121
Chapter 12: Developing Strategies for Multiplication and Division Computation
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) Representing a product of two factors may depend on the methods student experienced. What
representation of 37 × 5 below would indicate that the student had worked with base-ten?
A) An array with 5 × 30 and 5 × 7.
B) 5 groups of 30 lines and 5 groups of 7 dots.
C) 5 circles with 37 items in each.
D) 37 + 37 + 37 + 37 + 37 + 37 + 37.
2) What invented strategy is represented by a student multiplying 58 × 6 by adding 58 + 58 to get
116 and then adding another 116 to get 232 and then adding another 116 to find the product of
348.
A) Partitioning.
B) Clusters.
C) Complete number.
D) Compensation.
3) What invented strategy is just like the standard algorithm except that students always begin
with the largest values?
A) Partitioning.
B) Clusters.
C) Complete number.
D) Compensation.
4) What compensation strategy works when you are multiplying with 5 or 50?
A) Clusters.
B) Partitioning the multiplier.
C) Array.
D) Half-then-double.
5) What statement below describes the cluster problem approach for multidigit multiplication?
A) Encourages the use of known facts and combinations.
B) Encourages the manipulation of only one of the factors.
C) Encourages the use of an open array.
D) Encourages the use of fair sharing.
6) This model uses a structure that automatically organizes proportionate equal groups and offers
a visual demonstration of the commutative and distributive properties.
A) Clusters.
B) Missing Factor.
C) Area.
D) Open array.
122
7) When developing the written record for multiplication computation it is helpful to encourage
students to follow these suggestions EXCEPT:
A) Use sheets with base-ten columns.
B) Record partial products.
C) Record the combined product on one line.
D) Mark the subdivisions of the factors.
8) Division may be easier for students if they are familiar with the concepts. All of the statements
below are related to division of whole numbers EXCEPT:
A) Partitioning.
B) Fair sharing.
C) Compensating.
D) Repeated subtracting.
9) Cluster problems are an approach to developing the missing-factor strategy and capitalize on
the inverse relationship between multiplication and division. All of equations below represent
clusters that would help solve 381 divided by 72 EXCEPT:
A) 81 × 70
B) 10 × 72
C) 5 × 70
D) 4 × 72
10) Which of the following is a strategy that is more applicable for multiplying single digits than
multidigits?
A) Compatible numbers.
B) Doubling.
C) Partitioning.
D) Complete number.
11) 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) 46 × 3 = 46 × 2 (double) + 46 = 92 + 46 = 138
D) 27 × 4 is about 30 (27 + 3) × 4 = 120; then subtract out the extra 3 × 4, so 120 -12 = 108
12) Identify the statement that represents what might be voiced when using the missing-factor
strategy.
A) When no more tens can be distributed a ten is traded for ten ones.
B) Seven goes into three hundred forty-five how many times?
C) What number times seven will be close to three hundred forty-five with less than seven
remaining?
D) Split three hundred forty-five into 3 hundred, four tens and five ones.
13) Developing the standard algorithm for division teachers should use all of the following
guides EXCEPT:
A) Partial quotients with a visual model.
123
B) Partition or fair share model.
C) Explicit trade method.
D) Area model.
14) An intuitive idea about long division with two digit divisors is to round up the divisor. All of
examples below support this idea EXCEPT:
A) Think about sharing base-ten pieces.
B) Underestimate how many can be shared.
C) Pretend there are fewer sets to share than there really are.
D) Multiples of 10 are easier to compare.
15) One strategy for teaching computational estimation is to ask for information, but no answer.
Which statement below would be an example of NOT gathering information?
A) Is it more or less that 1,000?
B) Is it between $400 and $700?
C) Is one of these right?
D) Is your estimate about how much?
16) What is the purpose of using a side bar chart in multidigit division?
A) Easier to come up with the actual answer.
B) Uses a doubling strategy for considering the reasonableness of an answer.
C) Increases the mental computation needed to find the answer.
D) Uses the explicit trade notation.
17) What is the reason why mental calculations estimates are more complex?
A) They require a deep knowledge of how numbers work.
B) They require a solid knowledge of division procedures.
C) They require a deep knowledge of partitioning.
D) They require a solid knowledge of multiplication procedures.
18) A number line can be helpful with teaching this estimation strategy.
A) Front end.
B) Compatible.
C) Rounding.
D) Mental computation.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
19) Identify and discuss methods for supporting students’ development of the standard algorithm
for division.
20) Discuss the use of the cluster problem approach to help students with multiplication and
division computation?
