Question 1

Given the value for n , what is the function that produces the following data?

Accepted Answer

A) 2 n 
B) 2 n + 2 
C) n + 1 
D) 3 n - 1 
A) 2 n 
B) 2 n + 2 
C) n + 1 
D) 3 n - 1

Question 2

Under what circumstance, if any, is the following statement true?
8 + 7 = 3

Accepted Answer

A) It can never be true. 
B) If the equal sign were changed to a less than symbol. 
C) If this were related to the number of hours on a clock. 
D) If 8 and 7 were both decreased by 5. 
A) It can never be true. 
B) If the equal sign were changed to a less than symbol. 
C) If this were related to the number of hours on a clock. 
D) If 8 and 7 were both decreased by 5.

Question 3

Give three specific examples of different types of patterns that a teacher can use to introduce algebraic ideas to young children.

Accepted Answer

1. Number patterns: Teachers can use num

Question 4

The pattern below is referred to as what?
3, 9, 27, 81, …

Accepted Answer

A) the multiples of 3 
B) the cubes of 3 
C) the factors of 3 
D) the powers of 3 
A) the multiples of 3 
B) the cubes of 3 
C) the factors of 3 
D) the powers of 3

Question 5

In this pattern, what is the value of p when n = 10?

Accepted Answer

A) 15 
B) 60 
C) 50 
D) 55 
A) 15 
B) 60 
C) 50 
D) 55

Question 6

A child asks you what a function is. Give several specific examples that you would use to explain this important algebraic concept to her.

Accepted Answer

A function is a rule or relationship bet

Question 7

Using clock arithmetic, what is 6 + 7 = ?

Accepted Answer

A) 11 
B) 12 
C) 1 
D) 2 
A) 11 
B) 12 
C) 1 
D) 2

Question 8

What are the next two terms of the pattern below?
2, 1, 4, 3, 6, 5, …

Accepted Answer

A) 8, 7 
B) 7, 8 
C) 4, 7 
D) 7, 4 
A) 8, 7 
B) 7, 8 
C) 4, 7 
D) 7, 4

Question 9

Explain the role that patterning plays in helping develop children's algebraic reasoning.

Accepted Answer

Patterning plays a crucial role in helpi

Question 10

Research has shown that young children:

Accepted Answer

A) are incapable of understanding the role that variables play in equation solving. 
B) must have extensive practice with variables in order to understand them. 
C) must have a teacher who has an extensive background in algebra in order for the teacher to help children understand variables. 
D) can use variables to represent unknowns and then solve for the numbers that the variables represent. 
A) are incapable of understanding the role that variables play in equation solving. 
B) must have extensive practice with variables in order to understand them. 
C) must have a teacher who has an extensive background in algebra in order for the teacher to help children understand variables. 
D) can use variables to represent unknowns and then solve for the numbers that the variables represent.

Question 11

Which of the following is not a function?

Accepted Answer

A) {(A, 1), (B, 2), (C, 3)} 
B) {(A, 1), (B, 1), (C, 3)} 
C) {(A, 1), (B, 2), (B, 3), (C, 1), (C, 2)} 
D) {(A, 2), (B, 2), (C, 2)} 
A) {(A, 1), (B, 2), (C, 3)} 
B) {(A, 1), (B, 1), (C, 3)} 
C) {(A, 1), (B, 2), (B, 3), (C, 1), (C, 2)} 
D) {(A, 2), (B, 2), (C, 2)}

Question 12

Suppose that t = the number of tiles in a problem-solving situation, and a child tells you that 3 t means 3 tiles. How can you explain to him that his reasoning is faulty?

Accepted Answer

To explain to the child why the reasonin

Question 13

What are some specific ways that a teacher can introduce the idea of variables without actually using letters for variables?

Accepted Answer

One way a teacher can introduce the idea

Question 14

Explain some of the difficulties children have with understanding the role of the equal sign in equations.

Accepted Answer

Children often struggle with understandi

Question 15

For younger children, the equal sign in an equation may mean all of the following except for :

Accepted Answer

A) "The answer is coming." 
B) "Get ready to do something." 
C) "The left side is balanced with the right side of the equation." 
D) "Perform the operation on all of the numbers on the left side of the equal sign and put the result on the right side." 
A) "The answer is coming." 
B) "Get ready to do something." 
C) "The left side is balanced with the right side of the equation." 
D) "Perform the operation on all of the numbers on the left side of the equal sign and put the result on the right side."

Question 16

The best way to get children to understand equations is to give them:

Accepted Answer

A) five examples of equations to solve. 
B) balance scales to manipulate. 
C) familiar formulas such as those for area. 
D) nonexamples of equations, such as inequalities. 
A) five examples of equations to solve. 
B) balance scales to manipulate. 
C) familiar formulas such as those for area. 
D) nonexamples of equations, such as inequalities.

Question 17

Algebra in elementary school is best understood as:

Accepted Answer

A) a simplified version of high school algebra. 
B) focusing on the finding and extending of patterns. 
C) pre-algebra. 
D) a natural extension of other content standards. 
A) a simplified version of high school algebra. 
B) focusing on the finding and extending of patterns. 
C) pre-algebra. 
D) a natural extension of other content standards.

Question 18

The following are true statements concerning patterning and functions except for :

Accepted Answer

A) children who are able to form patterns build a foundation for the algebraic concept of functions. 
B) the ability to generalize a relationship from specific data is a hallmark of algebraic reasoning. 
C) patterns follow from functions. 
D) patterning is the concept of functions that is central to algebra. 
A) children who are able to form patterns build a foundation for the algebraic concept of functions. 
B) the ability to generalize a relationship from specific data is a hallmark of algebraic reasoning. 
C) patterns follow from functions. 
D) patterning is the concept of functions that is central to algebra.

Question 19

NAEP: The terms in this sequence are the squares of consecutive odd numbers:
1, 9, 25, 49, 81, …
The same rule is applied to each number in the given pattern. What is the sixth number in the pattern?

Accepted Answer

A) 40 
B) 100 
C) 121 
D) 144 
A) 40 
B) 100 
C) 121 
D) 144

Question 20

PISA: The illustration below shows the footprints of a man walking.
   
The pace length, p , is the distance between the rear of two consecutive footprints. 
For men, the formula n / p = 140 gives an approximate relationship between n and p where 
n = number of steps per minute, and 
p = pace length in meters 
If the formula applies to Heiko's walking and Heiko takes 70 steps per minute, what is Heiko's pace length? Be sure to show your work.

Accepted Answer

The answer of PISA: The illustration below shows the footprints...

Given the value for n , what is the function that produces the following data?

Under what circumstance, if any, is the following statement true? 8 + 7 = 3

Give three specific examples of different types of patterns that a teacher can use to introduce algebraic ideas to young children.

The pattern below is referred to as what? 3, 9, 27, 81, …

In this pattern, what is the value of p when n = 10?

A child asks you what a function is. Give several specific examples that you would use to explain this important algebraic concept to her.

Using clock arithmetic, what is 6 + 7 = ?

What are the next two terms of the pattern below? 2, 1, 4, 3, 6, 5, …

Explain the role that patterning plays in helping develop children's algebraic reasoning.

Research has shown that young children:

Which of the following is not a function?

Suppose that t = the number of tiles in a problem-solving situation, and a child tells you that 3 t means 3 tiles. How can you explain to him that his reasoning is faulty?

What are some specific ways that a teacher can introduce the idea of variables without actually using letters for variables?

Explain some of the difficulties children have with understanding the role of the equal sign in equations.

For younger children, the equal sign in an equation may mean all of the following except for :

The best way to get children to understand equations is to give them:

Algebra in elementary school is best understood as:

The following are true statements concerning patterning and functions except for :

NAEP: The terms in this sequence are the squares of consecutive odd numbers: 1, 9, 25, 49, 81, … The same rule is applied to each number in the given pattern. What is the sixth number in the pattern?

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

Extending Understanding of Common and Decimal Fractions

Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

Investigating Probability

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Exam 15: Thinking Algebraically

Given the value for n , what is the function that produces the following data?

Under what circumstance, if any, is the following statement true? 8 + 7 = 3

Give three specific examples of different types of patterns that a teacher can use to introduce algebraic ideas to young children.

The pattern below is referred to as what? 3, 9, 27, 81, …

In this pattern, what is the value of p when n = 10?

A child asks you what a function is. Give several specific examples that you would use to explain this important algebraic concept to her.

Using clock arithmetic, what is 6 + 7 = ?

What are the next two terms of the pattern below? 2, 1, 4, 3, 6, 5, …

Explain the role that patterning plays in helping develop children's algebraic reasoning.

Research has shown that young children:

Which of the following is not a function?

Suppose that t = the number of tiles in a problem-solving situation, and a child tells you that 3 t means 3 tiles. How can you explain to him that his reasoning is faulty?

What are some specific ways that a teacher can introduce the idea of variables without actually using letters for variables?

Explain some of the difficulties children have with understanding the role of the equal sign in equations.

For younger children, the equal sign in an equation may mean all of the following except for :

The best way to get children to understand equations is to give them:

Algebra in elementary school is best understood as:

The following are true statements concerning patterning and functions except for :

NAEP: The terms in this sequence are the squares of consecutive odd numbers: 1, 9, 25, 49, 81, … The same rule is applied to each number in the given pattern. What is the sixth number in the pattern?

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

Extending Understanding of Common and Decimal Fractions

Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

Investigating Probability

Filters