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Berkeley Heights Public Schools

Remedial Summer School Program

Mathematics Curriculum

Grades Kindergarten through 7th

Revised: 2012

Michele Gardner, Director of Special Education

Kindergarten Math

|Week 1 |Topic: Number and Numerical Operations |

| |Count with stable order by ones 1-31. |

| |Count backwards with stable order by one from 10-1 |

| |Count on with stable order by ones from any given number 10 or less |

| |Topic: Counting Quantity |

| |Demonstrate one to one correspondence |

| |Demonstrate conservation of one-digit numbers. (number remains the same even if objects are rearranged) |

| |Use the cardinality rule (when a set is counted, the last counting word said indicates the total value of|

| |the set and not just the name of the last object counted) |

|Week 2 |Topic: Number Relationships |

| |Recognize patterned arrangements of objects without counting (dice and dominos) |

| |Determine numbers that are one or two more or one or two less than a number |

| |Form digits 0-9 |

| |Topic: Number Relationships |

| |Compare sets and numbers to 10 |

| |Use models to join quantities (sums to 10) |

| |Use ordinal numbers to identify position of numbers to 5th position |

| |Order numbers to 31 |

|Week 3 |Topic: Concepts of Time |

| |Explain yesterday, today, tomorrow |

| |List the days of the week in order |

| |Tell time using the hour hand (o’clock) |

| |Topic: Spatial Abilities, Shape Relationships, and Patterns |

| |Demonstrate eye-motor coordination (trace an outline) |

| |Demonstrate visual discrimination (determine which 2-D shapes are the same |

| |Identify, draw, or construct straight lines and curved lines. |

| |Identify simplex 2-D shapes by their appearance as a whole. |

| |Analyze, Match, and Create patterns. |

|Week 4 |Topic: Location and Movement and Size |

| |Describe location using vocabulary (front, back, above, below, between, next to, top, bottom, same side, |

| |different side, inside and outside) |

| |Compare lengths of objects using terminology such as, long, longer, longest, short, shorter, shortest, |

| |tall, taller, tallest. |

| |Review |

At the beginning of each session, students should participate in the daily calendar activities. (See handout on calendar routine)

Manipulatives for each week:

Week One

Counting bears

Number cards

Assorted Objects for counting (animals, people, vehicles)

Week Two

Dominos

Foam Dice

Assorted objects (animals, people, cars)

Links (addition)

Week Three

Pattern blocks

Unifix cubes

Cuisinaire Rods

Geoboards

Week Four

Cuisinaire Rods

First Grade Math

|Week 1 |Topic: Numbers and Numerical Operations |

| |Count forwards with stable order to 100 |

| |Count on with stable order by any number 100 or less |

| |Count backward with stable order by ones from 20 or less |

| |Skip count with stable order beginning at one by 2s, 5s and 10s |

| |Topic: Time |

| |List the months of the year in order |

| |Identify the seasons in order |

| |Identify how the calendar is the continuous count of days |

| |Tell time to the hour and half-hour using the hour hand and hour face |

|Week 2 |Topic: Whole Numbers: Addition and Subtraction |

| |Use number models to develop a concrete understanding of joining quantities (___ + ___ = ___) |

| |Use number models to develop a concrete understanding of separating quantities (___ - ___ = ___) |

| |Develop and use addition and subtraction vocabulary |

| |Make combinations for 10 |

| |Use doubles facts |

| |Topic: Identify and Count Money |

| |Recognize and identify coins by name |

| |Use the words dollar and cent |

| |Use the ¢ and $ symbols |

|Week 3 |Topic: Whole Numbers: Addition and Subtraction |

| |Verbalize stories related to addition and subtraction |

| |Solve situational stories related to addition and subtraction |

| |Create situational stories related to addition and subtraction |

| |Topic: Compare Values |

| |Compare sets and numbers to 50 |

| |Use vocabulary and symbols: greater than/less than/equal (, =) |

|Week 4 |Topic: Measurement |

| |Compare lengths of objects using terminology such as long, longer, longest, short, shorter, shortest |

| |Using a ruler correctly, measure to the nearest inch |

| |Review |

• Utilize math games to supplement fact practice and/or worksheets

Second Grade Math

|Week 1 |Time |

| |Tell time using the analog and digital clock. |

| |Tell time to five minutes. |

| |Review calendar skills. (Vocabulary- ordinal numbers) |

| |Money |

| |Identify value of groups of mixed bills and coins. |

| |Represent amounts of money with different combinations of coins. |

|Week 2 |Number and Numerical Operations |

| |Skip count with stable order beginning at one by 1’s, 5’s, and 10’s. |

| |Skip count with stable order from any number by 10’s, and 100’s. |

| |Skip count with stable order beginning at 1 by 25’s. |

| |Review use of number grid as a mathematical tool. |

| |Addition and Subtraction Facts |

| |Solve and create situational problems involving addition and subtraction. (Word Problems) Vocabulary |

| |review- total, unit, label, number model. |

| |Review use of parts-and-total diagrams and comparison diagrams and change diagram. |

| |Vocabulary review- (sum, addend, difference, even numbers, odd numbers.) |

|Week 3 |Place Value |

| |Count by tens and ones. |

| |Use a place chart. |

| |Generate equivalent representatives for a number (e.g. 37= 3 tens and 7 ones or 2 tens and 17 ones or 1 |

| |ten and 27 ones or 37 ones). |

| |Use vocabulary and symbols: greater than/less than/equal (,=) |

| |Estimation of Quantity (Number Sense) and Rounding |

| |Explain the concept of rounding. (Vocabulary 5 and above give it a shove, 4 and below- let it go). |

| |Round to the nearest 10. |

|Week 4 |Patterns and Functions and Number Representation. |

| |Review completing Frames and Arrows diagrams with one or two rules. |

| |Review completing Function Machines. |

| |Review completing various kinds of Collection box diagrams. |

• During each daily session students should review basic facts (ie. addition and subtraction)

• Utilize math games to supplement fact practice and/or worksheets

Third Grade Math

|Week 1 |Time |

| |Tell time to the minute using the hour and minute hand |

| |Tell time using the analog or digital clock |

| |Solve and create situational problems involving telling time and elapsed time |

| |Game ideas: Time Rolls On |

| |Money |

| |Identify value of mixed bill and coins |

| |Represent amounts of money with different combinations of coins |

| |Make change for a dollar or less |

| |Make change for more than a dollar |

| |Make change by counting up |

| |Game ideas: Ways to make a Dollar, Change for a Dollar |

|Week 2 |Number and Numerical Operations |

| |Round to any whole number place value |

| |Use a place value chart |

| |Order three digit numbers |

| |Generate equivalent representation of a number (37=3 tens and 7 ones, or 2 tens and 17 ones) |

| |Explain and write the concept of expanded notation (1,024= 1,000+20+4 or 2,000+500+6= 2,506) |

| |Game ideas: Number Top It |

| |Addition and Subtraction of Whole Numbers |

| |Use multiples of ten/ fact extensions (7+8=15, 70+80=150) |

| |Use regrouping to solve multi-digit addition problems |

| |Use regrouping to solve multi-digit subtraction problems |

| |Estimate sums and differences using a variety of methods |

| |Solve word problems involving addition and subtraction |

| |Game ideas: Addition Top It, Name that Number, Addition or Subtraction Slap Facts |

|Week 3 |Multiplication |

| |Stress basic facts |

| |Use models to develop a concrete understanding of equal quantities |

| |Explain the connection between skip counting with multiples and multiplication |

| |Develop understanding of multiplication using a repeated addition model |

| |Develop understanding of multiplication using an array model |

| |Solve word problems involving multiplication |

| |Vocabulary that students should be familiar with: product, factor, multiple |

| |Game ideas: Multiplication BINGO, Baseball Multiplication, Multiplication Top-It, Multiplication War, |

| |Circles and Stars, Roll a Rectangle |

| |Division |

| |Explain the division concept with a sharing or partition model (ie. Share 12 cookies among 4 friends |

| |12/4=3) |

| |Explain the division concept using arrays |

| |Explain the concept of a leftover or a remainder |

| |Solve word problems involving division |

| |Vocabulary that students should be familiar with: dividend, divisor, quotient |

|Week 4 |Linear Measurement |

| |Measure to the nearest inch and ½ inch |

| |Measure to the nearest centimeter |

| |Measure perimeter & area |

| |Fractions |

| |Use models to develop a concrete understanding of a fraction of a region or a set |

| |Explain how a fraction is a fair share |

| |Use fraction notation |

| |Vocabulary that students should be familiar with: numerator, denominator |

| |Review |

| |Review topics as needed |

| |Solve word problems where the correct operation needs to be determined—1-2 step problem solving |

• At the beginning of each session, students should review basic facts (ie. Single digit addition, subtraction, and multiplication facts)

• Utilize math games to supplement fact practice and/or worksheets

Suggested manipulatives:

• Regular playing cards, Judy clocks, Play money, # grids, Place value charts, Fact triangles/fact cards

Fourth Grade Math

|Week 1 |Topic: Number sense, Place Value and addition and subtraction of Whole Numbers |

| |Read/write numbers to hundreds-millions |

| |Explain and write the concept of expanded notation |

| |(1,024 = 1,00+20+4 or 2,00 + 500+ 6 = 2,506) |

| |Use regrouping to solve multi-digit addition and subtraction problems |

| |Use regrouping to solve subtraction problems with zeroes |

|Week 2 |Topic: Multiplication |

| |Use multiplication vocabulary: multiple, multiples, times groups, factors and product. Review/recall |

| |basic facts in the times table through twelve |

| |Use an algorithm to solve multi-digit multiplication problems using 1 digit and 2 digit multipliers |

| |Topic: Division |

| |Use division vocabulary: divide, divisor, dividend, quotient and remainder. Review/recall basic facts in |

| |the times table through twelve |

| |Use an algorithm to solve multi-digit division problems using 1 and 2 digit divisors |

|Week 3 |Topic: Problem Solving Applying Addition, Subtractions, Multiplication and Division Strategies |

| |Use problem solving steps and strategies for solving number stories (key words, mnemonics) |

| |Solve situational problems involving multi-digit addition, subtraction, multiplication and division |

| |Solve division word problems and interpret the remainder |

| |Topic: Measurement |

| |Measure to the nearest ½ inch, ½ centimeter |

|Week 4 |Topic: Fractions |

| |Vocabulary: numerator & denominator |

| |Equivalent fractions: use models to develop concrete understanding of equivalent fractions |

| |Comparing fractions: use models to develop concrete understanding of equivalent fractions. |

| |Order fractions or mixed numerals with common denominators |

| |Topic: Decimals |

| |Use the decimal place value chart (tenths hundredths, thousandths) |

| |Addition and subtraction of decimals |

• At the beginning of each session, students should review basic facts (ie. Single digit addition, subtraction, and multiplication facts)

• Utilize math games to supplement fact practice and/or worksheets

Materials needed:

• Math Decks

• Grid paper

• Place value chart

• Ruler

• Pattern blocks

Games:

• Top It

• Multiplication Baseball

• Name that Number (place value)

Fifth Grade Math

|Week 1 |WHOLE NUMBERS AND DECIMALS |

| |Identify place value of whole numbers and decimals. Round whole numbers to nearest te, hundred, and |

| |thousand AND round decimals to nearest whole number, tenth and hundredth. |

| |Compare and order whole numbers and decimals using symbols and =. Make magnitude estimates by |

| |rounding to the greatest place value for sums, differences, products and quotients. |

| |Reinforce skills presented in week 1 using Everyday Math games and manipulatives. GAME DAY- Friday |

|Week 2 |COMPUTATION |

| |Solve addition and subtraction problems involving whole numbers and decimals. Include word problems. |

| |Solve multiplication problems involving whole numbers and decimals. Include word problems. |

| |Solve division problems involving whole numbers and decimals. Include word problems. |

| |Reinforce skills presented in week 2 using Everyday Math games and manipulatives. GAME DAY-Friday |

|Week 3 |FRACTIONS |

| |Use common denominators to create equivalent fractions and simplify to lowest terms. Change improper |

| |fractions to mixed and whole numbers AND mixed and whole numbers into improper fractions. Compare and |

| |order fractions and mixed numbers. |

| |Add fractions and mixed numbers with same and different denominators. Include word problems. |

| |Subtract fractions and mixed numbers with same and different denominators. Include word problems. |

| |Reinforce skills presented in week 3 using Everyday Math games and manipulatives. GAME DAY-Friday |

|Week 4 |FRACTIONS, COORDINATE GRAPHS, AREA/PERIMETER |

| |Convert fractions to decimals and percents. |

| |Use a ruler to read fractions (halves, fourths, eighths, sixteenths). Draw and measure line segments |

| |with a ruler. |

| |Locate ordered number pairs on 4-quadrant coordinate grids. Find area and perimeter of squares, |

| |rectangles, parallelograms, and triangles. |

| |Reinforce skills presented in week 4 using Everyday Math games and manipulatives. GAME DAY-Friday |

Sixth Grade Math

|Week 1 |Geometry |

| |Reasoning with Angle Measures |

| |Find angle measures by reasoning with supplementary and vertical angle definitions |

| |Find angle measures by reasoning with sums of angle measures in triangles and quadrangles |

| |Parallel Lines and Angle Relationships |

| |Explore relationships between angles formed by parallel lines cut by a transversal |

| |Find missing measures of angles |

| |Classify parallel, perpendicular, and intersecting lines |

| |Area and Perimeter of Polygons |

| |Prove and calculate formulas of area and perimeter for squares, rectangles, parallelograms, triangles, |

| |and trapezoids |

| |Calculate area and circumferences of a circle |

| |Measurement |

| |Conversions |

| |Memorize common measurement conversions |

| |Calculate conversions within the standard measurement system |

| |Convert between standard and metric measurement systems |

| |Measuring Objects |

| |Measure objects accurately |

| |Discern appropriate unit of measurement |

|Week 2 |Rates, Ratios and Units |

| |Rates, Rate Tables, and Unit Rates |

| |Use the per-unit rate and rate table method of solving rate problems |

| |Introduce proportions as models for rate situations |

| |Create rate tables generated from real-life experiences |

| |Ratios |

| |Review notations for and meanings of ratios |

| |Solve problems involving part-to-part and part-to-whole ratios |

| |Solving Rate Problems |

| |Solving Rate Problems with Proportions |

| |Use proportions to model and solve rate problems |

| |Solving Proportions by Cross-Multiplication |

| |Introduce cross multiplication as a way to test whether two fractions are equivalent |

| |Use cross multiplication to solve proportions |

|Week 3 |Rational Number Uses and Operations |

| |Adding and Subtracting Fractions |

| |Review adding and subtracting fractions with like and unlike denominators |

| |Adding and Subtracting Mixed Numbers with Like and Unlike Denominators |

| |Adding and subtracting mixed numbers with like denominators |

| |Extend addition and subtraction to mixed numbers with like denominators |

| |Multiplication of Fractions and Mixed Numbers |

| |Use multiplication of fractions algorithm to solve multiplication of fraction problems |

| |Multiply mixed numbers by using the renaming mixed numbers as fractions method |

| |Equation Laws and Order of Operations |

| |Number Sentences |

| |Review relation symbols, number sentences, and equations |

| |Translate between English and number sentence |

| |Solving Simple Equations |

| |Solve equations by trial and error and by cover-up method |

|Week 4 |Probability |

| |Probability of Independent Events |

| |Identify likelihood of probability of one or more independent events |

| |Tree Diagrams and Venn Diagrams |

| |Use tree diagrams and Venn diagrams to help calculate the probabilities of the outcomes of chance events |

| |Compare actual results of a simulation to expected outcomes |

| |Discrete Math |

| |Explore combinations of outcomes |

| |Discuss use of graphic organizer to solve practical problems |

| |Review |

*Include daily review of multiplication and division facts.

Seventh Grade Math

|Week 1 |Algebraic Expressions and Integers |

| |Integers and Absolute Value |

| |Represent, graph, and order integers |

| |Find opposites and absolute values |

| |Adding, Multiplying, Subtracting, Dividing Integers |

| |Use visual models and rules to add, subtract, multiply, and divide integers |

| |Simplify integer expressions using order of operations |

|Week 2 |Solving One-Step Equations and Inequalities |

| |Solving Equations (one-step) |

| |Solve one-step equations using addition and subtraction |

| |Solve one-step equations using multiplication and division |

| |Solving Inequalities (one-step) |

| |Solve one-step inequalities using addition and subtraction |

| |Solve one-step inequalities using multiplication and division |

|Week 3 |Properties of Exponents and Geometry |

| |Operations with Exponents |

| |Use order of operations with exponents |

| |Multiply and divide expressions containing exponents |

| |Use properties of exponents to simplify expressions |

| |Scientific Notation |

| |Write and evaluate numbers in scientific notation |

| |Calculate with scientific notation |

| |Geometry |

| |Identify characteristics of quadrilaterals |

| |Identify polygons and parts of polygons and find their perimeter |

| |Calculate area and volume for squares, rectangles, triangles, and rectangular solids |

|Week 4 |Fractions, Proportions, and Percents |

| |Solving Problems Using Percents |

| |Solve percent word problems |

| |Comparing and Adding Fractions |

| |Find the least common multiple |

| |Compare fractions |

| |Add fractions with and without common denominators |

| |Converting Between Fractions and Percents |

| |Identify equivalent fractions and percents |

| |Convert a fraction into a percent |

| |Convert a percent into a fraction |

| |Review |

*Include daily review of multiplication/division facts.

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