Lesson | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

IM® 6-8 Math v.360, an IM v.360 curriculum, is ©2024 by Illustrative Mathematics®, and licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

IM 6-8 Math v.360, an IM v.360 curriculum, is a derivative of IM 6-8 Math.

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics®, and is ©2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) . OUR's 6-8 Math Curriculum is available at https://openupresources.org/math-curriculum/ .

Adaptations and updates to IM 6-8 Math v.360 are ©2024 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution-Noncommercial 4.0 International License (CC BY-NC 4.0).

Adaptations to add additional English language learner supports are ©2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The second set of English assessments (marked as set “B”) are ©2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) .

Spanish translation of the “B” assessments are ©2020 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Navigation

6-8 Grade 6 Unit 4 Lesson 4

Gradeband

K-5 Math •6-8 Math 9-12 Math

Course

•Grade 6 Grade 7 Grade 8

Unit

Unit 1 Unit 2 Unit 3 •Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

Lesson

Lesson 1 Lesson 2 Lesson 3 •Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17

K-5
6-8
9-12

Grade 6
Grade 7
Grade 8

Accelerated 6
Accelerated 7

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17

Settings

Language

Audience

family

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

English
Español

teacher
student
family

Lesson 4

4.1 Warm-up 4.2 Activity Student Lesson Summary

Unit 4, Lesson 4

How Many Groups? (Part 1)

Grade 6

4.1

Warm-up

Equal-size Groups

Write a multiplication equation and a division equation for each sentence or diagram.

Eight $5 bills are worth $40.
There are 9 thirds in 3 ones.

Are You Ready for More?

4.2

Activity

Reasoning with Pattern Blocks

Your teacher will give you pattern blocks as shown here. Use them to answer the questions.

Four pattern blocks: One large yellow hexagon, one blue rhombus, one red trapezoid, and one green triangle.

If a hexagon represents 1 whole, what fraction does each of the following shapes represent? Be prepared to show or explain your reasoning.
- 1 triangle
- 1 rhombus
- 1 trapezoid
- 4 triangles
- 3 rhombuses
- 2 hexagons
- 1 hexagon and 1 trapezoid
Here are Elena’s diagrams for and . Do you think these diagrams represent the equations? Explain or show your reasoning.

Two diagrams of pattern blocks: The first is of one red hexagon composed of two red trapezoids. The diagram is labeled with the equation 2 times one half equals 1. The second diagram is of two blue hexagons where each hexagon is composed of three blue rhombuses. The second diagram is labeled with the equation 6 times, one third, equals 2.
Use pattern blocks to represent each multiplication. Sketch or trace the blocks to record your representation. Remember that a hexagon represents 1 whole.
Answer each question. If you get stuck, consider using pattern blocks.
1. How many s are in 4?
2. How many s are in ?
3. How many s are in 2?

Student Lesson Summary

Some problems that involve equal-size groups also involve fractions. Here is an example: “How many s are in 2?” We can express this question with multiplication and division equations.

Pattern-block diagrams can help us make sense of such problems. Here is a set of pattern blocks.

Four pattern blocks: One large yellow hexagon, one blue rhombus, one red trapezoid, and one green triangle.

If the hexagon represents 1 whole, then a triangle must represent , because 6 triangles make 1 hexagon. We can use the triangle to represent the in the problem.

Two figures of pattern blocks. Each figure is 6 triangles in the shape of a hexagon.

Twelve triangles make 2 hexagons, which means there are 12 groups of in 2.

If we write the 12 in the place of the “?” in the original equations, we have:

Glossary

None

Have feedback on the curriculum?

Help us improve by sharing suggestions or reporting issues.

Submit Feedback

Are You Ready for More?