Question 1

Counting precedes whole-number learning of addition and subtraction.What is another term for counting fraction parts?

Accepted Answer

A) Equalizing. 
B) Iterating. 
C) Partitioning. 
D) Sectioning. 
A) Equalizing. 
B) Iterating. 
C) Partitioning. 
D) Sectioning. B

Question 2

Comparing fractions involves the knowledge of the inverse relationship between number of parts and size of parts.The following activities support the relationship EXCEPT:

Accepted Answer

A) Iterating. 
B) Equivalent fraction algorithm. 
C) Estimating. 
D) Partitioning. 
A) Iterating. 
B) Equivalent fraction algorithm. 
C) Estimating. 
D) Partitioning. B

Question 3

The part-whole construct is the concept most associated with fractions,but other important constructs they represent include all of the following EXCEPT:

Accepted Answer

A) Measure. 
B) Reciprocity. 
C) Division. 
D) Ratio. 
A) Measure. 
B) Reciprocity. 
C) Division. 
D) Ratio. B

Question 4

What is the definition of the process of partitioning?

Accepted Answer

A) Equal shares. 
B) Equal-sized parts. 
C) Equivalent fractions. 
D) Subset of the whole. 
A) Equal shares. 
B) Equal-sized parts. 
C) Equivalent fractions. 
D) Subset of the whole.

Question 5

The term improper fraction is used to describe fractions greater than one.Identify the statement that is true about the term improper fraction.

Accepted Answer

A) Is a clear term,as it helps students realize that there is something unacceptable about the format. 
B) Should be taught separately from proper fractions. 
C) Are best connected to mixed numbers through the standard algorithm. 
D) Should be introduced to students in a relevant context. 
A) Is a clear term,as it helps students realize that there is something unacceptable about the format. 
B) Should be taught separately from proper fractions. 
C) Are best connected to mixed numbers through the standard algorithm. 
D) Should be introduced to students in a relevant context.

Question 6

Locating a fractional value on a number line can be challenging but is important for students to do.All of the statements below are common errors that students make when working with the number line EXCEPT:

Accepted Answer

A) Use incorrect notation. 
B) Change the unit. 
C) Use incorrect subsets. 
D) Count the tick marks rather than the space. 
A) Use incorrect notation. 
B) Change the unit. 
C) Use incorrect subsets. 
D) Count the tick marks rather than the space.

Question 7

The way we write fractions is a convention with a top and bottom number with a bar in between.Posing questions can help students make sense of the symbols.All of the questions would support that sense making EXCEPT:

Accepted Answer

A) What does the denominator in a fraction tell us? 
B) What does the equal symbol mean with fractions? 
C) What might a fraction equal to one look like? 
D) How do know if a fraction is greater than,less than 1? 
A) What does the denominator in a fraction tell us? 
B) What does the equal symbol mean with fractions? 
C) What might a fraction equal to one look like? 
D) How do know if a fraction is greater than,less than 1?

Question 8

Complete this statement,"Comparing two fractions with any representation can be made only if you know the..".

Accepted Answer

A) Size of the whole. 
B) Parts all the same size. 
C) Fractional parts are parts of the same size whole. 
D) Relationship between part and whole. 
A) Size of the whole. 
B) Parts all the same size. 
C) Fractional parts are parts of the same size whole. 
D) Relationship between part and whole.

Question 9

Teaching considerations for fraction concepts include all of the following EXCEPT:

Accepted Answer

A) Iterating and partitioning. 
B) Procedural algorithm for equivalence. 
C) Emphasis on number sense and fractional meaning. 
D) Link fractions to key benchmarks. 
A) Iterating and partitioning. 
B) Procedural algorithm for equivalence. 
C) Emphasis on number sense and fractional meaning. 
D) Link fractions to key benchmarks.

Question 10

What does a strong understanding of fractional computation relies on?

Accepted Answer

A) Estimating with fractions. 
B) Iteration skills. 
C) Whole number knowledge. 
D) Fraction equivalence. 
A) Estimating with fractions. 
B) Iteration skills. 
C) Whole number knowledge. 
D) Fraction equivalence.

Question 11

All of the following are fraction constructs EXCEPT:

Accepted Answer

A) Part-whole. 
B) Measurement. 
C) Iteration. 
D) Division. 
A) Part-whole. 
B) Measurement. 
C) Iteration. 
D) Division.

Question 12

The following visuals/manipulatives support the development of fractions using the area model EXCEPT:

Accepted Answer

A) Pattern blocks. 
B) Tangrams. 
C) Cuisenaire rods. 
D) Geoboards. 
A) Pattern blocks. 
B) Tangrams. 
C) Cuisenaire rods. 
D) Geoboards.

Question 13

Fraction misconceptions come about for all of the following reasons.The statements below can be fraction misconceptions EXCEPT.

Accepted Answer

A) Many meanings of fractions. 
B) Fractions written in a unique way. 
C) Students overgeneralize their whole-number knowledge 
D) Teachers present fractions late in the school year. 
A) Many meanings of fractions. 
B) Fractions written in a unique way. 
C) Students overgeneralize their whole-number knowledge 
D) Teachers present fractions late in the school year.

Question 14

A _______ is a significantly more sophisticated length model than other models.

Accepted Answer

A) Number line. 
B) Cuisenaire rods. 
C) Measurement tools. 
D) Folded paper strips. 
A) Number line. 
B) Cuisenaire rods. 
C) Measurement tools. 
D) Folded paper strips.

Question 15

Equivalent fraction models are important for students to have in several contexts.Identify two models and an example of how they can be used for teaching equivalence.

Accepted Answer

Equivalence models and examples of how t

Question 16

Models provide an effective visual for students and help them explore fractions.Identify the statement that is the definition of the length model.

Accepted Answer

A) Location of a point in relation to 0 and other values. 
B) Part of area covered as it relates to the whole unit. 
C) Count of objects in the subset as it relates to defined whole. 
D) A unit or length involving fractional amounts. 
A) Location of a point in relation to 0 and other values. 
B) Part of area covered as it relates to the whole unit. 
C) Count of objects in the subset as it relates to defined whole. 
D) A unit or length involving fractional amounts.

Question 17

What is a common misconception with fraction set models?

Accepted Answer

A) There are not many real-world uses. 
B) Knowing the size of the subset rather than the number of equal sets 
C) Knowing the number of equal sets rather than the size of subsets 
D) There are not many manipulatives to model the collections. 
A) There are not many real-world uses. 
B) Knowing the size of the subset rather than the number of equal sets 
C) Knowing the number of equal sets rather than the size of subsets 
D) There are not many manipulatives to model the collections.

Question 18

Researchers have described a number of reasons that students have a tendency to struggle with fraction concepts.Name two of these reasons,and describe a method a teacher might use to address each.

Accepted Answer

Traditional instruction has not focused

Question 19

What does it mean to write fractions in simplest term?

Accepted Answer

A) Finding equivalent numerators. 
B) Finding equivalent denominators. 
C) Finding multipliers and divisors. 
D) Finding equivalent fractions with no common whole number factors. 
A) Finding equivalent numerators. 
B) Finding equivalent denominators. 
C) Finding multipliers and divisors. 
D) Finding equivalent fractions with no common whole number factors.

Question 20

How do you know that 46= 23 ? Identify the statement below that demonstrates a conceptual understanding.

Accepted Answer

A) They are the same because you can simplify 46 and get 23. 
B) Start with 23 and multiply the top and bottom by 2 and you get 46. 
C) If you have 6 items and you take 4 that would be 46.You can make 6 groups into 3 groups and 4 into 2 groups and that would be 23 . 
D) If you multiply 4 x 3 and 6 x 2 they're both 12. 
A) They are the same because you can simplify 46 and get 23. 
B) Start with 23 and multiply the top and bottom by 2 and you get 46. 
C) If you have 6 items and you take 4 that would be 46.You can make 6 groups into 3 groups and 4 into 2 groups and that would be 23 . 
D) If you multiply 4 x 3 and 6 x 2 they're both 12.

Exam 15: Developing Fraction Concepts

Counting precedes whole-number learning of addition and subtraction.What is another term for counting fraction parts?

Comparing fractions involves the knowledge of the inverse relationship between number of parts and size of parts.The following activities support the relationship EXCEPT:

The part-whole construct is the concept most associated with fractions,but other important constructs they represent include all of the following EXCEPT:

What is the definition of the process of partitioning?

The term improper fraction is used to describe fractions greater than one.Identify the statement that is true about the term improper fraction.

Locating a fractional value on a number line can be challenging but is important for students to do.All of the statements below are common errors that students make when working with the number line EXCEPT:

The way we write fractions is a convention with a top and bottom number with a bar in between.Posing questions can help students make sense of the symbols.All of the questions would support that sense making EXCEPT:

Complete this statement,"Comparing two fractions with any representation can be made only if you know the..".

Teaching considerations for fraction concepts include all of the following EXCEPT:

What does a strong understanding of fractional computation relies on?

All of the following are fraction constructs EXCEPT:

The following visuals/manipulatives support the development of fractions using the area model EXCEPT:

Fraction misconceptions come about for all of the following reasons.The statements below can be fraction misconceptions EXCEPT.

A _______ is a significantly more sophisticated length model than other models.

Equivalent fraction models are important for students to have in several contexts.Identify two models and an example of how they can be used for teaching equivalence.

Models provide an effective visual for students and help them explore fractions.Identify the statement that is the definition of the length model.

What is a common misconception with fraction set models?

Researchers have described a number of reasons that students have a tendency to struggle with fraction concepts.Name two of these reasons,and describe a method a teacher might use to address each.

What does it mean to write fractions in simplest term?

How do you know that 46= 23 ? Identify the statement below that demonstrates a conceptual understanding.

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 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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