Question 1

What is a reason for students to create graphs of functions?

Accepted Answer

A) They are representing them in the manner that makes it the hardest to visualize relationships between patterns. 
B) They should be provided to them with examples within a real-life context. 
C) They should place the independent variable (step number)along the vertical axis. 
D) They should always be given specific data,equations,or numbers. 
A) They are representing them in the manner that makes it the hardest to visualize relationships between patterns. 
B) They should be provided to them with examples within a real-life context. 
C) They should place the independent variable (step number)along the vertical axis. 
D) They should always be given specific data,equations,or numbers. B

Question 2

Describe two different ways you could determine whether a function is linear.Describe how these two methods relate to one another,and a possible classroom activity that would help students to see this connection.

Accepted Answer

By examining the ratio of the changes between the independent and dependent variables and then graphing the values,they will see a connection between the fact that proportional changes in the independent and dependent variables results in a consistently linear slope in the graph.This could also lead to a more in-depth discussion of how proportional situations will always result in a linear graph and pass through the origin.

Question 3

Using expressions and variables in elementary classrooms should be evident with all of the following EXCEPT:

Accepted Answer

A) Involve situation with a specific unknown. 
B) Express it in symbols. 
C) Use letters in place of an open box. 
D) Use specific data,numbers and equations. 
A) Involve situation with a specific unknown. 
B) Express it in symbols. 
C) Use letters in place of an open box. 
D) Use specific data,numbers and equations. D

Question 4

Describe three different ways algebra can be connected to other areas of the mathematics curriculum.

Accepted Answer

There are many potential correct answers

Question 5

The statements below are students' views of equations EXCEPT.

Accepted Answer

A) Relational-structural view 
B) Relational-computational view 
C) Correspondence-relational view 
D) Operational view 
A) Relational-structural view 
B) Relational-computational view 
C) Correspondence-relational view 
D) Operational view

Question 6

Growing patterns can be represented in multiple ways.Identify the representation below that actually illustrates covariation.

Accepted Answer

A) A table. 
B) Symbols. 
C) Physical model. 
D) Graph. 
A) A table. 
B) Symbols. 
C) Physical model. 
D) Graph.

Question 7

Making sense of properties of the operations is a part of learning about generalizations.Identify the statement below that a student might use to explain the associative property of addition.

Accepted Answer

A) " When you add three number you can add the first two and then add the third or add the second and third and then the first.Either way you get the same answer". 
B) " When you add two number in any order you will get the same answer". 
C) " When you have a subtraction problem you can think addition by using the inverse". 
D) "When you add zero to any number you get the number you started with". 
A) " When you add three number you can add the first two and then add the third or add the second and third and then the first.Either way you get the same answer". 
B) " When you add two number in any order you will get the same answer". 
C) " When you have a subtraction problem you can think addition by using the inverse". 
D) "When you add zero to any number you get the number you started with".

Question 8

Identify the true statement for all proportional relationships.

Accepted Answer

A) They can only be represented accurately with an equation. 
B) They will always show in a graph as a straight line that passes through the origin. 
C) They will always have a positive slope. 
D) They are more challenging for students to generalize than a non-proportional one. 
A) They can only be represented accurately with an equation. 
B) They will always show in a graph as a straight line that passes through the origin. 
C) They will always have a positive slope. 
D) They are more challenging for students to generalize than a non-proportional one.

Question 9

Three of these are the strands of algebraic thinking described by Blanton and Kaput.Which one is not considered a strand by itself?

Accepted Answer

A) Structures in the number system. 
B) Meaningful use of symbols. 
C) Mathematical modeling. 
D) Patterns,relations and functions. 
A) Structures in the number system. 
B) Meaningful use of symbols. 
C) Mathematical modeling. 
D) Patterns,relations and functions.

Question 10

The term algebraic thinking is used instead of the term algebra because algebraic thinking goes beyond the topics that are typically found in an algebra course.All of the ideas below could be used as "algebraified" activity EXCEPT:

Accepted Answer

A) Familiar formulas for measuring a geometric shape. 
B) Data from census reports and survey. 
C) Experiments that look for functional relations. 
D) Strategies for model-based problems. 
A) Familiar formulas for measuring a geometric shape. 
B) Data from census reports and survey. 
C) Experiments that look for functional relations. 
D) Strategies for model-based problems.

Question 11

Complete this statement,"The use of a two-pan balance scale or semi-concrete drawings of a balance help develop a strong understanding of..".

Accepted Answer

A) Pattern identification. 
B) Function patterns. 
C) Abstract concept of equality. 
D) Conjecture. 
A) Pattern identification. 
B) Function patterns. 
C) Abstract concept of equality. 
D) Conjecture.

Question 12

All of the statements below relate students' understanding of the equal sign EXCEPT:

Accepted Answer

A) Understanding or confusion with the equal sign does not usually cause difficulties understanding the process of solving equations. 
B) Because of their early experiences,many students tend to believe the equal sign represents "and the answer is". 
C) The equal sign is one of the principle methods of representing important relationships within the number system. 
D) The equal function can be represented concretely by a number balance scale,which can lead to deeper conceptual understanding. 
A) Understanding or confusion with the equal sign does not usually cause difficulties understanding the process of solving equations. 
B) Because of their early experiences,many students tend to believe the equal sign represents "and the answer is". 
C) The equal sign is one of the principle methods of representing important relationships within the number system. 
D) The equal function can be represented concretely by a number balance scale,which can lead to deeper conceptual understanding.

Question 13

Students need to be familiar and use the language to describe functions of graphs.All of vocabulary below will support the knowledge of functions EXCEPT:

Accepted Answer

A) Discrete are isolated or selected values. 
B) Covariational is the input generated by the output 
C) Range is the corresponding possible values for the dependent variable. 
D) Domain is the possible values of the independent variable. 
A) Discrete are isolated or selected values. 
B) Covariational is the input generated by the output 
C) Range is the corresponding possible values for the dependent variable. 
D) Domain is the possible values of the independent variable.

Question 14

This method of recording can help students think about how two quantities vary from step to step.

Accepted Answer

A) Grid paper. 
B) Hundreds chart. 
C) Table. 
D) Open number line. 
A) Grid paper. 
B) Hundreds chart. 
C) Table. 
D) Open number line.

Question 15

Patterns are found in all areas of mathematics.Below are examples of repeating patterns EXCEPT:

Accepted Answer

A) Patterns that have core the repeats. 
B) Patterns in number i.e.place value. 
C) Patterns in seasons,days,music. 
D) Patterns in skip counting. 
A) Patterns that have core the repeats. 
B) Patterns in number i.e.place value. 
C) Patterns in seasons,days,music. 
D) Patterns in skip counting.

Question 16

What is one method that students can use to show that they are generalizing properties?

Accepted Answer

A) Symbols. 
B) Written examples. 
C) Equations with numbers. 
D) Model with manipulatives. 
A) Symbols. 
B) Written examples. 
C) Equations with numbers. 
D) Model with manipulatives.

Question 17

Mathematical modeling is one of the eight Standards for Mathematical Practice.Three of the statements reference the true meaning of mathematical modeling.Identify the one that is often mistaken for modeling.

Accepted Answer

A) Links classroom mathematics to everyday life. 
B) Process of choosing appropriate mathematics for situations. 
C) Visual models,such as manipulatives and drawings of pattern. 
D) Analyzing empirical situations to better understand. 
A) Links classroom mathematics to everyday life. 
B) Process of choosing appropriate mathematics for situations. 
C) Visual models,such as manipulatives and drawings of pattern. 
D) Analyzing empirical situations to better understand.

Question 18

All of the following are examples of algebraic thinking a young student would demonstrate in kindergarten EXCEPT:

Accepted Answer

A) Acting out a situation. 
B) Recognizing patterns in sounds (clapping). 
C) Applying properties of addition. 
D) Adding and subtracting with fingers. 
A) Acting out a situation. 
B) Recognizing patterns in sounds (clapping). 
C) Applying properties of addition. 
D) Adding and subtracting with fingers.

Question 19

These patterns are technically referred to as sequences and they involve a step-to-step progression.

Accepted Answer

A) Recursive. 
B) Covariational. 
C) Correspondence. 
D) Linear. 
A) Recursive. 
B) Covariational. 
C) Correspondence. 
D) Linear.

Question 20

A tool called __________________,is normally thought of as teaching numeration but can help students to connect place value and algebraic thinking.

Accepted Answer

A) Open number line. 
B) Grid paper. 
C) Calculator. 
D) Hundreds chart. 
A) Open number line. 
B) Grid paper. 
C) Calculator. 
D) Hundreds chart.

Exam 14: Algebraic Thinking, equations, and Functions

What is a reason for students to create graphs of functions?

Describe two different ways you could determine whether a function is linear.Describe how these two methods relate to one another,and a possible classroom activity that would help students to see this connection.

Using expressions and variables in elementary classrooms should be evident with all of the following EXCEPT:

Describe three different ways algebra can be connected to other areas of the mathematics curriculum.

The statements below are students' views of equations EXCEPT.

Growing patterns can be represented in multiple ways.Identify the representation below that actually illustrates covariation.

Making sense of properties of the operations is a part of learning about generalizations.Identify the statement below that a student might use to explain the associative property of addition.

Identify the true statement for all proportional relationships.

Three of these are the strands of algebraic thinking described by Blanton and Kaput.Which one is not considered a strand by itself?

The term algebraic thinking is used instead of the term algebra because algebraic thinking goes beyond the topics that are typically found in an algebra course.All of the ideas below could be used as "algebraified" activity EXCEPT:

Complete this statement,"The use of a two-pan balance scale or semi-concrete drawings of a balance help develop a strong understanding of..".

All of the statements below relate students' understanding of the equal sign EXCEPT:

Students need to be familiar and use the language to describe functions of graphs.All of vocabulary below will support the knowledge of functions EXCEPT:

This method of recording can help students think about how two quantities vary from step to step.

Patterns are found in all areas of mathematics.Below are examples of repeating patterns EXCEPT:

What is one method that students can use to show that they are generalizing properties?

Mathematical modeling is one of the eight Standards for Mathematical Practice.Three of the statements reference the true meaning of mathematical modeling.Identify the one that is often mistaken for modeling.

All of the following are examples of algebraic thinking a young student would demonstrate in kindergarten EXCEPT:

These patterns are technically referred to as sequences and they involve a step-to-step progression.

A tool called __________________,is normally thought of as teaching numeration but can help students to connect place value and algebraic thinking.

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

Developing Strategies for Multiplication and Division Computation

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