Question 1

Which of the following is a true statement about standard algorithms?

Accepted Answer

A) Students will frequently invent them on their own if they are given the time to experiment. 
B) They cannot be taught in a way that would help students understand the meaning behind the steps. 
C) In order to use them,students should be required to understand why they work and explain their steps. 
D) There are no differences between various cultures. 
A) Students will frequently invent them on their own if they are given the time to experiment. 
B) They cannot be taught in a way that would help students understand the meaning behind the steps. 
C) In order to use them,students should be required to understand why they work and explain their steps. 
D) There are no differences between various cultures. C

Question 2

Modern technology has made computation easier.Identify the true statement below.

Accepted Answer

A) But mental computation strategies can be faster than using technology. 
B) And recent studies have found that a very low percentage of adults use mental math computation in everyday life. 
C) And mental computation contributes to diminished number sense. 
D) So the ability to compute fluently without technology is no longer needed for most people. 
A) But mental computation strategies can be faster than using technology. 
B) And recent studies have found that a very low percentage of adults use mental math computation in everyday life. 
C) And mental computation contributes to diminished number sense. 
D) So the ability to compute fluently without technology is no longer needed for most people. A

Question 3

The models listed below are used to support the development of invented strategies EXCEPT:

Accepted Answer

A) Jump strategy. 
B) Split strategy. 
C) Take-Away strategy. 
D) Shortcut strategy. 
A) Jump strategy. 
B) Split strategy. 
C) Take-Away strategy. 
D) Shortcut strategy. D

Question 4

Cultural differences are evident in algorithms.What reason below supports teaching for mathematics?

Accepted Answer

A) Notational algorithms. 
B) Customary algorithms. 
C) Mental algorithms. 
D) Invented algorithms. 
A) Notational algorithms. 
B) Customary algorithms. 
C) Mental algorithms. 
D) Invented algorithms.

Question 5

The general approach for teaching the subtraction standard algorithm is the same as addition.What statement below would not be a problem when using the standard algorithm for addition?

Accepted Answer

A) Develop the written record. 
B) Begin with models. 
C) Trades made after the column in the left has been done. 
D) Exercises with zeros. 
A) Develop the written record. 
B) Begin with models. 
C) Trades made after the column in the left has been done. 
D) Exercises with zeros.

Question 6

The Common Core State Standards states that student should learn a variety of strategies.These strategies should be based on all of the following EXCEPT:

Accepted Answer

A) Place value. 
B) Sophisticated thinking. 
C) Properties of operations. 
D) Prior to the standard algorithm. 
A) Place value. 
B) Sophisticated thinking. 
C) Properties of operations. 
D) Prior to the standard algorithm.

Question 7

All of the following provide an example of a method used for computation EXCEPT:

Accepted Answer

A) Standard algorithms. 
B) Student-invented strategies. 
C) Discourse modeling. 
D) Computational estimation. 
A) Standard algorithms. 
B) Student-invented strategies. 
C) Discourse modeling. 
D) Computational estimation.

Question 8

Students who have learned this strategy for their "basic facts" can use it effectively with solving problems with multidigit numbers.

Accepted Answer

A) Jump strategy. 
B) Shortcut strategy. 
C) Think addition strategy. 
D) Split strategy. 
A) Jump strategy. 
B) Shortcut strategy. 
C) Think addition strategy. 
D) Split strategy.

Question 9

There are important things to remember when teaching the standard algorithm.Identify the statement that does not belong.

Accepted Answer

A) Good choice in some situations. 
B) Require written record first. 
C) Require concrete models first. 
D) Explicit connections are made between concept and procedure. 
A) Good choice in some situations. 
B) Require written record first. 
C) Require concrete models first. 
D) Explicit connections are made between concept and procedure.

Question 10

Complete the statement,"When creating a classroom environment appropriate for inventing strategies..".

Accepted Answer

A) The teacher should immediately confirm that a student's answer is correct,in order to build his/her confidence. 
B) The teacher should attempt to move unsophisticated ideas to more sophisticated thinking through coaching and questioning. 
C) The teacher should discourage student-to-student conversations in order to provide students with a quiet environment to think. 
D) The teacher should encourage the use of naked numbers as a starting point. 
A) The teacher should immediately confirm that a student's answer is correct,in order to build his/her confidence. 
B) The teacher should attempt to move unsophisticated ideas to more sophisticated thinking through coaching and questioning. 
C) The teacher should discourage student-to-student conversations in order to provide students with a quiet environment to think. 
D) The teacher should encourage the use of naked numbers as a starting point.

Question 11

Describe the three types estimation and give an example of how they could be used in teaching computational estimation.

Accepted Answer

Types of e

Question 12

All of the statements below represent the differences between invented strategies and standard algorithms EXCEPT:

Accepted Answer

A) A range of flexible options. 
B) Left-handed rather than right-handed. 
C) Number oriented rather than digit oriented. 
D) Basis for mental computation and estimation. 
A) A range of flexible options. 
B) Left-handed rather than right-handed. 
C) Number oriented rather than digit oriented. 
D) Basis for mental computation and estimation.

Question 13

When a problem has a number that is a multiple of ___ or close to ___it is an example of a problem that you leave one number intact and subtract from it.

Accepted Answer

A) 85 - 35 
B) 85 - 64 
C) 85 - 29 
D) 85 - 56 
A) 85 - 35 
B) 85 - 64 
C) 85 - 29 
D) 85 - 56

Question 14

Complete the statement,"A mental computation strategy is a simple..".

Accepted Answer

A) Left-handed method. 
B) Invented strategy. 
C) Standard algorithm. 
D) One right way. 
A) Left-handed method. 
B) Invented strategy. 
C) Standard algorithm. 
D) One right way.

Question 15

Often siblings and family members are pushing the use of the standard algorithm while students are learning invented strategies.What is the course of action for a teacher?

Accepted Answer

A) Insist on invented strategies. 
B) Require students demonstrate both standard and invented strategies. 
C) Expect them to be responsible for the explanation of why any strategy works. 
D) Memorize the steps. 
A) Insist on invented strategies. 
B) Require students demonstrate both standard and invented strategies. 
C) Expect them to be responsible for the explanation of why any strategy works. 
D) Memorize the steps.

Question 16

The ten-structure of the number system is important to extend students thinking beyond counting.All of the activities below reference a strategy for calculation EXCEPT:

Accepted Answer

A) Using decade number. 
B) Odd or even. 
C) Up over 10. 
D) Add on to get to 10. 
A) Using decade number. 
B) Odd or even. 
C) Up over 10. 
D) Add on to get to 10.

Question 17

An open number can be used effectively for thinking about addition and subtraction.All of the reasons below support the use of an open number line EXCEPT:

Accepted Answer

A) Is less flexible than a numbered line. 
B) Eliminates confusion with hash marks and spaces. 
C) Less prone to computational errors. 
D) Helps with modeling student thinking. 
A) Is less flexible than a numbered line. 
B) Eliminates confusion with hash marks and spaces. 
C) Less prone to computational errors. 
D) Helps with modeling student thinking.

Question 18

All of the following could be examples of invented strategies for obtaining the sum of two-digit numbers EXCEPT:

Accepted Answer

A) Adding on tens and then ones (For example,to solve 24 + 35,think 24 + 30 = 54 and 5 more makes 59.) 
B) Using nicer numbers to estimate (For example,to solve 24 + 47,think 24 is close to 25 and 47 is closer to 45 so 24 + 47 = 25 + 45 = 70.) 
C) Moving some to make 10 (For example,to solve 24 + 35,move 6 from 35 to make 24 + 6 and then add 30 to the remaining 29.) 
D) Adding tens and adding ones then combining (For example,to solve 24 + 35,think 20 + 30 = 50 and 4 + 5 = 9 so 50 + 9 = 59.) 
A) Adding on tens and then ones (For example,to solve 24 + 35,think 24 + 30 = 54 and 5 more makes 59.) 
B) Using nicer numbers to estimate (For example,to solve 24 + 47,think 24 is close to 25 and 47 is closer to 45 so 24 + 47 = 25 + 45 = 70.) 
C) Moving some to make 10 (For example,to solve 24 + 35,move 6 from 35 to make 24 + 6 and then add 30 to the remaining 29.) 
D) Adding tens and adding ones then combining (For example,to solve 24 + 35,think 20 + 30 = 50 and 4 + 5 = 9 so 50 + 9 = 59.)

Question 19

What strategy for computational estimation after adding or subtracting do you adjust to correct for digits or numbers that were ignored?

Accepted Answer

A) Front-end. 
B) Rounding. 
C) Compatible numbers. 
D) Over and under. 
A) Front-end. 
B) Rounding. 
C) Compatible numbers. 
D) Over and under.

Question 20

Identify two or more ways that an open number line can be used to support the use of invented strategies.

Accepted Answer

An open number line can support learning

Exam 12: Developing Strategies for Addition and Subtraction Computation

Which of the following is a true statement about standard algorithms?

Modern technology has made computation easier.Identify the true statement below.

The models listed below are used to support the development of invented strategies EXCEPT:

Cultural differences are evident in algorithms.What reason below supports teaching for mathematics?

The general approach for teaching the subtraction standard algorithm is the same as addition.What statement below would not be a problem when using the standard algorithm for addition?

The Common Core State Standards states that student should learn a variety of strategies.These strategies should be based on all of the following EXCEPT:

All of the following provide an example of a method used for computation EXCEPT:

Students who have learned this strategy for their "basic facts" can use it effectively with solving problems with multidigit numbers.

There are important things to remember when teaching the standard algorithm.Identify the statement that does not belong.

Complete the statement,"When creating a classroom environment appropriate for inventing strategies..".

Describe the three types estimation and give an example of how they could be used in teaching computational estimation.

All of the statements below represent the differences between invented strategies and standard algorithms EXCEPT:

When a problem has a number that is a multiple of ___ or close to ___it is an example of a problem that you leave one number intact and subtract from it.

Complete the statement,"A mental computation strategy is a simple..".

Often siblings and family members are pushing the use of the standard algorithm while students are learning invented strategies.What is the course of action for a teacher?

The ten-structure of the number system is important to extend students thinking beyond counting.All of the activities below reference a strategy for calculation EXCEPT:

An open number can be used effectively for thinking about addition and subtraction.All of the reasons below support the use of an open number line EXCEPT:

All of the following could be examples of invented strategies for obtaining the sum of two-digit numbers EXCEPT:

What strategy for computational estimation after adding or subtracting do you adjust to correct for digits or numbers that were ignored?

Identify two or more ways that an open number line can be used to support the use of invented strategies.

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 Multiplication and Division 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

Filters

When a problem has a number that is a multiple of _ or close to _it is an example of a problem that you leave one number intact and subtract from it.