Chapter 12: 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
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) Which of the following is NOT an example of a method used to compute a solution?
a) Standard algorithms
b) Student-invented strategies
c) Discourse modeling
d) Computational estimation
3) Which of the following is NOT a benefit of student-developed strategies?
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) 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) Student-to-student conversations should be discouraged, in order to provide students with a quiet
environment to think.
d) The degree to which students feel safe to make mistakes is not an important factor.
6) All of the following could be examples of student-developed 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.)
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
7) The concept of “think addition” to aid in subtracting large numbers works the same as when subtracting
small numbers.
8) The take away strategy for subtraction can be easy if the subtracted number is a multiple of ten or close to
one.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
9) When students solve problems that involve ___________________________ or crossing ten, if they are
using the standard algorithm, they must regroup or trade.
10) As with any algorithm, students must first be exposed to addition from a _____________________
approach, which must then be connected to a more abstract approach.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
11) Which of the following is NOT true about strategies for developing the subtraction
algorithm?
a) Students should begin with models only.
b) The teacher should anticipate that there will be difficulties with zeros.
c) After the procedure is completely understood with models, then students should begin developing
the written record.
d) The general approach is completely different from that used to develop the addition algorithm.
12) Which of the following is a true statement regarding computational estimation?
a) We can use calculators, so it’s not really that necessary.
b) Its under representation in many textbooks can cause someone to incorrectly assume it’s not very
important.
c) Teachers should define for and accept from students only one correct estimation.
d) Examples of real-life context are not needed.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
13) ______________________________estimation is a strategy, most appropriate for addition or subtraction,
that only takes into account the leftmost digit and pretends the remaining numbers are all zeros.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
14) Provide an addition or subtraction problem and a potential student–invented strategy that could be used to
compute it. Explain why a student-invented strategy could be valuable. Describe a method you could use to
encourage the development and/or use of this method.
Chapter 12