Subject/Grade Level: Algebra/6th Grade
Grade Level: 5 Title: Number and Operations Dominant concept: Logic Time Frame:
Enduring Understanding: Students will apply algorithms to add, subtract, multiply, and divide fluently.
Essential Questions: 1. What is the relationship between multiplication and division?
2. How are prime and composite numbers classified?
3. Why is estimating important?
| | |Vocabulary Development | |Instructional Activities/ | |
|Concept/Topic |Indicators | |Assessment Strategies |Extension Activities |Resources |
|Standard 5-2: |5-2.1 Analyze the magnitude of a digit on the basis of its |Sample, repeating decimal,|Teacher made assessments |Play Top It |EM 1.1, 2.2, 2.3, 2.10, 5.5, 5.7, 7.2, |
|The student will demonstrate |place value, using whole numbers and decimal numbers |number and word notation, |Observations | |7.3 |
|through the mathematical |through thousandths. |power of 10 |Slate assessments | | |
|processes an understanding of | | |Class discussions | | |
|the place value system; the | | | | | |
|division of whole numbers; the | | | | | |
|addition and subtraction of | | | | | |
|decimals; the relationships | | | | | |
|among whole numbers, fractions,| | | | | |
|and decimals; and accurate, | | | | | |
|efficient, and generalizable | | | | | |
|methods of adding and | | | | | |
|subtracting fractions. | | | | | |
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| |5-2.2 Apply an algorithm to divide whole numbers fluently. |dividend, divisor, |Teacher made assessments |Division Top-It & Division Dash (EM) |EM 4.1, 4.2, 4.4, 4.5, 4.6, 5.7 |
| | |quotient, multiples, |Observations | | |
| | |partial quotient, |Slate assessments | | |
| | |quotient, remainder, |Class discussions | |Study Island |
| | | |Exit slips | | |
| |5-2.3 Understand the relationship among the divisor, |remainder, even number, |Teacher observations |Division Dash (EM Games) |EM 1.4, 1.5, 4.1, 4.3 |
| |dividend, and quotient. |odd number, divisible by |Exit slips |Factor Bingo (EM games) | |
| | |factor rainbow, divisible |Class discussions |Factor Rainbows | |
| | |by, | |Factor Captor (1-110 Grid) (EM) | |
| | |quotient, divisibility | | | |
| | |rule | | | |
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| |5-2.4 Compare whole numbers, decimals, and fractions by |whole (ONE, or unit), |Teacher made assessments |Number Top-It w/Decimals (EM) |EM 5.1, 5.2, 5.5, 5.6, 5.7, 5.8, 5.9, |
| |using the symbols , and =. |denominator, numerator, |Observations |Build-It |6.10, 8.1, 8.2 |
| | |unit fraction, improper |Slate assessments |Smartboard Lesson: Comparing-Ordering Fractions |Study Island |
| | |fraction, mixed number, |Class discussions |Frac-Tac-Toe | |
| | |percent, quick common |Exit slips | | |
| | |denominator, simplest form| | | |
| |5-2.5 Apply an algorithm to add and subtract decimals |place, value, digit, |Teacher made assessments |Frac-Tac-Toe, High Number Toss (Decimal Version) (EM) |EM 2.3, 2.4, 2.5 |
| |through thousandths. |algorithm, partial-sums |Observations |Addition Top It | |
| | |method, place value, |Slate assessments |Subtraction Target Practice | |
| | |expanded notation, column |Class discussions | | |
| | |–addition method, |Exit slips | | |
| | |trade-first method, | | | |
| | |minuend, subtrahend, | | | |
| | |difference, | | | |
| | |partial-difference | | | |
| | |algorithm , number | | | |
| | |sentence, true number | | | |
| | |sentence, false number | | | |
| | |sentence, variable, open | | | |
| | |number sentence, relation | | | |
| | |symbol, operation symbol, | | | |
| | |solution | | | |
| |5-2.6 Classify numbers as prime, composite, or neither. |composite number, prime |Teacher made assessments |Develop a strategy for Factor Captor |EM 1.6, 1.8, 1.9, 12.1 |
| | |number, unsquaring a |Observations |Factor Captor & Factor Bingo (EM Games) |BrainPop |
| | |number, square root, |Slate assessments |Name that Number | |
| | |square-root key, |Class discussions | | |
| | |name-collection box, |Exit Slips | | |
| | |factor string, length of | | | |
| | |factor string, prime | | | |
| | |factorization, factor tree| | | |
| |5-2.7 Generate strategies to find the greatest common |factor, product, factor |Slate assessments |engage/fractions/ |EM 1.3 , 6.9, 6.10, 8.1, 8.4, 12.1 |
| |factor and the least common multiple of two whole numbers. |pair, common denominator, |Teacher made assessments |SmartBoard Lesson – “Factors & Multiples” | |
| | |unlike denominators, |Teacher observations |Multiplication Top It (EM game) |Discovery Education |
| | |greatest common factor, |Exit Slips |Factor Captor | |
| | |least common factor, | | | |
| | |factor tree, prime | | | |
| | |factorization | | | |
| |5-2.8 Generate strategies to add and subtract fractions |equivalent fractions, |Teacher made assessments |Fraction Top-It, Frac-Tac-Toe, Mixed Number Spin |EM 5.2, 5.4, 6.8, 6.9, 6.10, 8.2, 8.3 |
| |with like and unlike denominators. |slide rule, slider, |Observations | | |
| | |holder, common |Slate assessments | | |
| | |denominators, unlike |Class discussions | | |
| | |denominators | | | |
| |5-2.9 Apply divisibility rules for 3, 6, and 9. |factor rainbow, divisible |Teacher observations |Factor Captor & Factor Bingo (EM games) |EM 1.5, 1.9, 4.1, 4.2, 4.4, 8.1 |
| | |by, quotient, divisibility|Class discussions |Factor Rainbows |Study Island |
| | |rule | |Practice using divisibility rules | |
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Title: Algebra Dominant concept: Logic
Enduring Understanding: Students will comprehend that number patterns and relationships can be represented using variables.
Essential Questions: 1. What are the essential steps for solving algebraic equations?
2. How can missing numbers (whole numbers or decimals) be identified in a sentence?
3. Differentiate between associative, commutative, and distributive properties.
|Standard 5-3: |5-3.1 Represent numeric, algebraic, and geometric patterns|square array, square |Teacher made assessments |Exponent Ball (EM) |EM 1.6, 1.7, 4.7, 5.6, 7.1, 7.2, 7.3, |
|The student will demonstrate |in words, symbols, algebraic expressions, and algebraic |number, exponential |Observations |Students create arrays for numbers using one inch tiles. Complete a chart on prime & |7.4, 7.5, 8.10, 10.3 |
|through the mathematical |equations. |notation, exponent key, |Slate assessments |composite #s. | |
|processes an understanding of | |exponent, variable, |Class discussions |Algebra Election | |
|the use of patterns, relations,| |standard notation, base, |Exit Slips |First to 100 | |
|functions, models, structures, | |factor, power of a number,| | | |
|and algebraic symbols to | |expression, ambiguous, | | | |
|represent quantitative | |nested parenthesis, order | | | |
|relationships and will analyze | |of operations, unit | | | |
|change in various contexts. | |fraction, unit percent, | | | |
| | |algebraic expression | | | |
| |5-3.2 Analyze patterns and functions with words, tables, |Standard notation, |Teacher made assessments |Hidden Treasures Game |EM 1.7, 4.7, 7.1, 7.2, 7.3, 9.1, 10.4,|
| |and graphs. |exponential notation, |Observations | |10.6, 10.7 |
| | |base, exponent, factor, |Slate assessments | | |
| | |power of a number, |Class discussions | | |
| | |expanded notation, rate, |Exit slips | | |
| | |formula, variable line | | | |
| | |graph, coordinates, | | | |
| | |mystery graph | | | |
| |5-3.3 Match tables, graphs, expressions, equations, and |bar graph, circle or pie |Teacher made assessments |Bill Bug Game - |EM 5.9, 6.4, 7.4, 9.1, 10.4, 10.5, |
| |verbal descriptions of the same problem situation. |graph, coordinate grid, |Observations | |10.6, 10.7 |
| | |axis, origin, ordered pair|Slate assessments | | |
| | |of numbers, vertical axis,|Class discussions | | |
| | |horizontal axis, |Exit slips | | |
| | |coordinate, predict | | | |
| |5-3.4 Identify applications of commutative, associative, |rectangular array, number |Teacher made assessments |Have students bring in examples of arrays from pictures, magazines, environment |EM 1.2, 7.5 |
| |and distributive properties with whole numbers. |model, Commutative |Slate assessments – draw on slates | | |
| | |Property of Multiplication|(teacher observations) | | |
| | | |Exit Slips | | |
| |5-3.5 Analyze situations that show change over time. |Rate, formula, variable, |Teacher made assessments |Students will integrate science into this math |EM 10.4, 10.5, 10.6, 10.7 |
| | |line graph, geyser, |Observations |lesson (graph motion of an object) | |
| | |predict |Slate assessments | | |
| | | |Class discussions | | |
Title: Geometry Dominant concept: Space
Enduring Understanding: Students will be able to recognize shapes and angles in their environment and identify them.
Essential Questions: 1. What characteristics does a shape have to have to be congruent or similar?
2. Describe the qualities of an obtuse, acute, and right angle.
3. Differentiate between translations, rotation, and reflection.
|Standard 5-4: |5-4.1 Apply the relationships of quadrilaterals to make |equilateral triangle, |Teacher made assessments |Polygon Capture (EM) |EM 3.4, 3.6, 3.7, 3.9, 3.10, 9.4 |
|The student will demonstrate |logical arguments about their properties. |isosceles triangle, |Observations | Island |
|through the mathematical | |scalene triangle, |Slate assessments |ex.htm | |
|processes an understanding of | |congruent, radius, |Class discussions |(google area and perimeter games) | |
|congruency, spatial | |diameter, pentagon, |Exit slips | | |
|relationships, and | |perimeter, area, square | | | |
|relationships among the | |units, base, height, | | | |
|properties of quadrilaterals. | |formula, variable | | | |
| |5-4.2 Compare the angles, side lengths, and perimeters of |regular polygon, |Teacher made assessments |Angle Tangle (EM) |EM 3.3, 3.6, 3.8, 9.2, 9.3 | |
| |congruent shapes. |tessellation, regular |Observations | | | |
| | |tessellation, tessellate, |Slate assessments | | | |
| | |tessellation vertex |Class discussions | | | |
| |5-4.3 Classify shapes as congruent. |equilateral triangle, |Teacher made assessments |Polygon Capture (EM) |EM 3.6, 3.8 Study Island |
| | |isosceles triangle, |Observations | | |
| | |scalene triangle, |Slate assessments | | |
| | |congruent |Class discussions | | |
| | | |Exit slips | | |
| |5-4.4 Translate between two-dimensional representations and|Ordered number pair, |Teacher made assessments |Hidden Treasure |EM 9.8, 9.9, 11.1, 11.2 |
| |three-dimensional objects. |coordinates, opposite of a|Observations |Dinosaur Dog Math Game – | |
| | |number, translation, |Slate assessments |3-D Shape Sort | |
| | |reflection, prism, |Class discussions | | |
| | |pyramid, cylinder, cone, | | | |
| | |sphere, geometric solid, | | | |
| | |surface, edge, vertex, | | | |
| | |polyhedron, apex, base | | | |
| |5-4.5 Predict the results of multiple transformations on a |Ordered number pair, |Teacher made assessments |Hidden Treasure |EM 9.2, 9.3 |
| |geometric shape when combinations of translation, |coordinates, opposite of a|Observations |Dinosaur Dog Math Game – | |
| |reflection, and rotation are used. |number, translation, |Slate assessments | | |
| | |reflection |Class discussions | | |
| |5-4.6 Analyze shapes to determine line symmetry and/or |Symmetry |Teacher made assessments |Polygon Capture (EM) |EM 3.7, 9.2, 9.3 |
| |rotational symmetry. | |Observations | | |
| | | |Slate assessments | | |
| | | |Class discussions | | |
| | | |Exit slips | | |
Title: Measurement Dominant concept: Space
Enduring Understanding: Students will be able to measure accurately using a variety of measuring devices.
Essential Questions: 1. Differentiate between area and volume.
2. How do units within a system relate to each other?
3. What types of problems are solved with measurement?
|Standard 5-5: |5-5.1 Use appropriate tools and units to measure objects to|radius, diameter, vertical|Teacher made assessments |Angle Tangle (EM) |EM 3.5, 4.3, 5.3, 6.2, 8.2 |
|The student will demonstrate |the precision of one-eighth inch. |(opposite) angles, |Observations |Smartboard Lesson | |
|through the mathematical | |adjacent angles, map |Slate assessments |Students measure various objects in the classroom with a ruler. |Smartboard Tools (ruler) |
|processes an understanding of | |legend, map key, map |Class discussions |Build-It | (Fraction |
|the units and systems of | |direction symbol, map |Exit slips | |Frenzy) |
|measurement and the application| |scale, fraction stick, | | | |
|of tools and formulas to | |equivalent fractions, | | | |
|determine measurements. | |Fathom, cubit, fair game | | | |
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| |5-5.2 Use a protractor to measure angles from 0 to 180 |acute angle, obtuse angle,|Teacher made assessments |Angle Tangle (EM) |EM 3.3, 3.4, 3.5, 3.6, 5.10, 6.3 |
| |degrees. |right angle, straight |Observations |Use a protractor to measure angles |Study Island |
| | |angle, reflex angle, |Slate assessments | | |
| | |Geometry Template, arc, |Class discussions | | |
| | |Percent Circle, sector, |Exit slips | | |
| | |Span, normal span, great | | | |
| | |span, stem-and-leaf plot, | | | |
| | |stem leaf, angle of | | | |
| | |separation | | | |
| |5-5.3 Use equivalencies to convert units of measure within |Liter (L), capacity, quart|Teacher made assessments |Students will learn the mnemonic |EM 9.10 |
| |the metric system: converting length in millimeters, |(qt.), cup ©, milliliter |Observations |“King Henry Died Monday Drinking Chocolate Milk” | |
| |centimeters, meters, and kilometers; converting liquid |(mL), cubic centimeter, |Slate assessments |to convert metric units. | |
| |volume in milliliters, centiliters, liters, and kiloliters;|volume of a container |Class discussions |Project: Students will make a “Gallon Man” to | |
| |and converting mass in milligrams, centigrams, grams, and | | |Convert standard units. | |
| |kilograms. | | | | |
| |5-5.4 Apply formulas to determine the perimeters and areas |Area, square units, base, |Teacher made assessments | 9.4, 9.5, 9.6, 9.7 |
| |of triangles, rectangles, and parallelograms. |height, formula, variable,|Observations |ea/index.htm | |
| | |personal references, |Slate assessments |(google area and perimeter games) | |
| | |rectangle method, |Class discussions | | |
| | |perpendicular, altitude, | | | |
| | |longitude, latitude | | | |
| |5-5.5 Apply strategies and formulas to determine the volume|Volume, cubic unit, |Teacher made assessments |3-D Shape Sort (EM) |EM 9.8, 9.9 |
| |of rectangular prisms. |rectangular prism, face, |Observations | | |
| | |base (of a rectangular |Slate assessments | | |
| | |prism), height (of a |Class discussions | | |
| | |rectangular prism), prism,| | | |
| | |face | | | |
| |5-5.6 Apply procedures to determine the amount of elapsed |Common denominator, unlike|Teacher made assessments |Story problems |EM 2.5, 6.9 |
| |time in hours, minutes, and seconds within a 24-hour |denominators |Observations | | |
| |period. | |Slate assessments | | |
| | | |Class discussions | | |
| |5-5.7 Understand the relationship between the Celsius and |Thermometer, Celsius, |Teacher made assessments |Everyday Math worksheet |Science Lab (for schools with a |
| |Fahrenheit temperature scales. |Fahrenheit, degrees |Observations | |science teacher) |
| | | |Slate assessments | |Collect weather data/convert |
| | | |Class discussions | | |
| |5-5.8 Recall equivalencies associated with length, liquid |Liter (L), capacity, quart|Teacher made assessments |Students will learn the mnemonic |EM 9.10 |
| |volume, and mass: |(qt.), cup ©, milliliter |Observations |“King Henry Died Monday Drinking Chocolate Milk” | |
| |10 millimeters = 1 centimeter, 100 centimeters = 1 meter, |(mL), cubic centimeter, |Slate assessments |to convert metric units. | |
| |1000 meters = 1 kilometer; |volume of a container |Class discussions |Project: Students will make a “Gallon Man” to | |
| |10 milliliters = 1 centiliter, 100 centiliters = 1 liter, | | |Convert standard units. | |
| |1000 liters = 1 kiloliter; and | | | | |
| |10 milligrams = 1 centigram, 100 centigrams = 1 gram, 1000 | | | | |
| |grams = 1 kilogram. | | | | |
Title: Data and Probability Dominant concept: Chance
Enduring Understanding: Students will understand probability and how it affects their daily lives.
Essential Questions: 1. What is probability and how do I use it?
2. Is the mean and median always the same?
3. How is the probability of an event determined and described?
|Standard 5-6: |5-6.1 Design a mathematical investigation to address a |Minimum, maximum, mode, |Teacher made assessments |Landmark Shark |EM 2.5, 2.6, 3.2, 6.1, 6.6 |
|The student will demonstrate |question. |median, landmark, line |Observations | | |
|through the mathematical | |plot |Slate assessments | | |
|processes an understanding of | | |Class discussions | | |
|investigation design, the | | |Exit slips | | |
|effect of data-collection | | | | | |
|methods on a data set, the | | | | | |
|interpretation and application | | | | | |
|of the measures of central | | | | | |
|tendency, and the application | | | | | |
|of basic concepts of | | | | | |
|probability. | | | | | |
| |5-6.2 Analyze how data-collection methods affect the nature|Census, sample, |Teacher made assessments |Student collected surveys |EM 2.5, 3.1, 6.1, 6.2, 6.3, 6.5 |
| |of the data set. |population, survey, |Observations | | |
| | |frequency table |Slate assessments | | |
| | | |Class discussions | | |
| |5-6.3 Apply procedures to calculate the measures of central|estimate, median, |Teacher made assessments |Landmark Shark (EM) |EM 2.1, 2.5, 3.9, 5.11, 6.1, 6.4, 6.6 |
| |tendency (mean, median, and mode). |stimulus, reaction time, |Observations |Measures of Control Tendency –Smartboard Lesson |Project: Record temperature for 7 days & |
| | |mean (average), mode, |Slate assessments | |find the mean, median & mode. Record data |
| | |range, minimum, maximum |Class discussions | |on line graph |
| | | |Exit slips | | |
| |5-6.4 Interpret the meaning and application of the measures|Minimum, maximum, mode, |Teacher made assessments |Cardio Activity, M&M’s or Skittles Activity |EM 3.2, 6.1, 6.6 |
| |of central tendency. |median, landmark, line |Observations | | |
| | |plot |Slate assessments | | |
| | | |Class discussions | | |
| | | |Exit slips | | |
| |5-6.5 Represent the probability of a single-stage event in |impossible, certain, |Teacher made assessments |“Probability” smartboard lesson |EM 2.6, 2.7, 6.5, 6.6, 12.2, 12.4, 12.5 |
| |words and fractions. |Probability Meter Poster |Observations | | |
| | |magnitude estimate, |Slate assessments | | |
| | |sample, population, |Class discussions | | |
| | |multiplication counting | | | |
| | |principle, tree diagram, | | | |
| | |equally likely, ratio | | | |
| |5-6.6 Conclude why the sum of the probabilities of the |impossible, certain, |Teacher made assessments |M&M’s or Skittles activity |EM 5.10, 12.2 |
| |outcomes of an experiment must equal 1. |Probability Meter Poster |Observations | | |
| | |magnitude estimate, |Slate assessments | | |
| | |sample, population, |Class discussions | | |
| | |multiplication counting | | | |
| | |principle, tree diagram, | | | |
| | |equally likely, ratio | | | |
Grade 5: Enduring Understanding and Essential Questions
Title: Number Theory Dominant concept: Logic Time Frame: 3 weeks
Enduring Understanding: Multiplication and division are inverse properties and they help students understand the relationship between multiplication and division (Connections)).
Essential Questions: 1. Explain how to find the GCF and the LCM of two whole numbers.
2. How are the divisor, dividend, and quotient related?
3. Describe the difference between prime and composite numbers.
Title: Estimation & Computation Dominant concept: Reasoning Time Frame: 3 weeks
Enduring Understanding: Students will understand that numerical computations and their results must be judged for reasonableness/correctness.
Essential Questions: 1. How do you calculate mean, median, and mode?
2. Explain procedures for adding and subtracting numbers with decimals.
3. When would estimating sums and differences be beneficial?
Title: Geometry Explorations Dominant concept: Space Time Frame: 3 weeks
Enduring Understanding: Students will be able to recognize shapes and angles in their environment and identify them.
Essential Questions: 1. What characteristics does a shape have to have to be congruent or similar?
4. Describe the qualities of an obtuse, acute, and right angle.
Title: Division Dominant concept: Logic Time Frame: 3 weeks
Enduring Understanding: Students will be able to divide whole numbers.
Essential Questions 1. How do you know if a number is divisible by 3, 6, and 9?
2. What are the parts of a division problem?
3. What is the purpose of dividing?
Title: Fractions, Decimals, & Percents Dominant concept: Reasoning Time Frame: 3 weeks
Enduring Understanding: Students will be able to identify and use fractions, decimals, & percents.
Essential Question: 1. What is a fraction? Decimal? Percent?
2. How do fractions, decimals, & percents affect our daily lives?
3. How are fractions, decimals, & percents alike/different?
Title: Using Data: Add & Subtract Fractions Dominant concept: Reasoning Time Frame: 3 weeks
Enduring Understanding: Students will be able to read and construct a graph to represent data collected.
Essential Questions: 1. How do I construct and interpret different types of graphs.
2. How do I decide which graph to use to report different types of data?
3. How do I use landmarks (mean, median, mode) to interpret data?
Title: Exponents & Negative Numbers Dominant concept: Logic Time Frame: 3 weeks
Enduring Understanding: Students will be able to identify place value will be able to work algebraic expressions using
the order of operations.
Essential Questions: 1. How do I write whole numbers in standard and exponential notation?
2. What is an exponent?
3. Why do algebraic expressions have to be worked in a certain order (order of operations0>
Title: Fractions & Ratios Dominant concept: Chance Time Frame: 3 weeks
Enduring Understanding: Students will be able to identify and compare fractions.
Essential Questions: 1. How do I identify and compare fractions?
2. How do I add and subtract fractions?
Title: Coordinates, Area, Volume, & Capacity Dominant concept: Space Time Frame: 3 weeks
Enduring Understanding: Students will be able to plot points on a coordinate grid.
Essential Questions: 1. How do I plot points on a coordinate grid using ordered pairs.
2. How do I find the area of geometric figures?
Title: Using Data: Algebra Concepts & Skills Dominant concept: Logic Time Frame: 3 weeks
Enduring Understanding: Students will be able to read a table or graph.
Essential Questions: 1. How do I create and solve algebraic equations?
4. How do I read a table or graph?
Title: Volume Dominant concept: Space Time Frame: 3 weeks
Enduring Understanding: Students will be able to identify a 2 dimensional and a 3-dimensional figure.
Essential Questions: 1. How do I identify a 3-dimensional geometric figure?
2. What is the difference between a 2-dimensional figure and a 3-dimensional figure.
Title: Probability, Ratios, & Rates Dominant concept: Chance Time Frame: 3 weeks
Enduring Understanding: Students will understand probability and how it affects their daily lives.
Essential Questions: 1. What is probability and how do I use it?
2. What is the greatest common factor?
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