Question 1

What is the least common multiple (LCM)for 36 and 48?

Accepted Answer

A) 288 
B) 144 
C) 192 
D) 576 
A) 288 
B) 144 
C) 192 
D) 576 B

Question 2

The following statements below concerning the least common multiple (LCM)are all true except for:

Accepted Answer

A) The LCM is used to find the common denominator of fractions. 
B) The LCM of 24, 36, and 70 is 23 × 32 × 5 × 7. 
C) The LCM is used to reduce fractions down to lowest terms. 
D) The LCM is confusing to children because this "least" number can be larger than any of the numbers under consideration. 
A) The LCM is used to find the common denominator of fractions. 
B) The LCM of 24, 36, and 70 is 23 × 32 × 5 × 7. 
C) The LCM is used to reduce fractions down to lowest terms. 
D) The LCM is confusing to children because this "least" number can be larger than any of the numbers under consideration. C

Question 3

Explain how you would help children make the transition between common fractions and decimal fractions.

Accepted Answer

To help children make the transition between common fractions and decimal fractions, I would use a variety of hands-on and visual aids to demonstrate the relationship between the two.

First, I would start by using visual representations such as fraction bars or circles to show how a fraction can be represented as a decimal. For example, I would show that 1/2 is the same as 0.5, and 1/4 is the same as 0.25. This visual representation helps children see the connection between the two forms.

Next, I would provide plenty of practice problems that require converting between fractions and decimals. This could include simple exercises like converting 1/4 to a decimal, or more complex problems like converting 3/5 to a decimal. By practicing these conversions, children can become more comfortable with the process and develop a deeper understanding of the relationship between fractions and decimals.

I would also use real-life examples to show how decimals are used in everyday situations. For example, I might show how prices at the grocery store are often listed in decimal form, or how measurements such as 1.5 meters are used in construction. By connecting decimals to real-world applications, children can see the practical value of understanding and being able to convert between fractions and decimals.

Overall, by using visual aids, providing plenty of practice, and connecting decimals to real-life examples, I would help children make a smooth transition between common fractions and decimal fractions.

Question 4

John wants to get ⅔ of his money out of the bank, but he has to pay his brother ⅙ of that. Which of the following statements shows what John would have left of the amount he took out of the bank, after paying his brother?

Accepted Answer

A) ⅔ - ⅙ 
B) ⅔ × ⅙ 
C) 1 - (⅔ × ⅙) 
D) ⅔ × ⅚ 
A) ⅔ - ⅙ 
B) ⅔ × ⅙ 
C) 1 - (⅔ × ⅙) 
D) ⅔ × ⅚

Question 5

Accepted Answer

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

Question 6

What is a correct expansion of 37.206?

Accepted Answer

A) (3 × 102)+ (7 × 100)+ (2 × 101)+ (6 × 103) 
B) (3 × 10)+ (7 × 100)+ (2 × 1)+ (0 × 10−1)+ (6 × 10−2) 
C) (3 × 101)+ (7 × 100)+ (2 × 10−1)+ (6 × 10−3) 
D) (3 × 10)+ (7 × 1)+ (2 × 0.1)+ (6 × 0.01) 
A) (3 × 102)+ (7 × 100)+ (2 × 101)+ (6 × 103) 
B) (3 × 10)+ (7 × 100)+ (2 × 1)+ (0 × 10−1)+ (6 × 10−2) 
C) (3 × 101)+ (7 × 100)+ (2 × 10−1)+ (6 × 10−3) 
D) (3 × 10)+ (7 × 1)+ (2 × 0.1)+ (6 × 0.01)

Question 7

"Lining up the decimal points" is the rote rule that children learn when adding and subtracting decimal fractions. The reasoning behind this rule is:

Accepted Answer

A) children are following the "one place value at a time" rule when adding and subtracting, similar to what they followed with whole numbers. 
B) children will not add together or subtract the wrong numbers. 
C) that base-10 blocks won't be necessary for conceptual understanding in this case. 
D) that real-life examples won't be necessary for conceptual understanding in this case. 
A) children are following the "one place value at a time" rule when adding and subtracting, similar to what they followed with whole numbers. 
B) children will not add together or subtract the wrong numbers. 
C) that base-10 blocks won't be necessary for conceptual understanding in this case. 
D) that real-life examples won't be necessary for conceptual understanding in this case.

Question 8

12 - 8.34 =

Accepted Answer

A) 4.66 
B) 3.66 
C) 4.34 
D) 6.34 
A) 4.66 
B) 3.66 
C) 4.34 
D) 6.34

Question 9

A student solved 
   
 by subtracting 6 - 4 to obtain 2 and 
   
 to obtain 
   
. She then subtracted 
   
 to get 
   
. Is this a legitimate algorithm? Will it always work? Explain why or why not.

Accepted Answer

The answer of A student solved 
   
 by...

Question 10

A half-gallon of milk is poured into 16 equal-sized containers. Which of the following is true with respect to this statement?

Accepted Answer

A) This is an example of the partitive model. 
B) This is an example of the repeated addition model. 
C) This is an example of the measurement model. 
D) The correct mathematical statement for this situation is ½ × 16. 
A) This is an example of the partitive model. 
B) This is an example of the repeated addition model. 
C) This is an example of the measurement model. 
D) The correct mathematical statement for this situation is ½ × 16.

Question 11

Common fractions with denominators of factors of 2s and 5s only are known as:

Accepted Answer

A) repeating decimals. 
B) terminating decimals. 
C) both repeating and terminating decimals. 
D) neither repeating nor terminating decimals. 
A) repeating decimals. 
B) terminating decimals. 
C) both repeating and terminating decimals. 
D) neither repeating nor terminating decimals.

Question 12

Given the problem below, which of the following is not a correct strategy to illustrate this problem?
Juan practiced piano for ¾ hour on Tuesday, Wednesday, and Thursday. How long did he practice altogether?

Accepted Answer

A) Take 3 fraction strips 1 unit long and mark off  ¾ of each strip. Lay the pieces together end to end and then separate them into halves and fourths. Add all the halves together and fourths together until all possible wholes and fractions are left. 
B) Use a clock to mark off the ¾ hours, starting at 12:00 and continuing around the clock marking off ¾ portions until ending up at 2:30. 
C) Using a number line, starting at 0, marking off the number line in fourths, then marking off ¾ units three times. 
D) Use fraction squares, shade in ¾ on each, then adding together the pieces, forming wholes and fractional parts. 
A) Take 3 fraction strips 1 unit long and mark off  ¾ of each strip. Lay the pieces together end to end and then separate them into halves and fourths. Add all the halves together and fourths together until all possible wholes and fractions are left. 
B) Use a clock to mark off the ¾ hours, starting at 12:00 and continuing around the clock marking off ¾ portions until ending up at 2:30. 
C) Using a number line, starting at 0, marking off the number line in fourths, then marking off ¾ units three times. 
D) Use fraction squares, shade in ¾ on each, then adding together the pieces, forming wholes and fractional parts.

Question 13

A student multiplied 5½ × 3¼, but was not sure of his answer. Which of the following mathematical statements that he listed on his paper has the same meaning as the given problem?

Accepted Answer

A) (5 × 3)+ (½ × ¼) 
B) (5 + ½)× 3 × ¼ 
C) (5 × ½)+ (3 × ¼) 
D) (5 + ½)× (3 + ¼) 
A) (5 × 3)+ (½ × ¼) 
B) (5 + ½)× 3 × ¼ 
C) (5 × ½)+ (3 × ¼) 
D) (5 + ½)× (3 + ¼)

Question 14

How could you explain the density property to children?

Accepted Answer

Density is a measure of how tightly pack

Question 15

Everett found out that the exchange rate between Singapore dollars and South African rand was: 
1 SGD = 4.2 ZAR 
Everett changed 3,000 Singapore dollars into South African rand at this exchange rate. How much money in South African rand did Everett get?

Accepted Answer

The answer of Everett found out that the exchange rate...

Question 16

Accepted Answer

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

Question 17

Tyrone asked Mr. Jones what the answer to 0.7 × 0.3 would be. Which of the following is the best method that Mr. Jones could use to help Tyrone understand this problem conceptually?

Accepted Answer

A) Mr. Jones could tell him to count the number of decimal places to the right of each decimal, then to multiply the two numbers as if they were whole numbers, and count back that number of places from the right. 
B) Mr. Jones could tell him to use base-10 pieces for each decimal, by laying down 7 longs 3 times, then to go back one decimal. 
C) Mr. Jones could tell him to change each decimal into fractions, multiply out the fractions, then change back into decimals. 
D) Mr. Jones could tell him to add 7 tenths three times, then to divide by one tenth. 
A) Mr. Jones could tell him to count the number of decimal places to the right of each decimal, then to multiply the two numbers as if they were whole numbers, and count back that number of places from the right. 
B) Mr. Jones could tell him to use base-10 pieces for each decimal, by laying down 7 longs 3 times, then to go back one decimal. 
C) Mr. Jones could tell him to change each decimal into fractions, multiply out the fractions, then change back into decimals. 
D) Mr. Jones could tell him to add 7 tenths three times, then to divide by one tenth.

Question 18

Illustrate and describe how tangrams can be used to develop the concepts of ½ and ¼ .

Accepted Answer

Tangrams can be used to develop the conc

Question 19

9.6 × 4.23 =

Accepted Answer

A) 40.68 
B) 4.068 
C) 406.8 
D) 4068.0 
A) 40.68 
B) 4.068 
C) 406.8 
D) 4068.0

Question 20

Accepted Answer

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

What is the least common multiple (LCM)for 36 and 48?

The following statements below concerning the least common multiple (LCM)are all true except for:

Explain how you would help children make the transition between common fractions and decimal fractions.

John wants to get ⅔ of his money out of the bank, but he has to pay his brother ⅙ of that. Which of the following statements shows what John would have left of the amount he took out of the bank, after paying his brother?

What is a correct expansion of 37.206?

"Lining up the decimal points" is the rote rule that children learn when adding and subtracting decimal fractions. The reasoning behind this rule is:

12 - 8.34 =

A student solved by subtracting 6 - 4 to obtain 2 and to obtain . She then subtracted to get . Is this a legitimate algorithm? Will it always work? Explain why or why not.

A half-gallon of milk is poured into 16 equal-sized containers. Which of the following is true with respect to this statement?

Common fractions with denominators of factors of 2s and 5s only are known as:

Given the problem below, which of the following is not a correct strategy to illustrate this problem? Juan practiced piano for ¾ hour on Tuesday, Wednesday, and Thursday. How long did he practice altogether?

A student multiplied 5½ × 3¼, but was not sure of his answer. Which of the following mathematical statements that he listed on his paper has the same meaning as the given problem?

How could you explain the density property to children?

Everett found out that the exchange rate between Singapore dollars and South African rand was: 1 SGD = 4.2 ZAR Everett changed 3,000 Singapore dollars into South African rand at this exchange rate. How much money in South African rand did Everett get?

Tyrone asked Mr. Jones what the answer to 0.7 × 0.3 would be. Which of the following is the best method that Mr. Jones could use to help Tyrone understand this problem conceptually?

Illustrate and describe how tangrams can be used to develop the concepts of ½ and ¼ .

9.6 × 4.23 =

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

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

Exam 13: Extending Understanding of Common and Decimal Fractions

What is the least common multiple (LCM)for 36 and 48?

The following statements below concerning the least common multiple (LCM)are all true except for:

Explain how you would help children make the transition between common fractions and decimal fractions.

John wants to get ⅔ of his money out of the bank, but he has to pay his brother ⅙ of that. Which of the following statements shows what John would have left of the amount he took out of the bank, after paying his brother?

What is a correct expansion of 37.206?

"Lining up the decimal points" is the rote rule that children learn when adding and subtracting decimal fractions. The reasoning behind this rule is:

12 - 8.34 =

A student solved by subtracting 6 - 4 to obtain 2 and to obtain . She then subtracted to get . Is this a legitimate algorithm? Will it always work? Explain why or why not.

A half-gallon of milk is poured into 16 equal-sized containers. Which of the following is true with respect to this statement?

Common fractions with denominators of factors of 2s and 5s only are known as:

Given the problem below, which of the following is not a correct strategy to illustrate this problem? Juan practiced piano for ¾ hour on Tuesday, Wednesday, and Thursday. How long did he practice altogether?

A student multiplied 5½ × 3¼, but was not sure of his answer. Which of the following mathematical statements that he listed on his paper has the same meaning as the given problem?

How could you explain the density property to children?

Everett found out that the exchange rate between Singapore dollars and South African rand was: 1 SGD = 4.2 ZAR Everett changed 3,000 Singapore dollars into South African rand at this exchange rate. How much money in South African rand did Everett get?

Tyrone asked Mr. Jones what the answer to 0.7 × 0.3 would be. Which of the following is the best method that Mr. Jones could use to help Tyrone understand this problem conceptually?

Illustrate and describe how tangrams can be used to develop the concepts of ½ and ¼ .

9.6 × 4.23 =

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

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