Download MA318, Review Guide

MA318, Review Guide for Exam II
0. Explain why the integers are closed under addition and subtraction. Are the integers closed under
multiplication and division? Explain.
1. Give a definition for , the set of rational numbers, = {_______________________________________}
2. Under what operations is the set closed? Explain
a
3. What are the three different perspectives from which to view the fraction ?
b
4. The most commonly used conceptualization in the K-8 curriculum is the part-whole concept. Explain what
the part-whole conceptualization means. When teaching the part-whole concept, what two ideas must be
emphasized?
5. When first teaching about fractions (equivalent, addition, subtraction, etc.) what manipulative would you
use (unit, parts, etc.)? Why?
2
6. Use a set model to explain what means.
3
7. What is the Fundamental Law of Fractions? Why is this “fundamental”?
1
7
8. Find a fraction that is less than
away from .
100
8
9. Explain the “Density Property”.
9
as a mixed fraction? Explain this process illustrating with a manipulative.
6
2
11. How do you write 3 as a improper fraction? Explain this process illustrating with a manipulative.
3
12. For each of the problems below, use fraction circles, Cuisenaire rods, or pattern blocks for solving. On the
exam, you must use each manipulative at least once. Make sure you are explicit about your answer; show that
you can use the manipulatives to effectively explain each problem.
3 1
1 1
a.  = ______
b. 1  = ______
4 2
6 3
2 1
5
c. 1 * = ______
d.  2 = ______
3 2
6
10. How do you write
13. The product of a fraction and 5 is the same as 5 subtracted from the fraction. Find the fraction.
1
2
to both the numerator and denominator of , simplify and reduce. What fraction results?
10
5
2
1
b. Multiply both the numerator and denominator of by
, simplify and reduce. What fraction results?
5
10
1
15.
a. If the rectangle
has a value of 1 , show 1:
3
14. a. Add
b. If the diagram
has a value of
1
1
, show :
3
2
c. On the number line below, mark the approximate location of 1.
0
1
2
3
16. For each problem, write the number statement including the operation(s) , , , or  that you used to
solve the problem. Then compute the solution.
a. A patient requires 3/4 of an ounce of medicine each day. If the bottle contains 12 ounces, how many days’
supply does the patient have?
Number Statement _______________________Answer _______________________
b. Kareem had 12 gallons of ice cream in the freezer for his party. Last night Brad and Mary ate 3/4 of a
gallon. How much ice cream is left?
Number Statement _______________________Answer _______________________
c. The Pool family is driving home from a friend’s house, and Rachel and Elizabeth are restless. They ask,
“How far do we have to go?” Their father replies that they have gone 12 miles and they are 3/4 of the way
there. What is the distance from the Pool home to their friend’s home?
Number Statement _______________________Answer _______________________
d. Karla has 3/4 of an acre of land for her garden. She has divided the garden into 12 equal regions. What is
the size of each region?
Number Statement _______________________Answer _______________________
.