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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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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

Section BRepresenting and Interpreting 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.

Section CLinear Functions and Rates of Change

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.

Section DCylinders and Cones

Section EDimensions and Spheres

Section FLet's Put It to Work

Unit 5 Resources

Student Materials

7

Connecting Representations of Functions

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

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.

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.

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.

22

Volume as a Function of . . .

I can compare functions about volume represented in different ways.