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

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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.

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Adaptations and additions to create IM 6–8 Math v.360 Accelerated are ©2025 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY-NC 4.0).

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6-8 Accelerated 7 Unit 8 Lesson 7

Gradeband

K-5 Math •6-8 Math 9-12 Math

Course

Accelerated 6 •Accelerated 7

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

K-5
6-8
9-12

Accelerated 6
Accelerated 7

Grade 6
Grade 7
Grade 8

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

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Unit 8, Lesson 7

A Proof of the Pythagorean Theorem

Accelerated 7

Practice

Problem 1
Student Task Statement
Use the areas of the two identical squares to explain why without doing any calculations.

2 decomposed squares. On left square is decomposed into square with side length = 5, 2 rectangles with sides = 12 and 5, and square with side length = 12. On right square is decomposed into a square with side length = 13 and 4 right triangles with sides = 5, 12, 13.

Lesson 7 Resources

Student Materials Student Materials in Spanish

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Problem 2

Student Task Statement

Find the exact value of each variable that represents a side length in a right triangle.

5 right triangles.

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Problem 3

Student Task Statement

In each part, and represent the length of a leg of a right triangle, and represents the length of its hypotenuse. Find the unknown length, given the other two lengths.

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Problem 4

ForLesson 13: Adding and Subtracting with Scientific Notation

Student Task Statement

In 2015, there were roughly high school football players and professional football players in the United States. About how many times more high school football players are there? Explain how you know.

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Problem 5

ForLesson 5: Square Roots on the Number Line

Student Task Statement

Each number is between which two consecutive integers?

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