Question 1

Which is an example of the compensation strategy?

Accepted Answer

A) 63 × 5 = 63 + 63 + 63 + 63 + 63 = 315 
B) 27 × 4 = 20 × 4 + 7 × 4 = 80 + 28 = 108 
C) 46 × 3 = 46 × 2 (double)+ 46 = 92 + 46 = 138 
D) 27 × 4 is about 30 (27 + 3)× 4 = 120; then subtract out the extra 3 × 4,so 120 -12 = 108 
A) 63 × 5 = 63 + 63 + 63 + 63 + 63 = 315 
B) 27 × 4 = 20 × 4 + 7 × 4 = 80 + 28 = 108 
C) 46 × 3 = 46 × 2 (double)+ 46 = 92 + 46 = 138 
D) 27 × 4 is about 30 (27 + 3)× 4 = 120; then subtract out the extra 3 × 4,so 120 -12 = 108 D

Question 2

Which of the following is a strategy that is more applicable for multiplying single digits than multidigits?

Accepted Answer

A) Compatible numbers. 
B) Doubling. 
C) Partitioning. 
D) Complete number. 
A) Compatible numbers. 
B) Doubling. 
C) Partitioning. 
D) Complete number. B

Question 3

What compensation strategy works when you are multiplying with 5 or 50?

Accepted Answer

A) Clusters. 
B) Partitioning the multiplier. 
C) Array. 
D) Half-then-double. 
A) Clusters. 
B) Partitioning the multiplier. 
C) Array. 
D) Half-then-double. D

Question 4

This model uses and a structure that automatically organizes proportionate equal groups and offers a visual demonstration of the commutative and distributive properties.

Accepted Answer

A) Clusters. 
B) Missing Factor. 
C) Area. 
D) Open array. 
A) Clusters. 
B) Missing Factor. 
C) Area. 
D) Open array.

Question 5

What is the reason why mental calculations estimates are more complex?

Accepted Answer

A) They require a deep knowledge of how numbers work. 
B) They require a solid knowledge of division procedures. 
C) They require a deep knowledge of partitioning. 
D) They require a solid knowledge of multiplication procedures. 
A) They require a deep knowledge of how numbers work. 
B) They require a solid knowledge of division procedures. 
C) They require a deep knowledge of partitioning. 
D) They require a solid knowledge of multiplication procedures.

Question 6

What invented strategy is represented by a student multiplying 58 x 6 by adding 58 + 58 to get 116 and then adding another 116 to get 232 and then adding another 116 to find the product of 348.

Accepted Answer

A) Partitioning. 
B) Clusters. 
C) Complete number. 
D) Compensation. 
A) Partitioning. 
B) Clusters. 
C) Complete number. 
D) Compensation.

Question 7

Division may be easier for students if they are familiar with the concepts.All of the statements below are related to division of whole numbers EXCEPT:

Accepted Answer

A) Partitioning. 
B) Fair sharing. 
C) Compensating. 
D) Repeated subtracting. 
A) Partitioning. 
B) Fair sharing. 
C) Compensating. 
D) Repeated subtracting.

Question 8

Identify the statement that represents what might be voiced when using the missing-factor strategy.

Accepted Answer

A) When no more tens can be distributed a ten is traded for ten ones. 
B) Seven goes into three hundred forty-five how many times? 
C) What number times seven will be close to three hundred forty-five with less than seven remaining? 
D) Split three hundred forty-five into 3 hundred,four tens and five ones. 
A) When no more tens can be distributed a ten is traded for ten ones. 
B) Seven goes into three hundred forty-five how many times? 
C) What number times seven will be close to three hundred forty-five with less than seven remaining? 
D) Split three hundred forty-five into 3 hundred,four tens and five ones.

Question 9

An intuitive idea about long division with two digit divisors is to round up the divisor.All of examples below support this idea EXCEPT:

Accepted Answer

A) Think about sharing base-ten pieces. 
B) Underestimate how many can be shared. 
C) Pretend there are fewer sets to share than there really are. 
D) Multiples of 10 are easier to compare. 
A) Think about sharing base-ten pieces. 
B) Underestimate how many can be shared. 
C) Pretend there are fewer sets to share than there really are. 
D) Multiples of 10 are easier to compare.

Question 10

What statement below describes the cluster problem approach for multidigit multiplication?

Accepted Answer

A) Encourages the use of known facts and combinations. 
B) Encourages the manipulation of only one of the factors. 
C) Encourages the use of an open array. 
D) Encourages the use of fair sharing. 
A) Encourages the use of known facts and combinations. 
B) Encourages the manipulation of only one of the factors. 
C) Encourages the use of an open array. 
D) Encourages the use of fair sharing.

Question 11

When developing the written record for multiplication computation it is helpful to encourage students to follow these suggestions EXCEPT:

Accepted Answer

A) Use sheets with base-ten columns. 
B) Record partial products. 
C) Record the combined product on one line. 
D) Mark the subdivisions of the factors. 
A) Use sheets with base-ten columns. 
B) Record partial products. 
C) Record the combined product on one line. 
D) Mark the subdivisions of the factors.

Question 12

What invented strategy is just like the standard algorithm except that students always begin with the largest values?

Accepted Answer

A) Partitioning. 
B) Clusters. 
C) Complete number. 
D) Compensation. 
A) Partitioning. 
B) Clusters. 
C) Complete number. 
D) Compensation.

Question 13

A number line can be helpful with teaching this estimation strategy.

Accepted Answer

A) Front end. 
B) Compatible. 
C) Rounding. 
D) Mental computation. 
A) Front end. 
B) Compatible. 
C) Rounding. 
D) Mental computation.

Question 14

Developing the standard algorithm for division teachers should used all of the following guides EXCEPT:

Accepted Answer

A) Partial quotients with a visual model. 
B) Partition or fair share model. 
C) Explicit trade method. 
D) Area model. 
A) Partial quotients with a visual model. 
B) Partition or fair share model. 
C) Explicit trade method. 
D) Area model.

Question 15

Cluster problems are an approach to developing the missing-factor strategy and capitalize on the inverse relationship between multiplication and division.All of equations below represent clusters that would help solve 381 divided by 72 EXCEPT:

Accepted Answer

A) 81 x 70 
B) 10 x 72 
C) 5 x 70 
D) 4 x 72 
A) 81 x 70 
B) 10 x 72 
C) 5 x 70 
D) 4 x 72

Question 16

What is the purpose of using a side bar chart in multidigit division?

Accepted Answer

A) Easier to come up with the actual answer. 
B) Uses a doubling strategy for considering the reasonableness of an answer. 
C) Increases the mental computation needed to find the answer. 
D) Uses the explicit trade notation. 
A) Easier to come up with the actual answer. 
B) Uses a doubling strategy for considering the reasonableness of an answer. 
C) Increases the mental computation needed to find the answer. 
D) Uses the explicit trade notation.

Question 17

One strategy for teaching computational estimation is to ask for information,but no answer.Which statement below would be an example of NOT gathering information?

Accepted Answer

A) Is it more or less that 1000? 
B) Is it between $400 and $700? 
C) Is one of these right? 
D) Is your estimate about how much? 
A) Is it more or less that 1000? 
B) Is it between $400 and $700? 
C) Is one of these right? 
D) Is your estimate about how much?

Question 18

Identify and discuss methods for supporting students' development of the standard algorithm for division.

Accepted Answer

Methods for supporti

Question 19

Representing a product of two factors may depend on the methods student experienced.What representation of 37 x 5 below would indicate that the student had worked with base-ten?

Accepted Answer

A) An array with 5 x 30 and 5 x 7. 
B) 5 groups of 30 lines and 5 groups of 7 dots. 
C) 5 circles with 37 items in each. 
D) 37 + 37 + 37 + 37 + 37 + 37 + 37. 
A) An array with 5 x 30 and 5 x 7. 
B) 5 groups of 30 lines and 5 groups of 7 dots. 
C) 5 circles with 37 items in each. 
D) 37 + 37 + 37 + 37 + 37 + 37 + 37.

Exam 13: Developing Strategies for Multiplication and Division Computation

Which is an example of the compensation strategy?

Which of the following is a strategy that is more applicable for multiplying single digits than multidigits?

What compensation strategy works when you are multiplying with 5 or 50?

This model uses and a structure that automatically organizes proportionate equal groups and offers a visual demonstration of the commutative and distributive properties.

What is the reason why mental calculations estimates are more complex?

What invented strategy is represented by a student multiplying 58 x 6 by adding 58 + 58 to get 116 and then adding another 116 to get 232 and then adding another 116 to find the product of 348.

Division may be easier for students if they are familiar with the concepts.All of the statements below are related to division of whole numbers EXCEPT:

Identify the statement that represents what might be voiced when using the missing-factor strategy.

An intuitive idea about long division with two digit divisors is to round up the divisor.All of examples below support this idea EXCEPT:

What statement below describes the cluster problem approach for multidigit multiplication?

When developing the written record for multiplication computation it is helpful to encourage students to follow these suggestions EXCEPT:

What invented strategy is just like the standard algorithm except that students always begin with the largest values?

A number line can be helpful with teaching this estimation strategy.

Developing the standard algorithm for division teachers should used all of the following guides EXCEPT:

Cluster problems are an approach to developing the missing-factor strategy and capitalize on the inverse relationship between multiplication and division.All of equations below represent clusters that would help solve 381 divided by 72 EXCEPT:

What is the purpose of using a side bar chart in multidigit division?

One strategy for teaching computational estimation is to ask for information,but no answer.Which statement below would be an example of NOT gathering information?

Identify and discuss methods for supporting students' development of the standard algorithm for division.

Representing a product of two factors may depend on the methods student experienced.What representation of 37 x 5 below would indicate that the student had worked with base-ten?

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

Algebraic Thinking, equations, and Functions

Developing Fraction Concepts

Developing Strategies for Fraction Computation

Developing Concepts of Fractions and Decimals

Proportional Reasoning

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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