Chapter 23: Developing Concepts of Exponents, Integers, and Real Numbers
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) When developing understanding of exponents
a) It is important to use physical models, such as squares and cubes.
b) The order of operations is not important.
c) Teachers just need to teach students about the symbolic nature of exponents.
d) Students should be taught that exponents are a shortcut for repeated addition.
2) The expression “Please Excuse My Dear Aunt Sally”
a) Is an obscure phrase that is not at all helpful.
b) Refers students somewhat to the order of operations in an expression or equation.
c) Does not help students remember which operation comes first.
d) Refers students to the left to right computations of parentheses, exponents, multiplication, division,
addition and subtraction.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
3) Students should be aware of the fact that some calculators don’t perform the order of operations and they should
know how to compensate for that fact.
4) Students can gain an understanding of negative exponents by examining a pattern and seeing how the evaluated
product always becomes negative when the exponent becomes negative.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
5) Representing very large or very small numbers requires exercises in converting from standard form to
____________________ notation.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
6) Which of the following would NOT help a student understand the concept behind scientific notation?
a) Examining patterns that arise when inputting very large and small numbers into a calculator
b) Researching real-life examples of very large and small numbers
c) Asking them to perform computation on very large and small numbers that are not in scientific notation,
so they can see how difficult it is
d) Simply telling them “the exponent with the 10 tells how many places to move the decimal point” and
nothing else
7) Students have almost daily interactions with negative numbers in real world examples. Which of the following
will NOT involve a discussion of integer operations?
a)
Debits and credits with accounts
b)
The effects of a percentage of discount at a department store
c)
Below zero temperatures
d) The yardage earned and lost in a football game
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
8) Because students who have not been introduced to integers have only seen the negative sign in the context of
subtraction, they can find the negative concept difficult to understand at first.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
9) If using the model of the addition of integers with the number line and arrow method, all of the following
statements are true EXCEPT
a) Each addend’s magnitude needs to be presented on the number line.
b) If two positive numbers are added, then the length of the two line segments representing these numbers
would be the sum of their individual lengths.
c) A model of the sum of negative number and a positive number would always result in a negative
number.
d) A line segment pointing to the left would indicate a negative number.
10) Which of the following is NOT a correct concept involving integer addition and subtraction?
a) A negative unit and a positive unit combine to make 0
b) Subtracting a negative number is equivalent to adding a positive number
c) Adding a negative number is the same as subtracting a positive number
d) An addition problem or subtraction problem that has a negative and a positive number always has a
result of a negative number.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
11) Many of the same models and concepts that students use to gain conceptual understanding of multiplying and
dividing positive numbers are applicable to those operations with negative numbers, as well.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
12) A rational number is any number that can be represented as a _____________________.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
13) Which of the following is an irrational number?
a) 3.5
b) –2
c) π
d) 1/2
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
14) The square roots of numbers that are not perfect squares do not have any real-life applications.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
15) Describe an activity that could help students gain a conceptual understanding of a real number concept.
Chapter 23