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Elementary and Middle School Mathematics: Teaching Developmentally

John A. Van de Walle, Karen S. Karp, Jennifer M. Bay-Williams

Chapter 18

Proportional Reasoning - all with Video Answers

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Chapter Questions

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Problem 1

Describe the idea of a ratio in your own words. Explain how your idea fits with each of the following statements:
a. A fraction is a ratio.
b. Ratios can compare things that are not at all alike.
c. Ratios can compare two parts of the same whole.
d. Rates such as prices or speeds are ratios.

Nick Johnson
Nick Johnson
Numerade Educator
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Problem 2

Describe a situation in which the comparison involved could be interpreted both additively and multiplicatively. Why is it important to include both types of reasoning when introducing ratios?

Nick Johnson
Nick Johnson
Numerade Educator
01:23

Problem 3

What is covariation? Give an algebraic and geometric example of covariation.

Rithvik Manne
Rithvik Manne
Numerade Educator
00:56

Problem 4

Make up a realistic proportional situation that can be solved mentally by a scale-factor approach and another that can be solved mentally by a unit-rate approach.

Jaida L
Jaida L
Numerade Educator
01:50

Problem 5

Consider this problem: If 50 gallons of fuel oil cost $\$ 56.95$, bow much can be purchased for $\$ 100$ ? Draw a sketch to illustrate the proportion, and set up the equation in two different ways. One equation should equate within ratios and the other between ratios.

Cory Kuzinski
Cory Kuzinski
Numerade Educator