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6-8 Accelerated 7 Unit 8

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Accelerated 7

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Curriculum

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.

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 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).

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).

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Unit 8

Student Learning Targets

Accelerated 7

Section ASide Lengths and Areas of Squares

1

The Areas of Squares

I can find the area of a tilted square on a grid by using methods like “decompose and rearrange” and “surround and subtract.”
I can find the area of a triangle.

2

Side Lengths and Areas

I can explain what a square root is.
If I know the area of a square, I can express its side length using square root notation.

3

Square Roots

I can find exact and approximate side lengths of squares.

4

Rational and Irrational Numbers

I know what a rational number is and can give an example.
I know what an irrational number is and can give an example.

Section BThe Pythagorean Theorem

Section CRepresentations of Rational and Irrational Numbers

Section DLet's Put It to Work

Unit 8 Resources

Student Materials Student Materials in Spanish

5

Square Roots on the Number Line

I can find a decimal approximation for square roots.
I can plot square roots on the number line.
When I have a square root, I can reason about which two whole numbers it is between.

6

Finding Side Lengths of Triangles

I can explain what the Pythagorean Theorem says.

7

A Proof of the Pythagorean Theorem

I can explain why the Pythagorean Theorem is true.
If I know the lengths of two sides, I can find the length of the third side in a right triangle.
When I have a right triangle, I can identify which side is the hypotenuse and which sides are the legs.

8

The Converse

I can explain why it is true that if the side lengths of a triangle satisfy the equation then it must be a right triangle.
If I know the side lengths of a triangle, I can determine if it is a right triangle or not.

9

Applications of the Pythagorean Theorem

I can use the Pythagorean Theorem to solve problems.

10

More Applications of the Pythagorean Theorem

I can recognize situations where the Pythagorean Theorem can be used to solve a problem.

11

Finding Distances in the Coordinate Plane

I can find the distance between two points in the coordinate plane.
I can find the length of a diagonal line segment in the coordinate plane.

15

When Is the Same Size Not the Same Size?

I can apply what I have learned about the Pythagorean Theorem to solve a more complicated problem.
I can decide what information I need to know to be able to solve a real-world problem using the Pythagorean Theorem.

12

Edge Lengths, Volumes, and Cube Roots

I can approximate cube roots.
I know what a cube root is.
I understand the meaning of expressions like .

13

Decimal Representations of Rational Numbers

I can write a fraction as a repeating decimal.
I understand that every number has a decimal expansion.

14

Infinite Decimal Expansions

I can write a repeating decimal as a fraction.
I understand that every number has a decimal expansion.