Question 1

The following statement are ways to define proportional reasoning EXCEPT:

Accepted Answer

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. 
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. B

Question 2

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

Accepted Answer

Restraining the path to computation allows students to -Need to understand the reasoning in order to find the missing value -Develop other strategies that will illustrate the problem that shows what covaries -Sketches will show the context and support the reasonableness of the solution -Employ scale factor and unit rate

Question 3

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

Accepted Answer

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. 
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. C

Question 4

Identify the problem below that is a constant relationship.

Accepted Answer

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? 
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 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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. 
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 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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. 
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 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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? 
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 12

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

Accepted Answer

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

Question 13

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:

Accepted Answer

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. 
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 14

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

Accepted Answer

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. 
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 15

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.

Accepted Answer

Ben and Mike were both dieting.Ben went

Question 16

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

Accepted Answer

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). 
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 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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. 
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 19

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

Accepted Answer

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

Exam 18: Proportional Reasoning

The following statement are ways to define proportional reasoning EXCEPT:

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

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

Identify the problem below that is a constant relationship.

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

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

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

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

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

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

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

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

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:

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

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.

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

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

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

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

Teaching Mathematics in the 21st Century

Exploring What It Means to Know and Do Mathematics

Teaching Through Problem Solving

Planning in the Problem-Based Classroom

Building Assessment Into Instruction

Teaching Mathematics Equitably to All Children

Using Technology Tools to Teach Mathematics

Developing Early Number Concepts and Number Sense

Developing Meanings for the Operations

Helping Students Master the Basic Facts

Developing Whole-Number Place-Value Concepts

Developing Strategies for Addition and Subtraction Computation

Developing Strategies for Multiplication and Division Computation

Algebraic Thinking, equations, and Functions

Developing Fraction Concepts

Developing Strategies for Fraction Computation

Developing Concepts of Fractions and Decimals

Developing Measurement Concepts

Geometric Thinking and Geometric Concepts

Developing Concepts of Data Analysis

Exploring Concepts of Probability

Developing Concepts of Exponents, integers, and Real Numbers

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