Question 1

A Canadian dollar is worth $0.90. How much is $10.00 worth in Canadian dollars?

Accepted Answer

A) about $11.00 
B) about $12.00 
C) a little more than $10.00 
D) about $9.00 
A) about $11.00 
B) about $12.00 
C) a little more than $10.00 
D) about $9.00

Question 2

The state that Mr. Smith lives in has a 6% sales tax. If he purchases a boat that costs $16,000, he must pay $960 in taxes. The correct term associated with the $960 is referred to as the:

Accepted Answer

A) base. 
B) rate. 
C) percentage. 
D) percent. 
A) base. 
B) rate. 
C) percentage. 
D) percent.

Question 3

Choose three of the meanings of ratios (part-whole sense, part-part-whole sense, relationship between two independent sets, ratio as a rate, probability relationships, or ratio as an operator)and explain the differences between them. Use examples to illustrate the differences.

Accepted Answer

Sure!

1. Part-Whole Sense: This meanin

Question 4

A common misconception students have when working with similar figures in geometry is that they want to add the lengths of segments, rather than multiply. How could you convince a student that multiplication is the proper operation?

Accepted Answer

To convince a student that multiplicatio

Question 5

PISA: Trinity is in the hospital and receives an injection of penicillin. Her body gradually breaks the penicillin down so that one hour after the injection only 60% of the penicillin will remain. The pattern continues: At the end of each hour only 60% of the penicillin that was present at the end of the previous hour remains active. Suppose Trinity is given a dose of 300 milligrams of penicillin at 0800 hours. Complete this table showing the amount of penicillin that will remain active in Trinity's body at intervals of one hour from 0800 until 1100 hours.

Accepted Answer

The answer of PISA: Trinity is in the hospital and...

Question 6

All of the following are true about proportional reasoning except for :

Accepted Answer

A) proportional reasoning involves understanding how quantities vary in relation to each other. 
B) proportional reasoning is an overarching principle of all mathematics and is central to all sub disciplines of mathematics. 
C) proportional reasoning is structurally an additive relationship. 
D) proportional reasoning is one of the most difficult topics for children to learn in mathematics. 
A) proportional reasoning involves understanding how quantities vary in relation to each other. 
B) proportional reasoning is an overarching principle of all mathematics and is central to all sub disciplines of mathematics. 
C) proportional reasoning is structurally an additive relationship. 
D) proportional reasoning is one of the most difficult topics for children to learn in mathematics.

Question 7

Explain two of the inherent difficulties students have when learning proportional reasoning.

Accepted Answer

Two inherent difficulties students have

Question 8

The price of a $5.00 hat is increased 20% to $6.00, then later, the hat is reduced back down to $5.00. Which of the following is a true statement?

Accepted Answer

A) The percent of decrease is the same as the percent of increase. 
B) The percent of decrease is less than the percent of increase. 
C) The percent of decrease is more than the percent of increase. 
D) The percent of increase followed by a percent of decrease cannot always be determined. 
A) The percent of decrease is the same as the percent of increase. 
B) The percent of decrease is less than the percent of increase. 
C) The percent of decrease is more than the percent of increase. 
D) The percent of increase followed by a percent of decrease cannot always be determined.

Question 9

Which equation can be used to solve the following problem: 
A tire shop sold 55% of its inventory in the last year. If it sold 2,500 tires last year, how many tires did the tire shop have in stock last year?

Accepted Answer

A) 0.55 × x = 2,500 
B) 0.55 × 2,500 = x 
C)    
D) 0.55 × x + 2,500 = 2,500 + x 
A) 0.55 × x = 2,500 
B) 0.55 × 2,500 = x 
C)    
D) 0.55 × x + 2,500 = 2,500 + x

Question 10

Which equation could be used to solve the problem below?
The number of students in a school increased by 150. The school originally had 500 students. By what percent did the number of students increase?

Accepted Answer

A) x % × 150 = 500 
B) x % × 500 = 150 
C)    
D)    
A) x % × 150 = 500 
B) x % × 500 = 150 
C)    
D)

Question 11

A square made with all seven tangram pieces is 2. Write the size of each of the other pieces using common fractions, decimal fractions, and percent.

Accepted Answer

Common fractions:
B: 1/4
C: 1/

Question 12

Changing 17 to a percent is equivalent to the value:

Accepted Answer

A) 0.17%. 
B) 0.0017%. 
C) 170%. 
D) 1700%. 
A) 0.17%. 
B) 0.0017%. 
C) 170%. 
D) 1700%.

Question 13

Explain the basic difference between using a rate table and using a multiples table when working with proportional reasoning.

Accepted Answer

When working with proportional reasoning

Question 14

TIMSS: If the ratio of 7 to 13 is the same as the ratio of x to 52, what is the value of x ?

Accepted Answer

A) 7 
B) 13 
C) 28 
D) 364 
A) 7 
B) 13 
C) 28 
D) 364

Question 15

Determining the chance of rolling a prime number (3:6)on a standard six-sided die with dots ranging from 1 to 6 is an example of which of the following meaning of ratios?

Accepted Answer

A) part-whole sense 
B) part-part sense 
C) ratio as a rate 
D) probability relationships 
A) part-whole sense 
B) part-part sense 
C) ratio as a rate 
D) probability relationships

Question 16

Explain how the "cross-product algorithm" for solving proportions can degrade students' understanding of proportional relationships.

Accepted Answer

The "cross-product algorithm" for solvin

Question 17

Performance Tasks: Pattern Blocks and Tangrams 
Use pattern blocks and tangrams to complete the tasks. Trace and mark your pieces to show your answers. 
A square made with all seven tangram pieces is designated as one. Write the size of each of the pieces using common fractions, decimal fractions, and percent.

Accepted Answer

To complete the performance tasks using

Question 18

Which example below uses the meaning of ratio called ratio as an operator?

Accepted Answer

A) A box of toys contains 3 airplanes and 4 toy soldiers. The ratio of airplanes to toy soldiers is 3:4. 
B) Traveling at 65 miles per hour can be written as 65:1. 
C) A model airplane has a scale factor of 100:1 on the box. So, if the real airplane is 200 feet long, the model would be 2 feet long. 
D) If it takes 4 eggs and 3 cups of flour to make a cake, this can be stated as a 4:3 ratio of eggs to flour. 
A) A box of toys contains 3 airplanes and 4 toy soldiers. The ratio of airplanes to toy soldiers is 3:4. 
B) Traveling at 65 miles per hour can be written as 65:1. 
C) A model airplane has a scale factor of 100:1 on the box. So, if the real airplane is 200 feet long, the model would be 2 feet long. 
D) If it takes 4 eggs and 3 cups of flour to make a cake, this can be stated as a 4:3 ratio of eggs to flour.

Question 19

Teacher Licensing Examination Questions
NAEP: On the road shown below, the distance from Granville to Concord is 60 miles.
 
What is the distance from Granville to Princeton?

Accepted Answer

A) 45 miles 
B) 75 miles 
C) 90 miles 
D) 105 miles 
A) 45 miles 
B) 75 miles 
C) 90 miles 
D) 105 miles

Question 20

Which option shows a between proportion based on the problem below?
Five shirts require 10 yards of cloth. How many yards of cloth will 15 shirts require?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

A Canadian dollar is worth $0.90. How much is $10.00 worth in Canadian dollars?

The state that Mr. Smith lives in has a 6% sales tax. If he purchases a boat that costs $16,000, he must pay $960 in taxes. The correct term associated with the $960 is referred to as the:

Choose three of the meanings of ratios (part-whole sense, part-part-whole sense, relationship between two independent sets, ratio as a rate, probability relationships, or ratio as an operator)and explain the differences between them. Use examples to illustrate the differences.

A common misconception students have when working with similar figures in geometry is that they want to add the lengths of segments, rather than multiply. How could you convince a student that multiplication is the proper operation?

All of the following are true about proportional reasoning except for :

Explain two of the inherent difficulties students have when learning proportional reasoning.

The price of a $5.00 hat is increased 20% to $6.00, then later, the hat is reduced back down to $5.00. Which of the following is a true statement?

Which equation can be used to solve the following problem: A tire shop sold 55% of its inventory in the last year. If it sold 2,500 tires last year, how many tires did the tire shop have in stock last year?

Which equation could be used to solve the problem below? The number of students in a school increased by 150. The school originally had 500 students. By what percent did the number of students increase?

A square made with all seven tangram pieces is 2. Write the size of each of the other pieces using common fractions, decimal fractions, and percent.

Changing 17 to a percent is equivalent to the value:

Explain the basic difference between using a rate table and using a multiples table when working with proportional reasoning.

TIMSS: If the ratio of 7 to 13 is the same as the ratio of x to 52, what is the value of x ?

Determining the chance of rolling a prime number (3:6)on a standard six-sided die with dots ranging from 1 to 6 is an example of which of the following meaning of ratios?

Explain how the "cross-product algorithm" for solving proportions can degrade students' understanding of proportional relationships.

Which example below uses the meaning of ratio called ratio as an operator?

Teacher Licensing Examination Questions NAEP: On the road shown below, the distance from Granville to Concord is 60 miles. What is the distance from Granville to Princeton?

Which option shows a between proportion based on the problem below? Five shirts require 10 yards of cloth. How many yards of cloth will 15 shirts require?

Elementary Mathematics for the 21st Century

Defining a Comprehensive Mathematics Program

Mathematics for Every Child

Learning Mathematics

Organizing Effective Instruction

Integrating Assessment

Developing Problem-Solving Strategies

Developing Concepts of Number

Extending Number Concepts and Number Systems

Developing Number Operations With Whole Numbers

Extending Computational Fluency With Larger Numbers

Developing Understanding of Common and Decimal Fractions

Extending Understanding of Common and Decimal Fractions

Thinking Algebraically

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

Investigating Probability

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Exam 14: Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

A Canadian dollar is worth $0.90. How much is $10.00 worth in Canadian dollars?

The state that Mr. Smith lives in has a 6% sales tax. If he purchases a boat that costs $16,000, he must pay $960 in taxes. The correct term associated with the $960 is referred to as the:

Choose three of the meanings of ratios (part-whole sense, part-part-whole sense, relationship between two independent sets, ratio as a rate, probability relationships, or ratio as an operator)and explain the differences between them. Use examples to illustrate the differences.

A common misconception students have when working with similar figures in geometry is that they want to add the lengths of segments, rather than multiply. How could you convince a student that multiplication is the proper operation?

All of the following are true about proportional reasoning except for :

Explain two of the inherent difficulties students have when learning proportional reasoning.

The price of a $5.00 hat is increased 20% to $6.00, then later, the hat is reduced back down to $5.00. Which of the following is a true statement?

Which equation can be used to solve the following problem: A tire shop sold 55% of its inventory in the last year. If it sold 2,500 tires last year, how many tires did the tire shop have in stock last year?

Which equation could be used to solve the problem below? The number of students in a school increased by 150. The school originally had 500 students. By what percent did the number of students increase?

A square made with all seven tangram pieces is 2. Write the size of each of the other pieces using common fractions, decimal fractions, and percent.

Changing 17 to a percent is equivalent to the value:

Explain the basic difference between using a rate table and using a multiples table when working with proportional reasoning.

TIMSS: If the ratio of 7 to 13 is the same as the ratio of x to 52, what is the value of x ?

Determining the chance of rolling a prime number (3:6)on a standard six-sided die with dots ranging from 1 to 6 is an example of which of the following meaning of ratios?

Explain how the "cross-product algorithm" for solving proportions can degrade students' understanding of proportional relationships.

Which example below uses the meaning of ratio called ratio as an operator?

Teacher Licensing Examination Questions NAEP: On the road shown below, the distance from Granville to Concord is 60 miles. What is the distance from Granville to Princeton?

Which option shows a between proportion based on the problem below? Five shirts require 10 yards of cloth. How many yards of cloth will 15 shirts require?

Elementary Mathematics for the 21st Century

Defining a Comprehensive Mathematics Program

Mathematics for Every Child

Learning Mathematics

Organizing Effective Instruction

Integrating Assessment

Developing Problem-Solving Strategies

Developing Concepts of Number

Extending Number Concepts and Number Systems

Developing Number Operations With Whole Numbers

Extending Computational Fluency With Larger Numbers

Developing Understanding of Common and Decimal Fractions

Extending Understanding of Common and Decimal Fractions

Thinking Algebraically

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

Investigating Probability

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