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Chapter 22: 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 students begin to work with exponents they often lack conceptual understanding.
Identify the method that supports conceptual versus procedural understanding.
A) Explore growing patterns with physical models.
B) Explore with whole numbers before exponents with variables.
C) Instruction on the order of operations.
D) Instruction should focus on exponents as a shortcut for repeated multiplication.
2) Order of operations extends working with exponents. What part of the order of operations is a
convention?
A) The meaning of the operation.
B) Multiplying before computing the exponent changes the meaning of the problem.
C) Working from left to right, using parenthesis.
D) PEMDAS.
3) The ideas below would guide student understanding of the concept behind scientific notation
EXCEPT:
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) Instructing them only on the movement of the decimal point “the exponent with the 10 tells
how many places to move the decimal point.”
4) Real-world contexts with negative numbers provide opportunities for discussion of integer
operations. What statement below would represent a quantity?
A) Timeline of Roman Empire rule.
B) Altitude above sea level.
C) Golf scores.
D) Gains and lost football yardage.
5) When using the number line method for the addition of integers, the following statements
relate to the number line method EXCEPT:
A) Each addend’s magnitude needs to be presented on the number line.
B) The position of the arrow indicates positive or negative integers.
C) A line segment pointing to the right could indicate a positive or negative number.
D) A line segment pointing to the left would indicate a negative number.
6) Identify the example of an irrational number.
A) 3.5
B) -2
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D)
7) Learning about exponents can be problematic. These are common misconceptions EXCEPT:
A) Think of the two values as factors.
B) Hear “five three times” and think multiplication.
C) Write the equation as 5 × 3 rather than 5 × 5 × 5.
D) Use repeated addition versus multiplication.
8) What is the primary reason to teach and use Scientific Notation?
A) Convenient way to represent very large or small numbers.
B) A number is changed to be the product of a number greater or equal to 1 or less than 10
multiplied by a power of 10.
C) Easiest way to convey the value of numbers in different contexts.
D) To determined by the level of precision appropriate for that situation.
9) The contexts below would support learning about very, very large numbers EXCEPT:
A) Distance from the planet Mercury to Mars.
B) Number of cells in the human body.
C) The estimated life span of a Bengal tiger.
D) Population of the European countries in 2011.
10) When students are learning and creating contexts for integer operations. Ask them to
consider the following questions EXCEPT:
A) Where am I now?
B) Where am I going?
C) Where did you start?
D) How far did you go?
11) For students to be successful in the division of integers they should competence in the
following concept?
A) Whole number division.
B) Division of fractions.
C) Relationship between multiplication and division.
D) Rules for dividing negative numbers.
12) The term rational numbers relates to all of examples below EXCEPT:
A) Fractions.
B) Decimals and percents.
C) Square roots.
D) Positive and negative integers.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
13) Describe a learning experience that can introduce students to irrational numbers.
14) Discuss the challenges of using number lines and counters to teach about magnitude and
direction of integers.
