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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).

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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).

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6-8 Grade 8 Unit 5

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

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

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Unit 5

Student Learning Targets

Grade 8

Section AInputs and Outputs

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.

Section BRepresenting and Interpreting Functions

Section CLinear Functions and Rates of Change

Section DCylinders and Cones

Section EDimensions and Spheres

Section FLet's Put It to Work

Unit 5 Resources

Student Materials Student Materials in Spanish

8

Linear Functions

I can determine whether a function is increasing or decreasing based on whether its rate of change is positive or negative.
I can explain in my own words how the graph of a linear function relates to its rate of change and initial value.

9

Linear Models

I can decide when a linear function is a good model for data and when it is not.
I can use data points to model a linear function.

10

Piecewise Linear Functions

I can create graphs of nonlinear functions with pieces of linear functions.

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

Tables, Equations, and Graphs of Functions

I can identify graphs that do, and do not, represent functions.
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.

5

More Graphs of Functions

I can explain the story told by the graph of a function.

6

Even More Graphs of Functions

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

7

Connecting Representations of Functions

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

11

Filling Containers

I can collect data about a function and represent it as a graph.
I can describe the graph of a function in words.

12

How Much Will Fit?

I know that volume is the amount of space contained inside a three-dimensional figure.
I recognize the following three-dimensional shapes: cylinder, cone, rectangular prism, and sphere.

13

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.

14

Finding Cylinder Dimensions

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

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

Volume as a Function of . . .

I can compare functions about volume represented in different ways.