Chapter 15 Chapter 15 It is important for students to recognize that, regardless of the context

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Chapter 15: Developing Fraction Concepts

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

answers the question.

1) The part-whole construct is the concept most associated with fractions, but other important constructs they

represent include all of the following EXCEPT

a) Measure

b) Reciprocity

c) Division

d) Ratio

ESSAY. Write your answer in the space provided or on a separate sheet of paper.

2) 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.

TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.

3) As long as the teacher is using models of fractions, it is not necessary to use a variety of kinds.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

answers the question

4) Which is NOT a category of fraction models?

a) Set

b) Area

c) Piecewise

d) Length

SHORT ANSWER. Write the word or phrase that best completes each statement or

answers the question.

5) _______________________________________ rods are a kind of length model that provide lots of

flexibility.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

answers the question

6) A number line is a very useful model for fractions because

a) It does not help build conceptual understanding that a fraction represents one number.

b) It allows comparisons of the fraction’s size relative to other numbers.

c) Due to its length, it is hard to connect it a real-life example, measurement.

d) It makes it difficult for students to see how one can find a fraction between any set of two

fractions.

SHORT ANSWER. Write the word or phrase that best completes each statement or

answers the question.

7) In a __________________________model, the whole is understood to be a collection of objects, and

subsets of the collection make up fractional parts.

TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.

8) It is important for students to recognize that, regardless of the context, 1/2 is always bigger than 1/3.

9) A common misconception between students is that fractional parts must be the same shape as well as the

same size.

SHORT ANSWER. Write the word or phrase that best completes each statement or

answers the question.

10) Dividing a shape into equal-sized pieces is called ________________________.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

answers the question

11) The process of iterating

a) Is not as important to conceptual understanding of factions as partitioning is.

b) Is not consistent with the concept of length.

c) Has a tendency to be more difficult for students when it is used with set models.

d) Is not a good way to help students make a transition from fractions to mixed numbers.

12) Improper fractions

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.

TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.

13) When estimating with fractions, it is important to keep in mind that students find estimation easier than

computation with fractions, so they don’t need a lot of practice. Time should be devoted to computation.

14) In the case of fraction equivalence, it is best to allow students the extra time to develop a conceptually-

based algorithm.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

answers the question

15) Which of the following is NOT an effective model of fraction equivalence?

a) The slope of a line

b) Shapes created on dot paper

c) Plastic, circular area models

d) Clocks

SHORT ANSWER. Write the word or phrase that best completes each statement or

answers the question.

16) The ______________________________________number property is essential to students’ understanding

of the equivalent fraction algorithm.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

answers the question

17) When comparing fractions

a) Students’ understanding of whole numbers and what makes a “bigger number” can result in

erroneous thinking.

b) The usual methods, finding common denominators and cross multiplying, help students develop

understanding of various fraction sizes, even when they have not invested a lot of thought into the

concept.

c) It is not helpful to compare the fractions to another common benchmark fraction.

d) Teachers should not add complication to students’ practice by asking them to compare fractions

that are equal.