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Unit 5 - Lesson 18 - Grade 8: Illustrative Mathematics

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Grade 8 Unit 5
Lesson 18: Scaling Two Dimensions
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 5
Lesson 18: Scaling Two Dimensions
CC BY 2021 Illustrative Mathematics®
Lesson: Scaling Two Dimensions

Tripling Statements (Warm Up)

m, n, a, b, and c all represent positive integers. Consider these two equations: m = a + b + c n = abc
1.

Which of these statements are true? Select all that apply.

2.

Create a true statement of your own about one of the equations.

A Square Base (Optional)

3.

Clare sketches a rectangular prism with a height of 11 and a square base and labels the edges of the base s. She asks Han what he thinks will happen to the volume of the rectangular prism if she
triples s.

Han says the volume will be 9 times bigger. Is he right? Explain or show your reasoning.

Playing with Cones (Optional)

There are many cones with a height of 7 units. Let r represent the radius and V represent the volume of these cones.
4.

Write an equation that expresses the relationship between V and r. Use 3.14 as an approximation for π.

5.

Predict what happens to the volume if you triple the value of r.

6.

Graph this equation.

7.

What happens to the volume if you triple r? Where do you see this in the graph? How can you see it algebraically?


Cool Down: Halving Dimensions

Halving Dimensions

There are many cylinders for which the height and radius are the same value. Let c represent the height and radius of a cylinder and V represent the volume of the cylinder.
8.

Write an equation that expresses the relationship between the volume, height, and radius of this cylinder using c and V.

9.

If the value of c is halved, what must happen to the value of the volume V?