Question 1

To guide students to develop a problem-based number sense approach for operations with fractions all of the following are recommended EXCEPT:

Accepted Answer

A) Address common misconceptions regarding computational procedures. 
B) Estimating and invented methods play a big role in the development. 
C) Explore each operation with a single model. 
D) Use contextual tasks. 
A) Address common misconceptions regarding computational procedures. 
B) Estimating and invented methods play a big role in the development. 
C) Explore each operation with a single model. 
D) Use contextual tasks. C

Question 2

Identify and discuss misconceptions that students bring from whole number operations to their learning of fraction operations.

Accepted Answer

Address common misconceptions.The above activity can be used to illustrate how division does not always result in a quotient that is smaller than the initial amount.

Question 3

Identify the manipulative used with linear models that you can decide what to use as the "whole".

Accepted Answer

A) Circular pieces. 
B) Number Line. 
C) Cuisenaire Rods. 
D) Ruler. 
A) Circular pieces. 
B) Number Line. 
C) Cuisenaire Rods. 
D) Ruler. C

Question 4

A ______ interpretation is a good method to explore division because students can draw illustrations to show the model.

Accepted Answer

A) Area. 
B) Set. 
C) Measurement. 
D) Linear. 
A) Area. 
B) Set. 
C) Measurement. 
D) Linear.

Question 5

This model is exceptionally good at modeling fraction multiplication.It works when partitioning is challenging and provides a visual of the size of the result.

Accepted Answer

A) Area model. 
B) Linear model. 
C) Set model. 
D) Circular model. 
A) Area model. 
B) Linear model. 
C) Set model. 
D) Circular model.

Question 6

What is helpful when subtracting mixed number fractions?

Accepted Answer

A) Deal with the whole numbers first and then work with the fractions. 
B) Always trade one of the whole number parts into equivalent parts. 
C) Avoid this method until the student fully understands subtraction of numbers less than one. 
D) Teach only the algorithm that keeps the whole number separate from the fractional part. 
A) Deal with the whole numbers first and then work with the fractions. 
B) Always trade one of the whole number parts into equivalent parts. 
C) Avoid this method until the student fully understands subtraction of numbers less than one. 
D) Teach only the algorithm that keeps the whole number separate from the fractional part.

Question 7

What is one of the methods for finding the product of fractional problems when one of the numbers is mixed number?

Accepted Answer

A) Change to improper fraction. 
B) Compute partial products. 
C) Linear modeling. 
D) Associative property. 
A) Change to improper fraction. 
B) Compute partial products. 
C) Linear modeling. 
D) Associative property.

Question 8

It is recommended that division of fractions be taught with a developmental progression that focuses on four types of problems.Which statement below is not part of the progression?

Accepted Answer

A) A fraction divided by a fraction. 
B) A whole number divided by a fraction. 
C) A whole number divided by a mixed number. 
D) A whole number divided by a whole number. 
A) A fraction divided by a fraction. 
B) A whole number divided by a fraction. 
C) A whole number divided by a mixed number. 
D) A whole number divided by a whole number.

Question 9

Common misconceptions occur because students tend to overgeneralize what they know about whole number operations.Identify the misconception that is not relative to fraction operations.

Accepted Answer

A) Adding both numerator and denominator. 
B) Not identifying the common denominator. 
C) Difficulty with common multiples. 
D) Use of invert and multiply. 
A) Adding both numerator and denominator. 
B) Not identifying the common denominator. 
C) Difficulty with common multiples. 
D) Use of invert and multiply.

Question 10

Different models are used to help illustrate fractions.Identify the model that can be confusing when you are learning to add fractions.

Accepted Answer

A) Area. 
B) Set. 
C) Linear. 
D) Length. 
A) Area. 
B) Set. 
C) Linear. 
D) Length.

Question 11

Each the statements below are examples of misconceptions students have when learning to multiply fractions EXCEPT:

Accepted Answer

A) Treating denominators the same as addition and subtraction. 
B) Matching multiplication situations with multiplication situations. 
C) Estimating the size of the answer incorrectly. 
D) Multiplying the denominator and not numerator. 
A) Treating denominators the same as addition and subtraction. 
B) Matching multiplication situations with multiplication situations. 
C) Estimating the size of the answer incorrectly. 
D) Multiplying the denominator and not numerator.

Question 12

Identify the problem that solving with a linear model would not be the best method.

Accepted Answer

A) Half a pizza is left from the 2 pizzas Molly ordered.How much pizza was eaten? 
B) Mary needs 3 13 feet of wood to build her fence.She only has 2 34 feet.How much more wood does she need? 
C) Millie is at mile marker 2 12.Rob is at mile marker 1.How far behind is Rob? 
D) What is the total length of these two Cuisenaire rods placed end to end? 
A) Half a pizza is left from the 2 pizzas Molly ordered.How much pizza was eaten? 
B) Mary needs 3 13 feet of wood to build her fence.She only has 2 34 feet.How much more wood does she need? 
C) Millie is at mile marker 2 12.Rob is at mile marker 1.How far behind is Rob? 
D) What is the total length of these two Cuisenaire rods placed end to end?

Question 13

Linear models are best represented by what manipulative?

Accepted Answer

A) Pattern Blocks. 
B) Circular pieces. 
C) Ruler. 
D) Number line. 
A) Pattern Blocks. 
B) Circular pieces. 
C) Ruler. 
D) Number line.

Question 14

Based on students experience with whole number division they think that when dividing by a fraction the answer should be smaller.This would be true for all of the following problems EXCEPT:

Accepted Answer

A) 16÷ 3 
B) 56÷ 3 
C) 36÷ 3 
D) 3÷56 
A) 16÷ 3 
B) 56÷ 3 
C) 36÷ 3 
D) 3÷56

Question 15

Adding and subtraction fractions should begin with students using prior knowledge of equivalent fractions.Identify the problem that may be more challenging to solve mentally.

Accepted Answer

A) Luke ordered 3 pizzas.But before his guests arrive he got hungry and ate 38 of one pizza.What was left for the party? 
B) Linda ran 1 12 miles on Friday.Saturday she ran 2 18 miles and Sunday 2 34.How many miles did she run over the weekend? 
C) Lois gathered 34 pounds of walnuts and Charles gathered 78 pounds.Who gathered the most? How much more? 
D) Estimate the answer to 1213+ 78. 
A) Luke ordered 3 pizzas.But before his guests arrive he got hungry and ate 38 of one pizza.What was left for the party? 
B) Linda ran 1 12 miles on Friday.Saturday she ran 2 18 miles and Sunday 2 34.How many miles did she run over the weekend? 
C) Lois gathered 34 pounds of walnuts and Charles gathered 78 pounds.Who gathered the most? How much more? 
D) Estimate the answer to 1213+ 78.

Question 16

Students are able to solve adding and subtracting fractions without finding a common denominator using invented strategies.The problems below would work with the invented strategies EXCEPT:

Accepted Answer

A) 34 + 18 
B) 12 - 18 
C) 56 - 17 
D) 23 + 12 
A) 34 + 18 
B) 12 - 18 
C) 56 - 17 
D) 23 + 12

Question 17

Estimation and invented strategies are important with division of fractions.If you posed the problem 16÷ 4 you would ask all of the questions EXCEPT:

Accepted Answer

A) Will the answer be greater than 4? 
B) Will the answer be greater than one? 
C) Will the answer be greater than 12? 
D) Will the answer be greater than 16? 
A) Will the answer be greater than 4? 
B) Will the answer be greater than one? 
C) Will the answer be greater than 12? 
D) Will the answer be greater than 16?

Question 18

What statement is true about adding and subtracting with unlike denominators?

Accepted Answer

A) Should be introduced at first with tasks that require both fractions to be changed. 
B) Is sometimes possible for students,especially if they have a good conceptual understanding of the relationships between certain fractional parts and a visual tool,such as a number line. 
C) Is a concept understood especially well by students if the teacher compares different denominators to "apples and oranges." 
D) Should initially be introduced without a model or drawing. 
A) Should be introduced at first with tasks that require both fractions to be changed. 
B) Is sometimes possible for students,especially if they have a good conceptual understanding of the relationships between certain fractional parts and a visual tool,such as a number line. 
C) Is a concept understood especially well by students if the teacher compares different denominators to "apples and oranges." 
D) Should initially be introduced without a model or drawing.

Question 19

All of the statements below are examples of estimation or invented strategies for adding and subtracting fractions EXCEPT:

Accepted Answer

A) Decide whether fractions are closest to 0,12,or 1. 
B) Look for ways different fraction parts are related. 
C) Decide how big the fraction is based on the unit. 
D) Look for the size of the denominator. 
A) Decide whether fractions are closest to 0,12,or 1. 
B) Look for ways different fraction parts are related. 
C) Decide how big the fraction is based on the unit. 
D) Look for the size of the denominator.

Question 20

Complete the statement,"Developing the algorithm for adding and subtracting fractions should..".

Accepted Answer

A) Be done side by side with visuals and situations. 
B) Be done with specific procedures. 
C) Be done with units that are challenging to combine. 
D) Be done mentally without paper and pencil. 
A) Be done side by side with visuals and situations. 
B) Be done with specific procedures. 
C) Be done with units that are challenging to combine. 
D) Be done mentally without paper and pencil.

Exam 16: Developing Strategies for Fraction Computation

To guide students to develop a problem-based number sense approach for operations with fractions all of the following are recommended EXCEPT:

Identify and discuss misconceptions that students bring from whole number operations to their learning of fraction operations.

Identify the manipulative used with linear models that you can decide what to use as the "whole".

A ______ interpretation is a good method to explore division because students can draw illustrations to show the model.

This model is exceptionally good at modeling fraction multiplication.It works when partitioning is challenging and provides a visual of the size of the result.

What is helpful when subtracting mixed number fractions?

What is one of the methods for finding the product of fractional problems when one of the numbers is mixed number?

It is recommended that division of fractions be taught with a developmental progression that focuses on four types of problems.Which statement below is not part of the progression?

Common misconceptions occur because students tend to overgeneralize what they know about whole number operations.Identify the misconception that is not relative to fraction operations.

Different models are used to help illustrate fractions.Identify the model that can be confusing when you are learning to add fractions.

Each the statements below are examples of misconceptions students have when learning to multiply fractions EXCEPT:

Identify the problem that solving with a linear model would not be the best method.

Linear models are best represented by what manipulative?

Based on students experience with whole number division they think that when dividing by a fraction the answer should be smaller.This would be true for all of the following problems EXCEPT:

Adding and subtraction fractions should begin with students using prior knowledge of equivalent fractions.Identify the problem that may be more challenging to solve mentally.

Students are able to solve adding and subtracting fractions without finding a common denominator using invented strategies.The problems below would work with the invented strategies EXCEPT:

Estimation and invented strategies are important with division of fractions.If you posed the problem 16÷ 4 you would ask all of the questions EXCEPT:

What statement is true about adding and subtracting with unlike denominators?

All of the statements below are examples of estimation or invented strategies for adding and subtracting fractions EXCEPT:

Complete the statement,"Developing the algorithm for adding and subtracting fractions should..".

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

Algebraic Thinking, equations, and Functions

Developing Fraction Concepts

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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