CC Course 1
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Throughout this course, you have learned to do a lot with fractions. You have used
fractions in multiplication, addition, and subtraction problems. You also modeled how to
divide equal shares of licorice between classmates and into groups of given sizes. In this
lesson, you will connect these ideas as you learn more about the operation of division and
as you make sense of fraction division. As you work on the problems in this lesson, ask
your teammates these questions to generate useful discussion:
 How can we represent this with a diagram?
 Is there another way to see it?
 What is it “part” of? What is the whole?
6-26. PIES FOR PERCUSSIONISTS
Troy is a proud drummer in the Minnie Mites Marching Band
and has invited his fellow drummers over for a party. When he
called to order three pies from the local bakery, he was told that
each pie would be cut into pieces that are each
of a pie.
Troy is wondering if he has ordered enough pie to share with
all the drummers.
1. How many pieces of pie will he have in all? Draw a picture to represent this
situation. Be prepared to explain your answer to the class.
2. This problem can be represented with a division sentence as well as several other
number sentences. Work with your team to find two or more number sentences to
describe this situation. Be sure that one of the number sentences uses division.
3. Including Troy, there will be 12 people at the party. If all three pies are shared
equally, what portion or part of one pie will each person get? Represent this
situation with two or more number sentences. Use the diagram from part (a) to
explain your answer.
6-27. Sarah had just made three fresh pies when she got a phone call from her boss,
Glenda.
o Glenda: How many pies do you have so far?
o Sarah:
Three.
o
Glenda: That’s only
of the number we need for today’s orders.
4. How many pies does the bakery need for the day? Draw a picture to represent
this situation and be prepared to explain your answer to the class.
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5. Work with your team to find at least two different ways to represent the situation.
Include at least one multiplication and one division number sentence.
6-28. Compare the division number sentences and the diagrams you drew to represent
them in problems 6-26 and 6-27. How are they similar? How are they different? How is
the meaning of your answer different in these two problems? Be ready to discuss your
ideas with the class.
6-29. Troy and Phillip both noticed that each time they represented a problem with a
division sentence, they could write a related multiplication sentence. Their team decided
to see if they could represent each situation below in four ways: with words, diagrams, a
multiplication number sentence, and a division number sentence.
Help them finish what they started by filling in the missing representations. Part (a) is
already completed.
0. Question in Words: How many quarter-pies make three whole pies?
Symbols (2 sentences): 3 ÷
= 12 and 3 · 4 = 12
Diagram:
Answer in Words: Twelve quarter-pies make three whole pies.
1. Question in Words: $5 is
of how much money?
Symbols (2 sentences):
Diagram:
Answer in Words:
2. Question in Words: How many half-dollars make $30?
Symbols (2 sentences):
Diagram:
Answer in Words:
3. Question in Words:
Symbols (2 sentences): 6 ÷
Diagram:
Answer in Words:
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= 4 and
·4=6
6-30. How is it that the same division problem, 3 divided by
, could be diagrammed in
different ways and the answer could seem to refer to different amounts? Consider this as
you think about the simple division problem 10 ÷ 4.
0. What does 10 ÷ 4 really mean? Work with your team to draw as many diagrams
as you can to represent 10 ÷ 4. For each diagram, write a word problem to
match. Be prepared to share your diagrams and problems with the class.
1. 10 ÷ 4 = 2
. Consider this answer in relation to your diagrams and problems
from part (a). Where do you see the 2
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in each diagram? In each case, what
does the answer of 2
mean?
2. How have you seen these different meanings for division in the previous problems
in this lesson and in Lesson 6.1.2? Discuss this with your team and be prepared to
explain your ideas to the class.
6-31. DIVIDE AND CONQUER: The Undoing Game
Troy knows that division and multiplication are inverse operations. In other words,
multiplication undoes division and division undoes multiplication. You can use
multiplication to check an answer to a division problem.
Troy challenged Phillip to the matching game, “Divide & Conquer.” He said to Phillip,
“I’ll ask you a division problem. You solve it and turn it around with a multiplication
sentence to prove your answer.”
When Troy said, “3 pies divided in eighths results in 24 pieces.” Phillip responded, “If I
eat
of a pie, 24 times, I’ve eaten 3 whole pies.
.”
State each problem below as a division problem. Then solve the problem and confirm
your solution by writing and stating the appropriate multiplication sentence.
0. If each box holds 5 books, how many boxes or partial boxes would be filled by 14
books?
1. How much does each person get if
pound of chocolate is shared equally
between 3 people?
6-32. LEARNING LOG
How are multiplication and division related? Include examples and
diagrams in your Learning Log that demonstrate the relationship.
Title this entry “Multiplication and Division” and label it with
today’s date.
6-33. Use a ruler to draw a line exactly 4 inches long and then mark every
Homework Help ✎
1. How many
inches are in 4 inches?
2. Now use the ruler to mark every
3. How many
inch.
inch. How many
inches are in 2 inches? in 3 inches?
inches are in 1 inch?
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6-34. Draw a diagram that shows how to divide 9 pieces of licorice into packages that
hold 5 pieces each. Then find 9 ÷ 5. Homework Help ✎
6-35. Audrey made the histogram below to show her recent bowling scores. Homework
Help ✎
1. How many games did she play in total?
2. Between what two values did most of her scores fall?
3. Challenge: What portion of her scores fell between 130 and 140?
6-36. Multiply the following fractions. Homework Help ✎
1.
2.
3.
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4.
6-37. Graph and connect the points (1, 1), (1, 5), (4, 5) and (4, 1) in the order listed and
then connect the last point you graphed to the first point. What is the length of each
side? What is the area of the shape that is formed? 6-37 HW eTool
(Desmos). Homework Help ✎
6-38. Draw a diagram to help calculate each of the following quotients (the answer to a
divison problem). Homework Help ✎
1. 4 ÷
2. 6 ÷
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6-39.
Jesse has five meters of twine and needs to cut it into lengths that
are each
of a meter long. How many lengths will he have? Express this problem in a
number sentence that uses division. Homework Help ✎
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6-40. Arrange each of these fractions on a number line:
.
Homework Help ✎
6-41. Multiple Choice:If a pizza is split evenly among 3 people, which of the following
is the most accurate description of the amount of the whole pizza each person should
receive? Explain your choice. Homework Help ✎
1. 0.33
2.
3. 33.3%
6-42. Draw generic rectangles to calculate each of the following products. What is each
product? Homework Help ✎
1. 11 · 33
2. 111 · 333