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6-8 Accelerated 7 Unit 6

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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 6
Accelerated 7

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Unit 6
Unit 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/ .

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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).

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 6

Student Learning Targets

Accelerated 7

Section ARepresenting and Interpreting Functions

1

Inputs and Outputs

I can write rules when I know input-output pairs.
I know how an input-output diagram represents a rule.

2

Introduction to Functions

I know that a function is a rule with exactly one output for each allowable input.
I know that if a rule has exactly one output for each allowable input, then the output depends on the input.

3

Equations for Functions

I can find the output of a function when I know the input.
I can name the independent and dependent variables for a given function and represent the function with an equation.

4

Graphs of Functions

I can explain the story told by the graph of a function.
I can use a graph of a function to find the output for a given input and to find the input(s) for a given output.

Section BPrisms and Cylinders

8

Slicing Solids

I can explain that when a three-dimensional figure is sliced it creates a face that is two dimensional.
I can picture different cross-sections of prisms and pyramids.

9

Volume of Right Prisms

I can explain why the volume of a prism can be found by multiplying the area of the base by the height of the prism.

10

Decomposing Bases for Area

I can calculate the volume of a prism with a complicated base by decomposing the base into quadrilaterals or triangles.

11

The Volume of a Cylinder

I can find the volume of a cylinder in mathematical and real-world situations.
I know the formula for volume of a cylinder.

Section CCones and Spheres

Section DLet's Put It to Work

Unit 6 Resources

Student Materials

5

Even More Graphs of Functions

I can draw the graph of a function that represents a real-world situation.

6

Connecting Representations of Functions

I can compare inputs and outputs of functions that are represented in different ways.

7

Linear Functions and Models

I can decide when a linear function is a good model for data and when it is not.
I can explain in my own words how the graph of a linear function relates to its rate of change and initial value.
I can use data points to model a linear function.

12

Finding Cylinder Dimensions

I can find missing information about a cylinder if I know its volume and some other information.

13

Surface Area of Right Prisms

I can decide whether I need to find the surface area or the volume, when solving a problem about a real-world situation.
I can picture the net of a prism to help me calculate its surface area.

14

Applying Volume and Surface Area

I can solve problems involving the volume and surface area of children’s play structures.

15

The Volume of a Cone

I can find the volume of a cone in mathematical and real-world situations.
I know the formula for the volume of a cone.

16

Finding Cone Dimensions

I can find missing information about a cone if I know its volume and some other information.

17

Scaling One Dimension

I can create a graph of the relationship between volume and height for all cylinders and cones with a fixed radius.
I can explain in my own words why changing the height by a scale factor changes the volume by the same scale factor.

18

Scaling Two Dimensions

I can create a graph representing the relationship between volume and radius for all cones (or cylinders) with a fixed height.
I can explain in my own words why changing the radius by a scale factor changes the volume by the scale factor squared.

19

Estimating a Hemisphere

I can estimate the volume of a hemisphere by calculating the volume of a shape I know is larger and the volume of a shape I know is smaller.

20

The Volume of a Sphere

I can find the volume of a sphere when I know the radius.

21

Cylinders, Cones, and Spheres

I can find the radius of a sphere if I know its volume.
I can solve mathematical and real-world problems about the volume of cylinders, cones, and spheres.

22

Building Prisms

I can build a triangular prism from scratch.

23

Volume as a Function of . . .

I can compare functions about volume represented in different ways.