Question 1

A bag of marbles has 5 red, 4 blue, and 7 green marbles. Which of the following fractions is not a part-whole representation?

Accepted Answer

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

Question 2

For health reasons people should limit their efforts, for instance, during sports, in order not to exceed a certain heartbeat frequency. For years, the relationship between a person's recommended maximum heart rate and the person's age was described by the following formula:   Recent research showed that this formula should be modified slightly. The new formula is as follows:   A newspaper article stated: "A result of the new formula is that the recommended maximum number of heart beats per minute for young people decreases slightly and for old people it increases slightly." From which age onward does the recommended maximum heart rate increase as a result of the introduction of the new formula? Show your work.

Accepted Answer

Answers will vary.

Question 3

Compare  
To 
  
.

Accepted Answer

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

Question 4

If a base-10 flat represents 1, then the unit represents:

Accepted Answer

A) 0.01. 
B) 0.1. 
C) 0.001. 
D) 0.0001. 
A) 0.01. 
B) 0.1. 
C) 0.001. 
D) 0.0001.

Question 5

The purpose in using the terms common fractions and decimal fractions is to:

Accepted Answer

A) let children know that they are commonly found in nature. 
B) help children understand that both types of numerals are used to represent fractional numbers. 
C) help children distinguish between these completely different types of numbers. 
D) decrease confusion about these complex numbers. 
A) let children know that they are commonly found in nature. 
B) help children understand that both types of numerals are used to represent fractional numbers. 
C) help children distinguish between these completely different types of numbers. 
D) decrease confusion about these complex numbers.

Question 6

The best way to teach children fractions and decimals is to:

Accepted Answer

A) teach them the rules first, then give them manipulatives to substantiate the rules. 
B) allow them to work with manipulatives, then teach them the rules. 
C) allow them to work with manipulatives, then have them make sketches, then to show them the rules. 
D) teach them the rules, then have them make sketches, then give them manipulatives. 
A) teach them the rules first, then give them manipulatives to substantiate the rules. 
B) allow them to work with manipulatives, then teach them the rules. 
C) allow them to work with manipulatives, then have them make sketches, then to show them the rules. 
D) teach them the rules, then have them make sketches, then give them manipulatives.

Question 7

Why should a teacher use the terms common fractions and decimal fractions rather than just the terms fractions and decimals ?

Accepted Answer

A teacher should use the terms common fr

Question 8

Improper fractions are:

Accepted Answer

A) fractions greater than 1. 
B) not equivalent to mixed numbers. 
C) fractions that should not be used in elementary school settings. 
D) algebraic fractions. 
A) fractions greater than 1. 
B) not equivalent to mixed numbers. 
C) fractions that should not be used in elementary school settings. 
D) algebraic fractions.

Question 9

How would you help a child who thinks that when you multiply two numbers the result is always larger than either of the two factors?

Accepted Answer

To help a child understand that multiply

Question 10

The concept of a fractional part of a set should only be introduced after children:

Accepted Answer

A) demonstrate that they can conserve number. 
B) have a good grasp of whole numbers. 
C) are skillful in counting objects in sets. 
D) all of these options are correct. 
A) demonstrate that they can conserve number. 
B) have a good grasp of whole numbers. 
C) are skillful in counting objects in sets. 
D) all of these options are correct.

Question 11

If the largest base-10 cube (10 units × 10 units × 10 units)represents 1, then the small unit (1 unit × 1 unit × 1 unit)represents:

Accepted Answer

A) 0.1. 
B) 0.001. 
C) 0.01. 
D) 0.0001. 
A) 0.1. 
B) 0.001. 
C) 0.01. 
D) 0.0001.

Question 12

Draw two different illustrations of improper fractions to explain why they are equivalent to mixed numerals.

Accepted Answer

Sure! Here are two different illustratio

Question 13

Equivalent fractions are best taught using:

Accepted Answer

A) units partitioned into equal-sized groups. 
B) sets partitioned into equal sized groups. 
C) comparison models. 
D) ratio models. 
A) units partitioned into equal-sized groups. 
B) sets partitioned into equal sized groups. 
C) comparison models. 
D) ratio models.

Question 14

Which of these coins or units of currency will NOT help students understand decimal fractions?

Accepted Answer

A) 5¢ 
B) 1¢ 
C) 10¢ 
D) $1 
A) 5¢ 
B) 1¢ 
C) 10¢ 
D) $1

Question 15

Which of the following has the fractions in ascending order?

Accepted Answer

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

Question 16

According to the research by Hunting, children have the most difficulty showing fractions that are:

Accepted Answer

A) part of a set of discrete objects. 
B) part of a whole. 
C) ratios. 
D) part of a continuous object such as a number line. 
A) part of a set of discrete objects. 
B) part of a whole. 
C) ratios. 
D) part of a continuous object such as a number line.

Question 17

If a child takes ½ of 12 cookies, this is an example of a situation represented by:

Accepted Answer

A) unit partitioned into equal-size parts. 
B) set partitioned into equal-size groups. 
C) comparison model. 
D) indicated division. 
A) unit partitioned into equal-size parts. 
B) set partitioned into equal-size groups. 
C) comparison model. 
D) indicated division.

Question 18

Explain what is meant by the indicated division representation of fractions.

Accepted Answer

The indicated division representation of

Question 19

Decimal fractions are similar to common fractions except that:

Accepted Answer

A) they are nonterminating, nonrepeating. 
B) they have denominators that are powers of ten. 
C) they are smaller than common fractions. 
D) they cannot be converted into percentages. 
A) they are nonterminating, nonrepeating. 
B) they have denominators that are powers of ten. 
C) they are smaller than common fractions. 
D) they cannot be converted into percentages.

Question 20

Taking a cake and dividing it into 6 equal slices is a situation represented by:

Accepted Answer

A) unit partitioned into equal-size parts. 
B) set partitioned into equal-size groups. 
C) expression of ratios. 
D) indicated division. 
A) unit partitioned into equal-size parts. 
B) set partitioned into equal-size groups. 
C) expression of ratios. 
D) indicated division.

A bag of marbles has 5 red, 4 blue, and 7 green marbles. Which of the following fractions is not a part-whole representation?

Compare To .

If a base-10 flat represents 1, then the unit represents:

The purpose in using the terms common fractions and decimal fractions is to:

The best way to teach children fractions and decimals is to:

Why should a teacher use the terms common fractions and decimal fractions rather than just the terms fractions and decimals ?

Improper fractions are:

How would you help a child who thinks that when you multiply two numbers the result is always larger than either of the two factors?

The concept of a fractional part of a set should only be introduced after children:

If the largest base-10 cube (10 units × 10 units × 10 units)represents 1, then the small unit (1 unit × 1 unit × 1 unit)represents:

Draw two different illustrations of improper fractions to explain why they are equivalent to mixed numerals.

Equivalent fractions are best taught using:

Which of these coins or units of currency will NOT help students understand decimal fractions?

Which of the following has the fractions in ascending order?

According to the research by Hunting, children have the most difficulty showing fractions that are:

If a child takes ½ of 12 cookies, this is an example of a situation represented by:

Explain what is meant by the indicated division representation of fractions.

Decimal fractions are similar to common fractions except that:

Taking a cake and dividing it into 6 equal slices is a situation represented by:

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

Extending Understanding of Common and Decimal Fractions

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

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 12: Developing Understanding of Common and Decimal Fractions

A bag of marbles has 5 red, 4 blue, and 7 green marbles. Which of the following fractions is not a part-whole representation?

Compare To .

If a base-10 flat represents 1, then the unit represents:

The purpose in using the terms common fractions and decimal fractions is to:

The best way to teach children fractions and decimals is to:

Why should a teacher use the terms common fractions and decimal fractions rather than just the terms fractions and decimals ?

Improper fractions are:

How would you help a child who thinks that when you multiply two numbers the result is always larger than either of the two factors?

The concept of a fractional part of a set should only be introduced after children:

If the largest base-10 cube (10 units × 10 units × 10 units)represents 1, then the small unit (1 unit × 1 unit × 1 unit)represents:

Draw two different illustrations of improper fractions to explain why they are equivalent to mixed numerals.

Equivalent fractions are best taught using:

Which of these coins or units of currency will NOT help students understand decimal fractions?

Which of the following has the fractions in ascending order?

According to the research by Hunting, children have the most difficulty showing fractions that are:

If a child takes ½ of 12 cookies, this is an example of a situation represented by:

Explain what is meant by the indicated division representation of fractions.

Decimal fractions are similar to common fractions except that:

Taking a cake and dividing it into 6 equal slices is a situation represented by:

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

Extending Understanding of Common and Decimal Fractions

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

Thinking Algebraically

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

Investigating Probability

Filters