# Curriculum for Grade 3

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### MODULE 1. Properties of Multiplication and Division and Solving Problems with Units of 2-5 and 10

Students build upon their knowledge of addition to identify factors (how many groups, how many objects in each group) and to compose and solve simple multiplication equations. They work with groups of 2-5 identical objects, beginning with models of identical concrete objects, such as bunches of bananas and fingers on a hand. As students progress, they work with more abstract objects (identical beads) and objects in an array.

A. Compose and solve a repeated addition equation based on a modelB. Compose a repeated addition equation based on a model and identify the number of "groups"C. Compose and solve a multiplication equation based on a model, a repeated addition equation, and the number of "groups"D. Compose and solve a multiplication equation based on a model and a repeated addition equationE. Arrange groups of objects into an array and determine the totalF. Compose and solve a multiplication equation based on a model of objects in an array

Students continue to work with concrete and more abstract objects to build models of division. They use the "dealing" method to create a given number of equal groups and also create groups of a given size. Based on these models, they answer the questions, "How many groups?" and "How many in each group?" They compose and solve division equations and determine the missing factor in multiplication problems.

A. Divide a set of objects into a given number of equal groups and identify the number of objects in each groupB. Compose and solve a division equation based on a model (Part 1)C. Divide a set of objects into equal groups of a given size and identify the number of groupsD. Compose and solve a division equation based on a model (Part 2)E. Arrange a group of objects into an array and compose a division equation based on the modelF. Determine the missing factor in a multiplication equation based on a modelG. Solve a missing factor multiplication equation based on a modelH. Solve a missing factor multiplication equation and a related division equation based on a model

A. Skip count by 2 (Level 1)B. Skip count by 3 (Level 1)C. Multiply by 2 with and without an array model (Level 1)D. Multiply by 3 with and without an array model (Level 1)E. Multiply by 2 to complete a pattern of equations (Level 1)F. Multiply by 3 to complete a pattern of equations (Level 1)G. Label arrays with equations to show the commutative property of multiplication by 2H. Label arrays with equations to show the commutative property of multiplication by 3I. Complete equations to show the commutative property of multiplication by 2 (Level 1)J. Complete equations to show the commutative property of multiplication by 3 (Level 1)K. Solve x2 multiplication equations (Level 1, Part 1)L. Solve x3 multiplication equations (Level 1, Part 1)M. Solve x2 multiplication equations (Level 1, Part 2)N. Solve x3 multiplication equations (Level 1, Part 2)O. Skip count by 2 (Level 2)P. Skip count by 3 (Level 2)Q. Multiply by 2 with and without an array model (Level 2)R. Multiply by 3 with and without an array model (Level 2)S. Multiply by 2 to complete a pattern of equations (Level 2)T. Multiply by 3 to complete a pattern of equations (Level 2)U. Complete equations to show the commutative property of multiplication by 2 (Level 2)V. Complete equations to show the commutative property of multiplication by 3 (Level 2)W. Label arrays with equations to show the distributive property of multiplication by 2 (Part 1)X. Label arrays with equations to show the distributive property of multiplication by 3 (Part 1)Y. Label arrays with equations to show the distributive property of multiplication by 2 (Part 2)Z. Label arrays with equations to show the distributive property of multiplication by 3 (Part 2)AA. Solve x2 multiplication equations (Level 2, Part 1)AB. Solve x3 multiplication equations (Level 2, Part 1)AC. Solve x2 multiplication equations (Level 2, Part 2)AD. Solve x3 multiplication equations (Level 2, Part 2)

Students use concrete and abstract objects to understand the concept of division. They then relate division to multiplication to help build understanding and fact fluency. Students begin by solving simple division equations (quotients to 5) and then advance to solving equations with quotients to 10.

A. Distribute objects equally to create a tape diagram (How many in each group?)B. Represent a tape diagram as a division equation (How many in each group?)C. Distribute objects equally to create a tape diagram (How many groups?)D. Represent a tape diagram as a division equation (How many groups?)E. Complete equations to relate multiplication to division (Part 1)F. Complete equations to relate multiplication to division (Part 2)G. Match a division fact to its related multiplication factH. Solve division equations by using the related multiplication factI. Solve division equations with a divisor of 2 (Level 1)J. Solve division equations with a divisor of 3 (Level 1)K. Solve division equations with a divisor of 2 or 3 (Level 1)L. Solve division equations with a divisor of 2 (Level 2)M. Solve division equations with a divisor of 2 (Level 3)N. Solve division equations with a divisor of 3 (Level 2)O. Solve division equations with a divisor of 3 (Level 3)

Building upon previous learning about multiplication and division, students apply their understanding to facts using 4 as a product or divisor. They work with familiar manipulatives and progression of skills to build understanding and fluency.

A. Skip count by 4B. Multiply by 4 with and without an array modelC. Multiply by 4 to complete a pattern of equationsD. Solve x4 multiplication equationsE. Represent a tape diagram as a multiplication equation (Level 1)F. Represent a tape diagram as a multiplication equation (Level 2)G. Label a tape diagram to represent a multiplication equationH. Identify factors and product in a multiplication equationI. Label arrays with equations to show the commutative property of multiplication (Level 1)J. Label arrays with equations to show the commutative property of multiplication (Level 2)K. Label tape diagrams with equations to show the commutative property of multiplicationL. Solve multiplication equations based on the commutative propertyM. Solve word problems using tape diagrams and multiplication equationsN. Solve division equations by using the related multiplication factO. Solve division equations with a divisor of 4 (Level 2)P. Solve division equations with a divisor of 4 (Level 1)

Building upon previous learning about multiplication and division, students apply their understanding to facts using 5 as a product or divisor and 10 as a product. They also develop understanding of the distributive property of multiplication and division. Students build connections between equations, arrays, tape diagrams, and word problems.

A. Skip count by 5B. Multiply by 5 with and without an array modelC. Multiply by 5 to complete a pattern of equationsD. Solve x5 multiplication equationsE. Solve division equations by using the related multiplication factF. Solve division equations with a divisor of 5 (Level 1)G. Solve division equations with a divisor of 5 (Level 2)H. Label arrays with equations to show the distributive property of multiplicationI. Complete expressions based on the distributive property of multiplicationJ. Compose a division equation based on an arrayK. Compose a division equation based on an array to show the distributive property of divisionL. Solve a division equation based on an array by using the distributive property of divisionM. Complete expressions based on the distributive property of divisionN. Skip count by 10O. Multiply by 10 to complete a pattern of equations (Level 1)P. Multiply by 10 to complete a pattern of equations (Level 2)Q. Solve x10 multiplication equationsR. Solve word problems using tape diagrams and division equations (Level 1)S. Solve word problems using tape diagrams and division equations (Level 2)

### MODULE 2. Place Value and Problem Solving with Units of Measure

Using a number line to provide context, students first determine the midway point between two round numbers. They then progress to rounding using the number line and the midway point. Finally, students round 2-, and 3-digit numbers to any given place value.

A. Determine the number that is halfway between two 2-digit numbers using a number lineB. Use = and ≈ to compare 2-digit numbersC. Round a 2-, or 3-digit number to its highest place value using a number lineD. Round a 2-, or 3-digit number to its highest place value using ≈E. Round a 2- or 4-digit number to the tens or hundreds place using a number lineF. Round a 3-digit number to various place values

### MODULE 3. Multiplication and Division with Units of 0, 1, 6-9, and Multiples of 10

Students enrich their understanding of multiplication and division by introducing the multiplication chart and the commutative property (or 'turnaround facts') of multiplication. They continue to build fact fluency, adding factors 6-9 to their repertoire.

A. Illustrate the commutative property by labeling arrays and tape diagramsB. Solve equations that illustrate the commutative propertyC. Determine missing products in a multiplication chart (factors to 5)D. Determine missing products in a multiplication chart (one factor > 5)E. Skip count by 6F. Determine multiples of 6 in a multiplication chartG. Skip count by 7H. Determine multiples of 7 in a multiplication chartI. Skip count by 8J. Determine multiples of 8 in a multiplication chartK. Skip count by 9L. Determine multiples of 9 in a multiplication chartM. Determine missing products in a multiplication chart (one factor > 5)N. Solve for an unknown represented by a letter in multiplication equationsO. Solve for an unknown represented by a letter in division equationsP. Match an equation containing an unknown to a statementQ. Solve for an unknown represented by a letter in multiplication and division equationsR. Compose and solve a multiplication equation based on a tape diagramS. Solve a multiplication word problem using a tape diagram

Students begin with familiar tasks taken to a more challenging level with higher factors. They deepen their understanding of the relationship between multiplication and division as well as their fact fluency.

A. Skip count by 6B. Determine multiples of 6 in a multiplication chartC. Determine products of 6 in a times table with and without an array modelD. Determine products of 6 in a times tableE. Solve division problems with a divisor of 6 based on its relationship to multiplicationF. Solve division problems with a divisor of 6 (Level 1)G. Solve division problems with a divisor of 6 (Level 2)H. Skip count by 7I. Determine multiples of 7 in a multiplication chartJ. Determine products of 7 in a times table with and without an array modelK. Determine products of 7 in a times tableL. Solve division problems with a divisor of 7 based on its relationship to multiplicationM. Solve division problems with a divisor of 7 (Level 1)N. Solve division problems with a divisor of 7 (Level 2)O. Solve multiplication equations using the break apart and distribute strategyP. Solve for an unknown represented by a letter in multiplication equationsQ. Solve for an unknown represented by a letter in division equationsR. Solve a word problem using a tape diagram and the relationship between multiplication and division

In addition to extending students' mastery of multiplication and division to include 8, they are also introduced to multi-step equations that use parentheses. Using illustrations and step-by-step instruction, students learn that parentheses and order of operations do not affect multiplication-only equations. They also continue to build their mastery of the break apart and distribute strategy.

A. Skip count by 8B. Determine multiples of 8 in a multiplication chartC. Determine products of 8 in a times table with and without an array modelD. Determine products of 8 in a times tableE. Solve division problems with a divisor of 8 based on its relationship to multiplicationF. Solve division problems with a divisor of 8 (Level 1)G. Solve division problems with a divisor of 8 (Level 2)H. Solve multi-step equations that include parentheses (Level 1)I. Compare similar multi-step equations with parentheses in different placesJ. Solve multi-step equations that include parentheses (Level 2)K. Identify a multi-step equation with parentheses that is solved correctlyL. Recognize the effect of parentheses on multi-step multiplication equations (Part 1)M. Recognize the effect of parentheses on multi-step multiplication equations (Part 2)N. Re-group factors with parentheses as a strategy to solve multi-step multiplication equations (Part 1)O. Re-group factors with parentheses as a strategy to solve multi-step multiplication equations (Part 2)P. Solve multiplication equations using the break apart and distribute strategy (Part 1)Q. Solve multiplication equations using the break apart and distribute strategy (Part 2)R. Solve division equations using the break apart and distribute strategy (Part 1)S. Solve division equations using the break apart and distribute strategy (Part 2)

Students apply and extend previous understanding to include 9 as a factor or divisor. We also introduce a strategy specifically for multiplying by 9.

A. Skip count by 9B. Determine multiples of 9 in a multiplication chartC. Determine products of 9 in a times table with and without an array modelD. Determine products of 9 in a times tableE. Solve division problems with a divisor of 9 based on its relationship to multiplicationF. Solve division problems with a divisor of 9 (Level 1)G. Solve division problems with a divisor of 9 (Level 2)H. Solve multiplication equations using the break apart and distribute strategyI. Solve multiplication equations using the 9 = 10-1 strategy

Students dig deeper into concepts of multiplication and division as they work with 1 and 0. In addition to working with these numbers as factors, dividends, and divisors, students use a letter to represent an unknown number in an equation and are introduced to let statements regarding such letters.

A. Compose a multiplication sentence (including 1x) to represent a modelB. Solve multiplication problems that use 1 as a factor (including 1 x n)C. Solve division problems that use 1 as a divisor (including n ÷ 1)D. Compose a multiplication sentence (including x1) to represent a modelE. Solve multiplication problems that use 1 as a factor (including n x 1)F. Solve division problems in which a number is divided by itselfG. Solve for an unknown (represented by a letter) in multiplication and division problems that include 1H. Compose a multiplication sentence (including x0) to represent a modelI. Solve multiplication problems that use 0 as a factor (including n x 0 and 0 x n)J. Solve division problems that use 1 as a dividend (including 0 ÷ n)K. Solve for an unknown (represented by a letter) in multiplication and division problems that include 0L. Determine whether a multiplication or division equation with an unknown represented by a letter is true based on a let statement

Building upon students' fact fluency with single-digit factors, we introduce multiplying a single-digit factor by a multiple of ten. Students relate word-based multiplication (e.g., 4 x 3 tens = 12 tens) to numeric equations (e.g., 4 x 30 = 120).

A. Solve for missing products on a multiplication chart in which 10 is a factorB. Relate a product of n tens to the product as a number n0C. Match numeric products to multiplication equations that use numbers and words (n tens)D. Use properties of multiplication to simplify and solve equationsE. Solve multiplication equations that have a single digit and a multiple of ten as factorsF. Solve for missing products on a multiplication chart that are square numbers

### MODULE 4. Multiplication and Area

Students are introduced to the very basics of area using tiling. They learn to use square units, measure sides of a rectangle, skip count rows of tiles, and rearrange tiles to form a different rectangle with the same area.

A. Identify 2-dimensional shapesB. Tile 2-dimensional shapes to compare their areaC. Determine and compare area by tiling with square unitsD. Identify shapes that have a given areaE. Determine area by tiling with square centimeters or inchesF. Determine area of a rectangle made by rearranging tiles from another rectangleG. Determine area by skip counting tiles in each row

Building upon the previous module, students start by skip counting tiles in a rectangle to determine its area. They then progress to multiplication using a tiled rectangle and one with only labeled measurements. Students rearrange tiles to determine the measurements of a different rectangle that has the same area. They also solve for an unknown side represented by a letter.

A. Multiply to find the area of a tiled rectangle (Level 1)B. Multiply to find the area of a tiled rectangle (Level 2)C. Determine the area of a rectangle by multiplying the lengths of the sides (Level 1)D. Determine the area of a rectangle by multiplying the lengths of the sides (Level 2)E. Determine the area of a rectangle by multiplying the lengths of the sides (Level 3)F. Determine the area of a rectangle based on the equal area of a different rectangleG. Determine the length of a side based on the area of a rectangle

Students dig deeper into their understanding of multiplication and area by using area models of rectangles. They compare parts to the whole, find missing parts, and manipulate equations to demonstrate properties. Exercises begin by using rectangles with gridlines and then advance to using those without.

A. Multiply to find area by splitting a rectangle into smaller parts (Level 1)B. Use the distributive property of multiplication to find the area of a rectangle split into smaller partsC. Subtract to find the area of a covered part of a rectangle (Level 1)D. Multiply or subtract to find areas of rectangles without gridlines (Level 2)

Students learn two different approaches to finding the area of a composite shape based on side lengths. In the first, they break the shape into smaller rectangles and add those areas together. In the second, they "complete" the shape to find the total area and then subtract the area of the "missing piece". Students begin by using shapes with unit squares shown and then progress to those without.

A. Determine area of a composite shape by splitting it into two rectangles and adding the areas (Part 1)B. Determine area of a composite shape by completing the rectangle and subtracting the area of the missing piece (Part 1)C. Determine area of a composite shape by completing the rectangle and subtracting the area of the missing piece (Part 2)D. Determine area of a composite shape by splitting it into two rectangles and adding the areas (Part 2)E. Determine the area of a composite shape using either the "break apart and add" or "complete and subtract" strategy

### MODULE 5. Fractions as Numbers on the Number Line

Students establish a foundation for understanding fractions by working with equal parts of a whole. They use halves, thirds, fourths, fifths, sixths, sevenths, and eighths of shapes including circles, rectangles, line segments, and other shapes. Students partition shapes, label sections, shade fractions, and even solve word problems involving equal sharing. Throughout the topic, they do not use fraction notation (e.g., 2 thirds).

A. Identify shapes that are partitioned into equal partsB. Identify and label halves, fourths, and eighthsC. Identify and label thirds, fifths, sixths, and seventhsD. Determine the number of equal parts needed to partition a shape into a given denominatorE. Identify the shaded portion of a shape as a unit fractionF. Sort shapes based on the unit fraction shadedG. Identify the shaded portion of a shapeH. Identify shapes that have a given portion shadedI. Partition and shade a shape to represent a given portionJ. Solve word problems involving equal parts of a whole

Students build upon their knowledge from Topic 5A to transition from word form to standard form in identifying fractions. They begin with unit fractions and advance to more complex fractions, including complements of a whole and improper fractions. Throughout the topic, students are presented with a variety of shapes, sizes, and colors of figures. While they do not use the term "improper fractions," they learn the underlying concept of fractional parts that form more than one whole.

A. Identify unit fractions written in standard formB. Label part of a figure with a unit fraction written in standard formC. Identify the part of a figure that is shaded with a unit fractionD. Identify figures that have a given unit fraction shadedE. Write a unit fraction to identify the shaded part of a figureF. Identify the shaded part of a figureG. Label the shaded part of a figure with a fraction written in standard formH. Shade parts of a figure to represent a given fractionI. Identify figures that have a given fraction shaded and fractions that represent the shaded part of a figureJ. Write a fraction to identify the shaded part of a figure (Level 1)K. Label the shaded part of a figure with a fraction written in standard form and word formL. Write a fraction to identify the shaded part of a figure (Level 2)M. Label shaded and unshaded parts of a figure (Level 1)N. Label shaded and unshaded parts of a figure (Level 2)O. Solve word problems involving complementary fractionsP. Determine the number of fractional parts in a wholeQ. Solve problems involving multiple wholes and improper fractionsR. Identify a set of figures whose shading represents an improper fractionS. Label a set of figures whose shading represents an improper fractionT. Divide and shade a set of figures to represent an improper fraction

Based on visual models, students learn that the more parts in a whole, the smaller each unit fraction. They then compare unit fractions using both words and symbols, and they relate the unit fraction to the whole.

A. Compare unit fractions based on a modelB. Compare unit fractions using <, =, and > with and without a modelC. Identify and label a unit fraction model that is greater or less than a given unit fraction modelD. Identify a whole based on a given unit fractionE. Build a whole using the correct number of unit fraction tiles

Students apply their understanding of fractions to numbers on a number line. They learn that there are numbers between the whole numbers on a number line and how to identify them. Using this tool, students are able to name equivalent whole number/fraction pairs, label fractions greater than 1, and compare fractions with unlike denominators.

A. Identify fractions on a number line and write 1 as a fractionB. Label fraction numerators on a number lineC. Label fractions on a number line (numerator and denominator)D. Segment a number line into fractions and place a given fraction on the number lineE. Place a given fraction on a number line visually (without hashmarks)F. Label fraction numerators on a number line in numbers greater than 1G. Identify a fraction that is equivalent to a whole number on a number lineH. Place fractions greater than 1 on a number lineI. Segment a number line into fractions and place a given fraction (greater than 1) on the number lineJ. Label fractions greater than 1 on a number lineK. Compare fractions with unlike denominators on a number lineL. Use <, =, or > to compare fractions with unlike denominators on a number line

Using familiar shaded models and the number line, students focus on concepts of equivalent fractions. They extend this understanding to include whole numbers and fractions greater than 1.

A. Create, label, identify, and compare equivalent fractionsB. Identify equivalent fractions using the number line (less than 1)C. Identify equivalent fractions using the number line (greater than 1)D. Label equivalent fractions on a number lineE. Label two equivalent fractions based on modelsF. Label three equivalent fractions based on modelsG. Label fractions equivalent to 1 wholeH. Write whole numbers as fractions (denominator of 1)I. Write whole numbers as fractions (various denominators)

Based on visual models, students learn to compare two fractions with the same numerator or two fractions with the same denominator. To do so, they apply their understanding of creating and naming fractions, as well as using the <, =, and > symbols.