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Chapter 11: Developing Strategies for Addition and Subtraction Computation
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) Modern technology has made computation easier. Identify the true statement below.
A) But mental computation strategies can be faster than using technology.
B) And recent studies have found that a very low percentage of adults use mental math
computation in everyday life.
C) And mental computation contributes to diminished number sense.
D) So the ability to compute fluently without technology is no longer needed for most people.
2) All of the following provide an example of a method used for computation EXCEPT:
A) Standard algorithms.
B) Student-invented strategies.
C) Discourse modeling.
D) Computational estimation.
3) All of the statements below are considered a benefit of invented strategies EXCEPT:
A) They require one specific set of steps to use them, which makes them easier to memorize.
B) They help reduce the amount of needed re-teaching.
C) Students develop stronger number sense.
D) They are frequently more efficient than standard algorithms.
4) Which of the following is a true statement about standard algorithms?
A) Students will frequently invent them on their own if they are given the time to experiment.
B) They cannot be taught in a way that would help students understand the meaning behind the
steps.
C) In order to use them, students should be required to understand why they work and explain
their steps.
D) There are no differences between various cultures.
5) Complete the statement, “When creating a classroom environment appropriate for inventing
strategies…”
A) The teacher should immediately confirm that a student’s answer is correct, in order to build
his/her confidence.
B) The teacher should attempt to move unsophisticated ideas to more sophisticated thinking
through coaching and questioning.
C) The teacher should discourage student-to-student conversations in order to provide students
with a quiet environment to think.
D) The teacher should encourage the use of naked numbers as a starting point.
6) Cultural differences are evident in algorithms. What reason below supports teaching for
mathematics?
A) Notational algorithms.
B) Customary algorithms.
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C) Mental algorithms.
D) Invented algorithms.
7) The models listed below are used to support the development of invented strategies EXCEPT:
A) Jump strategy.
B) Split strategy.
C) Take-Away strategy.
D) Shortcut strategy.
8) An open number can be used effectively for thinking about addition and subtraction. All of the
reasons below support the use of an open number line EXCEPT:
A) Is less flexible than a numbered line.
B) Eliminates confusion with hash marks and spaces.
C) Less prone to computational errors.
D) Helps with modeling student thinking.
9) The ten-structure of the number system is important to extend students thinking beyond
counting. All of the activities below reference a strategy for calculation EXCEPT:
A) Using decade number.
B) Odd or even.
C) Up over 10.
D) Add on to get to 10.
10) All of the following could be examples of invented strategies for obtaining the sum of two–
digit numbers EXCEPT:
A) Adding on tens and then ones (For example, to solve 24 + 35, think 24 + 30 = 54 and 5 more
makes 59.)
B) Using nicer numbers to estimate (For example, to solve 24 + 47, think 24 is close to 25 and
47 is closer to 45 so 24 + 47 = 25 + 45 = 70.)
C) Moving some to make 10 (For example, to solve 24 + 35, move 6 from 35 to make 24 + 6 and
then add 30 to the remaining 29.)
D) Adding tens and adding ones then combining (For example, to solve 24 + 35, think 20 + 30 =
50 and 4 + 5 = 9 so 50 + 9 = 59.)
11) Students who have learned this strategy for their “basic facts” can use it effectively with
solving problems with multidigit numbers.
A) Jump strategy.
B) Shortcut strategy.
C) Think addition strategy.
D) Split strategy.
12) When a problem has a number that is a multiple of ________ or close to ________ it is an
example of a problem that you leave one number intact and subtract from it.
A) 85 – 35
B) 85 – 64
C) 85 – 29
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D) 85 – 56
13) There are important things to remember when teaching the standard algorithm. Identify the
statement that does not belong.
A) Good choice in some situations.
B) Require written record first.
C) Require concrete models first.
D) Explicit connections are made between concept and procedure.
14) The general approach for teaching the subtraction standard algorithm is the same as addition.
What statement below would not be a problem when using the standard algorithm for addition?
A) Develop the written record.
B) Begin with models.
C) Trades made after the column in the left has been done.
D) Exercises with zeros.
15) The following statements are true regarding computational estimation EXCEPT:
A) Use the language of estimation- about, close, just about.
B) Focus on flexible methods.
C) Focus on answers.
D) Accept a range of estimates.
16) What strategy for computational estimation after adding or subtracting do you adjust to
correct for digits or numbers that were ignored?
A) Front-end.
B) Rounding.
C) Compatible numbers.
D) Over and under.
17) Complete the statement, “A mental computation strategy is a simple…”
A) Left-handed method.
B) Invented strategy.
C) Standard algorithm.
D) One right way.
18) Often siblings and family members are pushing the use of the standard algorithm while
students are learning invented strategies. What is the course of action for a teacher?
A) Insist on invented strategies.
B) Require students demonstrate both standard and invented strategies.
C) Expect them to be responsible for the explanation of why any strategy works.
D) Memorize the steps.
19) All of the statements below represent the differences between invented strategies and
standard algorithms EXCEPT:
A) A range of flexible options.
B) Left-handed rather than right-handed.
C) Number oriented rather than digit oriented.
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D) Basis for mental computation and estimation.
20) The Common Core State Standards states that student should learn a variety of strategies.
These strategies should be based on all of the following EXCEPT:
A) Place value.
B) Sophisticated thinking.
C) Properties of operations.
D) Prior to the standard algorithm.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
21) Identify two or more ways that an open number line can be used to support the use of
invented strategies.
22) Describe the three types estimation and give an example of how they could be used in
teaching computational estimation.
