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IM K-5 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 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).

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6-8 Accelerated 7 Unit 6 Lesson 5

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 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22 Lesson 23

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9-12

Accelerated 6
Accelerated 7

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Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9

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Lesson 3
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Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
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Lesson 5

5.1 Warm-up 5.2 Activity 5.3 Activity 5.4 Activity Student Lesson Summary

Unit 6, Lesson 5

Even More Graphs of Functions

Accelerated 7

5.1

Warm-up

Dog Run

Here are five pictures of a dog taken at equal intervals of time.

<p>A series of five photos. The first two are identical, depicting the dog sitting far from the camera. In the next three, the dog moves closer to the camera.</p>

Diego and Lin drew different graphs to represent this situation:

Diego's graph, quadrant 1, starts a small bit above the origin, begins with zero slope, then increases. — Diego's graph

Lin's graph, quadrant 1, starts further above the origin, stays constant, and then decreases. — Lin's graph

They both used time as the independent variable. What do you think each one used for the dependent variable? Explain your reasoning.

Are You Ready for More?

5.2

Activity

Which Graph Is It?

Standards Alignment

Building On

Addressing

8.F.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

View Full Standard

Building Toward

For each situation,

Name the independent and dependent variables.
Pick the graph that best fits the situation, or sketch the graph if one isn't provided.
Label the axes.
Answer the following question: Which quantity is a function of which? Be prepared to explain your reasoning.

Jada is training for a swimming race. The more she practices, the less time it takes for her to swim one lap.
Andre adds some money to a jar in his room each week for 3 weeks and then takes some out in week 4.

Are You Ready for More?

5.3

Activity

Sketching a Story about a Boy and a Bike

Standards Alignment

Building On

Addressing

8.F.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

View Full Standard

Building Toward

Your teacher will give you tools for creating a visual display. With your group, create a display that shows your response to each question.

Here is a story: “Noah was at home. He got on his bike and rode to his friend’s house and stayed there for a while. Then he rode home. Then he rode to the park. Then he rode home again.”

Create a set of axes, and sketch a graph of this story.
What are the two quantities? Label the axes with their names and units of measure. (For example, if this were a story about pouring water into a pitcher, one of your labels might say “volume (liters).”)
Based on your graph, is his friend’s house or the park closer to Noah’s home? Explain how you know.
Read the story and all your responses again. Does everything make sense? If not, make changes to your work.

Are You Ready for More?

5.4

Activity

Dog Bath

Standards Alignment

Building On

Addressing

8.F.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

View Full Standard

8.F.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

View Full Standard

Building Toward

Elena filled up the tub and gave her dog a bath. Then she let the water out of the tub.

Coordinate plane, horizontal, 0 to 30 by threes, vertical, 0 to 30 by threes. Graph consists of 3 connected segments. First, origin to (6 comma 24). Next to (18 comma 24), then to (30 comma 0).

The graph shows the amount of water in the tub, in gallons, as a function of time, in minutes. Add labels to the graph to show this.
When did she turn off the water faucet?
How much water was in the tub when she bathed her dog?
How long did it take for the tub to drain completely?
At what rate did the faucet fill the tub?
At what rate did the water drain from the tub?

Are You Ready for More?

Student Lesson Summary

Here is a graph showing Andre's distance as a function of time.

Piecewise linear graph, time, distance.

For a graph representing a context, it is important to specify the quantities represented on each axis. For example, if this is showing distance from home, then Andre starts at some distance from home (maybe at his friend’s house), moves farther away (maybe to a park), then returns home.

If instead the graph is showing distance from school, the story may be Andre starts out at home, moves farther away (maybe to a friend's house), then goes to school.

What could the story be if the graph is showing distance from a park?

Glossary

None

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Standards Alignment

Building On

Addressing

8.F.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

View Full Standard

Building Toward