3.1 Introducing Multiplication

21 lessons. Students represent and solve multiplication problems through the context of picture and bar graphs that represent categorical data.

Unit Overview

Unit learning goals

Students represent and solve multiplication problems through the context of picture and bar graphs that represent categorical data.

Unit at-a-Glance

Lesson learning goals

The teacher-facing learning goals below summarize, in teacher language, the mathematical, pedagogical, and language goals of each lesson.

Section

Teacher-facing learning goals

A: Interpret and Represent Data on Scaled Graphs

Lesson 1

Interpret picture graphs and bar graphs to generate questions (orally and in writing) about the data.

Lesson 2

Represent data using bar graphs and picture graphs.
Solve one- and two-step problems using addition and subtraction within 20.

Lesson 3

Interpret scaled picture graphs to generate questions (orally and in writing) about the data.

Lesson 4

Represent data using scaled picture graphs.

Lesson 5

Represent data using scaled bar graphs.

Lesson 6

Choose an appropriate scale for a bar graph that represents a given data set.

Lesson 7

Solve one-step "how many more" and "how many fewer" problems within 100, based on the data presented in scaled bar graphs.

Lesson 8

Solve one- and two-step "how many more" and "how many fewer" problems within 100, based on the data presented in scaled bar graphs.

B: From Graphs to Multiplication

Lesson 9

Build an understanding of multiplication as equal groups.
Represent a situation involving equal groups in a way that makes sense to students.

Lesson 10

Interpret a situation involving equal groups and represent it with a diagram.
Make sense of tape diagrams that represent multiplication.

Lesson 11

Write multiplication expressions to represent situations involving equal groups and diagrams.

Lesson 12

Represent and solve multiplication problems.

Lesson 13

Relate equations to multiplication situations and diagrams.
Write equations for multiplication situations and diagrams using a symbol for the unknown number.

Lesson 14

Relate equations to multiplication situations and diagrams using a symbol for the unknown number.
Write equations for multiplication situations and diagrams using a symbol for the unknown number.

Lesson 15

Solve multiplication problems.

C: Represent Multiplication with Arrays and the Commutative Property

Lesson 16

Build arrays with physical objects and describe them in terms of multiplication.
Describe an array as an arrangement of objects into rows with an equal number of objects in each row and into columns with an equal number in each column.

Lesson 17

Relate arrays to drawings of equal groups and describe them in terms of multiplication.

Lesson 18

Represent multiplication situations with arrays and multiplication expressions.

Lesson 19

Represent an array situation with an equation with a symbol for the unknown number.
Solve multiplication problems involving arrays.

Lesson 20

Describe the commutative property of multiplication using arrays.

Lesson 21 - Optional

Make choices and assumptions.
Represent data using scaled bar graphs to communicate results.
Solve real-world problems involving equal groups.

3.1 Unit Launch: Learning Narrative Video

The Unit Launch: Learning Narrative video for Grade 3, Unit 1 gives insight into the unit objectives, models and representations, possible student errors and misconceptions, and tips that might be used to help support student und...

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Full unit narrative

In this unit, students interpret and represent data on scaled picture graphs and scaled bar graphs. Then, they learn the concept of multiplication.

This is the first of four units that focus on multiplication. In this unit, students explore scaled picture graphs and bar graphs as an entry point for learning about equal-size groups and multiplication.

In grade 2, students analyzed picture graphs in which one picture represented one object and bar graphs that were scaled by single units. Here, students encounter picture graphs in which each picture represents more than one object and bar graphs that were scaled by 2 or 5 units. The idea that one picture can represent multiple objects helps to introduce the idea of equal-size groups.

Students learn that multiplication can mean finding the total number of objects in $a$ groups of $b$ objects each, and can be represented by $a\times b$ . They then relate the idea of equal groups and the expression $a\times b$ to the rows and columns of an array. In working with arrays, students begin to notice the commutative property of multiplication.

In all cases, students make sense of the meaning of multiplication expressions before finding their value, and before writing equations that relate two factors and a product.

Later in the unit, students see situations in which the total number of objects is known but either the number of groups or the size of each group is not known. Problems with a missing factor offer students a preview to division.

Throughout the unit, provide access to connecting cubes or counters, as students may choose to use them to represent and solve problems.

Throughout the unit

Students work toward fluency in multiplying by 2, 5, and 10. The How Many Do You See routine is used to encourage students to look for equal groups. It prompts students to subitize a group of dots as one unit, see the iterations of the groups, and skip-count to say the total number of dots they see in the image. This routine progresses from dots to drawings of equal groups to array formations.

Here is a sampling of the How Many Do You See warm-ups in the unit.

lesson 4	lesson 18

Number Talks are likewise designed to help students build fluency with equal groups and multiplication expressions. The sequence of expressions encourages students to relate multiplication to skip-counting. For example, in the sequence $1 \times 10$ , $2 \times 10$ , $3 \times 10$ , $4 \times 10$ , students can discover that the products increase in the same way as in skip-counting by 10. Some Number Talks elicit students' understanding of addition and subtraction within 100 in preparation for the work in an upcoming unit.

Here is a sampling of the Number Talk warm-ups in the unit.

lesson 5	lesson 15	lesson 19	lesson 20
$2+2+2+2$ $2+2+2+2+2+2+2+2$ $5+5+5+5$ $5+5+5+5+5+5+5+5$	$1\times 10$ $2\times 10$ $3\times 10$ $4\times 10$	$10\times 2$ $9\times 2$ $8\times 2$ $7\times 2$	$70-10$ $68-10$ $70-12$ $68-12$

lesson 5

lesson 15

lesson 19

lesson 20

$2+2+2+2$

$2+2+2+2+2+2+2+2$

$5+5+5+5$

$5+5+5+5+5+5+5+5$

$1\times 10$

$2\times 10$

$3\times 10$

$4\times 10$

$10\times 2$

$9\times 2$

$8\times 2$

$7\times 2$

$70-10$

$68-10$

$70-12$

$68-12$

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Assessments are available in print and digital formats with Spanish translations for equity and access in all instructional models.

Unit assessments

Section Checkpoints and checklists for observation of students can be found in the Teacher Resource Pack for this unit and on each section page. The end-of-unit assessment is below.

- CCSS.3.MD.B.3, CCSS.3.OA.A.1, CCSS.3.OA.A.3, CCSS.3.OA.A.4
3.1 End-of-Unit Assessment

This is the digital version of the end-of-unit assessment for Grade 3, Unit 1. Paper-based versions of this assessment are available in the Additional Materials tab. This assessment is intended to gauge students’ understanding of...
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- CCSS.3.MD.B.3, CCSS.3.OA.A.1, CCSS.3.OA.A.3, CCSS.3.OA.A.4
3.1 Evaluación final de la unidad

This is the digital version of the end-of-unit assessment for Grade 3, Unit 1. Paper-based versions of this assessment are available in the Additional Materials tab. This assessment is intended to gauge students’ understanding of...
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Printable versions

You can find the unit materials list, family letter, support for distance and unfinished learning, and print versions of the student workbook and teacher guide in the Additional resources section of this page.

Section and lesson materials

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Each unit is broken down into sections that identify the learning goals of the lessons within it.

Please click into Section A to explore a Lesson.

3.1 Section A: Interpret and Represent Data on Scaled Graphs

Lessons 1–8. Interpret scaled picture and bar graphs. Represent data using scaled picture and bar graphs. Solve one- and two-step story problems using addition and subtraction.

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3.1 Section B: From Graphs to Multiplication

Lessons 9–15. Represent and solve multiplication problems involving equal groups. Understand multiplication in terms of equal groups.

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3.1 Section C: Represent Multiplication with Arrays and the Commutative Property

Lessons 16–21. Represent and solve multiplication problems involving arrays.

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Additional resources

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Unit Materials

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The Planning Map gives a list of required materials, math language routines, instructional routines, and blackline master for each lesson in the unit, conveniently placing the materials in one location for efficiency in teacher preparation.

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3.1 Planning Map

A list of required materials, math language routines, instructional routines, and blackline masters for each lesson in the unit

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3.1 Monitoring Sheets

Find PDF and Microsoft Word templates to use for monitoring student progress towards the Grade 3, Unit 1 section goals.

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3.1 Unit Videos

Unit Launch and Inspire Math videos for Grade 3, Unit 1.

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3.1 Practice Problems

All of the digital practice sets for Grade 3, Unit 1, including a set devoted to the Pre-unit problems. Practice sets can also be found in the Additional resources section of the corresponding section page.

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3.1 Vocabulary

This lesson plan contains all of the vocabulary cards for terms introduced in Grade 3, Unit 1. Some ways to use this lesson plan include: Projecting or assigning to students as a review of vocabulary prior to the end-of-unit asse...

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3.1 Digital Cool-downs

All of the digital cool-downs for Grade 3, Unit 1. Cool-downs can also be found in the Additional Materials section of the corresponding lesson.

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3.1 Digital student task statements

All of the digital student task statements for Grade 3, Unit 1. These can also be found in the Additional Materials section of the corresponding lesson.

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Support for distance and unfinished learning

Unfinished Learning

3.1 Adaptation Pack

Grade 3, Unit 1 guidance for supporting students with accessing grade-level mathematics and addressing gaps in prior learning.

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Distance Learning

3.1 Section Planning Guide

Use this guide to inform distance learning planning for Grade 3, Unit 1 of IM K-5 Math version 1.
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3.1 Family Letter

Grade 3, Unit 1 family letter that teachers can copy and adapt. Each unit letter includes the mathematical focus of the unit and offers families ways in which they can support the learning at home.
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Home Connection

3.1 Unit Launch: Family Support Video

The Unit Launch: Family Support video for Grade 3, Unit 1 provides the background a family could need to support student learning throughout this unit. The Family Support video includes prior learning, vocabulary explanations, ma...

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3.1 Family Support Material

Print or share this guide to support families support their students with the key concepts and ideas in Grade 3, Unit 1. The guide also includes a Spanish language version.

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3.1 English Family Support Materials (PDF)

Print or share this guide to help families support their students with the key concepts and ideas in Grade 3, Unit 1 in English.
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3.1 Spanish Family Support Materials (PDF)

Print or share this guide to help families support their students with the key concepts and ideas in Grade 3, Unit 1.
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