# Curriculum for Grade 3

Students' strong foundation of math skills facilitates the shift to multiplication and division, moving from concrete procedures toward abstract thinking and automaticity.

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

### Topic A: Multiplication and the Meaning of the Factors

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.

#### Solve and re-write repeated addition equations

#### Complete statements describing equal groups and their totals

#### Use the multiplication sign

#### Compose and solve multiplication equations based on a model

#### Multiply based on a model of objects in rows

#### Compose and solve multiplication equations based on an array

#### Compose expressions and equations based on a model

### Topic B: Division as an Unknown Factor Problem

Students work with models of real-world objects to solve equal sharing problems. They are introduced to the division symbol. They use the "dealing" method to 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.

#### Use the division symbol

#### Compose and solve division equations based on a model

#### Model division equations and solve

#### Divide objects into groups

#### Compose division equations

#### Solve division word problems

### Topic C: Analyzing Arrays to Multiply Using Units of 2 and 3

#### Skip count by 2 (Level 1)

#### Skip count by 3 (Level 1)

#### Multiply by 2 with and without an array model (Level 1)

#### Multiply by 3 with and without an array model (Level 1)

#### Multiply by 2 to complete a pattern of equations (Level 1)

#### Multiply by 3 to complete a pattern of equations (Level 1)

#### Label arrays with equations to show the commutative property of multiplication by 2

#### Label arrays with equations to show the commutative property of multiplication by 3

#### Complete equations to show the commutative property of multiplication by 2 (Level 1)

#### Complete equations to show the commutative property of multiplication by 3 (Level 1)

#### Solve x2 multiplication equations (Level 1, Part 1)

#### Solve x3 multiplication equations (Level 1, Part 1)

#### Solve x2 multiplication equations (Level 1, Part 2)

#### Solve x3 multiplication equations (Level 1, Part 2)

#### Skip count by 2 (Level 2)

#### Skip count by 3 (Level 2)

#### Multiply by 2 with and without an array model (Level 2)

#### Multiply by 3 with and without an array model (Level 2)

#### Multiply by 2 to complete a pattern of equations (Level 2)

#### Multiply by 3 to complete a pattern of equations (Level 2)

#### Complete equations to show the commutative property of multiplication by 2 (Level 2)

#### Complete equations to show the commutative property of multiplication by 3 (Level 2)

#### Label arrays with equations to show the distributive property of multiplication by 2 (Part 1)

#### Label arrays with equations to show the distributive property of multiplication by 2 (Part 2)

#### Label arrays with equations to show the distributive property of multiplication by 3 (Part 1)

#### Label arrays with equations to show the distributive property of multiplication by 2 (Part 3)

#### Label arrays with equations to show the distributive property of multiplication by 3 (Part 2)

#### Solve x2 multiplication equations (Level 2, Part 1)

#### Solve x3 multiplication equations (Level 2, Part 1)

#### Solve x2 multiplication equations (Level 2, Part 2)

#### Solve x3 multiplication equations (Level 2, Part 2)

### Topic D: Division by 2 and by 3

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.

#### Distribute objects equally to create a tape diagram (How many in each group?)

#### Represent a tape diagram as a division equation (How many in each group?)

#### Distribute objects equally to create a tape diagram (How many groups?)

#### Represent a tape diagram as a division equation (How many groups?)

#### Complete equations to relate multiplication to division (Part 1)

#### Complete equations to relate multiplication to division (Part 2)

#### Match a division fact to its related multiplication fact

#### Solve division equations by using the related multiplication fact

#### Solve division equations with a divisor of 2 (Level 1)

#### Solve division equations with a divisor of 3 (Level 1)

#### Solve division equations with a divisor of 2 or 3 (Level 1)

#### Solve division equations with a divisor of 2 (Level 2)

#### Solve division equations with a divisor of 2 (Level 3)

#### Solve division equations with a divisor of 3 (Level 2)

#### Solve division equations with a divisor of 3 (Level 3)

### Topic E: Multiplication and Division by 4

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.

#### Skip count by 4

#### Multiply by 4 with and without an array model

#### Multiply by 4 to complete a pattern of equations

#### Solve x4 multiplication equations

#### Represent a tape diagram as a multiplication equation (Level 1)

#### Represent a tape diagram as a multiplication equation (Level 2)

#### Label a tape diagram to represent a multiplication equation

#### Identify factors and product in a multiplication equation

#### Label arrays with equations to show the commutative property of multiplication (Level 1)

#### Label arrays with equations to show the commutative property of multiplication (Level 2)

#### Label tape diagrams with equations to show the commutative property of multiplication

#### Solve multiplication equations based on the commutative property

#### Solve word problems using tape diagrams and multiplication equations

#### Solve division equations by using the related multiplication fact

#### Solve division equations with a divisor of 4 (Level 1)

#### Solve division equations with a divisor of 4 (Level 2)

### Topic F: Multiplication and Division by 5

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.

#### Skip count by 5

#### Multiply by 5 with and without an array model

#### Multiply by 5 to complete a pattern of equations

#### Solve x5 multiplication equations

#### Solve division equations by using the related multiplication fact

#### Solve division equations with a divisor of 5 (Level 1)

#### Solve division equations with a divisor of 5 (Level 2)

#### Label arrays with equations to show the distributive property of multiplication

#### Complete expressions based on the distributive property of multiplication

#### Compose a division equation based on an array

#### Compose a division equation based on an array to show the distributive property of division

#### Solve a division equation based on an array by using the distributive property of division

#### Complete expressions based on the distributive property of division

#### Skip count by 10

#### Multiply by 10 to complete a pattern of equations (Level 1)

#### Multiply by 10 to complete a pattern of equations (Level 2)

#### Solve x10 multiplication equations

#### Solve word problems using tape diagrams and division equations (Level 1)

#### Solve word problems using tape diagrams and division equations (Level 2)

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

### Topic A: Measuring Weight and Liquid Volume in Metric Units

Students use a scale and a pan balance with weights to determine the mass of objects. They learn to read a scale between labeled increments and to add and subtract mass measurements to solve problems. To learn how to measure capacity, students pour liquid into labeled containers. They learn the relationship between kilograms and grams and between liters and milliliters.

#### Measure the mass of objects in kilograms using a scale

#### Measure the mass of objects in kilograms using a pan balance

#### Measure the mass of objects in grams using a pan balance

#### Compare grams and kilograms

#### Tutorial: Drag the lace to match objects

#### Match the estimated mass in grams and kilograms to objects

#### Determine mass measurements on a scale that is only labeled in increments of 10

#### Add or subtract to compare or find the total mass of objects measured on a scale

#### Tutorial: Click on highlighted words to access definition

#### Determine visually which of two objects has a greater capacity

#### Measure capacity using non-standard units and liters

#### Measure capacity in liters

#### Measure capacity in milliliters

#### Measure capacity in milliliters

### Topic B: Rounding to the Nearest Ten and Hundred

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.

#### Determine the halfway point between tens on a number line (Level 1)

#### Determine the halfway point between tens on a number line (Level 2)

#### Determine whether a given number is greater or less than the halfway point between tens on a number line

#### Determine the halfway point between hundreds on a number line (Level 1)

#### Determine the halfway point between hundreds on a number line (Level 2)

#### Determine whether a given number is greater or less than the halfway point between hundreds on a number line

#### Use the ~ symbol when rounding a number to the nearest ten or hundred

#### Determine the nearest ten to a given number using a number line

#### Determine whether a given number rounds up or down to the nearest ten (Level 1)

#### Determine the nearest ten to a given number

#### Determine the nearest hundred to a given number

#### Round a given number to the nearest ten and to the nearest hundred

#### Round a given number to the nearest ten or to the nearest hundred

#### Determine whether a given number rounds up or down to the nearest ten (Level 2)

### Topic C: Two- and Three-Digit Measurement Addition Using the Standard Algorithm

Students review the standard algorithm for addition with regrouping and then use it to solve word problems involving measurements. As they progress, they receive fewer prompts to complete the standard algorithm.

#### Add 2-digit numbers using the standard algorithm with regrouping

#### Add 2-digit numbers using the standard algorithm with regrouping to solve word problems

#### Add 3-digit numbers using the standard algorithm with regrouping (Level 1)

#### Add 3-digit numbers using the standard algorithm with regrouping (Level 2)

#### Add 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 1)

#### Add 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 2)

#### Add 3-digit numbers using the standard algorithm with regrouping (Level 3)

#### Add 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 2)

### Topic D: Two- and Three-Digit Measurement Subtraction Using the Standard Algorithm

Students review the standard algorithm for subtraction with regrouping and then use it to solve word problems involving measurements. As they progress, they receive fewer prompts to complete the standard algorithm.

#### Subtract 2-digit numbers using the standard algorithm with regrouping

#### Subtract 2-digit numbers using the standard algorithm with regrouping to solve word problems

#### Subtract 3-digit numbers using the standard algorithm with regrouping (Level 1)

#### Subtract 3-digit numbers using the standard algorithm with regrouping (Level 2)

#### Subtract 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 1)

#### Subtract 3-digit numbers using the standard algorithm with regrouping (Level 3)

#### Subtract 3-digit numbers using the standard algorithm with regrouping (Level 4)

#### Subtract 3-digit numbers using the standard algorithm with regrouping to solve word problems (Level 2)

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

### Topic A: The Properties of Multiplication and Division

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.

#### Illustrate the commutative property by labeling arrays and tape diagrams

#### Solve equations that illustrate the commutative property

#### Determine missing products in a multiplication chart (factors to 5)

#### Determine missing products in a multiplication chart (one factor > 5)

#### Skip count by 6

#### Determine multiples of 6 in a multiplication chart

#### Skip count by 7

#### Determine multiples of 7 in a multiplication chart

#### Skip count by 8

#### Determine multiples of 8 in a multiplication chart

#### Skip count by 9

#### Determine multiples of 9 in a multiplication chart

#### Determine missing products in a multiplication chart (one factor > 5)

#### Solve for an unknown represented by a letter in multiplication equations

#### Solve for an unknown represented by a letter in division equations

#### Match an equation containing an unknown to a statement

#### Solve for an unknown represented by a letter in multiplication and division equations

#### Compose and solve a multiplication equation based on a tape diagram

#### Solve a multiplication word problem using a tape diagram

### Topic B: Multiplication and Division Using Units of 6 and 7

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.

#### Skip count by 6

#### Determine multiples of 6 in a multiplication chart

#### Determine products of 6 in a times table with and without an array model

#### Determine products of 6 in a times table

#### Solve division problems with a divisor of 6 based on its relationship to multiplication

#### Solve division problems with a divisor of 6 (Level 1)

#### Solve division problems with a divisor of 6 (Level 2)

#### Skip count by 7

#### Determine multiples of 7 in a multiplication chart

#### Determine products of 7 in a times table with and without an array model

#### Determine products of 7 in a times table

#### Solve division problems with a divisor of 7 based on its relationship to multiplication

#### Solve division problems with a divisor of 7 (Level 1)

#### Solve division problems with a divisor of 7 (Level 2)

#### Solve multiplication equations using the break apart and distribute strategy

#### Solve for an unknown represented by a letter in multiplication equations

#### Solve for an unknown represented by a letter in division equations

#### Solve a word problem using a tape diagram and the relationship between multiplication and division

### Topic C: Multiplication and Division Using Units up to 8

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.

#### Skip count by 8

#### Determine multiples of 8 in a multiplication chart

#### Determine products of 8 in a times table with and without an array model

#### Determine products of 8 in a times table

#### Solve division problems with a divisor of 8 based on its relationship to multiplication

#### Solve division problems with a divisor of 8 (Level 1)

#### Solve division problems with a divisor of 8 (Level 2)

#### Solve multi-step equations that include parentheses (Level 1)

#### Compare similar multi-step equations with parentheses in different places

#### Solve multi-step equations that include parentheses (Level 2)

#### Identify a multi-step equation with parentheses that is solved correctly

#### Recognize the effect of parentheses on multi-step multiplication equations (Part 1)

#### Recognize the effect of parentheses on multi-step multiplication equations (Part 2)

#### Re-group factors with parentheses as a strategy to solve multi-step multiplication equations (Part 1)

#### Re-group factors with parentheses as a strategy to solve multi-step multiplication equations (Part 2)

#### Solve multiplication equations using the break apart and distribute strategy (Part 1)

#### Solve multiplication equations using the break apart and distribute strategy (Part 2)

#### Solve division equations using the break apart and distribute strategy (Part 1)

#### Solve division equations using the break apart and distribute strategy (Part 2)

### Topic D: Multiplication and Division Using Units of 9

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

#### Skip count by 9

#### Determine multiples of 9 in a multiplication chart

#### Determine products of 9 in a times table with and without an array model

#### Determine products of 9 in a times table

#### Solve division problems with a divisor of 9 based on its relationship to multiplication

#### Solve division problems with a divisor of 9 (Level 1)

#### Solve division problems with a divisor of 9 (Level 2)

#### Solve multiplication equations using the break apart and distribute strategy

#### Solve multiplication equations using the 9 = 10-1 strategy

### Topic E: Analysis of Patterns and Problem Solving Including Units of 0 and 1

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.

#### Compose a multiplication sentence (including 1x) to represent a model

#### Solve multiplication problems that use 1 as a factor (including 1 x n)

#### Solve division problems that use 1 as a divisor (including n / 1)

#### Compose a multiplication sentence (including x1) to represent a model

#### Solve multiplication problems that use 1 as a factor (including n x 1)

#### Solve division problems in which a number is divided by itself

#### Solve for an unknown (represented by a letter) in multiplication and division problems that include 1

#### Compose a multiplication sentence (including x0) to represent a model

#### Solve multiplication problems that use 0 as a factor (including n x 0 and 0 x n)

#### Solve division problems that use 1 as a dividend (including 0 / n)

#### Solve for an unknown (represented by a letter) in multiplication and division problems that include 0

#### Determine whether a multiplication or division equation with an unknown represented by a letter is true based on a let statement

### Topic F: Multiplication of Single-Digit Factors and Multiples of 10

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).

#### Solve for missing products on a multiplication chart in which 10 is a factor

#### Relate a product of n tens to the product as a number n0

#### Match numeric products to multiplication equations that use numbers and words (n tens)

#### Use properties of multiplication to simplify and solve equations

#### Solve multiplication equations that have a single digit and a multiple of ten as factors

#### Solve for missing products on a multiplication chart that are square numbers

## MODULE 4. Multiplication and Area

### Topic A: Foundations for Understanding 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.

#### Identify 2-dimensional shapes

#### Tile 2-dimensional shapes to compare their area

#### Determine and compare area by tiling with square units

#### Identify shapes that have a given area

#### Determine area by tiling with square centimeters or inches

#### Determine area of a rectangle made by rearranging tiles from another rectangle

#### Determine area by skip counting tiles in each row

### Topic B: Concepts of Area Measurement

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.

#### Tutorial: Click on the book to see the multiplication table

#### Multiply to find the area of a tiled rectangle (Level 1)

#### Multiply to find the area of a tiled rectangle (Level 2)

#### Determine the area of a rectangle by multiplying the lengths of the sides (Level 1)

#### Determine the area of a rectangle by multiplying the lengths of the sides (Level 3)

#### Determine the area of a rectangle based on the equal area of a different rectangle

#### Determine the length of a side based on the area of a rectangle

### Topic C: Arithmetic Properties Using Area Models

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.

#### Multiply to find area by splitting a rectangle into smaller parts (Level 1)

#### Use the distributive property of multiplication to find the area of a rectangle split into smaller parts

#### Subtract to find the area of a covered part of a rectangle (Level 1)

#### Multiply or subtract to find areas of rectangles without gridlines (Level 2)

### Topic D: Applications of Area Using Side Lengths of Figures

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.

#### Determine area of a composite shape by splitting it into two rectangles and adding the areas (Part 1)

#### Determine area of a composite shape by completing the rectangle and subtracting the area of the missing piece (Part 1)

#### Determine area of a composite shape by completing the rectangle and subtracting the area of the missing piece (Part 2)

#### Determine area of a composite shape by splitting it into two rectangles and adding the areas (Part 2)

#### 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

### Topic A: Partition a Whole into Equal Parts

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).

#### Identify shapes that are partitioned into equal parts

#### Identify and label halves, fourths, and eighths

#### Identify and label thirds, fifths, sixths, and sevenths

#### Determine the number of equal parts needed to partition a shape into a given denominator

#### Identify the shaded portion of a shape as a unit fraction

#### Sort shapes based on the unit fraction shaded

#### Identify the shaded portion of a shape

#### Identify shapes that have a given portion shaded

#### Partition and shade a shape to represent a given portion

#### Solve word problems involving equal parts of a whole

### Topic B: Unit Fractions and their Relation to the 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.

#### Identify unit fractions written in standard form

#### Label part of a figure with a unit fraction written in standard form

#### Identify the part of a figure that is shaded with a unit fraction

#### Identify figures that have a given unit fraction shaded

#### Write a unit fraction to identify the shaded part of a figure

#### Identify the shaded part of a figure

#### Label the shaded part of a figure with a fraction written in standard form

#### Shade parts of a figure to represent a given fraction

#### Identify figures that have a given fraction shaded and fractions that represent the shaded part of a figure

#### Write a fraction to identify the shaded part of a figure (Level 1)

#### Label the shaded part of a figure with a fraction written in standard form and word form

#### Write a fraction to identify the shaded part of a figure (Level 2)

#### Label shaded and unshaded parts of a figure (Level 1)

#### Label shaded and unshaded parts of a figure (Level 2)

#### Solve word problems involving complementary fractions

#### Determine the number of fractional parts in a whole

#### Solve problems involving multiple wholes and improper fractions

#### Identify a set of figures whose shading represents an improper fraction

#### Label a set of figures whose shading represents an improper fraction

#### Divide and shade a set of figures to represent an improper fraction

### Topic C: Comparing Unit Fractions and Specifying the Whole

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.

#### Compare unit fractions based on a model

#### Compare unit fractions using <, =, and > with and without a model

#### Identify and label a unit fraction model that is greater or less than a given unit fraction model

#### Identify a whole based on a given unit fraction

#### Build a whole using the correct number of unit fraction tiles

### Topic D: Fractions on the Number Line

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.

#### Identify fractions on a number line and write 1 as a fraction

#### Label fraction numerators on a number line

#### Label fractions on a number line (numerator and denominator)

#### Segment a number line into fractions and place a given fraction on the number line

#### Place a given fraction on a number line visually (without hashmarks)

#### Label fraction numerators on a number line in numbers greater than 1

#### Identify a fraction that is equivalent to a whole number on a number line

#### Place fractions greater than 1 on a number line

#### Segment a number line into fractions and place a given fraction (greater than 1) on the number line

#### Label fractions greater than 1 on a number line

#### Compare fractions with unlike denominators on a number line

#### Use <, =, or > to compare fractions with unlike denominators on a number line

### Topic E: Equivalent Fractions

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.

#### Create, label, identify, and compare equivalent fractions

#### Identify equivalent fractions using the number line (less than 1)

#### Identify equivalent fractions using the number line (greater than 1)

#### Label equivalent fractions on a number line

#### Label two equivalent fractions based on models

#### Label three equivalent fractions based on models

#### Label fractions equivalent to 1 whole

#### Write whole numbers as fractions (denominator of 1)

#### Write whole numbers as fractions (various denominators)

### Topic F: Comparison, Order, and Size of Fractions

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.