Deck 18: Proportional Reasoning

Question 1

Creating ratio tables or charts helps students in all of the following ways EXCEPT:

A)Application of build up strategy.
B)Organize information.
C)Show nonproportional relationships.
D)Used to determine unit rate.

Answer 1

Show nonproportional relationships.

Question 2

A _____________ refers to thinking about a ratio as one unit.

A)Multiplicative comparison.
B)Ratio as a rate.
C)Cognitive task.
D)Composed unit.

Answer 2

Composed unit.

Question 3

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.

Answer 3

Ben and Mike were both dieting.Ben went from 200 to 180 pounds while Mike went from 240 to 219 pounds.Who was the more successful dieter? A student might incorrectly think Mike was more successful,because he lost 21 pounds and Ben only lost 20,because he is thinking additively.The teacher might need to use some of the strategies from

Question 4

What is the type of ratio that would compare the number of girls in a class to the number of students in a class?

A)Ratio as rates.
B)Ratio as quotients.
C)Ratio as part-whole.
D)Ratio as part-to-part.

Question 5

What statement below describes an advantage of using strip diagrams,bar models,fraction strips or length models to solve proportions?

A)A concrete strategy that can be done first and then connected to equations.
B)A strategy that connects ratio tables to graphs.
C)A common method to figure out how much goes in each equation.
D)A strategy that helps set up linear relationships.

Question 6

Complete this statement,"A ratio is a number that relates two quantities or measures within a given situation in a..".

A)Multiplicative relationship.
B)Difference relationship.
C)Additive relationship.
D)Multiplicative comparison.

Question 7

Using proportional reasoning with measurement helps students with options for finding what?

A)Conversions.
B)Similarities.
C)Differences.
D)Rates.

Question 8

The following statement are ways to define proportional reasoning EXCEPT:

A)Ratios as distinct entities.
B)Develop a specialized procedure for solving proportions.
C)Sense of covariation.
D)Recognize proportional relationships distinct from nonproportional relationships.

Question 9

Which of the following is an example of using unit ratemethod of solving proportions?

A)If 23= x15 ,find the cross products,30 = 3x,and then solve for x.x = 10.
B)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.
C)A square with a length of 2 inches was enlarged by a scale factor of 4 and is now 8 inches long.
D)If 5 candy bars cost $4.50,then 10 would cost $9.(Because 5 × 2 = 10,multiply $4.50 by 2).

Question 10

What should you keep in mind when comparing ratios to fractions?

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.

Question 11

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 14 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.

Question 12

The following are examples of connections between proportional reasoning and another mathematical strand EXCEPT:

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 14 of her Halloween candy and her sister also ate 12 of Sandy's candy.What fraction of Sandy's candy was left?

Question 13

Identify the problem below that is a constant relationship.

A)Janet and Jean were walking to the park,each walking at the same rate.Jean started first.When Jean has walked 6 blocks,Janet has walked 2 blocks.How far will Janet be when Jean is at 12 blocks?
B)Kendra and Kevin are baking muffins using the same recipe.Kendra makes 6 dozen and Kevin makes 3 dozen.If Kevin is using 6 ounces of chocolate chips,how many ounces will Kendra need?
C)Lisa and Linda are planting peas on the same farm.Linda plants 4 rows and Lisa plants 6 rows.If Linda's peas are ready to pick in 8 weeks,how many weeks will it take for Lisa's peas to be ready?
D)Two weeks ago,two flowers were measured at 8 inches and
12 inches,respectively.Today they are 11 inches and 15 inches tall.Did the 8-inch or 12-inch flower grow more?

Question 14

A variety of methods will help students develop their proportional thinking ability.All of the ideas below support this thinking EXCEPT:

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)Provide practice in cross-multiplication problems.

Question 15

Covariation means that two different quantities vary together.Identify the problem that is about a covariationbetween ratio.

A)Apples are 4 for $2.00.
B)2 apples for $1.00 and 1 for $0.50.
C)Apples at Meyers were 4 for $2.00 and at HyVee 5 for $3.00.
D)Apples sold 4 out of 5 over oranges.

Question 16

Posing problems for students to solve proportions situations with their own intuition and inventive method is preferred over what?

A)Scaling up and down.
B)Ratio tables.
C)Graphs.
D)Cross products.

Question 17

Discuss the reasoning behind "restraining the path to computation" for solving proportional problems.

Question 18

Which of the following is an example of using a 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 23= x15 ,find the cross products,30 = 3x,and then solve for x.x = 10.

Question 19

What is one method for students to see the connection between multiplicative reasoning and proportional reasoning?

A)Solving problems with rates.
B)Solving problems with scale drawings.
C)Solve problems with between ratios.
D)Solving problems with costs.