Question 1

The key word strategy sends a wrong message about problem solving.Identify the statement below that would be offered in support of the key word strategy.

Accepted Answer

A) Encourages children to ignore meaning and structure of problems. 
B) Many problems do not have key words. 
C) Encourage children to use a list of key words with corresponding operations. 
D) Many problems have key words that may be misleading. 
A) Encourages children to ignore meaning and structure of problems. 
B) Many problems do not have key words. 
C) Encourage children to use a list of key words with corresponding operations. 
D) Many problems have key words that may be misleading. C

Question 2

Remainders have an effect on all of the following EXCEPT:

Accepted Answer

A) Discarded leaving a smaller whole-number answer. 
B) Rounded to the nearest whole number for an approximate answer. 
C) Fractional part left over and not included in the whole-number answer. 
D) Force the answer to the next highest whole number. 
A) Discarded leaving a smaller whole-number answer. 
B) Rounded to the nearest whole number for an approximate answer. 
C) Fractional part left over and not included in the whole-number answer. 
D) Force the answer to the next highest whole number. C

Question 3

What number property is illustrated by the problem 16 × 12 = 16(10 + 2)= 160 + 32 = 192?

Accepted Answer

A) Associative. 
B) Commutative. 
C) Identity. 
D) Distributive 
A) Associative. 
B) Commutative. 
C) Identity. 
D) Distributive D

Question 4

Which problem is an example of the comparison,product unknown (multiplication)structure?

Accepted Answer

A) Barry's sandwich shop offers 3 kinds of meat and 2 kinds of bread.How many different sandwiches could he make if he uses one meat and one kind of bread for each? 
B) Barry saved $12 and Jill saved $6.Barry saved how many times as much money as Jill? 
C) This month,Barry saved 8 times as much as last month.Last month,he saved $3.How much did Barry save this month? 
D) Barry saved $24 total,and he saved $6 each month.For how many months had he been saving? 
A) Barry's sandwich shop offers 3 kinds of meat and 2 kinds of bread.How many different sandwiches could he make if he uses one meat and one kind of bread for each? 
B) Barry saved $12 and Jill saved $6.Barry saved how many times as much money as Jill? 
C) This month,Barry saved 8 times as much as last month.Last month,he saved $3.How much did Barry save this month? 
D) Barry saved $24 total,and he saved $6 each month.For how many months had he been saving?

Question 5

Which problem represents the compare,difference unknown structure?

Accepted Answer

A) Maryann had 3 library books before she checked out 2 more.How many did she have all together? 
B) Maryann had 5 library books before she returned 2 of them.How many does she have now? 
C) Maryann had 4 nonfiction books and 2 fiction.How many books does she have? 
D) Maryann had 9 library books and Jim had 4.How many more did Maryann have than Jim? 
A) Maryann had 3 library books before she checked out 2 more.How many did she have all together? 
B) Maryann had 5 library books before she returned 2 of them.How many does she have now? 
C) Maryann had 4 nonfiction books and 2 fiction.How many books does she have? 
D) Maryann had 9 library books and Jim had 4.How many more did Maryann have than Jim?

Question 6

All of the statements below are related to teaching multiplication and division EXCEPT:

Accepted Answer

A) What to do with remainders. 
B) Symbolism as a way to record thinking. 
C) Physical models,drawings and equations. 
D) Think addition as multiplication and take away as division. 
A) What to do with remainders. 
B) Symbolism as a way to record thinking. 
C) Physical models,drawings and equations. 
D) Think addition as multiplication and take away as division.

Question 7

Identify the problem that represents the join,result unknown structure.

Accepted Answer

A) Maryann had 3 library books before she checked out 2 more.How many did she have all together? 
B) Maryann had 5 library books before she returned 2 of them.How many does she have now? 
C) Maryann had 4 nonfiction books and 2 fiction.How many more nonfiction books does she have? 
D) Maryann had 9 library books and Jim had 4.How many more did Maryann have than Jim? 
A) Maryann had 3 library books before she checked out 2 more.How many did she have all together? 
B) Maryann had 5 library books before she returned 2 of them.How many does she have now? 
C) Maryann had 4 nonfiction books and 2 fiction.How many more nonfiction books does she have? 
D) Maryann had 9 library books and Jim had 4.How many more did Maryann have than Jim?

Question 8

Which problem is an example of the equal groups,number of groups unknown structure?

Accepted Answer

A) This month,Barry saved 8 times as much as last month.Last month,he saved $3.How much did Barry save this month? 
B) Barry's sandwich shop offers 3 kinds of meat and 2 kinds of bread.How many different sandwiches could he make if he uses one meat and one kind of bread for each? 
C) Barry saved $12 and Jill saved $6.Barry saved how many times as much money as Jill? 
D) Barry saved $24 total,and he saved $6 each month.For how many months had he been saving? 
A) This month,Barry saved 8 times as much as last month.Last month,he saved $3.How much did Barry save this month? 
B) Barry's sandwich shop offers 3 kinds of meat and 2 kinds of bread.How many different sandwiches could he make if he uses one meat and one kind of bread for each? 
C) Barry saved $12 and Jill saved $6.Barry saved how many times as much money as Jill? 
D) Barry saved $24 total,and he saved $6 each month.For how many months had he been saving?

Question 9

Identify the statement that is describes the importance for children to know the relationship between addition and subtraction.

Accepted Answer

A) Writing symbolic equations. 
B) Using the associative property. 
C) Mental mathematics. 
D) Using the same models or pictures. 
A) Writing symbolic equations. 
B) Using the associative property. 
C) Mental mathematics. 
D) Using the same models or pictures.

Question 10

Identify the reason why the equal sign can confuse children.

Accepted Answer

A) Relational symbol not operations. 
B) Means the answer is coming up. 
C) Operations symbol not relational. 
D) Means the answer is the same as. 
A) Relational symbol not operations. 
B) Means the answer is coming up. 
C) Operations symbol not relational. 
D) Means the answer is the same as.

Question 11

What is the importance of students knowing the commutative property?

Accepted Answer

A) Applies to addition and subtraction. 
B) Helps students master basic facts because,if they really understand it,it reduces the number of individual facts they have to memorize. 
C) Should be demonstrated with problems that have the same sums but different addends. 
D) Is a term that even very young students should memorize? 
A) Applies to addition and subtraction. 
B) Helps students master basic facts because,if they really understand it,it reduces the number of individual facts they have to memorize. 
C) Should be demonstrated with problems that have the same sums but different addends. 
D) Is a term that even very young students should memorize?

Question 12

What statement identifies the importance of using contextual problems as a primary teaching tool?

Accepted Answer

A) Children demonstrate procedural fluency. 
B) Children identify the structure of the situations. 
C) Children construct richer understanding of the operations. 
D) Children connect problems to school mathematics. 
A) Children demonstrate procedural fluency. 
B) Children identify the structure of the situations. 
C) Children construct richer understanding of the operations. 
D) Children connect problems to school mathematics.

Question 13

A good lesson built on a context or related to a story would have all of the qualities listed below EXCEPT:

Accepted Answer

A) Words,pictures and numbers are used to explain solution. 
B) Students can easily find a solution with mental mathematics. 
C) Students can find mistakes in other's written solutions. 
D) Designed to anticipate and develop mathematical models of the real world. 
A) Words,pictures and numbers are used to explain solution. 
B) Students can easily find a solution with mental mathematics. 
C) Students can find mistakes in other's written solutions. 
D) Designed to anticipate and develop mathematical models of the real world.

Question 14

Which problem represents the separate,start unknown structure?

Accepted Answer

A) Maryann had 3 library books before she checked out 2 more.How many did she have all together? 
B) Maryann had 5 library books before she returned 2 of them.How many does she have now? 
C) Maryann had some nonfiction books and 2 fiction.She now has 8 books.How many did she begin with? 
D) Maryann had 9 library books and Jim had 4.How many more did Maryann have than Jim? 
A) Maryann had 3 library books before she checked out 2 more.How many did she have all together? 
B) Maryann had 5 library books before she returned 2 of them.How many does she have now? 
C) Maryann had some nonfiction books and 2 fiction.She now has 8 books.How many did she begin with? 
D) Maryann had 9 library books and Jim had 4.How many more did Maryann have than Jim?

Question 15

The use of model-based problems that students can use counters,bar diagrams,or number lines helps with their problem solving skills.Identify the statement below that describes what the use of bar diagrams can demonstrate.

Accepted Answer

A) Modeling two parts in two separate piles. 
B) Measuring distances from zero. 
C) Generating mean-making space. 
D) Breaking the shape apart to show multiple parts. 
A) Modeling two parts in two separate piles. 
B) Measuring distances from zero. 
C) Generating mean-making space. 
D) Breaking the shape apart to show multiple parts.

Question 16

Complete this statement,"Constructing models of arrays draws attention to..".

Accepted Answer

A) Factors connection with rows and columns. 
B) Factors and product. 
C) Number of rows and columns. 
D) Connection with measurement of area. 
A) Factors connection with rows and columns. 
B) Factors and product. 
C) Number of rows and columns. 
D) Connection with measurement of area.

Question 17

What statement below is the description of a Part-part-whole?

Accepted Answer

A) Involve comparison of two quantities. 
B) Two parts that are conceptually or mentally combined into one whole. 
C) The change is the amount being removed. 
D) Initial action of joining start amount,a change amount and resulting amount. 
A) Involve comparison of two quantities. 
B) Two parts that are conceptually or mentally combined into one whole. 
C) The change is the amount being removed. 
D) Initial action of joining start amount,a change amount and resulting amount.

Question 18

Problems with the join and separate structures,with the start or initial amount unknown,tend to be the hardest for students to understand and accurately solve.Identify the reason for they are more challenging for children to use.

Accepted Answer

A) Children can model the physical action. 
B) Children can act out the situation. 
C) Children cannot use counters for the initial amount. 
D) Children cannot grasp a quantity represents two things at once. 
A) Children can model the physical action. 
B) Children can act out the situation. 
C) Children cannot use counters for the initial amount. 
D) Children cannot grasp a quantity represents two things at once.

Question 19

Present and discuss two reasons for using contextual problems to teach addition,subtraction,multiplication and division.

Accepted Answer

Reasons fo

Question 20

Why is it significant for students to use think-addition for subtraction rather than take-away?

Accepted Answer

A) Mastering subtraction facts. 
B) Mastering symbolic representations. 
C) Mastering problem solving strategies. 
D) Mastering model-based solutions. 
A) Mastering subtraction facts. 
B) Mastering symbolic representations. 
C) Mastering problem solving strategies. 
D) Mastering model-based solutions.

Exam 9: Developing Meanings for the Operations

The key word strategy sends a wrong message about problem solving.Identify the statement below that would be offered in support of the key word strategy.

Remainders have an effect on all of the following EXCEPT:

What number property is illustrated by the problem 16 × 12 = 16(10 + 2)= 160 + 32 = 192?

Which problem is an example of the comparison,product unknown (multiplication)structure?

Which problem represents the compare,difference unknown structure?

All of the statements below are related to teaching multiplication and division EXCEPT:

Identify the problem that represents the join,result unknown structure.

Which problem is an example of the equal groups,number of groups unknown structure?

Identify the statement that is describes the importance for children to know the relationship between addition and subtraction.

Identify the reason why the equal sign can confuse children.

What is the importance of students knowing the commutative property?

What statement identifies the importance of using contextual problems as a primary teaching tool?

A good lesson built on a context or related to a story would have all of the qualities listed below EXCEPT:

Which problem represents the separate,start unknown structure?

The use of model-based problems that students can use counters,bar diagrams,or number lines helps with their problem solving skills.Identify the statement below that describes what the use of bar diagrams can demonstrate.

Complete this statement,"Constructing models of arrays draws attention to..".

What statement below is the description of a Part-part-whole?

Problems with the join and separate structures,with the start or initial amount unknown,tend to be the hardest for students to understand and accurately solve.Identify the reason for they are more challenging for children to use.

Present and discuss two reasons for using contextual problems to teach addition,subtraction,multiplication and division.

Why is it significant for students to use think-addition for subtraction rather than take-away?

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

Helping Students Master the Basic Facts

Developing Whole-Number Place-Value Concepts

Developing Strategies for Addition and Subtraction Computation

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

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