NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 22
8•7
Lesson 22: Average Rate of Change
Classwork
Exercise
The height of a container in the shape of a circular cone is 7.5 ft., and the radius of its base is 3 ft., as shown. What is the
total volume of the cone?
Lesson 22:
Average Rate of Change
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M7-TE-1.3.0-10.2015
S.124
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 22
NYS COMMON CORE MATHEMATICS CURRICULUM
Time (in minutes)
8•7
Water Level (in feet)
1
2
3
4
5
6
7
7.5
Lesson 22:
Average Rate of Change
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M7-TE-1.3.0-10.2015
S.125
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 22
NYS COMMON CORE MATHEMATICS CURRICULUM
8•7
Problem Set
1.
Complete the table below for more intervals of water levels of the cone discussed in class. Then, graph the data on
a coordinate plane.
Time (in minutes)
Water Level (in feet)
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
Lesson 22:
Average Rate of Change
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M7-TE-1.3.0-10.2015
S.126
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 22
NYS COMMON CORE MATHEMATICS CURRICULUM
2.
8•7
Complete the table below, and graph the data on a coordinate plane. Compare the graphs from Problems 1 and 2.
What do you notice? If you could write a rule to describe the function of the rate of change of the water level of the
cone, what might the rule include?
𝑥
√𝑥
1
4
9
16
25
36
49
64
81
100
Lesson 22:
Average Rate of Change
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M7-TE-1.3.0-10.2015
S.127
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 22
8•7
3.
Describe, intuitively, the rate of change of the water level if the container being filled were a cylinder. Would we get
the same results as with the cone? Why or why not? Sketch a graph of what filling the cylinder might look like, and
explain how the graph relates to your answer.
4.
Describe, intuitively, the rate of change if the container being filled were a sphere. Would we get the same results
as with the cone? Why or why not?
Lesson 22:
Average Rate of Change
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M7-TE-1.3.0-10.2015
S.128
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.