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Chapter 13: Developing Strategies for Multiplication and Division Computation
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
1) Becoming fluent at breaking apart numbers in flexible ways is more important for multiplication than
addition, and the skill is dependent on students’ understanding of the __________________________
number property.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
2) Although many teachers worry that multiple representations of the same problem will confuse students,
research shows that, if students are shown a variety of methods from the beginning, they gain flexibility in
their problem-solving strategy use and, consequently, enhanced learning.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
3) Which of the following is NOT a useful strategy for multiplying by single digits?
a) Doubling
b) Compatible numbers
c) Partitioning
d) Complete number
4) Which is an example of the compensation strategy?
a) 63 × 5 = 63 + 63 + 63 + 63 + 63 = 315
b) 27 × 4 = 20 × 4 + 7 × 4 = 80 + 28 = 108
c) 27 × 4 is about 30 (27 + 3) × 4 = 120; then subtract out the extra 3 × 4, so 120 –12 = 108
d) 46 × 3 = 46 × 2 (double) + 46 = 92 + 46 = 138
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
5) When using ________________________________ to compute multi-digit multiplication problems,
students use facts and combinations they already know to find out more complex computation problems.
6) The _____________________________ , or connected array, can be a key visual representation of
multiplication that supports students’ conceptual understanding.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
7) Rather than using the confusing language of “carrying” the digit when multiplying, a teacher might want to
encourage students to use partial products.
8) Because division is frequently the most onerous of all computational operations, it is better to teach
students the standard algorithm rather than potentially confusing them with student-invented strategies.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
9) When developing the standard algorithm for division,
a) Teachers should avoid using a confusing algorithm based on repeated addition.
b) Teachers should have students use models after developing the written record.
c) The process of recording explicit trades can be less confusing to students than the more common
bringing down.
d) The expression “goes into” is very meaningful for kids.
10) Which of the following is a true statement regarding using estimation strategies?
a) It is much more useful to focus on the estimated answer than it is to focus on the process students
used to obtain the estimate.
b) The more practice students have with finding a variety of estimates for the same problem, the
more confused they will become.
c) If the teacher has ELL students, he or she should ensure the students understand the context of the
problem, then provide the numerical information before asking for an estimate.
d) The front-end strategy has been shown to be one of the most difficult for students to learn to use.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
11) In order to be truly useful in estimation, rounding must be flexible and conceptually understood by
students.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
12) The compatible numbers strategy
a) Is one of the least helpful strategies for estimating division problems.
b) Involves changing the numbers in the problems to make them more “friendly” to work with.
c) Is not easily applied to situations involving fraction, decimals, and rates.
d) Is not appropriate for estimating multiplication problems.
13) Calculators
a) Are not appropriate to use when students are learning to become more fluent estimators.
b) Don’t help students check the reasonableness of their estimates.
c) Are one of the reasons that estimation skills are so important, because students frequently make
mistakes involving hitting the wrong keys.
d) Can greatly reduce student engagement.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
14) When estimating with rational numbers, it is best to use other rational numbers. Otherwise, the estimate is
likely to be very inaccurate.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
15) Provide a multiplication or division problem and a potential strategy that could be used to compute it.
Explain why this strategy could be valuable. Describe an activity you could use to encourage the
development and/or use of this method.
