pair of students. |

| |Activity 2: Students select the cards that would be used to count by 5s and arrange them in |

| |ascending order. |

| |Activity 3: Students select the cards that would be used to count by 10s and arrange them in |

| |ascending order. |

| |Activity 4: Repeat any of the previous activities but require that cards be arranged with name |

| |side up. |

|M.1.1.6 Identify even and odd numbers. |Materials: Shuffled deck of flash cards from M.1.1.1 for each pair of students. |

| |Activity 1: Students sort the cards into piles of odd numbers and even numbers. |

| |Activity 2: Have students arrange the cards they sorted in Activity 1 into rows or columns in |

| |ascending order of card value. |

|M.1.1.7 Add whole numbers up to three digits (without|Materials: 3 dice for each pair of students. |

|carrying). |Activity: One student in each pair rolls the 3 dice at the same time, and rolls again if there |

| |are any 5s or 6s showing. When there are no 5’s or 6’s, the other student reads the number on |

| |the die farthest to the left and puts that number in the hundreds place. The number on the |

| |middle die goes in the tens place and the number on the die farthest to the right goes in the |

| |ones place. That process is repeated to get a second number for an addition problem. Then |

| |students reverse roles so that both students have an addition problem to solve. After they have |

| |done so, they check each other’s work, then show their problems and answers to the instructor. |

| |This exercise can be repeated as many times as students need to learn how to complete this type |

| |of calculation. |

|M.1.1.8 Demonstrate understanding of the concept of |Materials: Twenty toothpicks per student. |

|subtraction, i.e., as in taking away or separating, |Activity 1: Ask students to count out a given number of toothpicks, and then remove an assigned |

|from numbers up to twenty. |number from that pile and determine how many remain in the pile. Repeat with different values as|

| |many times as appropriate for adequate understanding. |

| |Activity 2: Ask students to count out a given number of toothpicks, and then remove toothpicks |

| |from that pile until an assigned number remain. Count how many were removed. Repeat with |

| |different values as many times as appropriate for adequate understanding. |

|M.1.1.9 Subtract whole numbers up to three digits |Materials: Decks of playing cards (with tens and face cards removed) so that each small group of|

|(without borrowing). |students has a deck. |

| |Activity 1: Explain that the aces will count as ones and jokers as zeros. Designate a student in|

| |each group to shuffle the deck of cards and deal each student two cards. Have each student in |

| |the group make a subtraction problem by subtracting the smaller number from the larger number |

| |with the other students checking to see that the subtraction was completed correctly. |

| |Activity 2: After students practice using two cards, then deal each student four cards, advising|

| |them to use the two cards with the larger numbers for the top number and the two with the |

| |smaller numbers as the bottom number and complete the subtraction problem. They can arrange the |

| |cards in what ever order they choose, i.e., if a students is dealt a 3, 5, 6, 9; their top |

| |number would be 69 or 96 and the bottom number would be 35 or 53 or if a student is deal a 0, 2,|

| |2, 7; their top number would be 27 or 72 and the bottom number would be 02 or 20. Students may |

| |use paper and pencil to solve the resulting problems, if needed. |

| |Activity 3: After students practice using four cards, increase the cards being dealt to five or |

| |six cards so that with five cards they can practice subtracting two digit numbers from three |

| |digit numbers and with six cards they can practice subtracting three digits numbers. |

|M.1.1.10 Demonstrate an understanding of the times |Materials: An assortment of pennies, nickels, and dimes for each student or group if students |

|tables for the numbers 1, 2, 5, and 10. |are working together. |

| |Activity 1: Ask students to determine how much money they will have if they count out a given |

| |number of a certain coin. Remind them to use multiplication to obtain that value. Repeat |

| |activity with different numbers and different value coins. |

| |Activity 2: To illustrate multiplication table for 2, ask students to raise both hands and |

| |determine how many human hands are in the air, in a given row, are female, etc. (If classroom |

| |includes amputees, change to human feet, ears, or eyes and change “raising hands” to “feet on |

| |the floor”, etc.). |

| |Activity 3: Ask how many coin sides there are on a given number of coins. Repeat with different |

| |numbers. |

|M.1.1.11 Halve even numbers up to 10 and double whole|Materials: Twenty toothpicks per pair of students. |

|numbers up to 10. |Activity 1: Ask how many toothpicks each student in a pair will get if each gets half of an |

| |assigned number. Have students count that number of toothpicks, then each take half of that |

| |number to verify each will have the same number with no toothpicks left over. |

| |Activity 2: Ask how many toothpicks will be used if each student of a pair gets an assigned |

| |number of toothpicks. Then have each student take that number of toothpicks, combine their |

| |toothpicks into a group, and count the total number of toothpicks selected. |

|M.1.1.12 Identify place value of ones, tens, and |Materials: One deck of I Have, Who Has place value cards for up to 17 students. You will need 2 |

|hundreds. |decks if you have more than 17 students. See Appendix C Template: M.1.1.12 Place Value |

| |Activity: Students pay a I Have, Who Has card game for practicing their place value skills for |

| |ones, tens, and hundreds. See Template: M.1.1.12 Place Value for additional instructions. |

|M.1.1.13 Identify basic functions (+, -, x, (, =, |Materials: One calculator per student or pair of students. |

|on/off) on the calculator and digits (0-9). |Activity: Have students identify the basic function keys on the calculator and then complete |

| |simple problems using the basic functions. |

|M.1.1.14 Identify fractional parts (1/4, 1/3, 1/2) |Materials: Cut strips of paper into 1” x 8.5” strips so that you have enough for each student to|

|and whole. |have at least four strips. |

| |Activity 1: Have students mark one strip as a whole. Then have them fold another strip in half |

| |and mark each part as 1/2, then fold another strip into thirds and mark each part as 1/3, then |

| |fold another strip into fourths and mark each part as 1/4. Discuss how as the denominator of the|

| |fraction gets larger the actual size of the fractional piece gets smaller. |

| |Materials: Appendix C Template M.1.1.14 Blank Circles. Make copies so that each student can have|

| |a sheet of 3 circles. Scissors for each student. |

| |Activity 2: Have students cut out one of the circles, and then cut it into halves. Repeat with |

| |another circle but cut into four equal size parts. Repeat on third circle but cut into three |

| |equal size parts. |

| |Materials: One worksheet per student showing circles with slices of size 1/2, 1/3, or 1/4. See |

| |Appendix C Template M.1.1.14 Fractional Circles. |

| |Activity 3: Have students label the fractional parts shown on their worksheet. Have students |

| |share things/examples from real life where one might want to divide something in half, in |

| |thirds, or in fourths. Share responses and ask for questions/discussion. |

| |Materials: Play Dough for each student, paper plate or wax paper to protect work surface, and |

| |plastic knife. |

| |Activity 4: Have students make several shapes using play dough and then cut each shape into |

| |different fractional parts. |

| |Materials: Several egg cartons and several dozen different colored plastic egg. |

| |Activity 5: Have students work in pairs to create specified mixtures of eggs to make a dozen, |

| |i.e., 1/2 blue and 1/2 pink or 1/3 yellow, 1/3 green, 1/3 blue or 1/2 blue, 1/4 yellow, 1/4 |

| |pink, etc. |

|M.1.1.15 Recognize currency (up to $20.00) and coins;|Materials: Sets of play money that includes pennies, nickels, dimes, quarters, $1 bills, $5 |

|count and trade pennies, nickels, dimes, and quarters|bills, $10 bills and $20 so that each pair of students would have money work with. |

|to 100 cents. |Activity 1: Ask each student to find and hold up a coin or bill of an assigned denomination. |

| |Repeat in random order until all denominations have been called out at least twice. |

| |Activity 2: Have students work in pairs to make at least 2 sets of three equivalencies. For |

| |example one group may show 10 pennies =2 nickels = 1 dimes and 4 $5 bills = 2 $10 bills = 1 $20 |

| |bill. Students may have many different variations. |

| |Activity 3: Assign a certain amount of money to be counted our. For example $18.24. Have |

| |students share the money combination they used to count out that amount of money. Repeat using |

| |different amounts of money until students can easily count different amounts up to $20.00. |

|M.1.1.16 Make and verify change. |Materials: Sets of play money that includes pennies, nickels, dimes, quarters, $1 bills, $5 |

| |bills, $10 bills and $20 so that each pair of students would have money work with. |

| |Activity 1: One student uses a $20 bill in a mock purchase of an item of the price the |

| |instructor writes on the chalkboard, and the other student chooses the correct change, which the|

| |purchaser then verifies. Repeat with differing purchase prices and paying with different amounts|

| |until all students can easily make change. |

|M.2.1 Measurement: Students will develop and apply concepts of standard measurements and use measurement tools to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.2.1.1 Recognize and record time to the nearest hour|Materials: An analog clock and a digital clock or pictures showing time that can be projected. |

|and half hour, from an analog and digital clock, |Activity: Ask students to record the times shown on the clocks including ‘am’ or ‘pm’. When you |

|including understanding the meaning between am and |show them the time on the close include phrases such as this is what time I went to bed last |

|pm. |night or this is the time that I ate breakfast this morning so that they can correctly indicate |

| |pm and am. After students have recorded their response write correct responses on the board and |

| |ask questions to generate discussion. |

|M.2.1.2 Interpret numeric representations of dates. |Materials: One calendar per student. |

| |Activity: After a date is written in numerical form on the chalkboard, each student is to locate|

| |that day on the calendar. If calendars are all for the same year, instructor can do quick checks|

| |by asking what day of the week that date falls on. Spot checks can also be done, or students can|

| |be asked to compare their finding with the finding of another student. |

|M.2.1.3 Understand use of standard US linear |Materials: One tape measure for each pair of students. |

|measurements (inches, feet). |Activity 1: Assign each pair an item two items to measure, such as windowpane, room wall, table |

| |length, chalkboard length, height of chair, etc. Have students record item measured and |

| |measurement obtained on board, and then rewrite that measurement in the alternate form (inches |

| |vs. feet and inches). Be sure two different pairs of students measure the same object, compare |

| |measurements, and if there is a disagreement in measurement or conversion from inches to feet or|

| |feet to inches, discuss to clarify understanding. |

| |Activity 2: Mark a point on the chalkboard and assign a pair of students to measure and mark end|

| |point for a given distance. Next pair should verify that measurement, and then repeat with a |

| |different measurement. Continue until every pair has made and verified at least two |

| |measurements. |

|M.2.1.4 Understand use of standard US capacity |Materials: Gallon containers filled with water for each pair of students. Also at least four |

|measurements (cups, pints, quarts, and gallons). |quart-size and pint-size containers and 1-cup measuring cups. |

| |Activity: One student pair is assigned to empty gallon into quart-size containers to determine |

| |how many it fills while another student pair pours a quart of water into pint-size containers |

| |and a third pair pours a pint of water into measuring cups. Each records how container sizes and|

| |how many are smaller containers are filled from the larger container. After returning the water |

| |to the one-gallon container, student pairs rotate assignments until all pairs have completed all|

| |three measurements. Follow with class discussion of how many ___ in a ____. |

|M.3.1 Geometry: Students will develop and apply concepts of geometric properties, relationships, and methods to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.3.1.1 Model and use directional and positional |Activity 1: Have students point to specific directions as called out by the instructor. Take |

|vocabulary appropriately. |time to observe problems and give explanations. |

| |Activity 2: Have students write the direction for a series of instructor demonstrations |

| |(pointing and/or with appropriate explanations, i.e., if I go to the women’s bathroom from here |

| |it will be on which side of the hall, when I leave the parking lot would I turn left or right to|

| |go to ___). Review responses with a show of hands so understanding can be gauged. Have students |

| |make up and ask similar questions. |

|M.3.1.2 Demonstrate an understanding of perimeter |Activity: Ask students to choose an item in the classroom and demonstrate what the perimeter |

|being the measure around the outside edges of squares|would be, i.e. for a desk they would show that the perimeter would be the distance around the |

|and rectangles. |edges, for the room the perimeter would be the distance around the walls, etc. |

|M.3.1.3 Identify and describe the properties of |Materials: Straightedge, protractor, compass, etc. for instructor to draw on chalkboard. |

|common two-dimensional shapes (square, circle, |Activity: Ask students to record if instructor sketches are straight or curved and the number of|

|rectangle, triangle) using everyday language |sides as instructor draws shapes and lines in different orientations. Ask for responses and |

|(straight, curved, etc.). |discuss each sketch before erasing any to make room for additional sketches. |

|M.4.1 Data Analysis and Probability: Students will develop and apply concepts of data analysis and probability to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.4.1.1 Identify and name various simple visual data |Materials: One copy per student of simple visual data taken from authentic publications |

|(graphs, charts, tables) found in authentic |(brochure, newspaper, magazine, etc). |

|publications. |Activity: Give each student an example of visual data and then have students identify the visual|

| |data assigned to them and giving at least two examples of why they decided it was that type. |

|M.4.1.2 Interpret data organized in basic categories |Materials: One copy per student of various visual data taken from authentic publications |

|and groupings. |(brochure, newspaper, magazine, etc). |

| |Activity: Ask students to interpret their assigned figure, and then explain what that figure |

| |illustrates. Ask other students to add additional details. Clarify explanation and answer |

| |student questions before proceeding to the next figure and a different volunteer. |

|M.4.1.3 Collect, label, and order numerical |Materials: With input from students, collect multiple scores for a given game, either from a |

|information for a particular purpose (e.g., to count |classroom activity or a newspaper. |

|and list stock). |Activity: Ask students to order the scores and write an appropriate label for the ordered |

| |scores. Upon completion, review different ways students chose to order the scores. If students |

| |appear to need more practice, repeat activity or assign appropriate homework. |

| |Materials: A small bag or cup of M&M’s for each student. |

| |Have students to list the “stock” in each bag or cup of M&M’s. |

|M.5.1 Algebra: Students will develop and apply concepts of basic algebra, patterns, relationships, and functions to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.5.1.1 Identify basic number patterns and |Materials: One Deck of flash cards numbered from 0 to 100 with numbers on one side for each pair|

|relationships inherent in addition and subtraction. |or small group of students. Can use M.1.1.3 Flash Cards to make the decks. |

| |Activity 1: Have students use their deck of cards to show a five card pattern for several of the|

| |following number patterns: repeated addition, i.e., adding one each time, adding two each time, |

| |etc.; repeated subtraction, i.e., subtracting one each time, three each time, etc.; consecutive |

| |odd numbers; consecutive even numbers; halving each time beginning with 80; doubling each time; |

| |tripling each time; etc. Have students share their sequence since answers will vary based on the|

| |card chosen for the first number in each sequence. |

| |Activity 2: Have students set up a card pattern similar to the ones used above or have them set |

| |up a patter where cards are missing within the pattern, such as 5, __, 15, __, ___, 30. When |

| |each group gets their pattern set up have students move from group to group to identify the next|

| |three numbers in the sequence or the missing number in the sequence and then describing the |

| |sequence, i.e., adding five each time or five times table. |

|M.5.1.2 Sort up to 20 objects or lists by color, |Materials: Approximately 20 buttons of various shapes, sizes, colors for each pair of students |

|shape, number, letter, or size. |Activity 1: Ask students to sort buttons by size, keeping those of identical size in the same |

| |group. After this exercise is completed and visually checked by instructor, ask students to sort|

| |their buttons by color. After color sorting is checked by instructor, have each student sort the|

| |buttons by first letter of their color, then explain to another student what color names they |

| |chose. |

| |Materials: One deck of playing cards per group of three students. |

| |Activity 2: After shuffling their deck, each group of three students should be told to divide |

| |the deck into 3 approximately equal groups, one per student in the group. Then have each student|

| |sort his/her cards by suit. After visually checked by instructor, have each student resort by |

| |color. After instructor checks color sorting, have each student sort his/her cards by size (tell|

| |them if they should consider Ace as one or as the highest card). |

|M.5.1.3 Understand and complete simple number |Materials: A picture that has multiple items, i.e., a picture that has many different animals or|

|sentences. |a picture that has different color flowers or different types of flowers, etc. for each small |

| |group of students. |

| |Activity: Assign a picture to each group of students. Have students work together to develop a |

| |story using number sentences about the items in their picture that they will share with the |

| |class. For example, they may say, “Our pictures is a picture of a farm. It has 3 goats, 5 pigs, |

| |and 1 cow for a total of 9 animals. It also has 2 small trees and 4 large trees for a total of 6|

| |trees. As one member of the group tells the story, have another member of the group write the |

| |number sentences on the board, i.e., 3 + 5 + 1 = 9 and 2 + 4 = 6. |

Mathematics Sample Teaching Activities

Level 2 – Grade Level 2.0 – 3.9

|M.1.2 Number Sense and Operations: Students will develop and apply concepts of number sense and operations to explore, analyze, and solve a variety |

|of mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.1.2.1 Read, write, order, and compare numbers in |Materials: Deck of playing cards with tens, face cards, and jokers removed. |

|the thousands including identifying place value. |Activity 1: Deal each student 4 cards. Have them record the numbers from the four cards on a |

| |piece of paper to make a number in the thousands. Ask each student to read their number. |

| |Activity 2: Using the same four cards from Activity 1, ask students to arrange the four |

| |cards/digits to make as large a number as possible, have them read their number. As the numbers |

| |are read record them on the board. After 5-6 students have read their numbers have students |

| |arrange the numbers from smallest to largest. |

|M.1.2.2 Demonstrate understanding of the concept of|Materials: Dime, penny, and play/monopoly dollar for each student. |

|addition (i.e., as in adding on or combining), |Activity 1: In pairs, students calculate how much money they have if they pool their money in |

|including the role of place value. |all combinations of 2 items (dime and penny, dollar and dime, dollar and penny). |

| |Activity 2: Make columns on chalkboard, and have each pair write their total in each column |

| |(values in each column should be the same). Then have students total the amount of money in the |

| |room (use statement such as “Let’s see how much we have if we pool our money to buy a pizza”). |

|M.1.2.3 Add whole numbers up to three digits using |Activity: Ask each student to count/sum the amount of money they have in change in their pocket|

|carrying. |or purse (those who do not have any may write a total from activity 1 in M.1.2.2). Then have |

| |students total the amount of money in the room (use statement such as “Let’s see how much we |

| |have if we pool our money to buy a pizza”). |

|M.1.2.4 Subtract whole numbers up to three digits |Materials: Play/monopoly money. |

|using borrowing and checking. Demonstrate an |Activity: Distribute $900 in play/monopoly money to each pair of students. Write a number on |

|understanding of how addition and subtraction |the chalkboard and tell them they have just received a bill for that amount of money; direct |

|relate to each other by checking answers using |them to calculate how much they will have left after they pay that bill. Direct them to add the |

|addition. |money they “paid” to the money they have left to check their computation. After they complete |

| |both calculations, have them count the money to “pay” the amount on the chalkboard, then count |

| |the money they have left to see if it matches their answer. Repeat this exercise several times, |

| |by changing the “cost” written on the chalkboard each time. |

|M.1.2.5 Demonstrate understanding of the concept of|Materials: Two dimes, pennies, and play/monopoly dollars for each student. |

|multiplication (i.e., as in repeated addition, |Activity: Direct students to put specific combinations of three of their money units in front |

|multiple groups, rows, and columns), including the |of them (and cover the rest), and ask what the total is (begin with two $1 and one dime). When |

|role of place value. |they agree, write that number on the chalkboard, then ask how much money would result from |

| |pooling the money from four students. Direct students to determine the total amount of exposed |

| |money by multiplying by 4. The class can then check that total by combining the exposed money |

| |and counting it. Repeat this exercise with several other combinations of three units, including |

| |one dollar, one dime, and one penny, two dollars and one penny, etc. and varying the number of |

| |students whose money is pooled. |

|M.1.2.6 Demonstrate an understanding of multiplying|Materials: 100 pennies and 10 dimes for each student. One worksheet per student listing items |

|by 10 and 100. |and purchase prices with every price being a multiple of 10 cents. |

| |Activity 1: Each student gets 100 pennies. The premise for this activity is that they are |

| |isolated in a place where all purchases are from vending machines that only take pennies. Direct|

| |students to make put enough pennies in stacks of 10 to purchase various items costing less than |

| |$1. After each “purchase”, student should fill in number of stacks and total number of pennies |

| |on worksheets ____ X 10 = ____. For last question in this activity, allow them to purchase 10 |

| |dimes with 10 stacks of 10 pennies and complete that problem on the worksheet. Discuss |

| |multiplication by 10 before proceeding to activity 2. |

| |Activity 2: Each student now has 10 dimes. The premise for this activity is that the vending |

| |machines have been upgraded to take dimes only. Direct students to put enough dimes in stacks of|

| |10 to purchase various items shown on the worksheet (each cost being between $2 and $10 but |

| |always whole dollars). After each “purchase”, student should fill in number of stacks and total |

| |number of dimes on worksheets, then write the number of pennies represented by each purchase. |

| |Discuss multiplication by 100 in the context of 1 cent times ___ dollars = ____ cents. |

|M.1.2.7 Multiply whole numbers up to three digits |Materials: Two hundreds, two tens, and two ones in play money for each student. |

|by one digit using carrying. |Activity: Direct students to put specific combinations of three of three bills in front of them|

| |(and cover the rest), and ask what the total is (begin with two $100 and one $10). When they |

| |agree, write that number on the board, then ask how much money would result from pooling the |

| |money from six students. The class can then check that total by combining the exposed money and |

| |counting it. Repeat this exercise with several other combinations of two of one unit and one of |

| |another, and varying the number of students whose money is pooled (up to 9 students). |

|M.1.2.8 Demonstrate understanding of the concept of|Materials: 30 toothpicks for each student. |

|division (i.e., as dividing a set into equal |Activity: Direct students to separate their toothpicks into two groups and point out how that |

|groups, or determining number of groups within a |relates to division of 30 by 2. Repeat this process by separating into 3 groups, then 5 groups, |

|set), including the role of place value. |then 6 groups. |

|M.1.2.9 Divide whole numbers up to hundreds by one |Materials: Box of toothpicks for each student. |

|digit. |Activity: Assign a number of toothpicks for students to select. After each student has counted |

| |out that many, tell them to divide the toothpicks into 2 groups and determine how many are in |

| |each group. Repeat exercise with 3 groups, 4 groups, etc. through 9 groups. |

|M.1.2.10 Use rounding and estimation for tens and |Materials: Template M.1.2.10 “Rounding in a Row for Addition” game. |

|hundreds. For example, estimate the sum of 406 and |Activity 1: Play the game according to the rules given on the template. |

|798 (nearest hundred) or estimate the difference |Activity 2: Allow student to make up different rules or a new game board. |

|between 836 and 425 (nearest ten). | |

|M.1.2.11 Demonstrate an understanding that even |Materials: Box of toothpicks for each student. |

|numbers can be paired and that odd numbers |Activity: Assign a number of toothpicks for students to select and verify that everyone knows |

|represent amounts that when paired have one |if the assigned number is even or odd. After each student has counted out that many, tell them |

|remaining. |to move two toothpicks at a time to a new pile. When everyone has finished, ask who has one |

| |toothpick left over. If any students have a different result than expected, have them repeat the|

| |exercise as part of a team of two students to demonstrate what happens with a correct count. |

|M.1.2.12 Know all pairs of numbers with a total of |Materials: Flash cards with pairs of numbers that add to ten, with one of those numbers on one |

|10. |side and the other number on the other side. One set for each pair of students: |

| |Activity: After shuffling the cards, one member of the student pair displays a card for the |

| |other student to read. When the second student states the value that must be added to the |

| |displayed number to result in a total of 10, the first student checks the answer by looking at |

| |the back side of the card, and proceeds to the next card if correct. Exercise should be repeated|

| |several times with cards reversed and reshuffled, and pair members switching roles. |

|M.1.2.13 Identify multiples of 2, 3, 4, 5, and 10 |Materials: Deck of playing cards (without jokers) for each group of 3, 4, or 5 students. |

|up to x 10. |Activity: Write on chalkboard that Jack = 11, Queen = 12, King = 13, and Ace = 14. Organize |

| |groups of 3, 4, or 5 students and give each group a deck of cards. Dealer rotates after each |

| |hand. After shuffling cards, dealer deals 5 cards to each player and puts the remaining cards in|

| |a “draw pile”. On each turn, a player can discard one card and draw a replacement from the draw |

| |pile. First player to show 5 cards that are all multiples of 2 wins. Then game is repeated with |

| |object being to show 5 cards that are all multiples of 3. If draw pile is exhausted without a |

| |winner, reshuffle and try again. Since each suit only contains two multiples of 5, 6 and 7 use |

| |double decks of cards for those multiples. Since each suit only contains one multiple or 8 and |

| |one of 9, this game is not suitable for learning those multiples. |

|M.1.2.14 Demonstrate an understanding of the times |Materials: A times table chart. |

|tables for the numbers 0 to 12. |Activity 1: Have students mark out all the times tables they know. Then have the mark out the |

| |reverse of the ones they know, i.e., if they know 3 x 12, then they also know 12 x 3. Discuss |

| |with students how little they have left to learn. |

| |Materials: small blocks, toothpicks, or buttons |

| |Activity 2: Ask students to demonstrate with the concrete objects different facts from the |

| |multiplication tables. For example, is they demonstrate 3 x 7 they should have three piles of 7 |

| |items in each pile or 7 piles of 3 items in each. Be sure they understand that 3 x 7 and 7 x 3 |

| |is the same total number of items. |

| |Materials: 1 Beach Ball. To prepare cover the inflated beach ball with circles by tracing |

| |circles using a 3-4 inch diameter pattern (a paper cup works well as a pattern) and a permanent |

| |marker. Inside each circle write math problems that focus on the skills you want to reinforce. |

| |Activity 3: Have participants form a circle. If you have a large group you can form several |

| |circles of 6 to 8 participants. Explain the rules of the game: |

| |Toss the ball to a player. |

| |The player who catches the ball must read aloud and answer the problem that is covered by the |

| |right thumb. |

| |That player then tosses the ball to another player. |

| |Continue to play ball as time allows. |

|M.1.2.15 Identify factoring of common numbers |Materials: Pair of dice for each pair of students. |

|(e.g., 12 = 4x3 = 2x6 = 2x2x3). |Activity: Pair members take turns rolling the two dice and identifying ways the sum of the |

| |numbers obtained from that roll can be factored. Other pair member verifies that those are |

| |factors and pair records number under name of pair member rolling the dice. Winner is pair |

| |member who has the highest total after each has ten turns. |

|M.1.2.16 Divide numbers by 10 and 100 and |Materials: 100 pennies and 10 dimes for each pair of students. Fifty $10 bills and twenty $100 |

|back-multiply to check results of division. |bills in play or monopoly money. |

| |Activity 1: Each pair of students gets 100 pennies and 10 dimes. Direct pairs to move all the |

| |pennies to one pair member and all the dimes to the other. Each time the instructor writes a |

| |multiple of 10 cents on the chalkboard, students determine how many dimes that represents, and |

| |trade coins accordingly. After each “exchange”, students should complete the expression ___ |

| |divide by 10 = ____ by putting the number of pennies in the first blank and the number of dimes |

| |in the last blank. Discuss division by 10 and point out the relationship to multiplication by 10|

| |before proceeding to activity 2. |

| |Activity 2: Each pair of students gets fifty $10 and twenty $100 bills in play or monopoly |

| |money. Each time the instructor writes an amount on the chalkboard, students determine how many |

| |$10 or $100 bills that represents, as directed by the instructor. One pair member counts that |

| |amount in $10 bills while the other counts that amount in $100 (roles should reverse after each|

| |problem). After each problem, each student should write the $___ divided by ___ = ___ ____ and |

| |put the amount of money shown on the chalkboard in the first blank, and the number and |

| |denomination ($1 or $10) in the last two blanks. Pair members should check each other’s work |

| |after each problem. After sufficient repetitions, discuss division by 10 and by 100 and point |

| |out the relationship to multiplication by 10 and by 100. |

|M.1.2.17 Identify and demonstrate an understanding |Materials: Two manipulative circles (such as felt backed), one divided into 6ths and one |

|of fractional parts including 1/8, 1/4, 1/3, 1/2, |divided into 8ths. One worksheet per student showing sketches of pies, some sliced into 6 pieces|

|and whole. |and some into 8 pieces. |

| |Activity: Show the relationship between number of slices and fraction of the circle. Have |

| |students color or shade 2 slices of an 8-piece pie to create ¼, two slices of a 6-piece pie to |

| |create 1/3, etc. |

|M.1.2.18 Demonstrate how fractions relate to |Materials: 20 play/monopoly money $1 bills for each pair of students. |

|multiplication and division (e.g., divide these 12 |Activity 1: Tell students that each pair member should take half of the money. After they |

|into 3 parts; 1/3 of 12 is 4, 2/3 is 8). |divide the money, ask how much each has, and point out the relationship between ½ and dividing |

| |by 2. |

| |Activity 2: Tell students to donate $2 to the bank, and divide the remaining $18 into thirds so|

| |they each get a third and the instructor gets a third. Ask how much each student still has and |

| |relate 1/3 of 18 to dividing by 3. |

| |Activity 3: Redistribute money so each pair of students has twelve $1 bills. Direct them to |

| |divide into halves and record the amount of money each gets. Then direct them to repeat this |

| |exercise after dividing into thirds, and again after dividing into fourths. Review the activity |

| |and discuss its objective. |

|M.1.2.19 Add and subtract common fractions with the|Materials: Make 3 fraction circles and copy one of each for each student, ex., using 1/3, 1/8/ |

|like denominators. |and 1/12 allows illustration of a range of fractions sizes. |

| |Activity 1: Direct students to shade or color one section of the 1/3 fraction circle. After |

| |students shade/color another 1/3 section slightly differently, ask the to add 1/3 + 1/3 (point |

| |out that this is just like adding 1 apple or whatever to another). Then ask what proportion of |

| |the circle is shaded. |

| |Activity 2: Ask students how many thirds are in the 1/3 fraction circle. After they agree that |

| |there are 3, ask them to subtract the number of shaded/colored thirds from 3 to find how many |

| |are not shaded. Direct them to verify that by looking at their circles. |

| |Activity 3: Repeat activities 1 and 2 with other fraction circles, and with variations such as |

| |3/8 + 3/8. Using the 1/8 and 1/12 circles will also provided the opportunity to point out how |

| |fractions can be reduced. |

|M.1.2.20 Identify improper fractions and mixed |Materials: Make 1 or 2 fraction circles, including the 1/3 fraction circle and copy one of each|

|numbers. |for each student. One pair of scissors per student. |

| |Activity: Cut the 1/3 fraction circle into the drawn slices of 1/3 and tell students to think |

| |of these as pizza slices. Have four or more students combine their slices and ask what the total|

| |number is. If they answer in an improper fraction, point that out to them and have the place the|

| |slices together to create an illustration of mixed numbers. Discuss the equivalency. Consider |

| |repeating by combining more slices or by working with a different fraction circle. |

|M.1.2.21 Identify and write amounts of money using |Materials: Play money including coins or monopoly money supplemented by coins. |

|decimals, words, and symbols. |Activity: Project or otherwise display a given amount of money, and direct students to write |

| |the amount including a dollar sign and decimal. After students have completed this for the first|

| |amount shown, clarify questions and repeat the exercise several times. |

|M.1.2.22 Demonstrate an understanding of decimal |Materials: Coins. |

|notation and place value by reading, writing, |Activity: Project or otherwise display an amount of money less than $1 and ask students to |

|ordering, and comparing decimals to two decimal |write that amount in decimal form. Assign that amount to an arbitrary color or as the price of |

|places. |an item, and repeat the exercise several times. Then ask students to list the colors or items |

| |with their values/prices in rank order and ask a series of questions, such as “Which is |

| |highest?”, “Is red higher than blue?”, etc. |

|M.1.2.23 Convert and express simple common |Materials: Copies of Template M.1.2.23 Fraction Ring |

|fractions as decimals. |Activity: Give students several copies of the fraction ring. Have them divide the fraction ring |

| |in half, discuss the percent, then divide the same ring in fourths, discuss the percent, then |

| |divide into eights and discuss the percent. Do a similar activity using another fraction ring |

| |and dividing into thirds, then sixths, then twelths. Then do another activity using another |

| |fraction ring and dividing into fifths, then tenths. Be sure to discuss what percent of the |

| |circle each fractional part uses. |

|M.1.2.24 Show relationship between decimal system |Materials: Five quarters and eleven dimes per student. |

|and money, i.e., show that 10¢ can be written as |Activity: Direct students to count and write the amount of money represented by five quarters, |

|$.10, 25¢ can be written as $.25, etc. |and the amount represented by eleven dimes. Verify that all students wrote those values |

| |correctly and write them on the chalkboard. Ask students to remove $1 from each stack of coins |

| |and express the amount of money remaining. Point out that 25 cents can be written as $.25 and 10|

| |cents as $.10. |

|M.2.2 Measurement: Students will develop and apply concepts of standard measurements and use measurement tools to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.2.2.1 Identify equivalent amounts of money using |Materials: One worksheet per student with drawings of bills and/or coins arranged in two |

|different bills and coins. |columns. Each amount shown on the left should match an item in the right column in total amount |

| |of money shown, but not in denomination. |

| |Activity: Direct students to complete the matching exercise. Then ask them to tell you the |

| |amount of money in a specific match as you record each amount on the chalkboard. |

|M.2.2.2 Read, record, and use date concepts |Materials: Calendars for each student. |

|(months, days of week) in common formats. |Activity: Students should refer to the calendar and record both the date and the day of the week|

| |as the instructor asks a series of questions, such as “What day of the week is March 17 on this |

| |year?”, “What is the date of the first Tuesday in April?”, etc. Pause occasionally to review |

| |answers and clarify. |

|M.2.2.3 Read, record, and understand time of day. |Materials: One handout per student showing a variety of times displayed on analog clock |

| |displays, supplemented with phrases such as “between breakfast and lunch”. |

| |Activity: Ask students to record times shown on the first three clock faces including ‘am’ or |

| |‘pm’. After sufficient work time, write correct responses on chalkboard and ask questions to |

| |generate discussion. Supplement with questions such as “How long until class should end?” Assign |

| |completion of worksheet as homework for instructor correction. |

|M.2.2.4 Telling time to the nearest minute. |Continue exercise from M.2.2.3. |

|M.2.2.5 Identify halves and whole numbers on a |Materials: One yardstick per pair of students. |

|ruler (inches) and develop personal reference point|Activity 1: Assign three measurements (one or two of them should include a half inch) to each |

|for one’s height. |pair of students and have them draw lines on those lengths on the chalkboard. Then have two of |

| |the pairs switch, measure the lines drawn by the other pair, and write that measurement on the |

| |board. Ask if that was the intended measurement. |

| |Activity 2: Ask for a volunteer who knows his or her height to report that height to the class. |

| |Ask the other students to write if they are shorter, taller, or the same height and estimate the |

| |height difference. Separately mark the heights of two students and measure the difference after |

| |asking students to guess the difference in height of those two students. |

|M.2.2.6 Identify halves and whole numbers on weight|Materials: One worksheet per student showing images of bathroom scale readouts and balance scale|

|scales (pounds) and develop personal reference |readouts. |

|point for one’s weight. |Activity: Direct students to write the number of pounds shown on the first image. After |

| |sufficient time, write the correct response on the chalkboard and evaluate understanding with |

| |questions and clarifications. Repeat with the next four images, and then assign the rest of the |

| |worksheet as homework. |

|M.2.2.7 Identify and select appropriate measures |Activity: Have students brainstorm things for appropriate measure, i.e., what measurement would |

|for capacity (cups, pints, quarts, and gallons) and|you use for the weight of an elephant, what weight would you use for a premature baby, what |

|weight (ounces, pounds, tons). |weight would you use to weight a bird, etc. For capacity, ask questions such as when you buy |

| |berries at the store how might they be packaged or if you are cooking for two people how might |

| |you measure the amount of rice to cook, etc. |

|M.2.2.8 Interpret temperature from Fahrenheit scale|Materials: One thermometer and one cup of ice water for each pair of students. Also, one |

|in various situations, including negative |worksheet per student (worksheet should include sketches of Fahrenheit thermometer scales |

|temperatures. |indicating temperatures of -15, 0, 15, 30, 80, 98 and 115. |

| |Activity 1: Direct students to record initial temperature (room temperature). Each pair should |

| |then place their thermometer in the cup of ice. One pair member should watch the clock and ask |

| |the other team member to read the temperature at one-minute intervals until there is no change |

| |(near 32 degrees). |

| |Activity 2: After pair members share and record the times and temperatures from activity 1 on |

| |their worksheet, direct them to read the temperatures shown on the worksheet and record those as |

| |indicated. This can be done in one class, with discussion to follow, or completed as homework for|

| |instructor correction. |

|M.2.2.9 Read and record time of day in 24-hour |Materials: Digital watch that can be programmed to show time in 24-hour format. |

|format. |Activity: As instructor projects different digital watch displays, changing the time setting |

| |before each projection, students record 24-hour format time in one column, and 12-hour format |

| |time, including am or pm, in other column. |

|M.2.2.10 Convert units of time: hours, minutes, and|Materials: Stopwatch. Worksheet for each student with problems stating numbers minutes and |

|seconds. |seconds to be converted into seconds, and numbers of hours and minutes to be converted into |

| |minutes. |

| |Activity: Time students in seconds to determine how long it takes for a given number to raise |

| |their hands to indicate they have completed the first problem on the worksheet. Tell students how|

| |many seconds you recorded and ask them to convert the time into minutes and seconds. Repeat for |

| |at least two more problems. Then tell them how many minutes their class has met or is scheduled |

| |to meet that month and ask them to convert into hours and minutes. |

|M.2.2.11 Identify customary US units of linear |Materials: rulers and measuring tapes |

|measurement and equivalents: inches, feet, yards, |Activity 1: Have students conduct measurements within the room and give their results in at least|

|and miles. |two forms, i.e., inches and feet, feet and yards, etc. |

| |Activity 2: Have students use a city map to get distances from one place to another. Then have |

| |them give the measurement in two different forms, i.e., feet and yards, yards and miles. |

|M.2.2.12 Measure length, width, height, and |Materials: Rulers or yardsticks for half the number of pairs of students, tape measures for the |

|perimeter in inches, feet, and yards using a ruler |other half. |

|or tape measure. |Activity: Assign the following items to have length and width measured with a ruler or |

| |yardstick: book, desk, and chalkboard. Assign the following items to be measured with a tape |

| |measure: wall (length), door (height), table (perimeter), and wastebasket (perimeter). |

| |Measurements should be recorded on chalkboard and verified by other pairs, then discussed. |

|M.2.2.13 Make rough-estimate approximations of |Materials: Chalkboard, unruled straight edge, or meter stick for student use, yardstick for |

|standard US measurements. |instructor use. |

| |Activity: Competition in which students each get a chance to draw, with help of a straight edge,|

| |3 distances on the chalkboard: 1 inch, 1 foot, and 1 yard. After each student completes this |

| |task, Instructor measures actual distance and and lists total inches over or under for that |

| |student. Winner is student with lowest error, unless a “run-off” competition seems appropriate, |

| |or instructor elects to give everyone a second try. Suggestion: award prize to winner, and |

| |perhaps to runner-up. |

|M.2.2.14 Read, interpret, and use map legends/keys.|Materials: Road maps and/or topographical maps for each pair of students. |

| |Activity: Ask questions such as “How many miles from ___ to ___?”, “How many miles are |

| |represented by one inch on this map?”, “How tall is ___?”, etc. |

|M.3.2 Geometry: Students will develop and apply concepts of geometric properties, relationships, and methods to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.3.2.1 Demonstrate an understanding of the |Materials: One round cookie and a knife for each pair of students. |

|concepts of sameness and halfness, i.e., identify |Exercise: Tell students to divide the cookie into half so that each will get the same amount. |

|and show where line(s) of symmetry (i.e., the lines|Point out that the student who does not cut the cookie gets to take first choice of halves. |

|that divide something into 2 equal parts) falls in |Discuss how halving created two equal amounts. Repeat the exercise with another cookie and roles |

|two-dimensional figures. |of pair members switched. |

|M.3.2.2 Use the four main compass directions (N, S,|Materials: A sign for each of the four main compass directions. |

|E, W) for spatial orientation. |Activity: Tape signs on classroom walls at approximately the direction of each compass signs. |

| |Have students face north, and ask which way and how far they need to turn to be facing east. |

| |Repeat with various other compass point combinations. |

|M.3.2.3 Define and correctly use the concept of |Materials: Rectangular items which can easily be stood upright, such as thick books. |

|horizontal and vertical positions. |Activity: After defining ‘horizontal’ and ‘vertical’ tell students to put the chosen items in a |

| |given position. Repeat until students appear to have mastered the concepts. |

|M.3.2.4 Follow a pattern or model to produce or |Materials: paper, scissors, directions for making a box. |

|reproduce a shape or object. |Activity: Have students look on the Internet to find directions to make a simple box. Ask them to|

| |make the box. |

|M.4.2 Data Analysis and Probability: Students will develop and apply concepts of data analysis and probability to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.4.2.1 Solve problems using simple graphs |Materials: A variety of simple graphs and tables. |

|(pictograph, bar, line, and circle), tables, or |Activity: Give each pair of students one of the graphs or tables. Ask each pair of student to |

|distances on maps. |write two questions about their graph or chart. When students have their questions written have |

| |them exchange with another pair of students and solve each other’s questions. |

|M.4.2.2 Identify, count, extract, and interpret | |

|pertinent data organized in lists, tables, and | |

|charts. | |

|M.4.2.3 Reorient, reorganize, and reformat simple |Materials: A variety of graphs and tables. |

|data, i.e., create a table to record and present |Activity: Give each pair of students one of the simple graphs or tables. Ask them to reorganize |

|numerical information. |or reformat the graphs to make the information easier to read. |

|M.4.2.4 Collect, label, and order numerical |Activity: Have students record the number of minutes of TV watched each day for 2 weeks. Then |

|information for a particular purpose (e.g., keep a |they could find the mean, median, and mode of their log. |

|log, etc.). | |

|M.4.2.5 Identify and interpret simple graphs, |Materials: A variety of simple graphs and tables. |

|tables, etc. |Activity: Allow each pair of students to select a graph or table and then write a brief story |

| |about the graph explaining what it means. |

|M.4.2.6 Read values on and make comparative | |

|statements about relative values on a simple bar | |

|graph. | |

|M.4.2.7 Develop an understanding of events as |Materials: Two dice for each pair of students. One worksheet per student with questions about |

|certain, impossible, likely, or unlikely to occur. |“chance” of particular outcomes on the roll of a die or a pair of dice. |

| |Activity: Complete first few worksheet questions as a group discussion, to include questions |

| |with answers of “certain” and “impossible”, such as chance of a sum of 13 on the two dice. |

|M.4.2.8 Determine the probability of simple events,|Materials: One die for each student. One worksheet per student with questions regarding |

|e.g., in the results of tossing a coin or rolling a|probability of particular outcomes on the roll of a die or a pair of dice. |

|die, etc. |Activity: Complete first few worksheet questions as a group. Worksheets should include questions|

| |where student records value from a die toss, and asks for probability of getting a higher value, |

| |etc. |

 

|M.5.2 Algebra: Students will develop and apply concepts of basic algebra, patterns, relationships, and functions to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.5.2.1 Recognize and create simple repeating |Materials: Deck of playing cards for each pair of students. |

|patterns using three or less items (e.g., color, |Activity: Direct students to turn over 3 cards from a shuffled deck until they get 3 consecutive|

|rhythmic, shape, number, and letter) and identify |cards of the same color. Repeat to get 3 consecutive face cards, 3 consecutive cards of the same |

|the unit being repeated. |suit, etc. Ask them to repeated items on the chalkboard. |

|M.5.2.2 Identify basic number patterns and |Materials: Writing paper or notebooks. |

|relationships inherent in multiplication and |Activity: Direct students to write numbers, as if counting, in rows of an assigned number of |

|division (e.g., identify halves, doubles, and |values and note the last number of each row (such as numbers ending in 5 or 0 if each row has 5 |

|triples of numbers). |numbers. Generate discussion of patterns observed. |

|M.5.2.3 Describe qualitative change, i.e., change |Materials: Records of number of daylight hours and average temperatures for several days (one |

|in the number of daylight hours or temperature over|copy per student pair). |

|time. |Activity: After assigning each pair of students a specific item, such as observing the pattern |

| |of change of average high temperature for days in April including how much daily change, have |

| |each pair describe the pattern they found to the class. |

|M.5.2.4 Interpret simple English word phrases, |Have students write the algebraic expression when you speak aloud the English words. |

|i.e., mathematical expressions, equations, and | |

|variables and write algebraic expressions. | |

|M.5.2.5 Recognize, interpret, and use basic |Materials: Make a set of cards with the symbol on one card and the name of the symbol on another |

|mathematical symbols (+, -, =, ) and recognize |card. |

|the different vocabulary used to represent each. |Activity 1: Mix up the cards and have students match the symbol with the name. |

| |Activity 2: Have students play “concentration” with the cards. |

|M.5.2.6 Translate simple mathematical expressions |Have students make up simple mathematical expressions, i.e., six is less than ten, five is |

|involving +, -, . |greater than two, two more than six, and write them on individual cards. Then shuffle the cards |

| |and have each pair of students translate the expressions into mathematical symbols. |

|M.5.2.7 Use a calculator to make basic calculations|Have students use a calculator and a menu or sale paper to determine the total cost to purchase |

|and solve simple addition, subtraction, |several items. |

|multiplication, and division problems and check | |

|solutions. | |

|M.5.2.8 Solve single step, real-life word problems |Have students write and solve word problems based on information from a menu or sale paper. |

|involving addition, subtraction, multiplication, | |

|and division using up to two digit whole numbers. | |

|M.5.2.9 Determine and use appropriate rounding and |Have students practice rounding using a sale paper or menu. |

|estimating techniques. Understand that the number | |

|"5" rounds up. | |

Mathematics Sample Teaching Activities

Level 3 – Grade Level 4.0 – 5.9

|M.1.3 Number Sense and Operations: Students will develop and apply concepts of number sense and operations to explore, analyze, and solve a variety |

|of mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.1.3.1 Read, write, order, and compare large whole|Activity: Give each student an index card with a large whole number on it. Give out play checks |

|numbers, i.e., thousands, millions, and billions. |that the student fills in with the number written numerically and in words. Have all students |

| |join together to put their checks in order from least to greatest. |

|M.1.3.2 Identify place value in large whole numbers|Activity: Collect large numbers from news stories and use them to practice place value and |

|and round off large whole numbers to nearest tens, |rounding. |

|hundreds, thousands, ten-thousands, | |

|hundred-thousands, million, etc. | |

|M.1.3.3 Interpret the inverse relationship between |Materials: Small bundle of toothpicks for each pair of students. |

|addition and subtraction and multiplication and |Activity 1: Both pair members count the number of toothpicks until they agree on the total. Then |

|division. |one takes part of the toothpicks from that group, keeping count, and the other determines how |

| |many toothpicks remain. Each writes that as a subtraction problem, and then writes the number of |

| |toothpicks in each group as an addition problem. Instructor asks if and why they obtained the |

| |original number when they completed the addition problem. |

| |Activity 2: Each pair divides their toothpicks into 3 equal size groups, discarding one of two |

| |toothpicks that are left over if necessary. Instructor explains the relationship of doing so to |

| |division, and then directs students to write the corresponding division problem. Then instructor |

| |asks what the group size multiplied by 3 would equal and directs students to write and solve that|

| |multiplication problem. Instructor asks if and why they obtained the original number when they |

| |completed the multiplication problem. This exercise can be repeated with division into 4 groups, |

| |5 groups, etc. |

| |Activity 3: Use the first letter of each word: Addition, a, all, add all the numbers. |

| |Subtraction, s, sorry or so long, subtract. Say so long to your money. Use play money. Multiply, |

| |m, more or many, because when multiply you have many more than when you started. Division, d, |

| |divide it into parts. |

|M.1.3.4 Demonstrate an understanding of the |Materials: 12 toothpicks per pair of students. |

|commutative and associative properties of addition |Activity: Each pair of students divides their toothpicks into 2 groups to verify that 2 X 6 = 12.|

|and multiplication (e.g., 2 pounds of meat at |Then they divide their toothpicks into 6 groups to verify that 6 X 2 equal 12. Repeat with 3 |

|$3/lb. costs the same as 3 pounds at $2/lb.). |groups of 4 toothpicks and 4 groups of 3 toothpicks. |

|M.1.3.5 Demonstrate an understanding of factors of |Materials: One box of toothpicks per pair of students. |

|numbers up to 100. |Activity 1: Assign student pairs specific numbers. Have them count that many toothpicks, then try|

| |to divide them into 2, 3, 4, etc. equal size piles. Each pair should report results to entire |

| |class, including writing factors on the chalkboard. |

| |Activity 2: Write the numbers 1-100 on blank index cards. Divide the cards between teams. Call |

| |out a number from 1-100 and have each team hold up any cards they have that are factors of that |

| |number. Write these factors on the board and show the multiplication relationship. |

| |Activity 3: Students work in groups of 2-4 using a highway map of North Carolina. Each group |

| |should plan a trip across the state, using the map’s scale to determine mileage from point to |

| |point. Students could also identify travel direction of each leg of the trip and locate |

| |attractions on the way (using map symbols). |

|M.1.3.6 Demonstrate an understanding of dividing by| |

|multi-digit numbers and interpreting remainder and | |

|expressing them as whole numbers, fractions, and | |

|decimals. | |

|M.1.3.7 Demonstrate an understanding of |Materials: One box of toothpicks for each pair of students. |

|back-multiplying to check results of division. |Activity 1: Direct pairs to count a specific number of toothpicks, and then divide those |

| |toothpicks into 3 equal size groups. Then ask what the group size multiplied by 3 would equal and|

| |whether any other number multiplied by 3 would give the same result. After class discussion of |

| |how back-multiplying can be used to check division answers, repeat the exercise with larger |

| |numbers of groups of toothpicks. |

| |Activity 2: Show the problem or make the division bracket. Tell students to remember to multiply|

| |everything outside the brackets when they finish dividing to find what is under the bracket. |

|M.1.3.8 Demonstrate an understanding of prime |Materials: 3 dice for each group of four to six students. |

|numbers and identify prime numbers up to 20. |Activity: Students take turns rolling the 3 dice and summing the 3 numbers that result from |

| |their roll. Direct students to roll again if the sum is greater than 20, and repeat until they |

| |get a sum of 20 or less. The student gets one point if that sum is a prime number and no points |

| |if it is not (group verifies if it is prime). First student to get 3 points wins, or students in |

| |the group can complete the round and have a roll-off if there is a tie. |

|M.1.3.9 Add and subtract whole numbers up to four |Activity: Use real-life materials, i.e, sale papers, menus, catalogs, etc. to make practice |

|digits using efficient methods and checking |problems. |

|answers. | |

|M.1.3.10 Multiply with two and three digit numbers | |

|using efficient written methods including checking | |

|answers. | |

|M.1.3.11 Identify and calculate equivalent |Materials: Three manipulative circles (such as felt backed), one divided into 6ths, one divided |

|fractions (fourths, thirds, halves, eighths, |into 8ths, and one divided into tenths. One worksheet per student showing sketches of pizzas, |

|fifths, and tenths) and simplify fractions to |some sliced into 6 pieces, some into 8 pieces and some into 10 pieces. |

|lowest terms. |Activity 1: Show the relationship between number of slices and fraction of the circle. On their |

| |worksheets, have students color or shade 2 slices of an 8-piece pizza to create ¼ and two slices |

| |of a 6-piece pizza to create 1/3. Then have them color two slices at a time of a 10-piece pizza |

| |to divide the pizza into 5ths. Continue with 2/4, 3/6, 4/10, etc. and discuss desirability of |

| |lowest term fractions. |

| |Materials: 100 pennies for each student. |

| |Activity 2: Teacher directs student to divide pennies into two piles of 60¢ and 40¢. Student |

| |then divides each pile into various parts as demonstrated by instructor using fourths, thirds, |

| |halves, eighths, fifths, and tenths. After I do, we do activities. Ask how many thirds in 60, how|

| |many eighths in 40, etc. |

|M.1.3.12 Convert improper fractions to mixed |Materials: One pair of scissors per pair of students. One worksheet per student showing drawings|

|numbers and mixed numbers to improper fractions. |of some circles divided into quarters and some divided into sixths. |

| |Activity: Have each pair of students cut three circles into fourths, then put the name of each |

| |student in class on one of the fourths. Ask how many fourths were used and write that on the |

| |chalkboard as an improper fraction. Then as how many pizzas the class would have to order if each|

| |student was to get ¼ pizza. Direct students to repeat the exercise with circles divided into |

| |sixths. |

|M.1.3.13 Add and subtract fractions (fourths, |Materials: Make fraction circles (1/2, 1/3, 1/6) and scissors for each pair of students. |

|thirds, halves, eighths, fifths, and tenths) using |Activity 1: Direct students to cut slices from different fraction circles for each exercise. |

|fractions that include like and unlike denominators|Start with halves and thirds fraction circles, and have students lay a ½ slice and a 1/3 slice on|

|and whole and mixed numbers. |the sixths fraction circle to see what result of ½ + 1/3. Then explain the addition of fractions |

| |with unlike denominators. Repeat with other fraction circle combinations. |

| |Exercise 2: Direct students to cut slices from different fraction circles for each exercise. |

| |Start with halves and thirds fraction circles, and have students lay a 1/3 slice and a ½ slice |

| |and compare the result to a 1/6 slice on the sixths fraction circle. Then explain the subtraction|

| |of fractions with unlike denominators. Repeat with other fraction circle combinations. |

|M.1.3.14 Multiply and divide by fractions (fourths,|Materials: Make fraction circles (1/4, 1/5, 1/3) and scissors for each pair of students. |

|thirds, halves, eighths, fifths, and tenths) using |Activity: Direct students to cut a ½ slice from the halves fraction circle, then try to cut it |

|fractions that include like and unlike denominators|into 2 equal parts. Have the place the results on the fourths fraction circle to evaluate their |

|and whole and mixed numbers. |results, then explain the multiplication of fractions. Direct students to repeat this exercise by|

| |dividing a ½ slice into thirds and looking at fraction circles to find the slice size that would |

| |result. Slice sizes that would be good choices for halving include ¼, 1/5, 2/3, 2/5, and ¾. |

|M.1.3.15 Relate multiplication of fractions and |Materials: Roll of quarters. |

|division, i.e., multiplying by 1/4 is equivalent to|Activity 1: Give each pair of students 8 quarters. Direct them to determine how many quarters |

|dividing by 4 and dividing by 1/4 is equivalent to |would be required for a vending machine purchase of an item costing $2.00. Demonstrate how this |

|multiplying by 4. |number can be calculated as ¼ X 2. |

| |Activity 2: Have students determine the number of items costing a quarter that can be purchased |

| |with $2 worth of quarters. |

|M.1.3.16 Express a relationship between two |Materials: 3 dice for each pair of students. |

|quantities as a fraction or fractional estimate, |Activity 1: One pair member rolls 2 of the dice and creates a 2-digit number by reading from |

|e.g., 54 of 352 graduates = 54/352 or about 1/6. |left to right, then rolls 3 dice to get a 3-digit number. Then the other pair member does the |

| |same thing. Then pair members work together to estimate a simple fraction to which that fraction |

| |might reduce. Pairs each report their results to the class and the class critiques their |

| |estimates. |

| |Activity 2: Same as Activity 1 except each student rolls all 3 dice twice. Direct students to |

| |use the smaller of the two numbers they generated from the two dice rolls as the fraction |

| |numerator and the larger as the denominator. |

|M.1.3.17 Identify quantities that are proportional.|Materials: A measuring cup for each group, a gallon of iced tea for each group, a clean |

| |container for each student in various shapes and sizes. |

| |Activity 1: Students measure 1 cup of drink in each container. Although in the containers they |

| |do not look the same, they are proportional. |

|M.1.3.18 Interpret the meaning of ratio and express|Materials: 2 pennies and 1 die (1 of a pair of dice) per student. |

|a relationship between two quantities as a ratio. |Activity: Direct students to observe one coin and write the ratio of 1 head:1 tail, then to |

| |observe one die and write the ratio of 1 “6”: 5 “not 6”. Ask how many sides of the die are even |

| |numbers and how many are odd, and what ratio they would write for that. Explain that ratios, like|

| |fractions, should be reduced, so they should write that as 1:1 rather than 3:3. Students can then|

| |practice writing ratios by listing the possible genders of two non-twin children. Verify that |

| |they show 4 possibilities in the “sample space”, then direct them to write ratios for boys:girls,|

| |same gender:not same, and both girls:other possibilites. |

|M.1.3.19 Read, write, order, and compare decimals |Materials: One copy of batting averages part of a Sports Section of a newspaper for each pair of|

|of up to three decimal places. |students. |

| |Activity 1: Explain that 3-digit batting averages are the proportion of hits per 1000 at bats. |

| |Assign a specific group of batting averages to each pair of students, such as the third highest |

| |batting average on each team, and ask them to make a ranked list showing batting average and |

| |players name (team optional), then explain the different in the batting averages of the top two |

| |players in their list. |

| |Materials: Deck of 100 flash cards (34 tenths, 33 hundredths, 33 thousandths) with number on one|

| |side and word name on the other. |

| |Activity 2: Shuffle and deal 10 cards to each player with number side up. 1st player reads the |

| |top card in his stack and 2nd player checks the word name on the back. Switch roles. |

| |Activity 3: Shuffle and deal 10 cards to each player name side up. At a signal, players display |

| |their cards in order from least to greatest. |

| |Activity 4: Deal all cards to each player name side up. Play the War game. |

|M.1.3.20 Identify place value for decimals (tenths,|Materials: Each pair should use the batting average list they created in M.1.3.19. |

|hundredths, and thousandths) and round decimals to |Activity: Explain that percentages without decimals are like batting averages rounded to the |

|one or two places or whole numbers. |nearest hundredth, and then have students round the batting averages to two places. |

|M.1.3.21 Compute percentages when part and whole |Materials: An assortment of coins. |

|are given using friendly numbers, e.g., 10%, 25%, |Activity: Use money to show the steps and relationship. One dollar is a whole. A dime is 10%. A |

|50%, and 75%. |quarter is 25%. Two quarters is 50%. Three quarters is 75%. A nickel is 5%. |

|M.1.3.22 Convert decimals to fractions and |Materials: 1 penny per student. |

|percents, fractions to decimals and percents, and |Activity: Ask students to write the probability of a head on one toss the pennies. After |

|percents to fractions and decimals. |sufficient time, ask how many wrote the answer as 1/2, how many wrote 50% and how many wrote .5. |

| |Show conversions between any pair of those answers and explain that all answers are correct. |

| |Direct students to write the probability of 2 heads if the penny is tossed twice as fraction, |

| |percent, and decimal. After allowing students to work for a minute or two, ask if everyone listed|

| |4 possible outcomes in their “sample space” just as they did with 2 children in M.1.3.18, and |

| |allow time for adjustments if they did not. Exercise can be repeated with probability of both |

| |girls in 2 children, probability that any year in the 1900s ends with a 0, and/or probability of |

| |all 3 girls in three non-twin children. |

|M.1.3.23 Add, subtract, multiply, and divide |Materials: Sales papers such as grocery store ads for each student. |

|numbers with decimals. |Activity 1: To practice addition, direct students to calculate total cost of 2 different items |

| |of different costs. Repeat exercise with 3 or more items of different cost. |

| |Activity 2: To practice subtraction, ask how much they would have left if they went to the |

| |grocery with $20 and purchased those items on a sales tax free day. |

| |Activity 3: To practice multiplication, direct students to calculate total cost if they buy 3 of|

| |the same item. Repeat exercise with 4 or more items of another item. Variations can include |

| |purchase of multiple items that are “buy one, get one free”. |

| |Activity 4: To practice multiplication, write the sales tax percent on the chalkboard and direct|

| |students to calculate sales tax on one or more of their previously assigned purchases. |

| |Activity 5: To practice division, direct students to calculate cost per item or cost per pound |

| |of something that is priced at 2 for ____. Repeat exercise with items that are 5 per ____, etc. |

|M.1.3.24 Read and write large numbers with decimals|Activity: Ask students to listen to the news and bring in the large numbers that were discussed. |

|(e.g., 12.6 million = 12,600,000). |Have them practice reading and writing those numbers. |

|M.1.3.25 Determine a fraction or percent of a |Materials: An assortment of plan money (bills and coins). |

|decimal, e.g., .25 = 1/4 = 25%, 1.5 = 1 1/2 = 150%,|Activity 1: Give out plastic coins and play paper money. Show how money amounts can be shown in |

|etc. |decimals (example: $.50), fractions (example: ½ dollar) and percents (example: 50% [50¢] of a |

| |dollar). |

|M.1.3.26 Understand and interpret the meaning of |Materials: 100 pennies for each student. Students work in groups of 3-6. |

|percent, i.e., percent represents a ratio of a part|Activity 1: Students make a circle of 100 pennies and then remove varying amounts from the |

|to a whole where the whole is 100. |circle. Explain 1%, 5%, etc. |

| |Activity 2: Students make a concentric circle with their pennies, 100 pennies in each layer. |

| |Compare fraction equivalents to percents. |

|M.1.3.27 Read, write, order, and compare simple |Materials: Set of cards with number on one side and word name on the other side. |

|percentages. |Activity 1: Deal 10 cards to each student, number side up (1%, 10%, 20%, 25%, 30%, 40%, 50%, |

| |75%, 90%, 100%). Have the students read the percent aloud to the game partner. |

| |Activity 2: Ask the students to place the cards in order from least to greatest. |

| |Activity 3: Shuffle all cards and play “War” to compare (greatest card wins). |

|M.1.3.28 Find given percents of any given number, |Activity: Discuss how percents are used in daily life, i.e. sales fax, social security tax, |

|i.e., what is 5% of 125?, what is 6.5% of 90?, etc.|federal tax, property tax, etc. Then use examples from real-life to practice finding percents. |

|M.2.3 Measurement: Students will develop and apply concepts of standard measurements and use measurement tools to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.2.3.1 Calculate units of time using a clock (both|Material: Clocks or watches and calendars, enough for each small group of students and train |

|12 and 24 hour) and a calendar. |schedule. |

| |Activity: Give the time in the 12 hour format and have students set their clock to the 24 hour |

| |time and vice versa. Have students use train schedules to plan a trip and use the calendar to |

| |find the date for arrival at each location. |

|M.2.3.2 Identify and select appropriate metric |Materials: One meter stick for each pair of students. One metric-labeled contains such as a |

|measurements including meters, liters, and grams. |2-liter soda bottle for each pair of students. One container with weight labeled in grams to put |

| |on the instructors desk/table. One worksheet per student of questions which ask the unit of |

| |measurement for items such as “length of wall”, “quantity of cough syrup”, and “weight of a |

| |coin”. |

| |Activity: Explain the function of each of the metric units. Direct students to answer the first |

| |3 questions on the worksheet. After sufficient time, ask for and discuss answers. Students can |

| |then be directed to complete and discuss more questions or complete the worksheet as homework for|

| |instructor correction. |

|M.2.3.3 Add, subtract, multiply, and divide sums of|Materials: Sales ads/price lists and worksheets with problems about total cost of 2 or more |

|money including decimal notation. |stated items, amount of discount on specific items, costs of a given number of items; one for |

| |each student |

| |Activity 1: Direct students to solve specific problems addition and multiplication problems on |

| |the worksheet. After sufficient time, discuss solutions to those problems; then direct students |

| |to determine the cost per person if items identified in a specific problem are being shared by 3 |

| |roommates. Division exercise can be repeated with a different number of roommates. Then direct |

| |students to solve other problems and discuss solutions. Some problems can be assigned for |

| |practice or homework to be corrected by the instructor. |

|M.2.3.4 Demonstrate an understanding of the |Activity: Discuss how distance, time and speed relate using examples such as students travelling |

|interrelation of distance, time, and speed and make|to and from class. Then have student make additional practice problems based on trips they have |

|simple calculations using distance, time, and speed|taken. |

|formula. | |

|M.2.3.5 Read and interpret map scales, legends, and|Materials: Road map with mileage table and for each pair of students. One worksheet per students|

|mileage tables. |with problems such as “How many miles from ___ to ___?” |

|  |Activity: Review use of map scales and demonstrate use of mileage table. Direct students to |

| |complete one problem that can be solved with mileage table and one that requires use of map |

| |scale, and then review solutions to those problems. Direct students to solve additional problems |

| |for review in class and/or as homework for instructor correction. |

|M.2.3.6 Measure with a standard ruler in inches and|Materials: Measuring device for each pair of students. half yardsticks and half meter sticks. |

|feet to 1/16 inch accuracy and a metric ruler in |Activity: Direct some pairs of students to measure selected items, such as chalkboard, window, |

|centimeters and millimeters. |door, or table, to 1/16 using the yardstick and write results on the chalkboard. Other pairs |

| |should measure the same items using the meter stick. Have pairs switch roles and verify |

| |measurements made by other pairs, noting disagreements on the chalkboard. Discuss differences or |

| |have a third pair repeat measurements that are significantly different. |

|M.2.3.7 Make informal comparisons between inches |Materials: Results of M.2.3.6. Yardstick and meter stick for each pair of students. |

|and centimeters including estimating the number of |Activity 1: Lead class discussion of specific comparisons by comparing measuring devices, |

|centimeters per inch. Create physical (bodily) |including yards vs. meters and inches vs. centimeters. Continue discussion by comparing results |

|benchmarks for units, e.g., fingernail = 1 cm; |of measurements for M.2.3.6. |

|thumb joint = 1 in. | |

|M.2.3.8 Convert and calculate with linear |Materials: measuring tools |

|measurements (inches, feet, yards, miles) and know |Activity: Have students make measures using one unit and then convert their measurement into |

|the relationship of familiar units, e.g., 12 inches|another unit, i.e., measure a table in inches, then calculate the number of feet or measure the |

|in a foot, 3 feet in a yard, 4 cups in a quart and |room width in feet, then calculate the inches or yards. |

|convert units of measure in the same systems. | |

|M.2.3.9 Use and apply concepts of weight and |Materials: Small balance beam scales. Empty container such as cup and/or quart, and different |

|capacity to solve problems, i.e., know the |weight materials such as water, popcorn, and popped corn. |

|difference between weight and capacity. |Activity: Direct one student to weigh empty container and record weight on chalkboard as other |

| |students watch. Direct another student to fill container with water, weigh, and record weight on|

| |chalkboard. Direct third student to do the same with popcorn, fourth to do the same with popcorn,|

| |etc. Have students subtract weight of empty container to get actual weight of different |

| |materials, and then discuss results with class. |

|M.2.3.10 Use, read, compare, and calculate with |Materials: Thermometer, ice, microwave, bowl |

|positive and negative Fahrenheit temperatures, |Activity: Have students use the thermometer to measure room temperature. Then, place the |

|i.e., know that temperature increases as it goes up|thermometer in ice water (using salt water may get the temperature below freezing). Then, heat |

|and decreases as it goes down and that the sign of |the ice water in the microwave to bring the temperature above room temperature. |

|the temperature changes when crossing the zero | |

|degree point. | |

|M.2.3.11 Calculate times using the appropriate |Activity: Have students calculate the length of their math class in hours, minutes, and seconds. |

|value and convert between time formats (including |Then move into calculations such as how many days, weeks or months it is until Christmas or how |

|elapsed time), i.e., know equivalencies for hours, |many decades it will be before they are old enough to begin getting Social Security, etc. |

|seconds, minutes, days, weeks, months, decades, and| |

|centuries. | |

|M.2.3.12 Directly measure perimeter in linear units|Activity 1: Decide how many square yards of carpet are necessary to carpet your classroom. |

|and area in square units (sq. in., sq. ft., sq. |Activity 2: Decide how many tiles of different dimensions (8” x 8”, 12” x 12” would be necessary|

|cm.). |to cover your classroom. |

|M.2.3.13 Estimate, measure, and compare weights |Materials: Containers of varying sizes and items students can measure and weight (beans, rice, |

|(pounds, ounces) using simple instruments, |corn, marbles, water, etc.) and some food packages that show weight (deli, meat, etc). |

|graduated in familiar units (ounces and pounds) and|Activity 1: Have students measure different objects and compute the weight in ounces and pounds. |

|know when to use appropriate measures. |Discuss the difference in dry measure and liquid measure. Have students practice measuring both. |

| |They should “see” that there are 4 cups in a quart, 4 quarts in a gallong, etc. Then ask students|

| |about the difference in the way package labels are written for weight, i.e., usually for meat it |

| |is not pounds and ounces but pounds in decimal form. Practice converting from one form to the |

| |other. |

| |Activity 2: Ask students what they would weigh using tons. If possible take students to a place |

| |that weights trucks and let them see how those scales work. Discuss the purpose of this, i.e., |

| |importance of trucks on our highways not to be overweight and a way to pay for a load (weighing |

| |the truck full, then empty, and calculating the weight of the load). |

|M.2.3.14 Convert and calculate using standard US | |

|units of weight: tons, pounds, ounces, etc. | |

|M.2.3.15 Convert and calculate using standard US | |

|units of capacity: ounces, quarts, and gallons. | |

|M.2.3.16 Demonstrate an understanding of the |Activity: Discuss when it is appropriate to use two-dimensional measurement versus square units. |

|concept of two-dimensional measurements and square | |

|units. | |

|M.2.3.17 Read analog and digital scales on |Materials: various analog and digital scales and measuring devices. |

|measuring devices including meters, gauges, scales,|Activity: Discuss with student show each device is used and then have them practice reading the |

|etc. using various types of units and calibrations.|devices. |

|M.3.3 Geometry: Students will develop and apply concepts of geometric properties, relationships, and methods to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.3.3.1 Recognize, identify, and describe basic |Activity: Have students identify and measure as many shapes as they can find in the classroom, |

|geometric shapes (triangle, square, circle, |building, and campus. Students should make notes and sketches of the shapes the find. Upon return|

|rectangle, hexagon, pentagon, and octagon). |to the classroom, have students draw some of the shapes they found to given dimensions. Ask |

| |students to compare their drawing to the actual item. |

|M.3.3.2 Draw two-dimensional (2-D) shapes of | |

|specific dimensions. | |

|M.3.3.3 Use informal visual methods to describe and| |

|compare shape, dimension, perimeter, area, angles, | |

|and sides in two- dimensional (2-D) and | |

|three-dimensional (3-D) objects. | |

|M.3.3.4 Identify properties, locations, and |Activity: Have students identify right angles in the classroom. Also identify two right angles, |

|functions of right angles, i.e., know that a right |i.e., a straight wall makes two right angles. Show what happens when you make four right angles |

|angle is 90 degrees or a quarter turn, that two |in the middle of a table, i.e., they fill the space. You can use painter tape for student to show|

|right angles make a straight line, and four right |right angles and straight angles. |

|angles fill a space. | |

|M.3.3.5 Use direction, distance, coordinates, |Materials: NC Highway Maps |

|latitude, longitude, simple scales, labels, |Activity: Have students work in groups of 2-4 using a highway map of North Carolina. Each group |

|symbols, and keys to read and use maps and plans. |should plan a trip across the state, using the map’s scale to determine mileage from point to |

| |point. Students may also identify travel direction of each leg of the trip and locate attractions|

| |on the way (using map symbols). |

|M.3.3.6 Use graph paper to draw two- dimensional |Activity: Have students use the drawings made for M.3.3.1 and draw several in a different |

|shapes in different orientations on a grid. |orientation using graph paper. |

|M.3.3.7 Calculate the area of squares, rectangles, |Materials: List of formulas and assortments of squares, rectangles and triangles. |

|and triangles and other common figures using given |Activity: Have students calculate the areas of the shapes given. Then have them find the student |

|formulas. |who has the same shape and size figure and compare areas. Have students to this for several |

| |different shapes. |

|M.3.3.8 Recognize, identify, and describe the |Materials: An assortment of everyday 3-dimensional items. |

|properties of common three-dimensional shapes, |Activity: Have students identify each item by its shape. |

|i.e., cube, cylinder, and sphere. | |

|M.3.3.9 Identify triangles based on their |Materials: paper triangles of various shapes and sizes and protractor. |

|properties, i.e., right, isosceles, equilateral, |Activity: have students sort the triangles into different piles based on visual inspections and |

|scalene, obtuse, and acute. |measurements and then have them explain how they know it is the identified triangle. |

|M.3.3.10 Identify common polygons of various |Materials: paper polygons of different shapes and sizes. |

|shapes, i.e., triangles, quadrilaterals, pentagons,|Activity: Have students sort the polygons into different piles based on visual inspections. Then |

|hexagons, and octagons. |have them explain how they know it is what it is. |

|M.3.3.11 Identify parallel, perpendicular, and |Activity 1: Have students give examples of parallel, perpendicular, and intersecting lines inside|

|intersecting lines. |the classroom. |

| |Activity 2: Take a field trip outside and have students give examples of parallel, |

| |perpendicular, and intersecting lines. |

|M.3.3.12 Describe characteristics of angles formed |Material: Painters tape, rolls for each small group of student. |

|by two intersecting lines, i.e., vertical, |Activity: Have students show the different items for this benchmark using the tape on tabletops. |

|supplementary, complementary, adjacent, and |If there is not room for each group to make all the different angles, then assign an angle for |

|corresponding/congruent. |each pair of student to make. |

|M.3.3.13 Identify angles of 90 and 45 degrees, |Materials: Use the paper triangles and polygons from the M.3.3.9 and M.3.3.10 activities. Have |

|right, acute, and obtuse. |students sort based on the size of the angles. |

|M.3.3.14 Use the secondary directions for spatial |Activity 1: Discuss real-life occupations and real-life situations in which people use secondary|

|orientation (e.g., NW, SW, NE, SE). |directions. |

| |Activity 2: Have the classroom marked with true N, S, E, W. Have the students stand at the |

| |beginning of the game facing N. The teacher will call out cardinal and secondary directions. Have|

| |the students then turn to the appropriate direction. Begin slowly and pick up speed as students |

| |“get it.” |

| |Materials: Compasses |

| |Activity 3: Give each student a compass rose. Mark “NORTH” as accurately as possible on a “sign” |

| |in the classroom. Have the students mark cardinal (N,S,E,W) and secondary (NE, SE, NW, SW) on |

| |their compass roses. Ask the students to list people and objects that are in all directions. |

| |These may be inside or outside the classroom. |

| |Activity 4: Have the students predict directions outside from the position of the sun. Check |

| |accuracy with a compass. |

| |Materials: NC Highway Maps |

| |Activity 5: Ask students to list towns or cities that are NW, SW, NE, SE of an indicated |

| |location. Then check and discuss answers. |

| |Materials: Globe |

| |Activity 6: Choose a major city – New York, Paris, London, etc. Have the students locate cities,|

| |lakes, rivers, mountains, etc. that are positioned NW, SE, NE, SW from the city. |

|M.3.3.15 Use a map with a coordinate grid. |Materials: NC Highway Maps |

| |Activity: Direct the students to work in groups of 2-4 to practice using the coordinate grid on |

| |a highway map of North Carolina. Teach “x” point and “y” point sequence in answers. Brainstorm a |

| |list of places that students would like to locate. |

|M.3.3.16 Create three-dimensional objects from |Activity: Model how to create a 3-D object from a 2-D drawing and then have students practice |

|two-dimensional representations. |doing it. For example, have student make a box or cup from a piece of paper. |

|M.4.3 Data Analysis and Probability: Students will develop and apply concepts of data analysis and probability to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.4.3.1 Identify, describe, and compare how a | |

|change in one variable relates to a change in a | |

|second variable, i.e., situations with | |

|constant/fixed and varying/variable rates of | |

|change. | |

|M.4.3.2 Demonstrate an understanding of the concept|Materials: Container of approximately 20 buttons of different sizes, shapes and colors for each |

|of categories such as shape, size, color, or yes/no|student |

|responses and know how to count each category for |Activity 1: In seating or alphabetical order, ask each question if he or she has done a |

|subtotals. |particular thing in the past 24 hours, such as wash dishes or gone grocery shopping. Make tally |

| |marks on chalkboard as students respond, then ask for help counting subtotals and verify that the|

| |two subtotals equal the total number of students present. |

| |Activity 2: Ask students to sort buttons by size, keeping those of identical size in the same |

| |group, then obtain subtotals of numbers of each size. After this exercise is completed and |

| |visually checked by instructor, ask students to sort their buttons by color and count subtotals. |

| |After instructor checks color sorting, direct each student sort his/her buttons by shape and |

| |count subtotals. Students should then add subtotals for each classification to verify that they |

| |all add to the same total. |

|M.4.3.3 Represent information so that it makes | |

|sense to others, i.e., demonstrate an understanding| |

|that information can be represented in different | |

|ways (list, table, or diagram) and the importance | |

|of labeling information. | |

|M.4.3.4 Demonstrate an understanding that when | |

|objects or responses are divided into categories, | |

|all data must be included in one and only one | |

|category; therefore, categories must identify | |

|distinct sets, i.e., find a total from subtotaled | |

|categories to verify inclusion of all data. | |

|M.4.3.5 Demonstrate an understanding of scatter | |

|plots, i.e., that each X in a line plot represents | |

|one and only one item or response; therefore, it is| |

|verifiable that the number of responses is equal to| |

|the number of X’s. | |

|M.4.3.6 Demonstrate an understanding that a graph |Materials: Paper, pencils, overhead projector, and markers. |

|is a visual representation and that a table |Activity 1: Teacher and student will discuss what students know about different types of math |

|arranges information in rows and columns. |graphs. Using the projector, the teacher will draw and explain how to read bar, picto, line, and |

| |pie graphs. The teacher needs to introduce 1 graph per day. Students will demonstrate |

| |comprehension through an in-class assignment. |

|M.4.3.7 Sort graphs and tables by type, i.e., know |Activity 1: Give each pair of students data from real-life situations. Have the students |

|that a bar graph uses bars of various heights to |generate a list of decision to be made about arranging the data in graphic form. Ask the class to|

|display amount, line graphs use lines to display |compile a list of different types of graphs and appropriate times to use each type of graph. Have|

|changes in amount, and circle or pie graphs |the students determine which type of graph would fit their data. |

|represent the whole. |Activity 2: From the list below, have students determine how to graph the data given. Why are |

| |some types of graphs more appropriate than others? Ex: Favorite soft drink (from choice of |

| |three), temperature in your city and temperature in another city for a two-week period, number of|

| |free throws successfully completed by two people, how students get to school – car, bus, foot. |

| |Activity 3: In groups of four, write an opinion question. For example: “Do you prefer Coke™, |

| |Pepsi™, or RC Cola™? Do you prefer Hardees™, McDonalds™, or Wendy’s™? Which team will you root |

| |for – NC State, Carolina, or Duke?” Develop a plan to gather data. Decide how many people to |

| |survey. What would be an appropriate sample? After gathering data, organize it and decide how to |

| |represent the information in graphic form. Create the graph. Present graphs to the class and |

| |explain to the class why you chose that type of data display. |

|M.4.3.8 Demonstrate an understanding that lists and| |

|tables can be ordered in different ways such as | |

|alphabetically, numerically, or randomly. | |

|M.4.3.9 Compare relative values on a bar graph, |Activity: Have students choose five or six Asian countries. For each country, find the |

|i.e., demonstrate an understanding that comparative|population, area, literacy rate, and an economic indicator such as GNP. Use each set of data to |

|statements such as greater than or less than can be|construct a comparative bar graph for the countries chosen. |

|made based on the height of the bars and relative | |

|numerical terms such as twice or half. | |

|M.4.3.10 Determine whether or not a graph/table |Materials: A variety of graphs and tables lamented for continued use. 5 to 10 question |

|connects to statements made in text using title, |worksheet for each lamented graph or table. Example questions: What does the Y axis represent? |

|data labels, and percent matches, i.e., know how to|What does the X axis represent? Where will you find _______? What is the purpose of this graph?|

|locate data labels in tables and graphs to verify |Activity 1: Have students work in groups of two or three giving each student a different graph |

|they match statements. |and accompanying worksheet. Students will work together to complete the worksheets. Allow each |

| |student to present one of the completed worksheets to the class or the instructor. |

|M.4.3.11 Support simple statements with data and | |

|know statements using “double” and “half” or fifty | |

|percent are accurate. | |

|M.4.3.12 Make observations, draw conclusions, |Materials: A variety of bar and circles graphs lamented for continued use. Bar and circle |

|compare, and extract information from bar and |graphs from periodicals or websites. |

|circle graphs. |Activity 1: Have students work in groups of two or three. Have each student explain their bar or|

| |circle graph to their partner, group or instructor. |

| |Activity 2: Have students write out their observations. Questions to consider: What were your |

| |observations? Explain your conclusion? How would you defend your conclusion? |

|M.4.3.13 Know that probability is the ratio of the | |

|potential successful outcomes to total | |

|possibilities and state probability as a ratio in | |

|multiple forms (colon, words, and fractions) with | |

|simple scenarios. | |

|M.4.3.14 Determine the probability of basic events |Materials: Deck of cards / Golf tees / An assortment of buttons / Bag of an assortment of |

|(e.g., in the results of drawing cards from a deck |candies, etc. |

|of cards, chance of baby being born on a certain |Activity 1: Pass out three or more different groups to the class. Have students count total |

|day of week, etc.) and express the likelihood of an|number of items and total number of like items in each grouping. Example Buttons: Have students|

|occurrence as a ratio, fraction, or percent. |categorize and count all the buttons, all the blue buttons, all the red buttons, etc. and |

| |determine a grand total. The instructor will retrieve items and draw one from the each grouping. |

| |Have students determine the probability of randomly picking the chosen item. You can request |

| |answer in ratio, fraction, or percent form. Students may work in groups or individually. Have the|

| |first group or student to complete the problem place answer upside down where other students |

| |cannot see the answer. Have 1st, 2nd, and 3rd, place winners. Prizes make a great incentive. |

|M.5.3 Algebra: Students will develop and apply concepts of basic algebra, patterns, relationships, and functions to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.5.3.1 Identify relationships and complete number | |

|sequences inherent in the addition and | |

|multiplication tables. | |

|M.5.3.2 Recognize and create repeating patterns and| |

|identify the unit being repeated using four or more| |

|items. | |

|M.5.3.3 Demonstrate an understanding that a |Materials: 1 toy car, 1 neutral colored house (zero/start), 10 each of 2 different colored |

|horizontal number line moves from left to right |houses (+/-). |

|using lesser to greater values and that intervals |Activities: Students will pick 4 random numbers between 1 and 10. The instructor will assign a |

|on a number line must follow a constant progression|positive or negative sign to each number. Students will move the car to the right (+) or to the |

|by values including negative and positive numbers |left (-) accordingly. Students will call out the answers by looking where the car stopped last. |

|and common fractions and decimals. | |

|M.5.3.4 Read and understand positive and negative | |

|numbers as showing direction and change on both | |

|horizontal and vertical number lines, i.e., | |

|demonstrate an understanding that a horizontal | |

|number line moves from left to right using lesser | |

|to greater values and that a vertical number line | |

|moves from the bottom up using lesser to greater | |

|values. | |

|M.5.3.5 Recognize and understand the commutative | |

|and associative properties of addition and | |

|multiplication by using them to rewrite | |

|expressions. | |

|M.5.3.6 Read, write, and simplify word expressions | |

|using algebraic notation for addition, subtraction,| |

|multiplication, division, and parentheses. | |

|M.5.3.7 Demonstrate an understanding that a |Materials: 20 pennies, bottle cap (variable), paper, and pencil. |

|variable represents a missing value in addition and|Activity: Write out a simple addition and subtraction equation, i.e. 2 + x = 6. Underneath the |

|subtraction expressions, e.g., substitute the value|equation place the appropriate amount of coins to represent the numbers and leave the variable |

|for the variable in one-step expressions using |blank. Note: Students should remove the 2 pennies from the left (leaving the bottle cap) and 2 |

|whole numbers when the value is given. |pennies from the right leaving 4. |

|M.5.3.8 Solve simple one-step equations by | |

|recognizing that addition and subtraction are | |

|inverse operations and that multiplication and | |

|division are inverse operations and knowing the | |

|unknown of simple equations can be found by using | |

|the inverse of the operation present. | |

|M.5.3.9 Demonstrate an ability to use the symbols >| |

|and < in number statements with larger numbers. | |

|M.5.3.10 Understand and use exponents to represent | |

|repeated multiplication, i.e., recognize that | |

|exponents indicate the number of times that the | |

|base is written as a factor. | |

|M.5.3.11 Read, write, and compute squares and cubes| |

|of whole numbers, i.e., 4(4) = 42 = 16 and 2(2)(2) | |

|= 23 = 8. | |

|M.5.3.12 Interpret and solve simple (one or two | |

|steps) real-life word problems involving addition, | |

|subtraction, multiplication, and division. | |

|M.5.3.13 Identify and apply simple formulas with | |

|one or two arithmetical steps for real-life | |

|contexts. | |

|M.5.3.14 Write an equation representing verbal | |

|situations with no more than two operations, i.e., | |

|translate simple word problems involving unknown | |

|quantities into simple equations. | |

|M.5.3.15 Develop flexibility in solving problems by| |

|selecting strategies, i.e., determine when and how | |

|to split a problem into simpler parts to make | |

|solving easier. | |

|M.5.3.16 Compute using the correct order of | |

|operations to solve problems including | |

|multiplication, division, addition, and subtraction| |

|(M, D, A, S). | |

|M.5.3.17 Apply estimation strategies and mental | |

|math to approximate solutions and then use a | |

|calculator to calculate solutions to contextual | |

|problems containing whole numbers and decimals to | |

|two places. | |

|M.5.3.18 Use the calculator to find squares, square| |

|roots, and cubes of whole number quantities, i.e., | |

|know the calculator keys that generate squares, | |

|square roots, and cubes of numbers. | |

Mathematics Sample Teaching Activities

Level 4 – Grade Level 6.0 – 8.9

|M.1.4 Number Sense and Operations: Students will develop and apply concepts of number sense and operations to explore, analyze, and solve a variety |

|of mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.1.4.1 Carry out calculations using addition, | |

|subtraction, multiplication, and division with | |

|numbers of any size using efficient written methods | |

|including ways to check answers, e.g., approximate | |

|calculations, estimation, etc. | |

|M.1.4.2 Identify the greatest common factor in a |Materials: Greatest Common Factor Venn Diagram (See Template M.1.4.2). |

|given number set. |Activity: Label each side of the Venn Diagram with the numbers being compared. Have students |

| |fill in the factors of the first number in the red circle and the factors of the second number |

| |in the blue circle. Fill in the overlapping part with the factors the numbers have in common. |

| |Multiply the numbers in the overlapping section to get the greatest common factor. |

|M.1.4.3 Identify prime numbers up to 100. |Materials: Calculator |

| |Activity: After showing students the definition of a prime number and giving several examples in|

| |the numbers 1 to 13, have students use the calculator to see which numbers from 14 to 100 are |

| |prime numbers. |

|M.1.4.4 Read, write, order, and compare fractions and| |

|mixed numbers. | |

|M.1.4.5 Recognize and use equivalent forms of common |Materials: Fraction bar set (kit or homemade paper strips) |

|fractions (e.g., 1/2 = 5/10). |Activity: Using the fraction bars, have students show the many ways they can represent the |

| |fractions 1/4, 1/3, 1/2, 2/3, 3/4 |

|M.1.4.6 Demonstrate an understanding of simple | |

|percent increase and decrease. | |

|M.1.4.7 Round decimals in practical contexts and |Materials: Collect grocery tickets or department store receipts. |

|verbal problems. |Activity 1: Teacher should highlight a few of the $ (dollar) or ¢ (cent) items for use. Ask the|

| |students to round off the decimal prices to the nearest tens, dollars, or tenths. Students can |

| |also compare the same items from like stores. |

|M.1.4.8 Multiply and divide with numbers involving |Material: A worksheet with various multiplication and division problems with decimals. |

|decimals, e.g., 2.5 x 3.6 and 3.2 ÷ .06 with pencil |Activity 1: Divide the class into two groups where ½ work problems using pencil and paper, the |

|and paper and using the calculator. |other ½ use calculators to solve the same problems. Compare answers and discuss discrepancies. |

|M.1.4.9 Use proportions to solve one-step real-life |Materials: Measuring spoons and cups. |

|problems, i.e., involving percents, dimensions, |Activity: Have students convert a recipe for making a pie for four people to making a pie for |

|scales, etc. |16 people. Ask the students to multiply each designated recipe 4 times the amount to increase |

| |the recipe. |

|M.1.4.10 Recognize and use equivalencies between |Materials: Two decks of flash cards. One set with fractions only and other set with equivalents|

|common fractions, decimals, and percents to find part|in decimals on one side and percents on the other side. |

|of whole-number quantities, i.e., know common |Activity 1: Have students divide into groups of 3’s. Place the fraction cards face down. Place |

|fraction, decimal, and percent equivalents, e.g., 50%|the decimal and percent cards face up, half decimals and half percents. Have the students take |

|= 1/2 = .5, 25% = .25 = 1/4, .75 = 75% = 3/4. |turns picking a fraction card and finding the equivalents. They will have one minute to find it.|

| |If the student gets it correct, he/she will earn a point. If it is incorrect, the other players |

| |have a chance to steal the point. The person with the most points will win the game. |

|M.1.4.11 Compute percents by finding the part, the |Materials: Explain the meaning of the words (of=multiply, is=equal, n=unknown, what=n, and what|

|percent, and the whole. |percent=n. |

| |Activity 1: Ask the students to change the percent problem into an equation to solve. |

| |Ex: What is 15% of $9.00? n = .15 x 9.00 (a number x a number – multiply) |

| |Ex: What percent of 50 is 20? n x 50/50 = 20/50 |

| |A number times an unknown, divide by the number with the unknown. |

|M.1.4.12 Use a calculator to calculate efficiently | |

|using whole numbers, fractions, decimals, and | |

|percents. | |

|M.2.4 Measurement: Students will develop and apply concepts of standard measurements and use measurement tools to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.2.4.1 Read, measure, estimate, calculate, and |Materials: Thermometers with Fahrenheit and Celsius. Fahrenheit to Celsius conversion formulas.|

|compare with and between Fahrenheit and Celsius |Activity 1: Divide students into two groups. One group works on Fahrenheit. The other group |

|temperatures using formulas provided. |works on Celsius. Each group estimates temperature in the room, outside, in the refrigerator, in|

| |a cup of coffee. Measure the temperature in each place. If students measure in Fahrenheit, |

| |convert to Celsius. If students measure in Celsius, convert to Fahrenheit. Share and compare |

| |answers between |

|M.2.4.2 Measure common three-dimensional shapes |Activity 1: Have students work in pairs to create a map of the classroom or other room familiar|

|(e.g., a room, window, box, etc.) and represent the |to the students. The map should include a scale, coordinate grid, compass rose, and symbols. |

|information as a scale drawing. |Remind students to include a title and a key. (This project could be done in steps as each item |

| |is discussed in the classroom. Example: Drawing to scale, outlining the space by measuring and |

| |creating an appropriate scale. This should be done in connection with the scale lesson.) |

| |Materials: Measuring tool (ex: tape measure, ruler, meter stick). |

| |Activity 2: Measure common 3-dimensional shapes (e.g. a room, window, box, etc.) and represent |

| |the information as a scale drawing. Give the students an object/area to measure. The students |

| |may be given a formula of measurement. |

|M.2.4.3 Use the language (meters to measure length, | |

|grams to measure mass, liters to measure volume) and | |

|prefixes (mili, centi, deci, deca, hecto, kilo) of | |

|metric units to describe environment. | |

|M.2.4.4 Make informal comparisons and estimations | |

|between grams and ounces, kilograms and pounds, and | |

|liters and quarts, i.e., 1 ounce is approximately 29 | |

|grams, a paper clip weighs about 1 gram, a kilogram | |

|is about 2.2 pounds, and a liter is a little larger | |

|than a quart (1.1 qts.). | |

|M.2.4.5 Calculate volume and surface area of basic |Materials: 1 cube, 1 oatmeal cylindrical box, 1 rectangular tissue box, measuring tape, ruler, |

|cubes, cylinders, and rectangular containers using |formula cards, construction paper, scissors, glue. |

|formulas provided. |Activity 1: Using formula cards measure, calculate, and record the volume of the cube, |

| |cylinder, and rectangular box. |

| |Activity 2: Measure the length of one side of the cube. Measure and cut out six squares of |

| |construction paper to fit. Using formula card, calculate the area of the square and write it on |

| |each square piece. Add the six areas for a total surface area. Paste the squares onto the cube. |

| |Using the formula card, calculate and record the total surface area of the cube. Do the two |

| |totals match? |

| |Activity 3: Measure the length and width of each side of the rectangular box. Measure and cut |

| |out a shape of construction paper to fit each side. Using the formula card, write the area of |

| |each piece. Add the six areas to get a total. Paste the shapes onto the box. Using the formula |

| |card, calculate, and record the total surface area of the rectangular box. Do the two totals |

| |match? |

| |Activity 4: Trace and cut two circles of construction paper to cover each end of the |

| |cylindrical box. Using the formula card, find the area of the circle and write it on each. |

| |Measure the height and circumference of the body of the box. Cut a piece of construction paper |

| |to fit. Using a formula card, calculate the area of the side piece. Write it on the shape. Add |

| |the three areas for a total. Paste the shapes to the box. Using the formula card, calculate and |

| |record the total surface area of the cylinder. Do the two totals match? |

|M.2.4.6 Calculate the perimeter and area of basic |Materials: 3 rectangular classroom tables and tape measure, GED formulas. |

|irregular or composite shapes, i.e., shapes formed by|Activity 1: Have students measure, calculate, and record the perimeter and area of each table. |

|a combination of rectangles and triangles using |Arrange the tables in each of the following patterns. Then have students measure the perimeter |

|formulas provided. |and area of each new arrangement and record their findings. Which gives the most seating places?|

| |Is there another way to arrange the tables? Which do you like best? |

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|M.2.4.7 Find equivalencies and solve problems using | |

|conversions of units of weight, length/width, and | |

|capacity. | |

|M.2.4.8 Interpret, calculate, apply rates, and |Materials: Map |

|estimate equivalencies involving time such as |Activity 1: Have students figure how long it will take to travel between two cities at different|

|velocity (mi/hr, ft/sec, m/sec), frequency |rates of speed. |

|(calls/hr), consumption (cal/day, kw/hr), flow | |

|(gal/min), change (degrees/min, inches/year), and | |

|unit rates (cents/min, $/sq. ft., mi/gal). | |

|M.2.4.9 Interpret and use scale drawings to solve |Materials: Graph paper, scrap paper, scissors |

|real-life problems. |Activity: Have students work in teams to create a scale drawing of a classroom. Cut shapes to |

| |represent beds, tables, dressers, etc. Have students decide how many teacher desks, student |

| |desks, and computers can be placed in the classroom. |

|M.2.4.10 Relate the measure of one object to another |Materials: Paper clip, cell phone, notebook, tennis balls, trash can |

|(e.g., this is about 3 times as long, 6 of these will|Activity: Have students use the paper clip, etc. to measure larger objects. Students should |

|fit in there) and plan linear spacing in a design |make comparisons using the different objects. Have students guess how many tennis balls will |

|(e.g., how many lines of what size can fit on a |fit in the trash can. |

|poster of a certain height?). | |

|M.3.4 Geometry: Students will develop and apply concepts of geometric properties, relationships, and methods to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.3.4.1 Identify and compare elements of a circle |Activity: Use circular tables or drawn circles to actually measure and map out the various |

|(center, radius, diameter, arc, circumference). |components of a circle. Cut out circles, then measure and cut the circles into quarter pieces. |

| |This will give a representation of the radius and circumference. Then bring them together to |

| |show the center. |

|M.3.4.2 Calculate circumference of a circle using |Materials: tape measures and an assortment of circular objects such as paper plates of varying |

|formulas provided. |sizes, plastic lids, etc. |

| |Activity: Have students calculate the circumference of several circles, then have them measure |

| |to check their answers. |

|M.3.4.3 Understand the relationship of angles when |Materials: protractors |

|you have a system of parallel lines cut by a |Activity: Draw a pair of parallel lines cut by a transverse line. Use a protractor to measure |

|transversal. |each angle. Compare the complementary angles around each intersection. Show how the pairs of |

| |angles equal 180° and how the angles add up in various pairs. Additionally, once all of the |

| |angles have been colored in, show the comparison of the angles in the different areas of |

| |intersection. |

|M.3.4.4 Show more than one line of symmetry in |Activity 1: Write the capital letters which have more than one line of symmetry. Draw the lines |

|complex shapes. |of symmetry. |

| |Materials: Magazine advertisements |

| |Activity 2: Have students look at an advertisement and determine lines of symmetry. Which ones |

| |have more than one line of symmetry? Watch for shapes within shapes and include those also. |

| |List, sketch, and/or draw the lines of symmetry. |

| |Activity 3: Look around the room and find 4 shapes which have more than one line of symmetry. |

| |Which ones have more than one line of symmetry. List, sketch, and draw the lines of symmetry. |

| |Activity 4: Walk outside and look for lines of symmetry in nature and in manmade objects. Which |

| |ones have more than one line of symmetry. List, sketch, and draw the lines of symmetry. |

|M.3.4.5 Interpret concepts of similarity and identify|Materials: Strips of paper |

|figures that are similar or congruent. |Activity: Give each student 3 strips of paper. Have students use the strip of paper to create a |

| |triangle by placing the strips together corner-to-corner. Have students compare their triangle |

| |to another student’s triangle. Are they congruent? Encourage students to prove the triangle are |

| |congruent using the definition of congruent triangles. |

|M.3.4.6 Demonstrate understanding of the 360–degree |Activity 1: Measure various angles and relate them to a 360 degree circle. |

|system of measuring angles and rotation. |Activity 2: Look around the room and find shapes which have angles. Which ones have more than |

| |one size angle? Watch for angles within angles. Estimate the size of the angles. List and draw |

| |the angles in a 360-degree circle. |

| |Activity 3: Do the same using a magazine advertisement. |

| |Activity 4: Do the same for objects outside. |

|M.3.4.7 Estimate the measure of an angle, accurately |Materials: Protractor, ruler, pencil. |

|measure an angle using a protractor, and draw angles |Activity: Use a protractor and ruler to draw 5 different size triangles with 2 given measures. |

|of specific measures using a protractor and ruler. |First have the students estimate the unknown angle. Then have students use a protractor and |

| |calculate the unknown angle. |

|M.3.4.8 Apply the Pythagorean Theorem using simple |Materials: basic right triangles of different sizes and rulers. |

|numbers and basic right triangles. |Activity: Give each pair of students a right triangle. Have them measure each side using the |

| |ruler. Then have them put the numbers for two of the sides into the Pythagorean Theorem and |

| |solve for the third side. Does their solution match their measurement? Is it close? Discuss what|

| |may cause minor errors. Have students solve for different sides, then have students do this with|

| |a different size right triangle. |

|M.4.4 Data Analysis and Probability: Students will develop and apply concepts of data analysis and probability to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.4.4.1 Develop and draw conclusions from tables and |Materials: Instructor needs tables and graphs from newspapers, magazines, or GED Social Studies|

|graphs using instructor or student selected |text so that students can develop skills. |

|information. |Activity: Have tables and graphs for students to analyze and predict outcomes and friends. |

|M.4.4.2 Gather data to answer a posed question and |Materials: Pens, pencils, and post-in-notes. |

|analyze and present data visually. |Activity: Students can suggest the data to be collected such as: Favorite color, type of |

| |shoes, color of hair, color of eyes, music, food, number of family members or siblings, etc. |

| |Write the responses/answers/data on the post-it-notes. Post them on a board in “like columns”. |

| |Analyze columns – how many of this and of that. |

|M.4.4.3 Demonstrate that a table can display the same|Materials: Cell phones, paper, text message logs (in cell phone). |

|data as a line or bar graph. |Activity: Have the students find the text message log in their cell phones. (Activity can |

| |target/tally number of incoming texts and/or outgoing texts.) Have the students tally how many |

| |texts have been sent (or received) for a period of 1 week. (1) Make a table showing each day of |

| |the week. Write the number of texts sent/received for each day of the week. (2) Using this table|

| |of information, have the student construct a bar graph to display this information, with the |

| |days of the week along the horizontal axis, the number of texts sent/received along the vertical|

| |axis (in intervals of twenty or ten). |

|M.4.4.4 Find the average (mean), median, mode, and |Activity: Have students guess the average number of siblings each class member has. Have the |

|range for a data set. Note: it is important for |students tally the number of siblings in each family. Using the data, calculate the mean, |

|students to recognize that mean and median numbers |median, and mode. Compare the actual results to the guess. |

|are considered “averages” and that averages represent| |

|numbers typical of the data that can support an | |

|argument. | |

|M.4.4.5 Identify the minimum, maximum, and spread of |Materials: Pens, pencils, students’, post-it-notes, board on which to stick the notes. |

|a data set and describe the effect of spread on mean |Activity: Have the students write their ages on the notes and place them on the board in |

|and median, i.e., know the minimum or maximum value |columns or in a number-line fashion. Ask, “What is the minimum age? What is the maximum age?” |

|can greatly affect the mean but will not affect the |The spread is the range between minimum and maximum. Remind the students that the median = the |

|median. |middle value (think: median strip is in the middle of the road). The mean is the average of all |

| |values. Determine the median (middle) value. Determine the mean (average) value. Then remove the|

| |lowest/highest value and see the difference on the mean. Did the median change? Why or why not? |

| |(This exercise could also be done with price values on store flyers.) |

|M.4.4.6 Demonstrate an understanding of line graphs, |Materials: Monthly electric bills for one year. |

|i.e., that lines going up mean increase, lines |Activity: Students will draw a line graph with months of the year along the horizontal axis and|

|tilting down mean decrease and that they can vary |the number of monthly kilowatt usage along the vertical axis (in intervals of about 50 or so). |

|over time, flat lines mean no change, and use |Students can connect the dots to form a line. Students can then discuss peaks, lows, trends, |

|specific vocabulary to describe trends, i.e., sharp |etc. |

|increase, plummeted, etc. | |

|M.4.4.7 Know when percent figures don’t add up to |Activity: Develop a pie chart with percents. Example: Pie chart entitled, “Modes of |

|100% and when numbers and percent figures (50%, 25%, |Transportation to School”, which displays modes such as: bus, private auto, parents, other. |

|10%) don’t match up, i.e., understand that circle |What is the percent of the other mode of transportation to school? What happens if the other |

|graphs represent 100%. |mode increases to 20%? |

|M.4.4.8 Recognize that some visual representations | |

|distort actual data (bar widths can provide | |

|misleading information) or see where authors of data | |

|reports can manipulate data to benefit themselves or | |

|malign others in provided materials and know how to | |

|recognize who produced a data report and how their | |

|interests might affect the report – conflict of | |

|interest. | |

|M.4.4.9 Reorient, reorganize, restate, summarize, or | |

|reformat report data (make graphs) for a particular | |

|purpose and audience. | |

|M.4.4.10 Determine and compare probabilities of |Materials: Develop a lottery for the class. Tickets are sold for a free pizza at the local |

|chance events (e.g., winning lottery prizes). |pizza establishment. Tickets cost $.10, and 100 tickets are sold. |

| |Activity: John buys 17 tickets. Jane buys 23 tickets. What is the probability that John will |

| |win? What is the probability that Jane will win? What is the probability that neither will win? |

|M.4.4.11 Calculate the possible combinations (a | |

|selection of items where order doesn’t matter) of up | |

|to five items in simple, practical situations (e.g., | |

|I have 4 tickets and 5 potential guests). | |

|M.4.4.12 Calculate the possible permutations (an | |

|arrangement of items/data in a certain order) of up | |

|to five elements in simple, practical situations | |

|(e.g., ways to sequence titles of 4 different colors | |

|in a pattern). | |

|M.5.4 Algebra: Students will develop and apply concepts of basic algebra, patterns, relationships, and functions to explore, analyze, and solve |

|mathematical and real-life problems. |

|Benchmark |Teaching Activities |

|M.5.4.1 Identify and use simple formulas from tables | |

|with one or two arithmetical steps for real-life | |

|contexts. | |

|M.5.4.2 Use graphs to analyze the nature of changes | |

|in quantities in linear relationships and use | |

|vocabulary to describe linear change (e.g., rises | |

|steadily, fall, gradually declines). | |

|M.5.4.3 Recognize and describe patterns in given sets| |

|of numbers in a functional relationship and how | |

|changes in one quantity can affect another. | |

|M.5.4.4 Demonstrate understanding of the Cartesian | |

|coordinate system. | |

|M.5.4.5 Use coordinate grid to identify and locate |Materials: Battleship game |

|specific points on the x- and y-axes. |Activity: Divide students into groups of 2 or teams. With the battleship game board divided |

| |into four quadrants, have students play Battleship with ships hidden in each quadrant. |

|M.5.4.6 Graph simple linear equations by generating a|Materials: 6 flash cards at each table with the same linear equation: x = 2, x = -1, x = 0, x |

|table of values from an equation and plotting the |= 1, x = 2, x = 3 on the front, y = solved answer on the back. Graph paper. |

|coordinates on a graph. |Activity 1: Ask students to solve for y and make a table representing the (x, y) coordinates. |

| |Activity 2: Have students plot points. Ask, “Is this a linear equation?” |

|M.5.4.7 Determine the slope of a line when given two | |

|points on the line or the equation of a line and | |

|relate it to change. | |

|M.5.4.8 Write the equation of a simple line when | |

|given two points or slope and one point. | |

|M.5.4.9 Demonstrate an understanding of like terms by|Materials: M&M’s and pennies. |

|combining like terms in simple algebraic expressions.|Activity 1: Give each student 5 pennies. Have the students add 1p + 1p, 1p + 2p, etc. Repeat |

| |with M&M’s. |

| |Activity 2: Have one student lay small groups of pennies down and another student write an |

| |algebraic equation to represent the expression. |

| |Activity 3: When the students are ready, use the pennies and M&M’s in the same expression, 2p +|

| |p + 3m + 2m, simplify. |

|M.5.4.10 Demonstrate an understanding of the order of| |

|operations and use the order of operations when | |

|simplifying algebraic expressions. | |

|M.5.4.11 Add and subtract integers, i.e., positive |Materials: Play money ($500/student), copy of a check registry. Hand out with a list of bill |

|and negative numbers. |amounts and paycheck amounts. Decks of cards. |

| |Activity 1: Hand out all the items above except the deck of cards. Explain to the students that|

| |the amounts of money you have/get are positive numbers, and the money used/spent is a negative |

| |number. Instruct them to put the $500 down at the top of the resister as a begging balance. Have|

| |them use the handout to add and subtract the bills and paychecks. |

| |Activity 2: In a game called Zero divide students into groups and give each group a deck of |

| |cards. Have students take out face cards. Instruct students to pass out 5 cards to each student.|

| |Black cards are positive, and red are negative. Sort cards by color and use rules for signed |

| |numbers to add and subtract numbers on cards to eliminate as many as possible until all cards |

| |have been added. The hand closest to 0 wins the game. This game can be used in a small group or |

| |involve the whole class. |

|M.5.4.12 Multiply and divide integers, i.e., positive| |

|and negative numbers. | |

|M.5.4.13 Calculate square roots of perfect squares, | |

|estimate within range of square root value, and | |

|demonstrate an understanding of how squaring and | |

|taking the square root are related. | |

|M.5.4.14 Evaluate, add, subtract, multiply, and | |

|divide expressions involving exponents. | |

|M.5.4.15 Demonstrate an understanding of scientific |Materials: Computer with Internet access, worksheet with large and small numbers (such as the |

|notation, i.e., a shorter way to write large or |distance of planets from the sun) |

|really small numbers. |Activity: Have students watch a YouTube video showing large and small numbers such as From |

| |Quarks to Outer Space. After instructor demonstration, have students complete the worksheet. |

|M.5.4.16 Demonstrate an understanding of and solve | |

|basic algebraic equations involving multiple steps, | |

|e.g., 3x + 25 = 100, 2x – 16 = 42, 3y+ 3 = 42, m/5 – | |

|25 = 200. | |

|M.5.4.17 Translate word phrases into algebraic | |

|expressions and vice versa. | |

|M.5.4.18 Demonstrate an understanding of substituting| |

|values into simple formulas and solving for the | |

|unknown value. | |

|M.5.4.19 Demonstrate understanding of the | |

|distributive property, e.g., 75 x 12 = 75 x 10 + 75 x| |

|2 and 2(a + 6) = 2a + 12 | |

|M.5.4.20 Read, write, order, and compare positive and|Activity: Disucss with students how negative numbers are used in daily life, i.e., negative |

|negative numbers and identify positive and negative |temperatures, debits to checking accounts, etc. |

|numbers on a number line. | |

|M.5.4.21 Solve real-life, multi-step word problems |Materials: Payroll stubs, sale papers, and catalogues. |

|involving money, measurement, and other contextual |Activity: Have students use payroll stubs to calculate the percent paid in different types of |

|situations using whole numbers, decimals, and |tax or insurance. Use sale papers to compare prices and find unit prices, sales tax, shipping |

|percents. For example, solve problems relating to |and handling fees, etc. |

|payroll deductions, computing and comparing unit | |

|pricing, rebates, discounts, deficits, sales taxes, | |

|shipping and handling fees, etc. | |

|M.5.4.22 Recognize and eliminate extraneous |Materials: Worksheets of word problems that have extra information. |

|information in word problems. |Activity: Have students work in pairs to identify the extra information. They do not need to |

| |solve the problems, only identify the extra information. Discuss why it is important to be able |

| |to identify this extra information, i.e., in real-life there is often more information than you |

| |need to solve a particular problem. |

Mathematics Glossary

Absolute value The distance a number is from zero on the number line.

Acute angle An angle of less than 90°

Acute triangle A triangle with three acute angles

Adjacent angle Angles that share a common side and vertex (corner point) but do not overlap

Algebraic expression A mathematical statement involving variables and/or numbers written in words or symbols, e.g., 3a + 5 or six plus seven times a number

Algebra/Functions The ability to represent and use variables; create and simplify expressions; create, solve, and apply equations and formulas; graph functions; use matrices; and apply algebraic skills and properties to realistic situations.

Analog clock A clock that has 12 equal divisions around the perimeter/ circumference, labeled 1 to 12 to represent hours. It has two hands that rotate around the center. The hour hand completes one revolution in 12 hours and the minute hand completes one revolution in one hour.

Angle A configuration of two line segments meeting at a point. The term is often used for the measure of rotation from one of the line segments to the other. In this sense, a right angle measures 90°, an acute angle is less than 90°, an obtuse angle is greater than 90° but less than 180°, and a reflex angle is greater than 180°.

Approximation A result that is not exact but sufficiently close to be useful in a practical context. Verb: approximate. Adverb: approximately.

Arc Part of the circumference of a circle

Area A measure of a surface or the space inside a plane figure. Measured in squares, e.g., square inches (in2), square feet (ft2), square centimeters (cm2), square meters (m2).

Area of circle Area = ( x radius2

Area of rectangle Area = length x width

Area of triangle Area = 1/2 base x height

Associative property Grouping does not matter in addition or multiplication, e.g., for numbers a, b, and c; A + (b + c) = (a + b) + c and a x (b x c) = (a x b) x c

Authentic Materials Real-life materials, i.e., materials which have not been specifically written for classroom use

Average Sometimes used synonymously with arithmetic mean, e.g., average = sum of quantities ( number of quantities

Average speed Average speed = total distance ( total time

Axis X axis is the horizontal (along) axis and the Y axis is the vertical (up) axis. If you are talking about both of them, they are called “axes.”

Axis of symmetry A line that makes one half of a figure fit (or map) exactly on the other half.

Bar chart/graph A statistical diagram made up of bars. Bars of equal width represent frequencies where the lengths are proportional to the frequencies. The bars may be presented vertically or horizontally.

Base (1) The base of a figure. (2) The counting system being used, e.g., base 10 is ordinary counting and base 4 is counting using only 0, 1, 2, and 3.

Binominal An algebraic expression containing two terms, e.g., 2a + 3b

Bisect Cut exactly in half

Bisector A line that divides another line or an angle exactly in half. A perpendicular bisector is a line that cuts another line exactly in half at right angles.

Block graph A statistical diagram made up of blocks. In its simplest form, where the class intervals are equal and rectangles have bases of the same size, the block graph can be considered as a bar chart, and the length of each rectangle represents the total in each class.

Borrow Regrouping from a greater place value to a lesser place value in order to subtract, e.g., one ten to ten ones.

Calculate efficiently Use knowledge of number systems and operations, e.g., use multiplication rather than repeated addition. In the context of using tools, to use available operations and functions, e.g., memory and constant functions on a calculator, sum formula in a spreadsheet for a range of cells, rather than addition of individual cells.

Cancel Divide the numerator (top) and denominator (bottom) of a fraction by the same number to make the fraction simpler

Capacity Volume, i.e., a measure in three dimensional spaces applied to liquids, materials that can be poured, or containers. Units include cubic inches (in3), cubic feet (ft3), cubic centimeters (cm3), cubic meters (m3). Note: a liter is 1000 cm3 (the volume of 1 kg of water).

Cardinal number A counting number, i.e., one, two, three, etc.

Cartesian coordinate system Also known as the rectangular coordinate system, it consists of two number scales (X axis and Y axis). Each scale is a number line drawn to intersect each other at zero.

Carry Regrouping from a lesser place value to a greater place value in order to add, e.g., ten ones to one ten.

Chart Visual organization and presentation of data in rows and columns

Circumference The perimeter of a circle, i.e., the distance all the way around a circle; if the radius of a circle is “r” units, and the diameter is “d” units, then the circumference is 2( r or (

Clockwise Moving the same direction as the hands of a clock move.

Coefficient The number in front of a variable, e.g., for the term 4a, the coefficient of a is 4.

Combination A selection of some or all of a number of different objects. It is an un-ordered collection of unique sizes in which the order of occurrence of the objects is not important.

Combined events A set of independent events with a single outcome. An independent event does not influence a subsequent event. For example, one throw of a die does not influence a second throw. Two throws of a die is a combined event with 36 possible outcomes (6 x 6). The probability of throwing two sixes is 1/36.

Common Something shared by both or all things

Common fraction A fraction where the numerator and denominator are both integers, also known as a simple or vulgar fraction.

Communicating mathematically The ability to use mathematical terms, notation, and symbols appropriately; organize and consolidate mathematical thinking through written and oral communication; and coherently communicate one’s mathematical thinking to others.

Commutative property Order does not matter in addition or multiplication, e.g., 2 + 3 = 3 + 2 and 2 x 3 = 3 x 2. Subtraction and division are not commutative.

Compass directions Any of 32 horizontal directions indicated on a compass, the 8 most used are north, south, east, west, northeast, northwest, southeast, and southwest.

Complementary angles Angles that add up to 90°

Composite shape An irregular shape which can be partitioned into two or more regular or simple shapes, e.g., an L-shape made up of two rectangles.

Congruent Two or more figures that are the exact same shape and the exact same size

Continuous data Data resulting from measurement, e.g., length, temperature. Continuous data can take any value between two values, and can only be measured approximately to a certain degree of accuracy. A line usually represents continuous data.

Consecutive numbers Numbers that follow one another, e.g., 4, 5, 6 are consecutive numbers; 1, 3, 5 are consecutive odd numbers; and 2, 4, 6 are consecutive even numbers

Coordinates Mathematical map reference to show the position of a point. Ordered pairs; the x coordinate comes first then the y coordinate; coordinates are always written in pairs within parentheses with a comma between the numbers, e.g., (3, 5) where 3 is the x coordinate and 5 is the y coordinate

Corresponding angles Angles between parallel lines and a transversal and are exact copies of one another. Corresponding angles are equal.

Counter clockwise Moving in the opposite direction of the hands on a clock

Cube (1) A three dimensional figure with six square faces (2) A number multiplied by itself and then by itself again, e.g., the cube of 3 is 3 x 3 x 3; cubed is written to the power of three, e.g., 2 cubed = 23 = 2 x 2 x 2

Cubic Unit Unit used to measure the volume of a solid e.g., length= 1 cm therefore volume= 1 cubic unit

Cylinder A circular prism

Data Information of a quantitative nature consisting of counts or measurements; where they refer to items or events that are separate and can be counted, the data are discrete; where they refer to quantities such as length or capacity that are measured, the data are continuous. Singular: datum.

Data Analysis The ability to collect data using appropriate samples; organize data into tables or lists; display data using appropriate graphs; analyze and interpret data using mean, median, mode, range, and measures of variation; and apply statistics in realistic situations.

Decimal Relating to base ten. Most commonly used synonymously with decimal fraction, where the number of tenths, hundredths, thousandths, etc. is represented as digits following a decimal point. The decimal point is placed at the right of the unit’s column. Each column after the decimal point is a decimal place. For example, the decimal fraction 0.275 is said to have three decimal places. The system of recording with a decimal point is decimal notation. U.S. currency is based on the decimal system.

Decimal places The number of figures after the decimal point, e.g., 3.45 has 2 decimal places and 0.098765 has 6 decimal places.

Decrease To make smaller

Denominator The bottom number of a fraction; tells the number of parts in a whole

Diagonal A straight line from one corner of a figure to another corner, going across the space inside

Diameter The distance across the middle of a circle; the diameter is twice the radius, i.e., d = 2r

Difference The answer to a subtraction problem, e.g., the difference between 3 and 5 is 2 (5 – 3 = 2).

Digit One of the symbols of a number system, i.e., most commonly the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For example, the number 38 is a two-digit number, but there are three digits in 3.75. The position of the digits conveys place value.

Digital clock A 12-hour clock that displays time in hours past midnight and midday and uses a.m. and p.m. to differentiate.

Direct proportion Two quantities or variables are in direct proportion when they increase or decrease in the same ratio. For example, if 3 apples cost $1.00 and 6 apples cost $2.00, then cost is in direct proportion to quantity, i.e., they both double, or both halve; expressed mathematically as y = kx where k is constant.

Discrete data Data resulting from a count of separate items or events, e.g., number of people

Distribution In recording data, the way values in a set of observations are arranged

Distribution table A statistical table showing the number of items in each group, sometimes called a frequency table

Distributive property Multiplication is distributive over addition and subtraction

Dividend The number being divided into equal parts

Divisor The number divided into the dividend

Equal angles Angles that have the exact same measure

Equation A mathematical statement that says two or more expressions are equal

Equilateral triangle A triangle with three equal sides and three equal angles

Equivalent fractions Fractions of equal value. For example, 6/12, 3/6, and 1/2 are equivalent.

Estimate To arrive at a rough answer by calculating with suitable approximations for numbers

Evaluate To work out the value of an expression when numbers have been substituted for variables

Even numbers Any integer that can be divided exactly by 2

Event Used in probability to describe the outcome of an action or happening

Exponent The number of times a number is multiplied by itself

Expression A mathematical statement involving variables and/or numbers written in words or symbols, e.g., length x width, a x b, or ab

Face The flat part of the outside of a solid

Factor A number that divides evenly into another, e.g., 24 = 3 x 8, so 3 and 8 are factors of 24. A prime factor is a factor that is a prime number.

Factorial Denoted by n!, a factorial is the product of all positive integers less than or equal to n, e.g., 5!= 1 x 2 x 3 x 4 x 5= 120

Factoring The process of expressing a given number (or expression) as the product of two or more numbers (or expressions).

Familiar Describes contexts, situations, numbers, measures, instruments, etc., of which the learner has some prior knowledge or experience.

Formula Any identity, general rule, or mathematical law; a sentence in which one variable is given in terms of other variables and/or numbers.

Fraction A way of showing (expressing) parts of a whole

Frequency table A statistical table that shows how many things are in each group, sometimes called a distribution table.

Fundamental Counting Principle A method used to calculate all of the possible combinations of a given number of events

Geometry The ability to identify, describe, construct, and apply geometric shapes and figures; identify and use concepts of congruence and similarity; use coordinate geometry, right triangle trigonometry, and transformations; and apply geometric properties and relationships in realistic situations.

Graph Visual representation comparing data from different sources over time

Grouped data Observed information arising from counts and grouped into non-overlapping intervals, e.g., number of people in different age groups with intervals 0-9, 10-19, 20-29, 30-39, 40-49, etc.

Hexagon A polygon with 6 sides

Histogram A statistical diagram, like a bar graph with no gaps, for showing continuous information.

Horizontal Straight across or parallel to the horizon

Hypotenuse The longest side of a right triangle, the side opposite the right angle

Improper fraction A fraction in which the numerator (top) is equal to or larger than the denominator (bottom)

Imperial unit A unit of measure. Units include inch, foot, yard, mile, acre, ounce, pound, stone, ton, pint, quart, and gallon.

Increase To make bigger

Independent event When the result of one event is not affected by the result of another event, e.g., If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events

Inequality Two or more things that are not equal. The common signs for inequality are < (is less than), > (is more than or greater than), < (is less than or equal to), and > (is more than or equal to)

Integer Any positive or negative whole number including zero.

Interest The extra amount added to money that is being lent, borrowed, or saved.

Intersection Where two or more lines meet or what two or more items have in common

Inverse operations Operations that, when they are combined, leave the entity on which they operate unchanged. Inverse operations include addition and subtraction (3 + 4 – 4 = 3) and multiplication and division (3 x 4 ( 4 = 3).

Inverse relationships When an equation is balanced or the same on either side of the equals (=) sign. Occurs in addition and subtraction, e.g., 7+3= 10 then 10-3=7 and 10-7=3 are also true and multiplication and division, e.g., 3x4=12 then 12(3=4.

Isosceles triangle A triangle with two equal sides and two equal angles (remember the angle that is between the two equal sides is NOT one of the equal angles).

Latitude Is measured from the equator, with positive values going north and negative numbers going south

L.C.M. Lowest common multiple. The lowest number that two or more other numbers will divide into.

Like fractions Fractions that have the same denominator

Line graph A diagram showing a relationship between two variables

Line symmetry Means the same as reflective symmetry. The property of a shape where one half is a reflection of the other; the ‘mirror line’ is the axis of symmetry or line of symmetry.

Longitude Is measured from the Prime Meridian (which is the longitude that runs through Greenwich, England), with positive values going east and negative values going west

Lowest terms A fraction is in lowest terms when no number will equally divide into both the numerator and denominator.

Mass A fundamental characteristic of a body relating to the amount of matter within it. Mass differs from weight. Under certain conditions a body can become weightless, whereas mass is constant.

Mathematical Connections The ability to make and use connections within mathematics and among mathematical ideas; and to recognize and apply mathematics in contexts drawn from other disciplines.

Mean A measure of average. The arithmetic mean is the sum of quantities divided by the number of quantities. For example, the arithmetic mean of 5, 6, 14, 15, and 45 is (5 + 6 + 14 + 15 + 45) ( 5 = 17.

Measurement The ability to measure, estimate, and apply units of quantity and size including length, area, volume, mass, time, temperature, and angle measure.

Measures of central tendencies A statistic describing a typical value of a numerical data set; i.e., mean, median, mode.

Median A measure of average; the middle number or value when all are arranged in order of size. Ex., the median of 5, 6, 14, 15, and 45 is 14. Where there is an even number of values, the median is the mean (average) of the two middle values. For example, the median of 5, 7, 7, 8, 14 and 45 is (7 + 8) ( 2 = 7.5.

Mental math Strategy for finding an answer without writing or using a calculator

Metric Relating to the decimal system of measurement based on the meter, kilogram, mile, and second

Metric unit Unit of measurement in the decimal system. Metric units include meter, centimeter, millimeter, kilometer, gram, and kilogram.

Mixed fraction A whole number and a fractional part expressed as a common fraction, e.g., 1 2/3 is a mixed fraction; also known as a mixed number

Mixed number A whole number and a fractional part expressed as a common fraction, e.g., 1 2/3 is a mixed number; also known as a mixed fraction.

Mode A measure of average. The most frequently occurring number in a set of data, for example, the mode of 5, 6, 6, 6, 7, 8 and, 10 is 6.

Monomials An expression with one term

Multiple Any number that has a given number as a factor is called a multiple of that factor, e.g., 12=6 x 2, 36=6 x 6 and 60=6 x 10; so 12, 36, and 60 are all multiples of 6.

Natural number A positive integer; a positive whole number

Negative number A number less than 0

Non-standard unit Unit of measure which is not fixed or widely agreed upon, e.g., pace—each person has a different pace.

Number bond A pair of numbers with a particular total, e.g., number bonds to ten mean all pairs of numbers with the total 10.

Number sense The ability to count; round numbers; represent and apply whole numbers, fractions, decimals, and percents using place value, pictures, equivalent forms, and properties; order numbers and identify their relative magnitude; and use number properties and proportional reasoning.

Numeral A symbol used to denote a number. The Roman numerals I, V, X, L, C, D and M represent the numbers one, five, ten, fifty, one hundred, five hundred, and one thousand. The Arabic numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in the Hindu-Arabic system giving numbers in the form that is widely used today.

Numerator The top number of a fraction; it tells how many parts of the whole were used.

Obtuse angle An angle that measures more than 90° but less than 180°

Octagon A polygon with 8 equal sides

Odd numbers Any integer that cannot be divided exactly by 2

Operations The ability to use mathematical operations to compute and estimate sums, differences, products, and quotients; use powers, roots, and proportions; and apply numbers and operations in realistic situations.

Order of operations The set of rules for finding the value of mathematical expressions.

Ordinal number A term that describes a position within an order, e.g., first, second, third, fourth … twentieth, etc.

Origin The point (0, 0) where the x axis crosses the y axis.

Parallel Always the same distance apart, e.g., parallel lines are always the same distance apart; they do not meet.

Pattern A systematic arrangement of numbers, shapes, or other elements according to a rule.

Patterns The ability to recognize, describe, and generalize a relationship and to create and extend a sequence.

Pentagon A plane figure with 5 sides

Percent Out of 100, written %.

Percentage A fraction expressed as the number of parts per hundred and recorded using the notation #%, e.g., one-half can be expressed as 50%, the whole can be expressed as 100%.

Perimeter The complete distance around the outside of a figure

Permutation An arrangement is called a permutation. It is the rearrangement of objects or symbols into distinguishable sequences. When we set things in order, we say we have made an arrangement. When we change the order, we say we have changed the arrangement. Each of the arrangements that can be made by taking some or all of a number of things is known as permutation.

Perpendicular At right angles

Pi ([pic]) The symbol used to denote the ratio of the circumference of a circle to its diameter, stands for 3.14 or 22/7.

Pictogram A statistical diagram made up of pictures. Suitable pictures/symbols/icons are used to represent objects.

Pictograph A representation of numerical data, as on a graph, where each value is represented by a proportional number of pictures. For large numbers, one symbol may represent a number of objects (one apple may represent 100 bushels); a part symbol then represents a rough proportion of the number (1/2 an apple represents 50 bushels).

Pie chart A statistical diagram shaped like a circular pie, with slices of pie showing amounts. The frequency or amount of each quantity is proportional to the angle at the center of the circle.

Place value The value of a digit that relates to its position or place in a number, e.g., in 1,321 the digits represent thousands, hundreds, tens, and ones respectively. The value of the 1 on the left is one thousand while the value of the 1 on the right is one.

Plot To represent graphically on a chart

Polygon A plane figure with many sides. Examples include triangle (3 sides), quadrilateral (4 sides), pentagon (5 sides), hexagon (6 sides), heptagon (7 sides), octagon (8 sides), nonagon (9 sides), and decagon (10 sides).

Prime number A prime number has exactly two factors, itself and 1. For example, 2 has factors 2 and 1, 3 has factors 3 and 1; however 6 is not a prime number because it has factors 2 and 3 in addition to 1 and 6.

Probability (1) The likelihood of an event happening; a measure of certainty. Probability is expressed on a scale from 0 to 1 either as a fraction, decimal, or percent. Where an event cannot happen, its probability is 0 and where it is certain, its probability is 1. The probability of scoring 1 with a fair die is 1/6 or about .167 or 16.7%.

Probability (2) The ability to apply measures of chance and likelihood including identifying possible outcomes, using simulations to calculate experimental probability, calculating theoretical probability of independent, dependent and compound events, and comparing experimental and theoretical probabilities.

Problem solving The ability to apply strategies to the solution of problems that arise in mathematics and other contexts; build new mathematical understanding through problem solving; and monitor, adapt, and reflect on the process of mathematical problem solving.

Product The answer to a multiplication problem, e.g., the product of 2, 3, and 4 is 24 (2 x 3 x 4).

Property Any attribute, e.g., one property of a square is that all sides are equal

Proportions An equation made up of two equal ratios.

Pythagorean Theorem Measure of the hypotenuse in a right triangle, the sum of the measure of the legs = the sum of the square of the hypotenuse, e.g., leg2 + leg2 = hypotenuse2 most often written as a2 + b2 = c2.

Quadratic equation An equation with a square term in it.

Quadrilateral A polygon with four sides and four interior angles.

Qualitative Descriptions or distinctions based on quality

Quantitative A measurement based on some quantity or number rather than on some quality

Quotient Answer to a division problem

Radius The distance from the center of a circle to the circumference; half the diameter.

Range A measure of spread in statistics; the difference between the least and greatest in a set of numerical data.

Ratio A comparison of quantities of the same kind, written a:b. For example, a mixture made up of two ingredients in the ratio 3:1 is 3 parts of the first ingredient to 1 part of the second; the first ingredient makes up 3/4 of the total mixture and the second makes up 1/4 of the total.

Reasoning The ability to make and investigate mathematical conjectures, develop and evaluate mathematical arguments and proofs, and apply deductive and inductive reasoning to logical arguments.

Reciprocal The reversal of a fraction, to turn upside down, e.g., the reciprocal of 2/3 is 3/2.

Rectangle A quadrilateral (four-sided polygon) with four right angles. The pairs of opposite sides are equal. Adjective: rectangular.

Reflex angle An angle that is more than 180 degrees but less than 360 degrees

Regular A polygon is a regular polygon if all the sides are equal and all the internal angles are equal, e.g., a regular quadrilateral is a square. When referring to a shape, the adjective ‘regular’ refers to common 2-D and 3-D shapes whose areas can be found using a formula, e.g., rectangle, circle, cylinder.

Remainder The number that is left in division problems, e.g., 18 ( 4=4 with a remainder of 2 since 4 does not divide into 18 equally.

Revolution All the way around, i.e., 360°

Right angle An angle of exactly 90°; one-quarter of a complete turn.

Roman Numerals Most common ones used today are I-1, V=5, X=10, L=50, C=100, D=500, and M=1000.

Rotation Turning a figure about a point, the point is called the center of rotation.

Rotational symmetry Where the shape or image can be rotated any number of times and it still looks the same

Round (verb) To express a number or measurement to a required degree of accuracy, e.g., 764 rounded to the nearest ten is 760.

Scale A measuring device usually consisting of points on a line with equal intervals.

Scalene triangle A triangle with no equal sides and no equal angles

Scientific notation A way of writing very large numbers and very small decimals in which the numbers are expressed as the product of a number between 1 and 10 and a power of 10.

Sequence A succession of terms formed according to a rule in which there is a definite relation between one term and the next and between each term and its position in the sequence, e.g., 1, 4, 9, 16, 25, etc.

Sign A symbol used to denote an operation, e.g., addition sign +, subtraction sign –, multiplication sign x, division sign (. In the case of directed numbers, the positive + or negative – sign indicates the direction in which the number is measured from the origin along the number line.

Simplify Work out to give the shortest possible answer

Speed Speed = distance ( time

Spread The difference between highest and lowest observed values in a set of data; range

Square number A number that can be expressed as the product of two equal numbers, e.g., 25 = 5 x 5, so 25 is a square number.

Square unit Unit used to measure the area of a two-dimensional figure; units needed to cover a surface.

Standard unit Units that are agreed upon throughout a community, e.g., the foot is a standard measure of length. Non-standard units are not widely agreed upon.

Straight angle An angle that measures 180 degrees

Substitute To assign a value to a variable

Sum Answer to an addition problem

Supplementary angles Angles which add up to 180 degrees

Symbol A letter, numeral, or other mark that represents a number, an operation or another mathematical idea. For example, V is the Roman symbol for 5 and > is the symbol for “is greater than.”

Symmetry A figure has symmetry if parts can be interchanged without changing the whole. A geometric figure may have reflective symmetry or rotational symmetry. Adjective: symmetrical.

Table An orderly arrangement of information, numbers, or letters usually in rows and columns.

Tally To make marks to represent objects counted.

Technology use The ability to effectively use calculators and computers to support the development of mathematical understanding, to solve mathematical problems, and to prepare students for the technologically-driven workplace.

Term One of the parts of an expression, e.g., 3a – 2 has two terms: 3a and -2

Translation Moving the position of an object so that it looks the same but is in a different place. It does not rotate, only moves left or right or up or down.

Transversal A line that intersects two or more lines in the same plane

Triangle A polygon with 3 sides

Trinomial An expression containing three terms, e.g., 3x2 – 4x + 5 has three terms: 3x2, -4x, and +5.

Unit One; a standard used in measuring, e.g., a meter is a metric unit of length.

Unit fraction A fraction that has 1 as the numerator and whose denominator is a non-zero integer, e.g., 1/2, 1/3.

Unit price The cost of one item.

Unlike fractions Fractions with different denominators

Variable A letter or symbol used to represent an unknown number

Venn diagram A picture showing sets. The elements of each set are put into a circle or oval shape.

Vertex Common endpoint of two rays that form an angle

Vertical Straight up and down

Volume The amount of space inside a solid; measured in cubes, e.g., cubic inches (in3), cubic centimeters (cm3).

Weight The force with which a body is attracted towards the earth’s center. In non-scientific contexts, weight is often used synonymously with mass (though technically different). Units of weight include pounds (lbs), ounces (oz), kilograms (kg), and grams (g).

X axis The horizontal (across) axis

X intercept The point at which a line crosses the x-axis on a coordinate graph; the ordered pair (x, 0)

Y axis The vertical (up/down) axis

Y intercept The point at which a line crosses the y-axis on a coordinate graph; the ordered pair (0, y)

Mathematics Internet Resources

Adults Learning Math Newsletter



Adult Numeracy Network



Aplus Math



Cool Math Games



Fun Brain



Math in Daily Life



Math Forum



Math Goodies



Math Playground



National Council of Teachers of Mathematics



NC Online Math Library



Science and Numeracy Special Collection, National Institute for Literacy LINCS

or

The Math Forum



The Numeracy List (electronic discussion list sponsored by the Adult Numeracy Network)



Resources for Teaching Technology/

Computer Literacy

| |Page |

|Technology/Computer Literacy Verification Checklists |199 |

|Technology/Computer Literacy Self Assessments |205 |

|Technology/Computer Literacy Sample Activities |212 |

|Technology/Computer Literacy Glossary |223 |

|Technology/Computer Literacy Internet Resources |233 |

| | |

Standard 1 - Technology/Computer Literacy Verification Checklist

|Student |Instructor |Date Enrolled |

| | | |

|Standard 1. The student will demonstrate knowledge of important issues of a technology-based society and exhibit ethical behaviors related to the |

|use of computers, digital resources, and other technologies. |

|Benchmark |Date |Initials |

|T.1.1.1 |Identify the computer as a machine that helps people communicate, work, and play. | | |

|T.1.1.2 |Recognize, discuss, and model correct use of common computer terms. | | |

|T.1.1.3 |Identify and discuss common features and functions of computer software and devices. | | |

|T.1.1.4 |Identify and discuss correct and responsible use and care of technology resources. | | |

|T.1.1.5 |Identify and discuss the uses of and changes in technology devices and the impact technological changes have had | | |

| |on business, transportation, communications, industry, and agriculture in the student’s local community and in | | |

| |society in general. | | |

|T.1.1.6 |Investigate computer/technology-related careers and occupations from the past, present, and future. | | |

|T.1.1.7 |Identify and discuss technology skills needed for the workplace now and in the future and how they impact the | | |

| |student as an adult learner today. | | |

|T.1.2.1 |Recognize and discuss the rights of ownership of computer-created and online work. | | |

|T.1.2.2 |Recognize, discuss, and model appropriate, responsible, ethical, and safe use of computers, mobile phones, | | |

| |wireless networks, LANs, and digital information (e.g., security, privacy, passwords, personal information), and | | |

| |recognize possible consequences of unethical behavior. | | |

|T.1.2.3 |Recognize and discuss how Copyright Laws and Fair Use Guidelines protect ownership of individual’s, group’s, and | | |

| |companies’ intellectual property and creative works and the importance of citing sources. | | |

|T.1.2.4 |Recognize and discuss consequences of misuse of copyrighted property and establish ethical guidelines for use of | | |

| |personal and copyrighted media (e.g., images, music, video, content, language), especially as related to use | | |

| |during class and for class projects and assignments. | | |

|T.1.3.1 |Recognize, discuss, and use terms and concepts related to networks (e.g., stand alone, network, file server, | | |

| |LANs, WANs, network resources) and protection of computers, networks, and information (virus protection, network | | |

| |security, passwords, firewalls, privacy laws). | | |

|T.1.3.2 |Investigate, recognize and discuss why computers, networks, and information must be protected from viruses, | | |

| |vandalism, and intrusion, both malicious and mischievous; discuss appropriate technology tools (virus software) | | |

| |used to protect them. | | |

|T.1.3.3 |Identify and discuss the benefits of non-networked and networked computers. | | |

|T.1.4.1 |Recognize, discuss, and use multi-tasking concepts (e.g., windows, toggle between two windows on the desktop, | | |

| |copy and paste data between two windows on the desktop). | | |

|T.1.4.2 |Recognize and discuss strategies for identifying, solving, and preventing minor hardware and software problems. | | |

Standard 2 - Technology/Computer Literacy Verification Checklist

|Student |Instructor |Date Enrolled |

| | | |

|Standard 2. The student will demonstrate an understanding of databases and ability to create databases. |

|Benchmark |Date |Initials |

|T.2.1.1 |Identify and discuss print (e.g., phone book) and electronic databases (e.g., automated circulation system, | | |

| |CD-ROM encyclopedias) as a way to collect, organize, and display data. | | |

|T.2.1.2 |Identify and discuss how and why databases are used in an information-intensive society (e.g., in education, | | |

| |government, business, community (grocery, pharmacy), and home). | | |

|T.2.1.3 |Identify and discuss database terms and concepts (e.g., sort, search, filter, keyword, data entry, field, record,| | |

| |list) using print and/or electronic databases to demonstrate. | | |

| T.2.2.1 |Plan, discuss, and use keyword searches or filters using one criterion in prepared electronic databases (e.g., | | |

| |automated circulation, encyclopedia, etc.). | | |

|T.2.2.2 |Use prepared databases to sort alphabetically/numerically in ascending/descending order. | | |

|T.2.2.3 |Modify prepared databases to enter/edit additional information and cite the source. | | |

|T.2.2.4 |Modify databases to organize, analyze, interpret data, and create reports (e.g., documents, multimedia project, | | |

| |and web pages). | | |

|T.2.3.1 |Use simple databases to locate, organize, analyze, evaluate, compare, and present information, citing sources of | | |

| |information. | | |

|T.2.3.2 |Using a prepared database, apply sort and search/filter functions to organize, analyze, interpret, and evaluate | | |

| |findings. | | |

|T.2.4.1 |Develop and use search strategies with two or more criteria to solve problems, make decisions, and report | | |

| |findings. | | |

|T.2.4.2 |Plan and develop a simple database to enter, edit, collect, organize, and display data. | | |

|T.2.4.3 |Use knowledge of database terms, concepts, functions, and operations to explain strategies used to plan and | | |

| |develop a simple database. | | |

|T.2.4.4 |Plan and develop database reports to organize data, create reports, and present findings, citing sources. | | |

|T.2.4.5 |Select and use appropriate database features and functions to collect, organize information, and create reports | | |

| |for use in other projects or media (e.g., documents, multimedia project, web pages), citing sources. | | |

Standard 3 – Technology/Computer Literacy Verification Checklist

|Student |Instructor |Date Enrolled |

| | | |

|Standard 3. The student will demonstrate an understanding of the ability to create, extract information from, and interpret spreadsheets. |

|Benchmark |Date |Initials |

|T.3.1.1 |Identify spreadsheets as a tool for organizing information. | | |

|T.3.1.2 |Recognize, discuss, and investigate how spreadsheets are used to process information (e.g., organize, calculate, | | |

| |graph data, solve problems, make predictions, and present data) in a variety of settings (e.g., schools, | | |

| |government, business, industry, communications, transportation, mathematics, science). | | |

|T.3.1.3 |Identify and discuss spreadsheet terms and concepts (e.g., collect, organize, classify, graph, display, cell, | | |

| |column, row, values, labels, chart, formula, sort, classify, bar graphs, line graphs, pie charts). | | |

|T.3.2.1 |Modify data in a prepared spreadsheet and observe the changes that occur to make predictions. | | |

|T.3.2.2 |Use spreadsheet software to enter, display, and identify types (text and numeric) of data. | | |

|T.3.2.3 |Recognize, discuss, and use graphs to display and interpret data in prepared spreadsheets. | | |

|T.3.3.1 |Modify or create and use spreadsheets to solve problems by performing calculations using simple formulas and | | |

| |functions (e.g., +, -, *, /, sum, average) and display data graphically. | | |

|T.3.3.2 |Use spreadsheet concepts and functions (e.g., median, range, mode) to calculate, represent, and explain data. | | |

|T.3.4.1 |Modify or create a spreadsheet by using the features and functions previously learned to analyze and interpret | | |

| |information, solve problems, make decisions, and support, display, and present findings, citing sources. | | |

|T.3.4.2 |Modify or create and use spreadsheets to calculate and graph data to incorporate into other documents or projects| | |

| |(e.g., word processing, multimedia, and web pages), citing sources. | | |

Standard 4 – Technology/Computer Literacy Verification Checklist

|Student |Instructor |Date Enrolled |

| | | |

|Standard 4. The student will demonstrate knowledge and skills in keyboarding, word processing, and desktop publishing. |

|Benchmark |Date |Initials |

|T.4.1.1 |Identify basic word processing terms. | | |

|T.4.1.2 |Identify, locate, and use letters, numbers, and special keys (e.g., arrow keys, space bar, shift, insert, enter/return, | | |

| |backspace, delete) on the keyboard. | | |

|T.4.1.3 |Identify, discuss, and use word processing as a tool to enter letters, numbers, words, and phrases. | | |

|T.4.1.4 |With a simple document, identify, discuss, and use menu/tool bar functions in word processing applications. | | |

|T.4.1.5 |Demonstrate correct finger placement for home row keys. | | |

|T.4.2.1 |Recognize and explain the advantages and disadvantages of using word processing to create documents. | | |

|T.4.2.2 |Identify, discuss, and use word processing as a tool to open, edit, print, and save documents. | | |

|T.4.2.3 |Identify and use basic word processing terms and concepts (e.g., desktop, menu, tool bar, document, text, line spacing, | | |

| |margins, spell check). | | |

|T.4.2.4 |Use the formatting toolbar to format and change the appearance of word processing documents. | | |

|T.4.2.5 |Use word processing as a tool to write, edit, and publish sentences, paragraphs, and stories. | | |

|T.4.3.1 |Use published documents (e.g., letter, memo, newspaper) to identify and discuss document design and layout as a class. | | |

|T.4.3.2 |Recognize and use menu and tool bar features to edit and make corrections to documents. | | |

|T.4.3.3 |Demonstrate knowledge of WP/DTP tools to develop documents, which include data imported from a spreadsheet or database. | | |

|T.4.3.4 |Identify, discuss, and use WP/DTP menu and tool bar terms and concepts to describe documents. | | |

|T.4.3.5 |Select and use WP/DTP menu and tool bar features to revise and change existing documents. | | |

|T.4.4.1 |Recognize, discuss, select, and use WP/DTP terms, concepts, features, and functions to develop edit/revise, and publish | | |

| |documents for a specific audience and purpose. | | |

|T.4.4.2 |Demonstrate knowledge of the advantages and disadvantages of using word processing to develop, publish, and present | | |

| |information to a variety of audiences. | | |

|T.4.4.3 |Demonstrate appropriate use of copyrighted materials in word processing documents. | | |

|T.4.4.4 |Use instructor prepared rubrics to evaluate the quality of published documents/projects for content, design, and | | |

| |appropriate use of resources. | | |

|T.4.4.5 |Use proper keyboarding techniques to improve accuracy, speed, and general efficiency in computer operation. | | |

Standard 5 – Technology/Computer Literacy Verification Checklist

|Student |Instructor |Date Enrolled |

| | | |

|Standard 5. The student will demonstrate an understanding of multimedia and ability to create multimedia presentations. |

|Benchmark |Date |Initials |

|T.5.1.1 |Identify and discuss components of multimedia. | | |

|T.5.1.2 |Use multimedia software to illustrate words, phrases, concepts, numbers, and symbols. | | |

|T.5.1.3 |Recognize and explain the advantages and disadvantages of using multimedia to develop products. | | |

|T.5.2.1 |Identify, discuss, and use common multimedia terms and concepts. | | |

|T.5.2.2 |Identify and discuss issues (e.g., personal information, images, content, language, and appropriateness and | | |

| |accuracy of information) and guidelines to consider in selection and use of materials for multimedia projects.| | |

|T.5.2.3 |Identify, discuss, and use multimedia tools (e.g., insert, import, create, edit, publish) to combine text and | | |

| |graphics. | | |

|T.5.2.4 |Demonstrate knowledge of multimedia tools and concepts used by media (e.g., games, video, radio/TV broadcasts,| | |

| |websites) to entertain, sell, and influence ideas and opinions. | | |

|T.5.3.1 |Identify, discuss, and cite various types of resources. | | |

|T.5.3.2 |Modify an existing multimedia story to include student narration. | | |

|T.5.3.3 |Use storyboard, menus, and branching to modify or create non-linear products, citing sources. | | |

|T.5.4.1 |Demonstrate knowledge of the advantages and disadvantages of using multimedia to develop, publish, and present| | |

| |information to a variety of audiences. | | |

|T.5.4.2 |Use menu and tool bar features to edit, modify, and revise multimedia projects to present information for a | | |

| |different audience or purpose than the original document intended. | | |

|T.5.4.3 |Plan, design, and develop a multimedia product using data (e.g., graphs, charts, database reports) to present | | |

| |information in the most effective way, citing sources. | | |

|T.5.4.4 |Create or modify and use rubrics to evaluate multimedia presentations for elements (e.g., organization, | | |

| |content, design, accuracy, purpose, appropriateness for target audience, presentation, effectiveness, ethical | | |

| |use of resources, citation). | | |

Standard 6 – Technology/Computer Literacy Verification Checklist

|Student |Instructor |Date Enrolled |

| | | |

|Standard 6. The student will demonstrate ability to utilize Internet and other telecommunications resources. |

|Benchmark |Date |Initials |

|T.6.1.1 |Identify and discuss the Internet as a source of information at school and home. | | |

|T.6.1.2 |Discuss the origin of the Internet. | | |

|T.6.1.3 |Explore Internet resources and information and discuss the variety and types of information found. | | |

|T.6.1.4 |Identify, discuss, and chart elements that make an online resource useful, appropriate, and safe. | | |

|T.6.2.1 |Identify, discuss, and use common terms/concepts used with the Internet, e.g., online, browser, World Wide Web, | | |

| |digital information, URL, keyword, search engine, navigation, resources, web address, web page, hyperlinks/links, | | |

| |bookmarks/favorites, webmaster, etc. | | |

|T.6.2.2 |Identify online resources as the work of individuals/groups/companies and discuss why citing resources is necessary. | | |

|T.6.2.3 |Identify and discuss Internet telecommunications as a tool for communication and collaboration (e.g., email, | | |

| |messaging, and videoconferencing). | | |

|T.6.2.4 |Use Internet resources to locate information then discuss and compare findings for usefulness. | | |

|T.6.2.5 |Cite sources of information (print and non-print) for a project. | | |

|T.6.3.1 |Plan, discuss, and use search strategies with two or more criteria to find information online. | | |

|T.6.3.2 |Identify, discuss, and use online collaborative tools (e.g., email, surveys, videoconferencing, wikis, documents) to | | |

| |collect and present data. | | |

|T.6.3.3 |Locate, select, organize, and present information from the Internet for a specific purpose and audience, citing | | |

| |sources. | | |

|T.6.3.4 |Recognize, discuss, and use email, videoconferencing, and/or web conferencing as a means of interactive | | |

| |communications. | | |

|T.6.4.1 |Recognize, discuss, and use terms and concepts associated with safe, effective, and efficient use of | | |

| |telecommunications, Internet, and networks (e.g., password, firewalls, spam, security, Fair Use, AUP/IUP's, IP | | |

| |address, Intranet, private networks, discussion forum, threaded discussion, LANS, WANs, netiquette, child predators, | | |

| |scammers, hackers). | | |

|T.6.4.2 |Select and justify use of appropriate collaborative tools (e.g., surveys, email, discussion forums, web pages, wikis, | | |

| |online videoconferencing, documents, etc.) to survey, collect, share, present, and communicate information for the | | |

| |intended audience and purpose. | | |

|T.6.4.3 |Plan, select, evaluate, interpret, and use information from a variety of digital resources to develop assignment, | | |

| |project, or presentation. | | |

|T.6.4.4 |Use evaluation tools as a guide to select and evaluate Internet resources and information for content and usefulness | | |

| |for intended audience and purpose. | | |

Standard 1 - Technology/Computer Literacy Self-Assessment

|Student |Instructor |Date Enrolled |

| | | |

|Please rate yourself on each of the following. Check only one box in each row. |

|Standard 1. The student will demonstrate knowledge of important issues of a technology-based society and exhibit ethical behaviors related to the use of |

|computers, digital resources, and other technologies. |

|Benchmark |Don’t |Know a |Know well|Can teach|

| |know |little | | |

|T.1.1.1 |Identify the computer as a machine that helps people communicate, work, and play. | | | | |

|T.1.1.2 |Recognize, discuss, and model correct use of common computer terms. | | | | |

|T.1.1.3 |Identify and discuss common features and functions of computer software and devices. | | | | |

|T.1.1.4 |Identify and discuss correct and responsible use and care of technology resources. | | | | |

|T.1.1.5 |Identify and discuss the uses of and changes in technology devices and the impact technological changes | | | | |

| |have had on business, transportation, communications, industry, and agriculture in the student’s local | | | | |

| |community and in society in general. | | | | |

|T.1.1.6 |Investigate computer/technology-related careers and occupations from the past, present, and future. | | | | |

|T.1.1.7 |Identify and discuss technology skills needed for the workplace now and in the future and how they impact| | | | |

| |the student as an adult learner today. | | | | |

|T.1.2.1 |Recognize and discuss the rights of ownership of computer-created and online work. | | | | |

|T.1.2.2 |Recognize, discuss, and model appropriate, responsible, ethical, and safe use of computers, mobile | | | | |

| |phones, wireless networks, LANs, and digital information (e.g., security, privacy, passwords, personal | | | | |

| |information), and recognize possible consequences of unethical behavior. | | | | |

|T.1.2.3 |Recognize and discuss how Copyright Laws and Fair Use Guidelines protect ownership of individual’s, | | | | |

| |group’s, and companies’ intellectual property and creative works and the importance of citing sources. | | | | |

|T.1.2.4 |Recognize and discuss consequences of misuse of copyrighted property and establish ethical guidelines for| | | | |

| |use of personal and copyrighted media (e.g., images, music, video, content, language), especially as | | | | |

| |related to use during class and for class projects and assignments. | | | | |

|T.1.3.1 |Recognize, discuss, and use terms and concepts related to networks (e.g., stand alone, network, file | | | | |

| |server, LANs, WANs, network resources) and protection of computers, networks, and information (virus | | | | |

| |protection, network security, passwords, firewalls, privacy laws). | | | | |

|T.1.3.2 |Investigate, recognize and discuss why computers, networks, and information must be protected from | | | | |

| |viruses, vandalism, and intrusion, both malicious and mischievous; discuss appropriate technology tools | | | | |

| |(virus software) used to protect them. | | | | |

|T.1.3.3 |Identify and discuss the benefits of non-networked and networked computers. | | | | |

|T.1.4.1 |Recognize, discuss, and use multi-tasking concepts (e.g., windows, toggle or copy and paste data between | | | | |

| |two windows on the desktop). | | | | |

|T.1.4.2 |Recognize and discuss strategies for identifying, solving, and preventing minor hardware and software | | | | |

| |problems. | | | | |

Standard 2 - Technology/Computer Literacy Self-Assessment

|Student |Instructor |Date Enrolled |

| | | |

|Please rate yourself on each of the following. Check only one box in each row. |

|Standard 2. The student will demonstrate an understanding of databases and ability to create databases. |

|Benchmark |Don’t |Know a |Know well|Can teach|

| |know |little | | |

|T.2.1.1 |Identify and discuss print (e.g., phone book) and electronic databases (e.g., automated circulation | | | | |

| |system, CD-ROM encyclopedias) as a way to collect, organize, and display data. | | | | |

|T.2.1.2 |Identify and discuss how and why databases are used in an information-intensive society (e.g., in | | | | |

| |education, government, business, community (grocery, pharmacy) and home). | | | | |

|T.2.1.3 |Identify and discuss database terms and concepts (e.g., sort, search, filter, keyword, data entry, | | | | |

| |field, record, list) using print and/or electronic databases to demonstrate. | | | | |

| T.2.2.1 |Plan, discuss, and use keyword searches or filters using one criterion in prepared electronic | | | | |

| |databases (e.g., automated circulation, encyclopedia, etc.). | | | | |

|T.2.2.2 |Use prepared databases to sort alphabetically/numerically in ascending/descending order. | | | | |

|T.2.2.3 |Modify prepared databases to enter/edit additional information and cite the source. | | | | |

|T.2.2.4 |Modify databases to organize, analyze, interpret data, and create reports (e.g., documents, multimedia| | | | |

| |project, web pages). | | | | |

|T.2.3.1 |Use simple databases to locate, organize, analyze, evaluate, compare, and present information, citing | | | | |

| |sources of information. | | | | |

|T.2.3.2 |Using a prepared database, apply sort and search/filter functions to organize, analyze, interpret, and| | | | |

| |evaluate findings. | | | | |

|T.2.4.1 |Develop and use search strategies with two or more criteria to solve problems, make decisions, and | | | | |

| |report findings. | | | | |

|T.2.4.2 |Plan and develop a simple database to enter, edit, collect, organize, and display data. | | | | |

|T.2.4.3 |Use knowledge of database terms, concepts, functions, and operations to explain strategies used to | | | | |

| |plan and develop a simple database. | | | | |

|T.2.4.4 |Plan and develop database reports to organize data, create reports, and present findings, citing | | | | |

| |sources. | | | | |

|T.2.4.5 |Select and use appropriate database features and functions to collect, organize information, and | | | | |

| |create reports for use in other projects or media (e.g., documents, multimedia project, web pages), | | | | |

| |citing sources. | | | | |

Standard 3 - Technology/Computer Literacy Self-Assessment

|Student |Instructor |Date Enrolled |

| | | |

|Please rate yourself on each of the following. Check only one box in each row. |

|Standard 3. The student will demonstrate an understanding of the ability to create, extract information from, and interpret spreadsheets. |

|Benchmark |Don’t |Know a |Know well|Can teach|

| |know |little | | |

|T.3.1.1 |Identify spreadsheets as a tool for organizing information. | | | | |

|T.3.1.2 |Recognize, discuss, and investigate how spreadsheets are used to process information (e.g., organize, | | | | |

| |calculate, graph data, solve problems, make predictions, and present data) in a variety of settings | | | | |

| |(e.g., schools, government, business, industry, communications, transportation, mathematics, science).| | | | |

|T.3.1.3 |Identify and discuss spreadsheet terms and concepts (e.g., collect, organize, classify, graph, | | | | |

| |display, cell, column, row, values, labels, chart, formula, sort, classify, bar graphs, line graphs, | | | | |

| |pie charts). | | | | |

|T.3.2.1 |Modify data in a prepared spreadsheet and observe the changes that occur to make predictions. | | | | |

|T.3.2.2 |Use spreadsheet software to enter, display, and identify types (text and numeric) of data. | | | | |

|T.3.2.3 |Recognize, discuss, and use graphs to display and interpret data in prepared spreadsheets. | | | | |

|T.3.3.1 |Modify or create and use spreadsheets to solve problems by performing calculations using simple | | | | |

| |formulas and functions (e.g., +, -, *, /, sum, average) and display data graphically. | | | | |

|T.3.3.2 |Use spreadsheet concepts and functions (e.g., median, range, mode) to calculate, represent, and | | | | |

| |explain data. | | | | |

|T.3.4.1 |Modify or create a spreadsheet by using the features and functions previously learned to analyze and | | | | |

| |interpret information, solve problems, make decisions, and support, display, and present findings, | | | | |

| |citing sources. | | | | |

|T.3.4.2 |Modify or create and use spreadsheets to calculate and graph data to incorporate into other documents | | | | |

| |or projects (e.g., word processing, multimedia, web pages), citing sources. | | | | |

Standard 4 - Technology/Computer Literacy Self-Assessment

|Student |Instructor |Date Enrolled |

| | | |

|Please rate yourself on each of the following. Check only one box in each row. |

|Standard 4. The student will demonstrate knowledge and skills in keyboarding, word processing, and desktop publishing. |

|Benchmark |Don’t |Know a |Know |Can teach|

| |know |little |well | |

|T.4.1.1 |Identify basic word processing terms. | | | | |

|T.4.1.2 |Identify, locate, and use letters, numbers, and special keys (e.g., arrow keys, space bar, shift, insert| | | | |

| |enter/return, backspace, delete) on the keyboard. | | | | |

|T.4.1.3 |Identify, discuss, and use word processing as a tool to enter letters, numbers, words, and phrases. | | | | |

|T.4.1.4 |With a simple document, identify, discuss, and use menu/tool bar functions in word processing | | | | |

| |applications. | | | | |

|T.4.1.5 |Demonstrate correct finger placement for home row keys. | | | | |

|T.4.2.1 |Recognize and explain the advantages and disadvantages of using word processing to create documents. | | | | |

|T.4.2.2 |Identify, discuss, & use word processing as a tool to open, edit, print, & save. | | | | |

|T.4.2.3 |Identify and use basic word processing terms and concepts (e.g., desktop, menu, tool bar, document, | | | | |

| |text, line spacing, margins, spell check). | | | | |

|T.4.2.4 |Use the formatting toolbar to format and change the appearance of word processing documents. | | | | |

|T.4.2.5 |Use WP as a tool to write, edit, & publish sentences, paragraphs, & stories. | | | | |

|T.4.3.1 |Use published documents (e.g., letter, memo, newspaper) to identify and discuss document design and | | | | |

| |layout as a class. | | | | |

|T.4.3.2 |Recognize & use menu & tool bar features to edit & make corrections to documents. | | | | |

|T.4.3.3 |Demonstrate knowledge of WP/DTP tools to develop documents, which include data imported from a | | | | |

| |spreadsheet or database. | | | | |

|T.4.3.4 |Identify, discuss, and use WP/DTP menu and tool bar terms and concepts (e.g., import, portrait, | | | | |

| |landscape, copy and paste between two documents, clipboard) to describe documents. | | | | |

|T.4.3.5 |Select & use WP/DTP menu & tool bar features to revise & change existing documents. | | | | |

|T.4.4.1 |Recognize, discuss, select, and use WP/DTP terms, concepts, features, and functions to develop, | | | | |

| |edit/revise, & publish documents for a specific audience & purpose. | | | | |

|T.4.4.2 |Demonstrate knowledge of the advantages and disadvantages of using word processing to develop, publish, | | | | |

| |and present information to a variety of audiences. | | | | |

|T.4.4.3 |Demonstrate appropriate use of copyrighted materials in word documents. | | | | |

|T.4.4.4 |Use instructor prepared rubrics to evaluate the quality of published documents/projects for content, | | | | |

| |design, and appropriate use of resources. | | | | |

|T.4.4.5 |Use proper keyboarding techniques to improve accuracy, speed, and general efficiency in computer | | | | |

| |operation. | | | | |

Standard 5 - Technology/Computer Literacy Self-Assessment

|Student |Instructor |Date Enrolled |

| | | |

|Please rate yourself on each of the following. Check only one box in each row. |

|Standard 5. The student will demonstrate an understanding of multimedia and ability to create multimedia presentations. |

|Benchmark |Don’t |Know a |Know well|Can teach|

| |know |little | | |

|T.5.1.1 |Identify and discuss components of multimedia. | | | | |

|T.5.1.2 |Use multimedia software to illustrate words, phrases, concepts, numbers, and symbols. | | | | |

|T.5.1.3 |Recognize and explain the advantages and disadvantages of using multimedia to develop products. | | | | |

|T.5.2.1 |Identify, discuss, and use common multimedia terms and concepts. | | | | |

|T.5.2.2 |Identify and discuss issues (e.g., personal information, images, content, language, and, | | | | |

| |appropriateness and accuracy of information) and guidelines to consider in selection and use of | | | | |

| |materials for multimedia projects. | | | | |

|T.5.2.3 |Identify, discuss, and use multimedia tools (e.g., insert, import, create, edit, publish) to combine | | | | |

| |text and graphics. | | | | |

|T.5.2.4 |Demonstrate knowledge of multimedia tools and concepts used by media (e.g., games, video, radio/TV | | | | |

| |broadcasts, and websites) to entertain, sell, and influence ideas and opinions. | | | | |

|T.5.3.1 |Identify, discuss, and cite various types of resources. | | | | |

|T.5.3.2 |Modify an existing multimedia story to include student narration. | | | | |

|T.5.3.3 |Use storyboard, menus, and branching to modify or create non-linear products, citing sources. | | | | |

|T.5.4.1 |Demonstrate knowledge of the advantages and disadvantages of using multimedia to develop, publish, and| | | | |

| |present information to a variety of audiences. | | | | |

|T.5.4.2 |Use menu and tool bar features to edit, modify, and revise multimedia projects to present information | | | | |

| |for a different audience or purpose than the original document intended. | | | | |

|T.5.4.3 |Plan, design, and develop a multimedia product using data (e.g., graphs, charts, database reports) to | | | | |

| |present information in the most effective way, citing sources. | | | | |

|T.5.4.4 |Create or modify and use rubrics to evaluate multimedia presentations for elements (e.g., | | | | |

| |organization, content, design, accuracy, purpose, appropriateness for target audience, presentation, | | | | |

| |effectiveness, ethical use of resources, citation). | | | | |

Standard 6 - Technology/Computer Literacy Self-Assessment

|Student |Instructor |Date Enrolled |

| | | |

|Please rate yourself on each of the following. Check only one box in each row. |

|Standard 6. The student will demonstrate ability to utilize Internet and other telecommunications resources. |

|Benchmark |Don’t |Know a |Know well|Can teach|

| |know |little | | |

|T.6.1.1 |Identify and discuss the Internet as a source of information at school and home. | | | | |

|T.6.1.2 |Discuss the origin of the Internet. | | | | |

|T.6.1.3 |Explore Internet resources and information and discuss the variety and types of information found. | | | | |

|T.6.1.4 |Identify, discuss, and chart elements that make an online resource useful, appropriate, and safe. | | | | |

|T.6.2.1 |Identify, discuss, and use common terms/concepts used with the Internet, e.g., online, browser, World | | | | |

| |Wide Web, digital information, URL, keyword, search engine, navigation, resources, web address, web | | | | |

| |page, hyperlinks/links, bookmarks/favorites, webmaster, etc. | | | | |

|T.6.2.2 |Identify online resources as the work of individuals/groups/companies and discuss why citing resources| | | | |

| |is necessary. | | | | |

|T.6.2.3 |Identify and discuss Internet telecommunications as a tool for communication and collaboration (e.g., | | | | |

| |email, messaging, and videoconferencing). | | | | |

|T.6.2.4 |Use Internet resources to locate information then discuss & compare findings. | | | | |

|T.6.2.5 |Cite sources of information (print and non-print) for a project. | | | | |

|T.6.3.1 |Plan, discuss, & use search strategies with two or more criteria to find information online. | | | | |

|T.6.3.2 |Identify, discuss, and use online collaborative tools (e.g., email, surveys, videoconferencing, wikis,| | | | |

| |documents) to collect and present data. | | | | |

|T.6.3.3 |Locate, select, organize, and present information from the Internet for a specific purpose and | | | | |

| |audience, citing sources. | | | | |

|T.6.3.4 |Recognize, discuss, and use email, videoconferencing, and/or web conferencing as a means of | | | | |

| |interactive communications. | | | | |

|T.6.4.1 |Recognize, discuss, and use terms and concepts associated with safe, effective, and efficient use of | | | | |

| |telecommunications, Internet, and networks (e.g., password, firewalls, spam, security, Fair Use, | | | | |

| |AUP/IUP's, IP address, Intranet, private networks, discussion forum, threaded discussion, LANS, WANs, | | | | |

| |netiquette, child predators, scammers, hackers). | | | | |

|T.6.4.2 |Select and justify use of appropriate collaborative tools (e.g., surveys, email, discussion forums, | | | | |

| |web pages, wikis, online videoconferencing, documents, etc.) to survey, collect, share, present, and | | | | |

| |communicate information for the intended audience and purpose. | | | | |

|T.6.4.3 |Plan, select, evaluate, interpret, and use information from a variety of digital resources to develop | | | | |

| |assignment, project, or presentation. | | | | |

|T.6.4.4 |Use evaluation tools as a guide to select and evaluate Internet resources and information for content | | | | |

| |and usefulness for intended audience and purpose. | | | | |

Technology/Computer Literacy Sample Activities

Standard 1, Levels 1-4, Grade Levels 0.0 – 8.9

|T.1 Technology & Society: The student will demonstrate knowledge of important issues of a technology-based society and exhibit ethical behaviors |

|related to the use of computers, digital resources, and other technologies. |

|Level |Benchmark |Sample Activities |

|T.1.1.1 |Identify the computer as a machine that helps people |Display pictures (from magazines or newspapers) to get students to think |

| |communicate, work, and play. |about how computers are used in everyday life. |

|T.1.1.2 |Recognize, discuss, and model correct use of common |Have students make a glossary of computer terms; this can be done using a |

| |computer terms. |database such as Microsoft Works (each student can add 1 or more records) or|

| | |with a word processor (each student can contribute to a common document). |

| | |Print the final product for each student to have as a reference of computer |

| | |terms. |

|T.1.1.3 |Identify and discuss common features and functions of |Have students add these terms to the glossary mentioned in standard T.1.1.2.|

| |computer software and devices. |Have students word process a paragraph about themselves. Have them give |

| | |their file a name, save, print, close the file, rename it, make a backup |

| | |copy, open the file again. |

| | |After performing these tasks, have students identify which processes |

| | |involved input and which involved output. |

| | |Note: This paragraph can be a good beginning of the year activity for |

| | |students to get to know each other and the instructor if students share |

| | |their paragraphs. The paragraphs can be displayed on a bulletin board; |

| | |later when digital camera skills are covered, students can add a photo of |

| | |themselves to their paragraphs. |

|T.1.1.4 |Identify and discuss correct and responsible use and care |Make a list of actions a person can take to care for technology resources. |

| |of technology resources. |Beside each action, list consequences that might occur if the resource is |

| | |mistreated. |

|T.1.1.5 |Identify and discuss the uses of and changes in technology|Have students make a chart (either on a word processor, paper, or |

| |devices and the impact technological changes have had on |blackboard) with 2 sections: 1950 to 1980 and Present Day. List technology |

| |business, transportation, communications, industry, and |common in each time period, attempting to compare like technologies (i.e., a|

| |agriculture in the student’s local community and society |map versus a GPS). |

| |in general. |Next, add a third column labeled “Impact on Society” and list how present |

| | |day technology has been influenced by each of the items. |

|T.1.1.6 |Investigate computer/technology-related careers and |The instructor can show 3 segments from videos (i.e., tv shows) of 3 time |

| |occupations from the past, present, and future. |periods (past, present, and future) and have students identify technology |

| | |used and how that technology has evolved. For example: in a video from the |

| | |past, the teacher could show a few minutes from the Andy Griffith Show when |

| | |phones were attached to a wall and an operator dialed the phone number. If |

| | |a futuristic video is not available, have students brainstorm what they |

| | |think could make devices function better. |

| | |Have students list careers that are now obsolete due to technological |

| | |changes, i.e., telephone operators. |

|T.1.1.7 |Identify and discuss technology skills needed for the |Have each student identify a career he/she would like to have and |

| |workplace now and in the future and how they impact the |investigate (either through the Internet or personal interview) what |

| |student as an adult learner today. |technology skills are needed for that career. Allow students to work with a|

| | |partner if there are common career goals in the class. |

|T.1.2.1 |Recognize and discuss the rights of ownership of |Give students a scenario where they are a writer who has poems posted |

| |computer-created and online work. |online; ask them how they would feel if someone copied their poems and |

| | |claimed that he/she wrote them. |

|T.1.2.2 |Recognize, discuss, and model appropriate, responsible, |Have students read articles about how bullying affects a person (e.g., |

| |ethical, and safe use of computers, mobile phones, |depression, suicide, anger). |

| |wireless networks, LANs, and digital information (e.g., |Show students “mock” emails and have students decide if they follow Internet|

| |security, privacy, passwords, personal information), and |etiquette guidelines. |

| |recognize possible consequences of unethical behavior. | |

|T.1.2.3 |Recognize and discuss how Copyright Laws and Fair Use |Have students correctly cite online sources with a project they complete |

| |Guidelines protect ownership of individual’s, group’s, and|(i.e., a PowerPoint or web page); show examples of MLA and APA citations. |

| |companies’ intellectual property and creative works and | |

| |the importance of citing sources. | |

|T.1.2.4 |Recognize and discuss consequences of misuse of |When creating projects, direct students to sites that are public domain |

| |copyrighted property and establish ethical guidelines for |(i.e., ). |

| |use of personal and copyrighted media (e.g., images, | |

| |music, video, content, and language), especially as | |

| |related to use during class and for class projects and | |

| |assignments. | |

|T.1.3.1 |Recognize, discuss, and use terms and concepts related to |Have students draw a diagram of a network, including a file server. Have |

| |networks (e.g., stand alone, network, file server, LANs, |them explain how software is distributed and how a site license works. |

| |WANs, network resources) and protection of computers, | |

| |networks, and information (virus protection, network | |

| |security, passwords, firewalls, privacy laws). | |

|T.1.3.2 |Investigate, recognize, and discuss why computers, |Have students discuss the different kinds of antivirus software available |

| |networks, and information must be protected from viruses, |and what they would choose for their own computer. |

| |vandalism, and intrusion, both malicious and mischievous; | |

| |discuss appropriate technology tools (virus software) used| |

| |to protect them. | |

|T.1.3.3 |Identify and discuss the benefits of non-networked and |Have students brainstorm the benefits of networked computers versus |

| |networked computers. |non-networked computers and vice versa (i.e., your computer at work may be |

| | |connected to email and the Internet whereas your computer at home may not be|

| | |connected to anything). |

|T.1.4.1 |Recognize, discuss, and use multi-tasking concepts (e.g., |Provide students with 2 word processed documents (2 poems) then have them |

| |windows, toggle between two windows on the desktop, and |cut and paste and copy and paste from 1 document to another. |

| |copy and paste data between two windows on the desktop). | |

|T.1.4.2 |Recognize and discuss strategies for identifying, solving,|Present students with scenarios where there is a hypothetical problem and |

| |and preventing minor hardware and software problems. |have students give suggestions of the origin of the problem (e.g., light off|

| | |on printer may mean that it is not plugged in or the power button is off). |

Technology/Computer Literacy Sample Activities

Standard 2, Levels 1-4, Grade Levels 0.0 – 8.9

|T.2 Databases: The student will demonstrate an understanding of databases and ability to create databases. |

|Level |Benchmark |Sample Activities |

|T.2.1.1 |Identify and discuss print (e.g., phone book) and |(1) Ask students to consider what might happen if a library had no catalog |

| |electronic databases (e.g., automated circulation system, |system. (2) Ask students to consider a common database that they use |

| |CD-ROM encyclopedias) as a way to collect, organize, and |(cookbook, phone book) and brainstorm reasons why it might be better in |

| |display data. |print form then why it might be better in electronic form. |

|T.2.1.2 |Identify and discuss how and why databases are used in an |As a whole class activity, have students list places in the community they |

| |information-intensive society (e.g., in education, |commonly go then tell how databases are used or might be used at that place.|

| |government, business, community (grocery, pharmacy, and |Give an example to begin. |

| |home). | |

|T.2.1.3 |Identify and discuss database terms and concepts (e.g., |Using index cards, have students create a database about an interest of |

| |sort, search, filter, keyword, data entry, field, record, |theirs, i.e., a movie collection, the cars they drive, music they collect, |

| |list) using print and/or electronic databases to |books read, etc. Each student will fill out 1 record/index card. This can |

| |demonstrate. |be done collectively as a class, thus building a large database students can|

| | |use as a reference. Solicit ideas on what fields will be needed. Discuss |

| | |definitions of fields, records, and files. Have students choose a field to |

| | |manually sort the database by then choose a criterion and manually filter |

| | |the database. |

| T.2.2.1 |Plan, discuss, and use keyword searches or filters using |Give students a prepared electronic database (e.g., dinosaurs, waterfalls, |

| |one criterion in prepared electronic databases (e.g., |U.S. presidents, etc.) and have them do a search then a filter. |

| |automated circulation, encyclopedia, etc.). | |

|T.2.2.2 |Use prepared databases to sort alphabetically/numerically |After performing the search in standard T.2.2.1, have students sort the data|

| |in ascending/descending order. |to alphabetize or put in numerical order and then do the same for the |

| | |filter. |

|T.2.2.3 |Modify prepared databases to enter/edit additional |Have students add a record to the database used in standard T.2.2.1 OR have |

| |information and cite the source. |students add a field to an existing record. Have students add another field|

| | |to cite the source of their information. |

|T.2.2.4 |Modify databases to organize, analyze, interpret data, and|After adding a record as started in standard T.2.2.1, sort the database. |

| |create reports (e.g., documents, multimedia project, web |Insert the database into a word processed document. |

| |pages). | |

|T.2.3.1 |Use simple databases to locate, organize, analyze, |Have students create an address book of their family and friends. |

| |evaluate, compare, and present information, citing sources| |

| |of information. | |

|T.2.3.2 |Using a prepared database, apply sort and search/filter |Have students use a prepared database to answer questions given by the |

| |functions to organize, analyze, interpret, and evaluate |instructor that use the sort and search functions to organize, analyze, |

| |findings. |interpret and evaluate their findings. |

|T.2.4.1 |Develop and use search strategies with two or more |Have students answer Who Am I? questions by giving them 2 or 3 questions |

| |criteria to solve problems, make decisions, and report |that require them to search and/or filter. For example, if they are |

| |findings. |creating a musician database, you could ask, “I am famous for rock and roll.|

| | |I am deceased. I was born in South Carolina.” |

|T.2.4.2 |Plan and develop a simple database to enter, edit, |Have students create an electronic database from the print database |

| |collect, organize, and display data. |completed in standard T.2.2.4. Sort the database by various fields and draw|

| | |conclusions from the sort. |

|T.2.4.3 |Use knowledge of database terms, concepts, functions, and |Have students create a simple database then share with the class how they |

| |operations to explain strategies used to plan and develop |created it, using terminology learned in class. |

| |a simple database. | |

|T.2.4.4 |Plan and develop database reports to organize data, create|After answering the Who Am I? questions described in T.2.4.1, have students |

| |reports, and present findings, citing sources. |show their search or filter to the class while explaining how they arrived |

| | |at their answer(s). |

|T.2.4.5 |Select and use appropriate database features and functions|Copy and paste the electronic database started in standard T.2.2.4 into a |

| |to collect, organize information, and create reports for |word-processed document. Students can make a “wanted” poster with their Who|

| |use in other projects or media (e.g., documents, |Am I questions listed. Have students insert a photo from the Internet onto |

| |multimedia project, web pages), citing sources. |the poster and cite the source. |

Technology/Computer Literacy Sample Activities

Standard 3, Levels 1-4, Grade Levels 0.0 – 8.9

|T.3 Spreadsheets: The student will demonstrate an understanding of the ability to create, extract information from, and interpret spreadsheets. |

|Level |Benchmark |Sample Activities |

|T.3.1.1 |Identify spreadsheets as a tool for organizing |Have students brainstorm ways that using a spreadsheet is more efficient |

| |information. |than using a calculator or paper and pencil. |

|T.3.1.2 |Recognize, discuss, and investigate how spreadsheets are |Give students examples of places where spreadsheets are used (e.g., bank or |

| |used to process information (e.g., organize, calculate, |hospital) and have them discuss how a spreadsheet might be used at that |

| |graph data, solve problems, make predictions, and present |location. |

| |data) in a variety of settings (e.g., schools, government,| |

| |business, industry, communications, transportation, | |

| |mathematics, science). | |

|T.3.1.3 |Identify and discuss spreadsheet terms and concepts (e.g.,|Have students open a prepared spreadsheet and identify the rows, columns, |

| |collect, organize, classify, graph, display, cell, column,|cells, and formula bar. Perform a sort to alphabetize or numerically |

| |row, values, labels, chart, formula, sort, classify, bar |arrange a column. |

| |graphs, line graphs, pie charts). | |

|T.3.2.1 |Modify data in a prepared spreadsheet and observe the |Using the spreadsheet in T.3.1.3, predict what would happen if a value in a |

| |changes that occur to make predictions. |numerical cell were increased or decreased then enter the value to check |

| | |predictions. Identify which cells changed and why. |

|T.3.2.2 |Use spreadsheet software to enter, display, and identify |Have students identify text and numbers in a prepared spreadsheet then enter|

| |types (text and numeric) of data. |their own text and numbers and discuss any changes. |

|T.3.2.3 |Recognize, discuss, and use graphs to display and |With the spreadsheet used in T.3.1.3, make an appropriate chart. |

| |interpret data in prepared spreadsheets. | |

|T.3.3.1 |Modify or create and use spreadsheets to solve problems by|Using the spreadsheet in T.3.1.3, have students add a row or column and |

| |performing calculations using simple formulas and |change formulas as needed then make a chart from the revised data. |

| |functions (e.g., +, -, *, /, sum, average) and display | |

| |data graphically. | |

|T.3.3.2 |Use spreadsheet concepts and functions (e.g., median, |Show students a spreadsheet (e.g., baseball batting averages) and have them |

| |range, mode) to calculate, represent, and explain data. |calculate the median, range, and mode and explain the differences among the |

| | |three values. |

|T.3.4.1 |Modify or create a spreadsheet by using the features and |Give students (can be done in groups if the class is large) M&Ms candy and |

| |functions previously learned to analyze and interpret |have them count the number of M&Ms they have for each color. Make a |

| |information, solve problems, make decisions, and support, |spreadsheet of their data. From the data, predict the percentages of each |

| |display, and present findings, citing sources. |color. Are some colors more common than others? Use the F11 key on the |

| | |keyboard to make a bar chart, either of all the data or a particular color. |

|T.3.4.2 |Modify or create and use spreadsheets to calculate and |Using the chart made in standard T.3.4.1, copy and paste it into an |

| |graph data to incorporate into other documents or projects|imaginary letter to the president of the M&M company. |

| |(e.g., word processing, multimedia, and web pages), citing| |

| |sources. | |

Technology/Computer Literacy Sample Activities

Standard 4, Levels 1-4, Grade Levels 0.0 – 8.9

|T.4 Desktop Publishing: The student will demonstrate knowledge and skills in keyboarding, word processing, and desktop publishing. |

|Level |Benchmark |Sample Activities |

|T.4.1.1 |Identify basic word processing terms. |Open a blank word document. Show students parts of the word processing |

| | |window, menus, etc. |

|T.4.1.2 |Identify, locate, and use letters, numbers, and special |Have students enter their name, address, and telephone number on separate |

| |keys (e.g., arrow keys, space bar, shift, insert, |lines using a word processor. |

| |enter/return, backspace, delete) on the keyboard. | |

|T.4.1.3 |Identify, discuss, and use word processing as a tool to |Adding to the document started in standard T.4.1.2, have students type a |

| |enter letters, numbers, words, and phrases. |paragraph about themselves, perhaps telling where they are from, what |

| | |hobbies they have, likes, and dislikes, etc. |

|T.4.1.4 |With a simple document, identify, discuss, and use |Have students type a sentence that includes their name and favorite hobby. |

| |menu/tool bar functions in word processing applications. |From the formatting toolbar, have them change the font type, font color, |

| | |font size, choose a word to boldface and italicize, underline a word, add |

| | |clip art, do a spell check, save, print, and make a back-up copy. |

|T.4.1.5 |Demonstrate correct finger placement for home row keys. |Have students type a few lines that contain only home row keys (won’t be |

| | |complete words). Example: asdfjkl; then type it backwards). |

|T.4.2.1 |Recognize and explain the advantages and disadvantages of |Show students several examples of non-print word processed documents, i.e., |

| |using word processing to create documents. |newspaper article, magazine article, book. Have them discuss ways that |

| | |these non-print documents can be created electronically. |

|T.4.2.2 |Identify, discuss, and use word processing as a tool to |Have students open a word-processed document that is easily recognized and |

| |open, edit, print, and save documents. |you have put out of order (e.g., a children’s poem or song such as Row, Row,|

| | |Row Your Boat). Have students cut and paste lines into the correct order |

| | |then have them copy and paste the entire poem or song so that they have 2 |

| | |copies. Save, make a backup copy, and print. |

|T.4.2.3 |Identify and use basic word processing terms and concepts |From the song or poem in standard T.4.2.2, add a title, double space the |

| |(e.g., desktop, menu, tool bar, document, text, line |body of the document, decrease the top, bottom, and side margins, and check |

| |spacing, margins, and spell check). |the document for correct spelling. |

|T.4.2.4 |Use the formatting toolbar to format and change the |From the song or poem in standard T.4.2.2, enlarge the font of the title, |

| |appearance of word processing documents. |boldface, center, and underline the title, change the font of the entire |

| | |document, and choose a line to italicize. |

|T.4.2.5 |Use word processing as a tool to write, edit, and publish |Add On Story Activity: Give students a “story starter” to type as the first |

| |sentences, paragraphs, and stories. |sentence in a story that they write. Give them a few minutes to type on the|

| | |story then have them stand up and go to another computer and add on to that |

| | |story. Students rotate several times before going back to finish their |

| | |story. Print and display stories if desired. |

|T.4.3.1 |Use published documents (e.g., letter, memo, newspaper) to|Show students examples of magazine articles, advertisements, and newspaper |

| |identify and discuss document design and layout as a |articles and have them discuss how the layout and choice of graphics |

| |class. |influences the viewer. |

|T.4.3.2 |Recognize and use menu and tool bar features to edit and |From the Add On Story started in standard T.4.2.5, add a clip art picture, |

| |make corrections to documents. |change the orientation to landscape, insert a header with student’s name, do|

| | |a spell check, and change a word using the thesaurus for ideas. |

|T.4.3.3 |Demonstrate knowledge of WP/DTP tools to develop |From the database made in standard T.2.4.2, copy and paste part or the |

| |documents, which include data imported from a spreadsheet |entire database into a word document. |

| |or database. | |

|T.4.3.4 |Identify, discuss, and use WP/DTP menu and tool bar terms |From the word document made in standard T.4.1.2, have students put the |

| |and concepts (e.g., import, portrait, landscape, copy and |document in landscape orientation and explain the process of copying and |

| |paste between two documents, clipboard) to describe |pasting from the spreadsheet to the word document. |

| |documents. | |

|T.4.3.5 |Select and use WP/DTP menu and tool bar features to revise|Give students a word processed file that is typed in a small, plain font. |

| |and change existing documents. |The document can be a poem they will recognize or lyrics to a popular song |

| | |to edit. If possible, use a desktop publishing program such as Microsoft |

| | |Publisher. Have students enhance the layout by changing the font, double |

| | |spacing, adding a title, etc. |

|T.4.4.1 |Recognize, discuss, select, and use WP/DTP terms, |Using a desktop publishing program such as Microsoft Publisher, have |

| |concepts, features, and functions (e.g., minimize |students create a brochure or newsletter based on a project they are doing. |

| |document, resize document, toggle between two open |An example might be a newsletter written from the point of view of a |

| |documents on the desktop, columns, tables, |character in a book. |

| |headers/footers, and using multiple files and/or | |

| |applications) to develop (e.g., design, format, layout), | |

| |edit/revise, and publish documents for a specific audience| |

| |and purpose. | |

|T.4.4.2 |Demonstrate knowledge of the advantages and disadvantages |Have students contrast the process of doing their newsletter or brochure in |

| |of using word processing to develop, publish, and present |standard T.4.4.1 using paper and pen versus desktop publishing and desktop |

| |information to a variety of audiences. |publishing versus word processing. Have them identify the target audience |

| | |for their newsletter or brochure. |

|T.4.4.3 |Demonstrate appropriate use of copyrighted materials in |With the newsletter or brochure made in standard T.4.4.1, have students cite|

| |word processing documents. |sources (information, images, etc.) |

|T.4.4.4 |Use instructor- prepared rubrics to evaluate the quality |Provide students with a rubric to evaluate various websites. |

| |of published documents/projects for content, design, and | |

| |appropriate use of resources. | |

|T.4.4.5 |Use proper keyboarding techniques to improve accuracy, |Have students keep a journal to practice keyboarding skills. You can have |

| |speed, and general efficiency in computer operation. |them turn it in or keep for personal reference. If students don’t know how |

| | |to begin, give them a question to start with such as, “If you could go on |

| | |any trip for free, where would you go?” or “If you could trade places with |

| | |anyone, who would you trade with?” or “What was the best day of your life?” |

| | |Advanced students might even want to start an online personal blog. |

Technology/Computer Literacy Sample Activities

Standard 5, Levels 1-4, Grade Levels 0.0 – 8.9

|T.5 Multimedia: The student will demonstrate an understanding of multimedia and the ability to create multimedia presentations. |

|Level |Benchmark |Sample Activities |

|T.5.1.1 |Identify and discuss components of multimedia. |Show students an advertisement from a printed medium such as a magazine or |

| | |newspaper. Point out the components in the ad such as text, color, photos, |

| | |clip art. Show students a TV or Internet commercial advertising the same |

| | |product and compare/contrast print media with multimedia. |

|T.5.1.2 |Use multimedia software to illustrate words, phrases, |Have students come up with an idea for an invention and then create an |

| |concepts, numbers, and symbols. |advertisement. For example, they might create a boat that can also function |

| | |as transportation on land. Have them identify their target audience and |

| | |point of view. Have students use a program such as Paint to illustrate |

| | |their products then insert their drawings into multimedia software such as |

| | |PowerPoint, Hypermedia, or Photo Story. |

|T.5.1.3 |Recognize and explain the advantages and disadvantages of |With the 2 forms of advertising (print and multimedia) viewed in standard |

| |using multimedia to develop products. |T.5.1.1, have students identify the advantages and disadvantages to both |

| | |forms of advertising. |

|T.5.2.1 |Identify, discuss, and use common multimedia terms and |As students create their advertisement in standard T.5.1.2, check for |

| |concepts. |understanding of multimedia terms. Discuss if their product is more |

| | |effective in a sequential or nonlinear format. |

|T.5.2.2 |Identify and discuss issues (e.g., personal information, |With their advertisement started in standard T.5.1.2, ask students to |

| |images, content, language, and, appropriateness and |justify their choices of images, sounds, persuasive language, etc. What do |

| |accuracy of information) and guidelines to consider in |they hope to accomplish with each component? |

| |selection and use of materials for multimedia projects. | |

|T.5.2.3 |Identify, discuss, and use multimedia tools (e.g., insert,|Using a document created without graphics, have students add text boxes, |

| |import, create, edit, publish) to combine text and |clip art, and photos. |

| |graphics. | |

|T.5.2.4 |Demonstrate knowledge of multimedia tools and concepts |Show a 30 second commercial to students (can be from TV or the Internet). |

| |used by media (e.g., games, video, radio/TV broadcasts, |Have students list visuals used to portray a message. Show the commercial to|

| |and websites) to entertain, sell, and influence ideas and |students again but have them close their eyes. Have students list ways the |

| |opinions. |creators used audio to portray a message. From whose point of view is the |

| | |commercial told? Who is the target audience? |

|T.5.3.1 |Identify, discuss, and cite various types of resources. |Have students make a section (e.g., a slide) in their multimedia |

| | |advertisement citing any music, images, videos, or information they used. |

|T.5.3.2 |Modify an existing multimedia story to include student |Have students narrate their advertisement for the product they created. |

| |narration. |Have them first make a script then target ways they can use their voice and |

| | |sound effects to “sell” their product. |

|T.5.3.3 |Use storyboards, menus, and branching to modify or create |Have students write a storyboard for a digital story that they will create |

| |non-linear products, citing sources. |with multimedia software. The storyboard can be done using index cards, a |

| | |word processor, or pencil and paper. The “story” does not have to be a |

| | |traditional story; it might be a belief, dream, or idea that they want to |

| | |digitally share. |

|T.5.4.1 |Demonstrate knowledge of the advantages and disadvantages |Using software such as Photo Story, iMovie, or Movie Maker, have students |

| |of using multimedia to develop, publish, and present |use the storyboard they created in standard T.5.3.3 to make a digital story.|

| |information to a variety of audiences. |Have students brainstorm non-multimedia methods to create the story; discuss|

| | |advantages and disadvantages of each method. |

|T.5.4.2 |Use menu and tool bar features to edit, modify, and revise|Have students share their digital stories with classmates, ideally using a |

| |multimedia projects to present information for a different|projector. Choose a different audience (e.g., city council or elementary |

| |audience or purpose than the original document intended. |school children) and discuss how you might adapt your project. |

|T.5.4.3 |Plan, design, and develop a multimedia product using data |With their digital story, have students correctly cite their resources |

| |(e.g., graphs, charts, database reports) to present |(information, images, sounds, videos, etc.). Students might also survey |

| |information in the most effective way, citing sources. |classmates about a topic interesting to the group (e.g., favorite genre of |

| | |music), insert data into a spreadsheet, make a chart from the data, and then|

| | |import the chart into a multimedia product. |

|T.5.4.4 |Create or modify and use rubrics to evaluate multimedia |Give rubrics to students to review or grade digital photo stories presented |

| |presentations for elements (e.g., organization, content, |by their classmates (standard T.5.4.2). |

| |design, accuracy, purpose, appropriateness for target | |

| |audience, presentation, effectiveness, ethical use of | |

| |resources, citation). | |

Technology/Computer Literacy Sample Activities

Standard 6, Levels 1-4, Grade Levels 0.0-8.9

|Standard 6. Internet and Telecommunications: The student will demonstrate an ability to utilize Internet and other telecommunications resources. |

|Level |Benchmark |Sample Activities |

|T.6.1.1 |Identify and discuss the Internet as a source of |Have students list ways to get information other than the Internet. Next, |

| |information at school and home. |have them list everyday uses of the Internet (e.g., libraries, email, |

| | |commerce, etc.) |

|T.6.1.2 |Discuss the origin of the Internet. |Have students use the Internet to discover who started the Internet. Have |

| | |them make a timeline of major advances and changes in the Internet (e.g., |

| | |when the World Wide Web began). |

|T.6.1.3 |Explore Internet resources and information and discuss the|Have students examine and discuss 2 or more different types of websites such|

| |variety and types of information found. |as a shopping site and a library or government site. |

|T.6.1.4 |Identify, discuss, and chart elements that make an online |Have students look at examples of web pages where information is reliable |

| |resource useful, appropriate, and safe. |and other web pages where information is unreliable. Make a chart to |

| | |pinpoint characteristics of reliable and unreliable web pages. |

|T.6.2.1 |Identify, discuss, and use common terms/concepts used with|Give students a list of the terms listed in this standard. Play the game, |

| |the Internet, e.g., online, browser, World Wide Web, |What Am I?, where students say 3 sentences in first person to describe their|

| |digital information, URL, keyword, search engine, |term without using the term itself, then ask their classmates, What Am I? |

| |navigation, resources, web address, web page, | |

| |hyperlinks/links, bookmarks/favorites, webmaster, etc. | |

|T.6.2.2 |Identify online resources as the work of |Choose a variety of websites for students to examine and determine who the |

| |individuals/groups/companies and discuss why citing |author is and discuss how they might cite resources from these pages. |

| |resources is necessary. | |

|T.6.2.3 |Identify and discuss Internet telecommunications as a tool|Have students list ways of communicating with others, i.e., telephone, |

| |for communication and collaboration (e.g., email, |postal service, etc. and compare/contrast with online methods of |

| |messaging, and videoconferencing). |communication, i.e., email, instant messaging, etc. |

|T.6.2.4 |Use Internet resources to locate information, then discuss|In groups, assign students a search engine (ex. Yahoo, AltaVista) and have |

| |and compare findings for usefulness. |them look up a topic the class decides on (e.g., baseball or movies). |

| | |Compare results from various search engines. |

|T.6.2.5 |Cite sources of information (print and non-print) for a |Have students make a bibliography from information gathered in standard |

| |project. |T.6.2.4. |

|T.6.3.1 |Plan, discuss, and use search strategies with two or more |Have students use the advanced search to find more information for standard |

| |criteria to find information online. |T.6.2.4 and then compare/contrast using simple versus advanced searches. |

|T.6.3.2 |Identify, discuss, and use online collaborative tools |Have students, in pairs or small groups, enter a page in a wiki such as |

| |(e.g., email, surveys, videoconferencing, wikis, |Wetpaint to share information about a topic that they choose in standard |

| |documents) to collect and present data. |T.6.4.1. |

|T.6.3.3 |Locate, select, organize, and present information from the|Have students present their wiki page from standard T.6.3.2. Have them cite|

| |Internet for a specific purpose and audience, citing |their information at the bottom of the wiki page. |

| |sources. | |

|T.6.3.4 |Recognize, discuss, and use email, videoconferencing, |If possible, have students Skype another group of students. Choose a topic |

| |and/or web conferencing as a means of interactive |to discuss and have them prepare questions to ask the other group. This |

| |communication. |activity could easily be integrated with other subjects. Compare and |

| | |contrast email and web conferencing. |

|T.6.4.1 |Recognize, discuss, and use terms and concepts associated |Divide topics into areas (e.g., personal safety or Internet etiquette) and |

| |with safe, effective, and efficient use of |have students choose a topic in pairs or groups (groups may already have |

| |telecommunications, Internet, and networks (e.g., |been chosen from standard T.6.3.2). Have students create an infomercial |

| |password, firewalls, Spam, security, Fair Use, AUP/IUP's, |using a product (e.g., newsletter, video, brochure, PowerPoint) to teach |

| |IP address, Intranet, private networks, discussion forum, |their classmates how to use the Internet safely. |

| |threaded discussion, LANS, WANs, netiquette, child | |

| |predators, scammers, hackers. | |

|T.6.4.2 |Select and justify use of appropriate collaborative tools |Using the infomercial from T.6.4.1, have students set up a discussion forum |

| |(e.g., surveys, email, discussion forums, web pages, |to get feedback on their product. |

| |wikis, online videoconferencing, documents, etc.) to | |

| |survey, collect, share, present, and communicate | |

| |information for the intended audience and purpose. | |

|T.6.4.3 |Plan, select, evaluate, interpret, and use information |When students create their infomercial in standard T.6.4.1, require them to |

| |from a variety of digital resources to develop assignment,|have a variety of types of resources (primary sources, secondary sources, |

| |project, or presentation. |commercial sites, non-profit sites, government sites, encyclopedias, forums,|

| | |discussion boards, etc.) |

|T.6.4.4 |Use evaluation tools as a guide to select and evaluate |With the infomercials created in standard T.6.4.1 or with the wiki pages |

| |Internet resources and information for content and |created in standard T.6.3.2, have students use a prepared rubric to evaluate|

| |usefulness for intended audience and purpose. |each other’s work. |

Technology/Computer Glossary

|Active cell |The thick-bordered cell where you can enter numbers or formulas in a spreadsheet. |

|Adobe Acrobat |A free software product from Adobe designed to view .pdf (portable document format) documents |

| |downloaded from the World Wide Web. |

|Adobe Photoshop |Software used to edit digital images and save them in a highly compressed format for the World Wide |

| |Web, PowerPoint presentations, or word processing documents. |

|Alignment |How your text conforms to the left and right margins of a page. The text can be right-aligned, |

| |centered, left-aligned, or fully-aligned/justified. |

|AND |A way to search for information using the words AND, OR, and NOT. Boolean logic was created by English |

| |mathematician George Boole 150 years ago. |

|Animated clip art |A moving clip art graphic. |

|Anti-Virus |An application designed to search for viruses and repair files on a computer. Norton and McAfee make |

| |anti-virus software. |

|Application/ Software |Programs that allow you to accomplish certain tasks such as write letters, analyze numbers, sort files,|

| |manage finances, draw pictures, and play games. |

|Arrow keys |The keys on computer keyboard used to move the cursor up, down, left, or right on the screen. |

|Ascending order |Organizing or sorting information in order from smallest to largest, or A-Z or 1-9. |

|Asynchronous |Literally not at the same time. Online courses, email, discussion lists, online bulletin boards, or |

| |wikis are examples of asynchronous communication. |

|AUP |A set of rules and guidelines that are set up to regulate Internet use and to protect the user. |

|(Acceptable Use Policy) | |

|Axis |A feature of a chart on which you can plot numbers. The horizontal line is called the X-axis and the |

| |vertical line is called the Y-axis. |

|Bar graph |One type of graph developed from spreadsheet data that uses parallel bars to compare data and changes |

| |in data over time. |

|Blog |Blog is short for web log. A web log is a journal that is frequently updated and intended for the |

| |general public. Blogs represent the personality of the individual author or sponsor. |

|Bold |A style of text that makes a letter or word darker and thicker to stand out in a document. |

|Bookmark |When you bookmark a page, you tell your web browser to remember that page’s address (URL, uniform |

| |resource locator) so that you can go back to it easily without having to type in the URL again. |

| |Bookmarks are called “favorites” in MS Internet Explorer. |

|Browser |Software which lets you view material designed for the World Wide Web. A browser usually displays |

| |documents created in Hypertext Markup Language (HTML), the language used for creating web pages. |

|Button bar |A box or strip of buttons on the screen that you click on with your mouse to accomplish a task. It |

| |provides shortcuts for commonly used commands. Most buttons contain small pictures (icons) that display|

| |what they do, such as a small printer that can be clicked on to print a document. Some programs let you|

| |choose to hide or display the button bar and mix and match buttons to customize the bar. Also known as |

| |a toolbar. |

|Buttons |A hot spot used in multimedia applications to navigate from one place to another or to activate |

| |elements (e.g., sound, movies, animation). |

|Calculate |The working of mathematical equations. Formulas that are usually used in spreadsheets allow the |

| |computer to automatically perform calculations. |

|Cell |The space at the intersection of a row and column in a spreadsheet. |

|Chart |A way to present information from a spreadsheet in the form of graphs or tables. |

|Circle graph |A picture showing the relationship of two or more sets of data using a circle. |

|Clip art |Drawings you can add to your documents or presentations. Clip art includes items such as cartoons, |

| |maps, symbols, and flags. Some software packages include clip art. Clip art can be purchased |

| |separately. |

|Column |The vertical divisions in a spreadsheet that are named with an alphabetical letter. |

|Compression |Reduction in the size of data in order to save space and time spent transferring the file. |

|Copy |To make an exact copy of information in your document so you can duplicate it in a new location. |

|CPU |The main chip that allows computers to do millions of calculations per second and makes it possible for|

|(Central Processing Unit) |users to write letters and balance a checkbook. |

|Credits |To give reference to the creator and source of the information used in a presentation. |

|Cursor |This is where the action is located on your screen, represented by a flashing line. When you type on |

| |the keyboard, the information appears at the cursor. |

|Database |Software application that manages large collections of information. A simple database might be a single|

| |file containing many records, with the same set of fields. Data can be sorted and searched by one or |

| |more criteria. |

|Delete |A key used to erase characters or text. |

|Descending order |Organizing or sorting information in order from largest to smallest, Z-A or 9-1. |

|Desktop |The background for the windows, menus, and dialog boxes on a PC. It is supposed to represent a desk. |

|Desktop publishing (DTP) |Using features of word processing/DTP software to format and produce documents, letters, reports, |

| |flyers, and newsletters with graphics. |

|Dialog Box |Also known as pop-up windows, these are small windows that appear when you perform an action, select an|

| |option, or need information. For example, dialog boxes ask questions like “Do you want to save this |

| |document?” or “Are you sure that you want to exit this program?” |

|Digital Subscriber Line (DSL) |Technology that provides digital data transmission over the local telephone network using high |

| |frequency lines. Download speeds range from 256 to 24,000 kilobits per second. |

|Digital Versatile Disc (DVD) |An optical disc storage media format mainly used for video and data storage. DVDs are the same size as |

| |a CD but can store six times more data. |

|Digital Video Recorder (DVR) |A device that records video in a digital format to a disk drive or other memory within a device. |

|Distance Education/Learning |Distance education or learning is planned learning that normally occurs in a different place from |

| |teaching and as a result requires special techniques of course design, special instructional |

| |techniques, special methods or communication by electronic and other technology as well as special |

| |organizational and administrative arrangements. |

|Domain |The part of an Internet address that identifies where a person’s account is located. For example, in |

| |the address jdoe@newcc.edu the domain is everything after the @ symbol. |

|Dots Per Inch |Computers can only fit a certain amount of information on to a monitor screen. This is measured in how |

| |many dots can be shown in one inch of screen space. PC monitors range from 60-120 dots per inch but |

| |usually cannot display more than 72 dpi. Because of this limitation, images over 72 dpi should not be |

| |posted to a web page. Viewers will not be able to see any difference and the larger file size will slow|

| |the download time. |

|Download |Transferring files or information from a remote computer to your computer. |

|Drop Down Menu |A menu showing a list of choices on a web page. When you click on or roll the mouse over a down menu, |

| |other choices appear and you can select your choice. |

|Email |Sending and receiving messages through a computer network. This process requires a computer, modem, or |

| |network connection, and an e-mail address. It is convenient because all messages are sent and received |

| |immediately over short or long distances. |

|Edit |To make changes in a document or presentation. |

|E-learning |A broad term that suggests any type of technology-mediated learning, from independent research to email|

| |conversations that contribute to personal or professional development. |

|Electronic Discussion |A way for topical discussions to continue outside of the classroom. Students can post messages to one |

| |another and the instructor electronically. |

|Email Attachments |Documents can be added to email messages. These attachments are not part of the message and must be |

| |read or viewed separately. Attachments do not have to be text documents; any computer file (images, |

| |programs, spreadsheets, etc.) can be attached to email. Most email programs allow you to attach |

| |information in this way. |

|Email Newsgroups |A method to facilitate discussion outside of class. Students subscribe to a group and send messages to |

| |other students in the group. The list is like an electronic bulletin board so students need to check it|

| |periodically to read the new messages. |

|Enter/Return |The key used to begin a new line in a word processor or to enter information into a spreadsheet. It is |

| |the same as clicking OK in a dialog box. |

|Entry bar |The field where information is entered in a spreadsheet. |

|Excel |A program in the Microsoft Office Suite that creates spreadsheets. |

|Export |To convert a file into a format other than the original format, e.g., export database files into Excel |

| |spreadsheets. |

|Facebook |A free-access social networking website that is operated and owned by Facebook, Inc. Users can join |

| |networks, add friends, send messages, update their profile, post pictures, and videos and is an |

| |interactive way to connect with other people. |

|Fetch |This is Macintosh’s method of moving files from one computer to another, similar to file transfer |

| |protocol (FTP). It is used to copy files from a personal computer to a server so they can be accessed |

| |by others. |

|Field |A place in a database record where a category of information can be entered or located. |

|File |1. Any document on a computer, e.g., movie, sound, or word files |

| |2. A set of related records in a database |

|File Extension |These are the three letters which come after the dot in the name of a file and tell the computer what |

| |kind of file it is. Examples are .jpg (image file), .doc (Microsoft Word document), .txt (text file). |

|File Size |The size of the file is the amount of disk storage space taken up by a file (measured in bytes). |

|File Transfer Protocol (FTP) |A method of transferring files from one computer to another or downloading files from Internet sites. |

|Firewall |Technology that prevents users from visiting inappropriate websites and protects the network from |

| |unauthorized users. |

|Firewire |A collection of wires that support data transfer from one part of a computer to another at a very high |

| |speed. Firewire is intended for devices that contain large amounts of data such as camcorders, disk |

| |drives, and DVD players. |

|Font |The shape and style of text. |

|Format |To set the margins, tabs, font, or line spacing in the layout of a document. |

|Freeware |Software written and then donated to the public, so anyone is free to copy and share it with their |

| |friends. This is not the same as shareware or commercial software, which is supposed to be purchased. |

|Gif |(Pronounced "jiff.") A file format for pictures, photographs, and drawings that are compressed so that |

|(Graphic Interchange Format) |they can be sent across telephone lines quickly. This format is widely used on electronic bulletin |

| |boards and the Internet. It is limited to 256 colors so it cannot be used for high-end desktop |

| |publishing. |

|Gigabyte (GB) |A unit of measure of hard disks and flash drives, the more gigabytes the more storage space. |

|Google Search |The most popular search engine on the Internet and owned by Google, Inc. |

|Graph |A picture that shows the relationship of one or more sets of numbers to each other. Some graph types |

| |are line, bar, area, and pie graphs. |

|Graphic |Images/pictures created, edited, and/or published using a computer. |

|Hacker |An unauthorized person who secretly gains access to computer files. |

|Hardware |A physical part of the computer system such as the keyboard, monitor, mouse, joystick, printer, |

| |speakers, etc. |

|Hard drive |A data storage device consisting of a drive and one or more hard disks, such as a tape drive and its |

| |tape or a CD/DVD disk drive and its CD or DVD disk. |

|Highlight or Select |To choose part of a document by clicking and dragging over it with the mouse to highlight the text. |

|Home page |The first page of a web address. The home page serves as a gateway to the rest of the website by |

| |providing links to other pages. |

|Home row |Keys on the keyboard with fingers of the left hand are A-S-D-F and fingers on the right hand are |

| |J-K-L-;. |

|Host |The name given to a computer directly connected to the Internet. Host computers are associated with |

| |computer networks, online services, or bulletin board systems. |

|HTML |Hypertext Markup Language is the code used to write most documents on the World Wide Web. HTML codes |

| |tell your browser how to arrange text and images on the computer screen. |

|HTTP |Hyper Text Transfer Protocol is the standard method used to transfer data from a server to a remote |

| |computer. Web addresses often begin with http:// indicating that the documents are written in html. The|

| |Internet relies on http to perform tasks, without it you would not be able to view web pages or check |

| |email. |

|Hyperlink or Hypertext |Special text or images on a web page that when clicked cause your browser to load another page of html.|

| |Text links are usually underlined in blue and image links often take the form of buttons. |

|Icon |A small graphic symbol that represents a program, file, or folder on a computer. Clicking on an icon |

| |causes the program to run, a folder to open, or the file to be displayed. |

|Illustration |Clip art, graphics, or drawings on a computer. |

|Import |To convert a file into another format usually within a new file, e.g., import html files into pdf |

| |documents. |

|Indent |To set the first line of a paragraph in from the margin in a word processing document. |

|Input/output or I/O |The communication between an information processing system (a computer) and the outside world (a human |

| |or another computer). Inputs are the signals or data received by the system and outputs are the signals|

| |or data sent from it. Keyboards and the mouse are input devices of a computer whereas monitors and |

| |printers are output devices of a computer. Modems and network cards can serve as both input and output |

| |devices. |

|Interactive Whiteboard |A whiteboard connected to a computer where the board can be used as a touch screen, handwriting can be |

| |converted to text, and words and pictures can be dragged around with your finger. Pages can also be |

| |saved, reordered, and printed. |

|Internet |Term given to the network of computers that provide information worldwide. |

|Internet Explorer |A web browser created by Microsoft used to view pages on the web. |

|Java Script |A scripting language developed by Netscape. Java Script can make web pages interactive by telling users|

| |whether they’ve filled out a form correctly, displaying animated images, or allowing images to change |

| |when users touch them with the mouse. |

|Jpeg |JPEGs are the most commonly used digital image. It is a standard for shrinking graphics so they can be |

|(Joint Photographic Experts Group) |sent faster between modems and take up less space on the hard drive. These graphics can be reduced to 5|

| |percent of their original size but the image quality deteriorates. However, compressing graphics to 30 |

| |or 40 percent of their original size results in minimal loss of quality. |

|Keyboard |The hardware device used to enter letters into the computer. |

|Keyword |A word or reference point used to describe content on a web page that search engines use to properly |

| |index the page. |

|Label |The term given to the words entered on a spreadsheet usually naming a column. |

|Landscape |The page setup that permits a document to be printed in a horizontal position. |

|Line graph |A graph used to display trends and compare data. |

|Line spacing |The space between lines of text. |

|Linear |Moving in a straight line or path; a multimedia presentation that moves in a straight line from image |

| |to image. |

|Links |Connections that bridge one image, page, or word to another by clicking on a highlighted word or |

| |phrase. |

|Listserv |A generic term for an electronic mailing list or e-list. |

|Math Symbols to Use When Searching |Symbols used in a search. = ≠ Greater than, Less than, Greater than or equal to, Less than or equal |

| |to, Not equal or equal. |

|Monitor |The device with a screen used to show computer images. |

|Mouse |A tool used to move the cursor and pointer around the screen. |

|Multimedia |To use a combination of text, pictures, sounds, movies, and/ or animation in a presentation. |

|Network |A system of connected computers that allows the sharing of files and equipment. There are two types of |

| |networks: local area network (LAN) and wide area network (WAN). |

|Non-linear |Not moving in a straight line or path; a multimedia presentation that transitions from one image to |

| |another in an order that is preset but not necessarily in a straight path - Example: a non-linear |

| |presentation can transition from image 1 to image 3 and back to image 1 using menus/branching. |

|NOT |A way to search for information using the words AND, OR, and NOT. Boolean logic was created by English |

| |mathematician George Boole 150 years ago. |

|Numeric Keypad |The portion of a keyboard, set up like an adding machine or calculator, used to enter numbers and |

| |equations quickly into the computer. |

|Online resources |Internet information available to a computer user. |

|Online safety |Precautions taken to protect personal information and images from being misused by others. |

|Online training |Web-based course, simulations, and/or learning interactions that are intentionally structured for |

| |training/skill development. |

|OR |A way to search for information using the words AND, OR, and NOT. Boolean logic was created by English |

| |mathematician George Boole 150 years ago. |

|Page Set Up |The term in reference to the way a document is formatted to print. |

|Password |A code for security purposes that allow access to a computer or the computer programs. |

|Paste |To insert the last information that was cut or copied into a document. Cut and paste can be used to |

| |move information within or between documents. |

|Pictogram |Pictures used to create a bar graph chart. |

|Pie graph |Circle graph divided into pieces that look like portions of a pie. |

|Plug-in |Software that allows you to use a variety of media. Some work within the browser and some require you |

| |to play a file outside the browser depending upon how your system is configured and what operating |

| |system you are using. A popular plug-in is Flash Player. |

|Pop-ups |A form of online advertising on the Internet intended to attract web traffic or capture email |

| |addresses. It works when Websites open a new web browser window to display advertisements. Pop-ups are |

| |usually generated by JavaScript. Certain types of downloaded content like images and free music can |

| |cause pop-ups. Your computer may already have pop-up blockers installed and will let you know when |

| |content is being blocked and how to allow it to be downloaded. |

|Portable keyboard |A small keyboard that students can use for any writing activity. Files are saved automatically and may |

| |be downloaded to a computer for formatting and saving or sent directly to a printer. |

|Portrait |The default page setup that prints the document vertically. |

|PowerPoint |A Microsoft Office program that allows the user to create visually appealing presentations. |

|Print |To put what is on the computer screen onto paper. It creates a paper copy of the document created on |

| |the computer. |

|Printer |A hardware device used to make a paper copy of what is created on the computer. |

|Probeware |Computer-assisted data collection tools. |

|Public Domain |Software written then donated to the public. Anyone can use and copy public domain software free of |

| |charge but it is not always the same quality as commercial software. |

|QuickTime |A multimedia framework capable of handling various formats of digital video, media clips, sound, text, |

| |animation, music, and interactive images. It is available for Mac OS, Mac OS X, and Microsoft Windows |

| |operating systems. |

|Record |A collection of related fields and entries. |

|Retrieve |Open a saved document. |

|Row |The horizontal divisions in a spreadsheet named with a number. |

|RSS (Really Simple Syndication) |Web feed formats used to publish frequently updated works such as blog entries, news headlines, audio, |

| |and video in a standardized format. An RSS document, also called a “feed” or “channel”, includes full |

| |or summarized text plus publishing dates and authorship. RSS formats are specified using XML. |

|Save |To store information on a disk, hard drive, flash drive, or CD for later use. Work should be saved |

| |often, every 5 or 10 minutes, to make sure your latest changes are safely recorded. |

|Save As |To save a document with a new name. |

|Search |To look for specific information on the Internet or computer. |

|Search Engines |A tool on the web that searches, gathers, and identifies information from a database based on keywords,|

| |indices, titles, and text. |

|Search strategies |There are 3 basic ways to begin a search: |

| |1. Try to guess the URL. |

| |2. Use Subject directories provided by some search engines. The selected resources are grouped by |

| |subject, categories, and subcategories that can be used for keyword search or to browse the categories.|

| |3. Use a search engine for large searches using unique keywords or combinations of keywords to narrow |

| |the search. |

|Security |Protection of computer, computer files, or a computer network from use without permission of the owner |

| |or owners. |

|Server |A special computer used to store programs and files, and then sends the information out to other |

| |computers one or all at a time. |

|Shareware |Software that can be tried before being purchase. |

|Short Message Service |A communication service standardized in the mobile communication system allowing the exchange of short |

| |text messages between mobile phone devices. SMS text messaging is the most widely used data |

| |application. |

|Software/Application |Programs that allow you to accomplish certain tasks such as write letters, analyze numbers, sort files,|

| |manage finances, draw pictures, and play games. |

|Sort |Arranging information in a specific order (usually ascending and descending). |

|Spreadsheets |Applications that can be used to calculate, analyze, and present data. Excel, in the Microsoft Office |

| |Suite, includes tools for organizing, managing, sorting, and retrieving data and testing "what if” |

| |statements. It also has a chart feature that displays numerical data as a graph. |

|Stand Alone Computer |A computer that does not rely upon any other computer or server to work. |

|Storyboard |A graphic organizer used for planning and developing a multimedia report/presentation. The contents, |

| |layout, and formatting of each card/slide and the linking together of the cards/slides. |

|Streaming |A method for transferring data continuously. Streaming allows you to display the data on your browser |

| |before the entire file is transmitted. For streaming to work, data must be received and sent to an |

| |application called a plug-in that processes the data and converts it to audio or video. |

|Synchronous |Learners are required to participate in a particular learning activity at the exact same time. For |

| |example, chat rooms, videoconferencing, and audio conferencing are designed to be synchronous. |

|Table |Columns and rows of cells that can be filled with text that are used to organize information. |

|Telecommunication |The act of sending and receiving information such as data, text, pictures, voice, and video. The |

| |exchange of information can be within a building or around the globe. |

|Text |Words on a page, screen, or within a document. |

|Text Messaging or Texting |A common term for the sending of short text messages from mobile phones or personal data assistants |

| |using English language slang, e.g., instead of saying “great!”, the user would text “gr8t” or “brb” for|

| |“be right back”. Texting uses SMS. |

|Thesaurus |A feature in most word processors used to replace a word in a document with one that is more suitable |

| |and adds variety to your writing. |

|Thumbnail |A tiny copy of a larger image used to give a general idea of what the image looks like before it is |

| |downloaded. |

|Twitter |Another free social networking website and micro-blogging service that enables users to send and read |

| |other users’ updates known as tweets. Tweets are text-based posts of up to 140 bytes in length. Users |

| |may have to pay SMS fees through their phone service. |

|Upload |The process of transferring a file from a personal computer to a server. It makes the file available to|

| |others. |

|URL Address |An address for documents on the World Wide Web. For example, is a URL. |

|(Uniform Resource Locator) | |

|USB Flash Drive |A memory data storage device integrated with a universal serial bus (USB) interface. Most flash drives |

| |are removable, rewritable, and weigh less than an ounce. Flash drives are replacing floppy disks as the|

| |storage device of choice. |

|User name |First part of an email address. Example: barberdb is the user name of the following email address: |

| |barberdb@newcc.edu |

|Value |The term for a number in a spreadsheet that can be added, subtracted, multiplied, or divided. |

|Vandalism |The intentional act of destroying computer files or computer networks. |

|Virtual |Occurring or existing primarily online. Examples include virtual community, virtual world, and virtual |

| |reality. |

|Virus |A computer program designed to damage computer files. |

|Wallpaper |Refers to an image used as a background on a computer screen, may also be called desktop picture or |

| |desktop background. |

|Web address |Universal Resource Locator (URL). Example: |

|Webcast |Allows many people in different locations to see, hear, and participate in a meeting or event as it is |

| |happening. A webcast should be used when there will be more than eight receiving sites or a large |

| |audience. |

|Wiki |A page or collection of web pages designed to allow anyone to contribute or modify the content. |

|Windows |A software operating system produced by Microsoft and is the most widely used operating system used on |

| |computers. |

|Word processing |Using keyboarding skills to produce documents such as letters, reports, manuals, and newsletters. |

|Word wrap |This occurs when you get to the end of a line and continue typing allowing the text to go to the next |

| |line. |

|Worm |A computer file designed to do damage that goes through a computer and possibly a network. |

|WWW |The section of the Internet that allows access to text, graphics, sound, and even video. A lot of free |

|(World Wide Web) |information can be found on the WWW. |

|WYSIWYG |WYSIWYG is an acronym for "What You See Is What You Get" and is pronounced "wizzy wig." WYSIWYG simply |

| |means that the text and graphics shown on your screen exactly match what is printed. |

Technology/Computer Literacy Internet Resources

Balliro, L., & Kamiya, A. (2007). Spotlight: Akira kamiya keeps the big picture in mind. Fieldnotes 17(1), 11. Retrieved August 25, 2008, from

This article discusses one man’s perspective on when and how to use technology in the classroom. He suggests starting with a teaching goal or something the student wants to learn then discuss what types of technology can be used to reach that goal. He also shares some safety tips to avoid being scammed on the Internet.

Carter, J., & Quann, S. (2003). Under construction, building web sites as a project-based learning activity for abe/esol classes: Tips for teachers. Retrieved July 30, 2008, from



This document describes how to build Web sites in ABE/ESOL classrooms by both teacher and student involvement. There is a chapter on getting started, planning the site, sample sites, building the site, reflection and assessment of the process and site, and final tips.

Carter, J., & Titzel, J. (2003, July). Technology in today’s abe classroom: A look at the technology practices and preferences of adult basic education teachers. Retrieved July 30, 2008, from

This document discusses the findings of a regional survey given to ABE programs across the northeastern U.S. The purpose was to find out how technology was being used in the classroom, what teachers want to use technology for , and what kinds of support or professional development are out there to help teachers achieve their goals.

Cohn, E. R., & Hibbitts, B. J. (2004, November). Beyond the electronic portfolio: A lifetime personal web space. Retrieved August 28, 2008, from

This article discusses the differences between electronic portfolios and lifetime personal Web spaces. It also offers legitimate reasons to choose a LPWS instead of the ePortfolio.

Cromley, J.G. (2000, December). Learning with computers: The theory behind the practice. Focus on Basics, 4(C). Retrieved July 19, 2008, from



This is an article discussing the theory behind the use of learning with computers especially geared toward Adult Basic Education (ABE) teachers. It discusses the limitations, effective uses, increased interest, interactivity, collaboration, accommodations, memorization, thinking tools, and implications of technology in the classroom.

International Society for Technology in Education (ISTE). (2007). Retrieved August 25, 2008, from

International Society for Technology in Education is a nonprofit organization advancing the effective use of technology in schools and teacher education. It serves as the home of the National Educational Technology Standards (NETS). These standards measure proficiency and goals for the knowledge, skills and attitudes needed to succeed in the Digital Age.

Kotrlik, J. W., & Redmann, D. H. (2005). Extent of technology integration in instruction by adult basic education teachers. Adult Education Quarterly, 55(3), 200-219. Retrieved September 3, 2008, from

This document discusses the integration of technology into the ABE classroom, the barriers and anxiety many ABE instructors encounter, and how to incorporate technology into their lesson plans despite their limited resources.

Manohar, U. (2008, May). Why is internet safety important? Retrieved March 26, 2009, from

This article discusses the importance of Internet safety including common dangers and risks.

Manohar, U. (2008, February). Internet safety. Retrieved March 26, 2009, from

Another article discusses the dangerous people waiting to prey upon unsuspecting victims on the Internet. It also discusses ways to achieve Internet safety.

Maran, R. (2003, September). 3D dictionary. MaranGraphics, Inc. Retrieved February 3, 2009, from

NCOnline. (2009). Retrieved February 2, 2009, from

The Website was created by the North Carolina Community College System Office. It is designed to provide Basic Skills educators with quick and easy access to a variety of state and national resources including a virtual library, online professional development, and information exchange.

Northwest Lincs Resource Site. Retrieved February 26, 2009, from

Oak, M. (2008, July). Ethical issues of internet privacy. (2009). Retrieved March 25, 2009, from

This article focuses on Internet privacy and the ethical issues it raises. It discusses whether third parties should be allowed to track visitors and how information is stored.

Oak, M. (2008, October). Rules for internet safety. Retrieved March 25, 2009, from

This article discusses Internet safety and how to implement safety measures for Internet use.

Oregon Technology ABS Advisory Group. (2005). Oregon adult basic skills technology plan 2005-2008. Retrieved August 20, 2008, from

This document describes the technology plan for the state of Oregon through 2008. With the support of the governor, the Oregon Technology ABS Advisory Group (OTAAG) and Oregon Council of Adult Basic Skills Development (OCABSD) put together a comprehensive plan to integrate technology and increase educational opportunities in all adult basic skills programs.

Stewart, D. (2003, December). Kaleidoscope. NC Wise OWL, North Carolina Department of Public Instruction. Retrieved February 26, 2009, from

Taylor, J. (2006, September). Techglossary. The Adult Literacy Education Wiki. Retrieved February 20, 2009, from

Using technology in basic skills: A bibliography of resources available from North Carolina Community College Literacy Resource Center. (2002). Retrieved September 3, 2008, from

This is a list of resources from the NCCC Literacy Resource Center. It is divided into resources for teachers and learners as well as some theory and policy resources.

Warlick, D. (2009, March). The art & technique of personal learning networks. Retrieved May 30, 2009, from

This is an on-going blog from David Warlick’s CoLearners Wiki. It discusses how to develop personal learning networks. There are web links, tools, and other blogs.

Appendices

| |Page |

|Appendix A – The Development Process |237 |

|Appendix B – Suggested Reading |241 |

|Appendix C – Templates for Mathematics Activities |249 |

|Templates included in PDF version only. | |

| | |

Appendix A: The Development Process

Reading and Writing Content Standards

Phase 1: First Draft (October – November, 2007)

Teams of adult educators met to write the first draft of the reading and writing content standards, and then continued to provide review, feedback, and comments for continuous improvement of the original draft. These teams consulted a variety of resources including the following states’ existing standards: Arizona, Florida, Massachusetts, Nevada, Ohio, Washington, and West Virginia. These content standards were developed in part from those states’ existing standards.

The writing team for Phase 1 included ABS Directors; Instructors and Coordinators for ABE, GED, AHS, ESL, CED, Family Literacy, and Distance Learning; Specialists in Assessment, Curriculum, Retention, and AHS; Trainers; and Certified Resource Specialists. Team members included:

Yvonne Alston – Vance Granville

Ian Brailsford – South Piedmont

Shari Brown – Caldwell CC & TI

Judith Byrd – Coastal Carolina

Peggy Campbell – Mitchell

Tammy Chavis – Robeson

Sherry Clarke – Mitchell

Dawn Cook – Sampson

Doris Creech – Vance Granville

Durwood Fisher – James Sprunt

Jackie Futrell – Durham Technical

Maurie Gabbert-Cole – Central Piedmont

Anita Green – Central Carolina

Curtis Hildt – Coastal Carolina

Katrina Hinson – Lenoir

Kim Hinton – Caldwell CC & TI

Janis Holden-Toruño – Fayetteville Tech

Libby Kisseih – Robeson

Velma Leavens – James Sprunt

Kristi Marlowe – Catawba Valley

Linda Monroe – Catawba Valley

Geraldine Nicholson – Vance Granville

Ellen Overington – Wake Technical

Loria Payne – Central Carolina

Delores Payseur – Gaston

Charles Pickett – James Sprunt

Amanda Powers – Pamlico

Carol Propst – Catawba Valley

Tammy Quick – Central Carolina

Maria Robles – Catawba Valley

Becky Sanders – Sandhills

Lynn Stevens – Central Piedmont

Candace Taylor – Sampson

Mary Tucker – Catawba Valley

Hazel Tysor – Central Carolina

Misty Wiggins – Lenoir

Mandy Williams – Caldwell CC & TI

Lisa Woodall, Gaston

Joyce Wooten – Catawba Valley

Phase 2: Review of First Draft (December, 2007 – February, 2008)

A review team of adult educators met at the NCCCS in Raleigh to refine the first draft. Those present were Ian Brailsford (South Piedmont), Sherry Clarke (Mitchell), Anita Green (Central Carolina), Janis Holden-Toruño (Fayetteville Tech), Ellen Overington (Wake Tech), Becky Sanders (Sandhills), and Misty Wiggins (Lenoir).

The edits and comments from this group were emailed to all writing team members for comments during January 2008. The edits/comments received were integrated into a second draft.

Phase 3: Content Standards Forums (March-April, 2008)

Content standards forums were held at three sites across the state the first week of March for review and feedback. During this process, the content standards document was reviewed by a total of 36 adult educators including part-time and full-time instructors, program coordinators, and directors. Each participant was given review forms and a draft copy of the standards document so that adult educators from their program could also complete reviews and mail them to the Adult Basic Skills Professional Development Project. The edits and suggestions received during this phase were integrated into a third draft.

Phase 4: Planning Training, Piloting, Field Testing, and Reviews (2008-2010)

In early 2008 all Adult Basic Skills program and Community-based Literacy organization directors were invited to send a Certified Resource Specialist to Advance Institute in May to begin the piloting process for the NC ABE Reading and Writing Content Standards. The following attended the Institute and developed additional real-life applications and an implementation plan for their programs.

Laurie Weston – Beaufort Community College (Coastal Region)

Mandy Williams – Caldwell Community College and Tech. Institute (Western Region)

Lauri Stilwell – Caldwell Community College and Tech. Institute (Western Region)

Anita Green – Central Carolina Community College (Southern Region)

Maurie Gabbert-Cole - Central Piedmont Community College (Piedmont Region)

Lynn Stevens – Central Piedmont Community College (Piedmont Region)

Jacqueline Futrell – Durham Technical Community College (Piedmont Region)

Amanda Powers - Pamlico Community College (Coastal Region)

Libby Kisseih – Robeson Community College (Southern Region)

Becky Sanders – Sandhills Community College (Southern Region)

Ellen Overington – Wake Technical Community College (Central Region)

A total of nine (9) Adult Basic Skills programs representing each region, eleven (11) facilitators, approximately 20 instructors, and about 100 students participated in the piloting process.

On November 3, 2008 a revised draft was sent to those piloting the content standards as well as other program throughout the state for review.

In September 2010 minor revisions were made to the content standards to allow alignment with the Student Achievement in Reading evidence-based reading program.

Phase 5: Statewide Implementation Training (Fall 2010, Spring 2011).

NC ABE Content Standards Implementation Training of Trainers was held in September. Revisions were made to the supplemental material. Online and face-to-face training was designed and deliver to the trainers. Implementation training is planned for Spring 2011. The NC ABE Reading and Writing Content Standards are housed on the ABSPD website and the NCOnline website for easy access.

Mathematics Content Standards

Phase 1: First Draft (August – November 2008)

Teams of adult educators met to write the first draft of content standards in mathematics, and then continued to provided review, feedback and comments for continuous improvement of the original draft. These teams consulted a variety of resources including the CASAS and the following states’ existing standards: Louisiana, Massachusetts, Nevada, Texas, Washington, West Virginia, Wisconsin, and Wyoming. These content standards were developed in part from those states’ existing standards.

The writing team for Phase 1 included ABS Directors, Instructors, and Coordinators for ABE, GED, AHS, ESL, CED, Family Literacy, and Distance Learning; Specialists in Assessment, Curriculum, Retention, and AHS; as well as Trainers and Certified Resource Specialists. Team members included:

|Debra Armstrong- Martin |Shannon Newlin- Alamance |

|Catina Blake- Martin |Ellen Overington- Wake Tech |

|Mary Bonner- Martin |Delores Payseur- Gaston |

|Ian Brailsford- South Piedmont |Gardy Perard- Durham Literacy Council |

|Shari Brown- Caldwell CC & TI |Joe Phipps- Martin |

|Geraldine Bryant- James Sprunt |Amanda Powers-Bennett- Pamlico |

|Sujatha Chittilla- Wayne |James Purnell- Wake Tech |

|Synthia Cooper- Durham Tech |Dick Robbins- Cape Fear Literacy Council |

|Joey Crotts- Alamance |Yaneta Sanchez-Brown- Durham Tech |

|Maurie Gabbert-Cole- Central Piedmont |Becky Sanders- Sandhills |

|Judy Gordon- Isothermal |Donna Shea- Sandhills |

|Phil Gowins- Durham Tech |Judith Smith- Beaufort County |

|Rebecca Graham- Sandhills |Lynn Stevens- Central Piedmont |

|Mary Ann Head- Isothermal |Wanda Sweeney- Sandhills |

|Elizabeth Hembree- Haywood |Stephanie Taylor- Vance Granville |

|Curtis Hildt- Coastal Carolina |Lynne Toepke- Coastal Carolina |

|Ruth Hils- Isothermal |Mary Tucker- Catawba Valley |

|Floyd Hinshaw- Alamance |Laurie Weston- Beaufort County |

|Kim Hinton- Caldwell CC & TI |Mandy Williams- Caldwell CC & TI |

|Bill Johnson- Johnston |Shelly Williams- Wayne |

|Kristi Marlow- Catawba Valley |Lisa Woodall- Gaston |

|Michelle Meischeid- Roanoke- Chowan |Shirl Woods- Durham Tech |

|Dale Miller- Lenoir | |

Phase 2: Content Standards Review (February 2009 – March 2009)

ABE educators in North Carolina were asked to review the NC ABE Mathematics Content Standards and respond online to a Review Survey. The respondents represented 33 community college ABS programs and 2 community-based organizations. Reviewers included program directors, program coordinators, part-time instructors, and full-time instructors. The edits and comments received were integrated into the document.

Phase 3: Field Testing/Piloting Project (March – December 2009)

The NC ABE Mathematics Content Standards were piloted in ABE classes and/or labs at Caldwell Community College, Haywood Community College, Central Piedmont Community College, Sandhills Community College, Beaufort Community College and Central Carolina Community College.

Phase 4: Development of Teaching Activities (January –September 2010)

Development of teaching activities to correspond to each benchmark was begun in January 2010. The Adult Basic Skills Professional Development Project at Appalachian State University facilitated the writing of these activities and continues to add additional activities. The following NC adult educators contributed to these activities: Dianne Barber (Appalachian State University), Barbara Carman (Fayetteville Tech CC), Karen Davenport (College of the Albemarle), Janet Derick (Wilkes CC), Jermaine Jones (Durham Tech CC), Elizabeth King (Central Carolina CC), Lynne Kreiser (Fayetteville Tech CC), Steve Schmidt (Appalachian State University), and Pat Warren (Piedmont CC).

Phase 4: State-wide Dissemination/Implementation (Fall 2010 – Spring 2011)

NC ABE Content Standards Implementation Training of Trainers was held in September. Revisions were made to the supplemental material. Online and face-to-face training was designed and deliver to the trainers. Implementation training is planned for Spring 2011. The NC ABE Mathematics Content Standards are housed on the ABSPD website and the NCOnline website for easy access.

Technology/Computer Literacy Content Standards

Phase 1: First Draft (Fall 2008)

Teams of adult educators met to write the first draft of content standards in Technology/Computer, and then continued to provided feedback and comments for continuous improvement of the original draft. These teams consulted a variety of resources including the NC Department of Public Instruction and West Virginia ABE Computer Literacy content standards. These content standards were developed in part from those existing standards.

The writing team for Phase 1 included ABS Directors, Instructors, and Coordinators for ABE, GED, AHS, ESL, CED, Family Literacy, and Distance Learning; Specialists in Assessment, Curriculum, Retention, and AHS; as well as Trainers and Certified Resource Specialists. Team members included:

Debra Armstrong- Martin

Catina Blake- Martin

Mary Bonner- Martin

Ian Brailsford- South Piedmont

Shari Brown- Caldwell CC & TI

Geraldine Bryant- James Sprunt

Sujatha Chittilla- Wayne

Synthia Cooper- Durham Tech

Joey Crotts- Alamance

Maurie Gabbert-Cole- Central Piedmont

Judy Gordon- Isothermal

Phil Gowins- Durham Tech

Rebecca Graham- Sandhills

Mary Ann Head- Isothermal

Elizabeth Hembree- Haywood

Curtis Hildt- Coastal Carolina

Ruth Hils- Isothermal

Floyd Hinshaw- Alamance

Kim Hinton- Caldwell CC & TI

Bill Johnson- Johnston

Kristi Marlow- Catawba Valley

Michelle Meischeid- Roanoke- Chowan

Dale Miller- Lenoir

Shannon Newlin- Alamance

Ellen Overington- Wake Tech

Delores Payseur- Gaston

Gardy Perard- Durham Literacy Council

Joe Phipps- Martin

Amanda Powers-Bennett- Pamlico

James Purnell- Wake Tech

Dick Robbins- Cape Fear Literacy Council

Yaneta Sanchez-Brown- Durham Tech

Becky Sanders- Sandhills

Donna Shea- Sandhills

Judith Smith- Beaufort County

Lynn Stevens- Central Piedmont

Wanda Sweeney- Sandhills

Stephanie Taylor- Vance Granville

Lynne Toepke- Coastal Carolina

Mary Tucker- Catawba Valley

Laurie Weston- Beaufort County

Mandy Williams- Caldwell CC & TI

Shelly Williams- Wayne

Lisa Woodall- Gaston

Shirl Woods- Durham Tech

Phase 2: Content Standards Review (Spring 2009)

ABE educators reviewed the NC ABE Technology/Computer Content Standards and respond online to a Review Survey. The reviewers represented 9 community college ABS programs, and included coordinators, instructors, and program directors with 60% teaching and 40% not teaching. Of the reviewers who teach, 90% currently integrate computer literacy or technology skills into their classes.

Phase 3: State-wide Dissemination/Implementation (Fall 2010, Spring 2011)

NC ABE Content Standards Implementation Training of Trainers was held in September with local program implementation training taking place in Spring 2011

Appendix B: Suggested Reading

Reading and Writing

This section is a list of publications related to teaching reading and/or writing. These resources were selected for those professionals who want additional research-based information to enhance their teaching, learning, and training endeavors. All listed websites were functional as of November 2010.

Aftel, M. (1996). The story of your life. New York, NY: Simon & Schuster.

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Assessment. (1992). Boone, NC: Adult Basic Skills Professional Development Project, Appalachian State University. [VHS Video/DVD].

Atwell, N. (1998). In the middle: New understanding about writing, reading and learning. Portsmouth, NH: Heinemann.

Bassoff, T. (n.d.). How to adjust your teaching styles for english language learners (ELL) in ESL/bilingual classrooms. Retrieved September 7, 2007, from

Beck, I. L., McKeown, M. G., & Kucan, L. (2002). Bringing words to life: Robust vocabulary instruction. New York, NY: Guilford.

Beckman, D., & Nowotny, W. (1995). The adult basic education teacher’s toolkit. Austin, TX: The Adult Education Professional Development and Curriculum Consortium.

Bender, S. (1995). Writing personal essays. Cincinnati, OH: Writer’s Digest Books.

Bleich, D. (1988). The double perspective. Urbana, IL: NCTE (National Council of Teachers of English).

Brown, O. M. (1996). Tips at your fingertips: Teaching strategies for adult literacy tutors. Newark, DE: International Reading Association.

Brown, R. (1993). Schools of thought. San Francisco, CA: Jossey-Bass Publishers.

Brueggeman, M. A. (1986, December). React first, analyze second: Using editorials to teach the writing process. Journal of Reading, 30(3), 234-239. (ERIC Document Reproduction Service No. EJ343683)

Cameron, J. (1998). The right to write. New York, NY: Jeremy P. Tarcher/Putnam.

Cheyney, A. B. (1984). Teaching reading skills through the newspaper (2nd ed.). Newark, DE: International Reading Association.

Coles, R. (1989). The call of stories. Boston, MA: Houghton Mifflin Company.

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New York, NY: Teacher’s College Press.

Conversations with beginning readers. (1995). Boone, NC: Adult Basic Skills Professional Development Project, Appalachian State University. [VHS Video/DVD].

Cooper, J. D. (1997). Literacy: Helping children construct meaning. Boston, MA: Houghton Mifflin Company.

Crystal, D., ed. (1995). The cambridge encyclopedia of the english language.

Cambridge, UK: Cambridge University Press.

Curtis, M. (2006). The role of vocabulary instruction in adult basic education. Review of adult learning and literacy. 6(3), 43-69.

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Curtis, M. E., & Longo, A. M. (1999). When adolescents can’t read: Methods and materials that work. Cambridge, MA: Brookline Books.

Davidson, J. L., Padak, N. D., & Padak, G. M. (1989). Reading, writing, thinking for life (Teachers’ manual, level 1, set 1). Monroe, NY: Trillium.

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Fried, R. L. (1995). The passionate teacher. Boston, MA: Beacon Press.

Fry, E. B. (2004, April). The vocabulary teacher’s book of lists. Hoboken, NJ: John Wiley & Sons, Inc.

Fry, E. B. (2006, April). The reading teacher’s book of lists (5th ed.). Hoboken, NJ: John Wiley & Sons, Inc.

Frye, P. (1999). Litstart: Strategies for adult literacy and esl tutors. Okemos, MI: Michigan Literacy, Inc.

Gardner, H. (1983). Frames of mind. New York, NY: Basic Books.

Gates, Jr., H. L. (1992). Loose canons. New York, NY: Oxford University Press.

Gilligan, C. (1982). In a different voice. Cambridge, MA: Harvard University Press.

Goldberg, B. (1996). Room to write. New York, NY: Jeremy P. Tracher/Putnam.

Goldberg, N. (1986). Writing down the bones. Boston, MA: Shambhala.

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Basic Books.

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Graves, M. F., & Watts-Taffe, S. M. (2002). The place of word consciousness in a research-based vocabulary program. In A. E. Farstrup & S. J. Samuels (Eds), What research has to say about reading instruction (3rd ed., pp. 140-165). Newark, DE: International Reading Association.

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Heath, S. (1983). Ways with words. Cambridge, UK: Cambridge University Press.

Henk, W., & Helteldt, J. (1987, April). How to develop independence in following written directions. Journal of Reading, 30(7), 602-07. (ERIC Document Reproduction Service No. EJ350556)

Hicks, K., & Wadlington, G. (1994, February). Bigger is better: Shared book experience with adults. Journal of Reading, 37(5), 422-23. (ERIC Document Reproduction Service No. EJ480997)

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Informal reading inventory. (1992). Boone, NC: Adult Basic Skills Professional Development Project, Appalachian State University. [VHS Video/DVD].

Jacobowitz, T. (1988, November). Using theory to modify practice: An illustration with SQ3R. Journal of Reading, 32(2), 126-31. (ERIC Document Reproduction Service No. EJ378628)

Jameson, J. (1995, August). Sixteen tips for working with adult beginning readers. Retrieved July 26, 2007, from

Jeremiah, M. (1988, November). Summaries improve comprehension (Open to suggestion). Journal of Reading 32(2), 170-73. (ERIC Document Reproduction Service No. EJ378636)

Jones, J., & Wilson, W. eds. (1987). An incomplete education. New York, NY: Ballantine Books.

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Kossack, S., & Hoffman, E. (1987, November). Use the news: A picture’s worth a thousand words: Comprehension processing via the comics. Journal of Reading, 31(2), 174-76. (ERIC Document Reproduction Service No. EJ359224)

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Lie, A. (1993, May). Open to suggestion. Journal of Reading 36(8), 656-61. (ERIC Document Reproduction Service No. EJ378636)

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Literate at age 44. Journal of Reading, 35(1), 38-42. (ERIC Document Reproduction Service No. EJ431148)

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Word identification. (1994). Boone, NC: Adult Basic Skills Professional Development Project, Appalachian State University. [VHS Video/DVD].

Zinsser, W. (1988). Writing to learn. New York, NY: Harper & Row.

Mathematics

Barber, D. B., Barber, W. D. (2007). Adult basic skills instructor training manual: Teaching math in context: A tool kit for adult basic skills instructors. Boone, NC: Adult Basic Skills Professional Development Project, Appalachian State University.

Barber, D. B., Knight, C. S., & Voss, J. F. (Eds.). (2004). Instructor training manual: Numeracy. Boone, NC: Adult Basic Skills Professional Development Project, Appalachian State University.

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Appendix C – Templates for Mathematics Teaching Activities

See the PDF version of this document for the templates.

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