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Chapter 17: Developing Concepts of Fractions and Decimals
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) The base-ten system and place value
a) Are not at all related to decimal numbers.
b) Of whole numbers should be reviewed with students as a way to connect previous knowledge to
the decimal place values.
c) Of whole numbers frequently involves regrouping, which is not needed in the decimal place value
system.
d) Of decimal numbers is not easily shown with models like that for whole numbers is.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
2) The role of the decimal point is to designate the _____________position by sitting just to the right of it.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
3) The 10 to 1 relationship of place value extends infinitely in both the whole number and decimal directions.
4) Decimal concepts are good for developing number sense, but don’t have connections to many real-life
situations.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
5) Name two methods that could help students develop the connection between fractions and decimals. Then
describe how these methods develop conceptual understanding.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
6) A good early method to help students see the connection between fractions and decimals is to
a) Show them how to use a calculator to divide the fraction numerator by the denominator to find the
decimal.
b) Be sure to use precise language when speaking about decimals, such as “point seven two.”
c) Show them how to round decimal numbers to the closest whole number.
d) Have them use base-ten models to build models of base-ten fractions.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
7) Results of NAEP exams reveal that students perform quite well when asked to convert between fractions
and decimals.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
8) The use of ___________________fractions, those to which students have had lots of exposure, can help
them see the connection between non-base-ten fractions and decimals.
9) 0, 1/2, and 1 are very good _____________________________ to which students can compare decimal
numbers, in order to better approximate their size.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
10) Which of the following statements regarding students’ use of calculators to find decimal equivalents from
fractions is NOT true?
a) Students can look for patterns from which fractions result in repeating versus terminating
decimals.
b) They always become too dependent on the technology.
c) This should only be done after students have a conceptual understanding of the connection
between the two formats.
d) They can generalize a pattern about fractions that have only nine digits in their denominators.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
11) The main purpose of activities that require comparing and ordering fractions and decimals is to create a
better understanding of place value and numeration concepts.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
12) Which of the following is a misconception some students have about comparing decimals?
a) The shorter the decimal number is, the bigger the amount it represents.
b) .003 and .03 are different amounts.
c) .4 is bigger than .6 because 1/4 is bigger than 1/6.
d) 0 is smaller than .36 because it had a digit in the ones place, while .36 does not.
13) Decimal estimation
a) Should be something that students can do well before they begin to compute decimals with pencil
and paper.
b) Is not very useful in everyday life.
c) Does not help students determine whether or not their computation results are reasonable.
d) Is not a domain in the Common Core State Standards.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
14) After students have become fluent at solving story problems with decimals, it’s important to see if they can
reason without a context.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
15) Which is true about the algorithm for decimal multiplication?
a) Students can discover the method by being given a series of multiplication problems with factors
that have the same digits, but decimals in different places.
b) It is too complicated for students to discover on their own, so they should just explicitly be shown
how to do it.
c) They should be shown how to estimate after they are shown the algorithm.
d) The repeated addition strategy that works for whole number multiplication is not applicable.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
16) Contrary to those of whole numbers, the algorithms for decimal multiplication and division have no
connection.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question
17) A percent is simply another way of expressing a fraction or decimal that is measured in ___________.
18) Models used to represent percentages include rational number __________, percent necklaces, and 10 × 10
grids.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
19) To promote conceptual understanding of percentages, teachers should do all of the following EXCEPT
a) Limit percentage to those that have familiar fraction equivalents
b) Require students to use models and drawings to support their solutions to problems
c) Have them memorize handy percent equations such as “percent times the base equals the part”
d) Provide lots of examples in contexts
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question
20) Common uses for _________ percentages in real-world situations include tips, taxes, and discounts.
