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9-12 Integrated Math 3 Unit 1 Lesson 8

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 Integrated Math 2 •Integrated Math 3

Unit

•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7

Modeling Prompts

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

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7

Modeling Prompts

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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

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Unit 1, Lesson 8

The Root of the Problem

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Integrated Math 3

Practice

Problem 1
Student Task Statement
A solid with a volume of 8 cubic units is dilated by a scale factor of to obtain a solid with volume of cubic units. Find the value of that results in a solid with each given volume.

216 cubic units

1 cubic unit

1,000 cubic units

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Problem 2

Student Task Statement

A solid has a volume of 7 cubic units. The equation represents the scale factor of by which the solid must be dilated to obtain a solid with a volume of cubic units. Select all points that are on the graph representing this equation.

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Problem 3

Student Task Statement

A solid with a surface area of 8 square units is dilated by a scale factor of to obtain a solid with a surface area of square units. Find the value of that leads to a solid with each given surface area.

512 square units
square unit
8 square units

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Problem 4

ForLesson 7: Scaling Solids

Student Task Statement

It takes of a roll of wrapping paper to completely cover all 6 sides of a small box that is shaped like a rectangular prism. The box has a volume of 10 cubic inches. Suppose the dimensions of the box are doubled.

How many rolls of wrapping paper will it take to cover all 6 sides of the new box?
What is the volume of the new box?

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Problem 5

ForLesson 7: Scaling Solids

Student Task Statement

A solid with a volume of 8 cubic units is dilated by a scale factor of . Find the volume of the solid for each given value of .

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Problem 6

ForLesson 6: Scaling and Unscaling

Student Task Statement

A figure has an area of 9 square units. The equation represents the scale factor of by which the solid must be dilated to obtain an image with area of square units. Select all points that are on the graph representing this equation.

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Problem 7

ForLesson 5: Scaling and Area

Student Task Statement

Noah edits the school newspaper. He is planning to print a photograph of a flyer for the upcoming school play. The original flyer has an area of 576 square inches. The picture Noah prints will be a dilation of the flyer using a scale factor of . What will be the area of the picture of the flyer in the newspaper?

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Lesson 8 Resources

Student Materials