Chapter 18 Chapter 18 Operations can be done with fractions while they can’t be done with ratios

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Chapter 18: Proportional Reasoning

SHORT ANSWER. Write the word or phrase that best completes each statement or

answers the question

1) A ______________ is a number that relates two quantities or measures within a given situation in a

multiplicative relationship.

2) Part-to-_________, part–to-whole, quotients, and rates are types of ratio.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

answers the question.

3) When comparing ratios to fractions keep in mind that

a) Conceptually, they are exactly the same thing.

b) They have the same meaning when a ratio is of the part-to-whole type.

c) They both have a fraction bar that causes students to mistakenly think they are related in some

way.

d) Operations can be done with fractions while they can’t be done with ratios.

4) In the scenario “Billy’s dog weighs 10 pounds while Sarah’s dog weighs 8 pounds“, the ratio 10/8 can be

interpreted in the following ways EXCEPT

a) For every 5 pounds of weight Billy’s dog has, Sarah’s dog has 4 pounds.

b) Billy’s dog weighs 1–1/4 times what Sarah’s dog does.

c) Sarah’s dog weighs 8 out of a total of 10 dog pounds.

d) Billy’s dog makes up 5/9 of the total dog weight.

SHORT ANSWER. Write the word or phrase that best completes each statement or

answers the question

5) According to Lamon (2006), a _________________________ thinker would understand how two amounts

vary in the same way.

6) Many learners confuse a(n) __________________________ situation, such as “Mary is 3 feet taller than

Billy,” for proportional situations.

ESSAY. Write your answer in the space provided or on a separate sheet of paper.

7) Construct an example of when confusing additive and proportional thinking could result in an incorrect

answer. Describe an incorrect process that a learner might follow. Describe a correct way to find the

solution and a way you might help the learner to see his error.

SHORT ANSWER. Write the word or phrase that best completes each statement or

answers the question

8) At Grocery Store A you can get 5 apples for $2. Grocery Store B has apples 3 for $1. 5 and 3 represent a

____________________ratio while $2 and $1 represent a “within” ratio.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

answers the question.

9) Which of the following is NOT an example of a connection between proportional reasoning and another

strand of mathematics?

a) The area of a rectangle is 8 square units and the length is four units long. How long is the width?

b) The negative slope of the line on the graph represents the fact that, for every 30 miles the car

travels, it burns one gallon of gas.

c) The triangle has been enlarged by a scale factor of 2. How wide is the new triangle if its original

width is 4 inches?

d) Sandy ate 1/4 of her Halloween candy and her sister ate ½ of it. What fraction of her candy was

left?

10) Which of the following is an example of using the unit ratio method of solving proportions?

a) Allison bought 3 pairs of socks for $12. To find out how much 10 pairs cost, find that $12 divided

by 3 is $4 a pair, and multiply $4 by 10 for a total of $40.

b) A square with a length of 2 inches was enlarged by a scale factor of 4 and is now 8 inches long.

c) If 5 candy bars cost $4.50, then 10 would cost $9. (Because 5 × 2 = 10, multiply $4.50 by 2)

d) If 2/3 = x/15, find the cross products, 30 = 3x, and then solve for x. x = 10.

11) Which of the following is an example of using the buildup strategy method of solving proportions?

a) Allison bought 3 pairs of socks for $12. To find out how much ten pairs cost, find that $12 divided

by 3 is $4 a pair, and multiply $4 by 10 for a total of $40.

b) A square with a length of 2 inches was enlarged by a scale factor of 4 and is now 8 inches long.

c) If 5 candy bars cost $4.50, then 10 would cost $9. (Because 5 × 2 = 10, multiply $4.50 by 2.)

d) If 2/3 = x/15, find the cross products, 30 = 3x, and then solve for x. x = 10.

12) Which of the following is NOT a method that will help students develop their ability to think

proportionally?

a) Provide ratio and proportional tasks within many different contexts.

b) Provide examples of proportional and non-proportional relationships to students and ask them to

discuss the differences.

c) Relate proportional reasoning to their background knowledge and experiences.

d) Explain to them how important cross-multiplying is.

SHORT ANSWER. Write the word or phrase that best completes each statement or

answers the question

13) _________________________ are a visual representation of the connection between algebra and

proportional reasoning.

14) A line segment and double line drawing model can help students solve a variety of ________________

problems.