In Lesson 6.1.3, you made sense of the answers to division problems. You paid particular attention to the meaning of each part of the division sentence. In this lesson, you will extend your understanding about dividing to include division of fractions by other fractions. As you work with your team, recall what you know about the relationship between multiplication and division and keep the following questions in mind.
How can we represent this problem with a diagram?
Can we represent it in more than one way?
Dria is writing a piece of music. She has decided to replace a
note which takes up
of a small section of the music called a measure, with
notes which each take up
of a measure. Work with your team to use diagrams to help you figure out how many
notes she will need. Then represent the problem and its solution with a mathematical division sentence and a diagram. Be prepared to describe your strategies to the class.
Malik was catching up on homework when he noticed that he got the same answer dividing
as he did when he multiplied
In other words,
. He asked his teammates, “Is dividing by
always the same as multiplying by 5?”
Liam drew the two diagrams below and wrote down
“Does it have something to do with the fact that there are
one-fifths in each whole,
wholes?” Liam asked.
“Or,” asked Malik, “Is it because
Discuss this with your team. Do Liam’s and Malik’s explanations both make sense? Why or why not? Can you think of any other ways to explain this?
Malik was looking at problem 6-43 and asked, “Does this work when both numbers are fractions? Can you find how many
s are in
?” What do you think? Refer back to the diagram you drew for problem 6-43. Be ready to explain your ideas.
DORA’S DOLLHOUSE, Part 1
Dora is building a dollhouse for her cousin. She needs several boards that are each
of a foot long. She went to the store and found that the lumber she needs is sold only in lengths of
feet. She laid a tape measure next to a board and drew the diagram below. The diagram is also available on the Lesson 6.1.4 Resource Page, “Dora’s Dollhouse”.
Work with your team to figure out how many of her
-foot boards she can cut from one
-foot piece of wood. Be prepared to explain how you got your answer and to show why it makes sense using the diagram.
After she cuts her boards, how much lumber will be left over from the
foot piece? What part of a
foot board is this? Show how you know.
Represent this situation with a division sentence.
DORA’S DOLLHOUSE, Part 2
Dora has taken a closer look at her blueprints and figured out that one
foot board is exactly
of the length of wood that she needs for her whole project.
What length of wood does she need for her project? Work with your team to use the second diagram on the Lesson 6.1.4 Resource Page, “Dora’s Dollhouse,” to help you make sense of this question.
Represent this question and its answer with division.
Compare this problem with the question and answer in problem 6-45. In what ways are these questions and answers the same? How are they different?
DIVISION AND AREA
The Ferndale High School Golden Eagles have a large playfield at their school that covers
of a square mile. One side of the playfield measures
Draw a diagram that shows this situation. Be sure to include labels.
What operation can you do to calculate the other dimension of the field? Write a number sentence for this operation.
What is the other dimension of the playing field?What strategy did you use?
For each of the division problems below, work with your team to:
Write a question in words that could be answered using the expression.
Draw a diagram that represents the problem and your question.
Find the quotient and explain what it means.
Be ready to explain your ideas to the class.
You may have noticed that one answer (quotient) in problem 6-48 is greater than one and that one of the answers is less than one, even though all of the numbers in the problem are less than one.
Work with your team to figure out why this makes sense. Be ready to explain your thinking.
Write and solve two new fraction division problems. Write one that has an answer less than one and another that has an answer greater than one. Be ready to share your problems with the class.
TEAM LEARNING LOG
In previous chapters, you explored the effects of multiplication. You enlarged and reduced figures by multiplying by numbers that were less than or greater than one. Today you will write a team Learning Log that describes the effects of division. With your team, discuss the following questions:
With your team, discuss the following questions:
Do division problems always result in an answer that is less
than or greater than the original number?
How does the size of the divisor (the number you are
dividing by) affect the answer?
Can the answer to a division problem be greater than the
Once you have agreed on the answers, write your conclusions in the form of a statement that you all agree is true about the effects of division. Then use your team statement to begin your own individual Leaning Log, but add your own examples to support and justify it. Title this Learning Log “The Effects of Division” and label it with today’s date.
Name the coordinates of each point shown in the graph at right using ordered pairs
At the school’s fall bake sale, all of the pies were cut into 6 pieces, so each person who bought a piece bought
of a pie. Each slice of pie sold for
. How much money did the school make if all eleven pies were sold? (In other words, find
Find the area and perimeter of a rectangle that is
meters. Homework Help ✎
Express each of the following numbers as a product of its prime factors. Use exponents to represent repeated multiplication, when applicable. An example is given below. Homework Help ✎
Copy the pattern below. Homework Help ✎
Draw the fifth and sixth figures on your paper.
Describe Figure 20.
How many dots will be in Figure 20?
Ms. Perez is giving her class a pizza party because every student completed the school‑wide book reading challenge. If an extra-large pizza costs
people, how much should Ms. Perez expect to pay for pizzas if her class has
students? Homework Help ✎
Solve each generic rectangle puzzle. Write your answer in the form:
(total length)(total width) = sum of individual area parts = total area. Homework Help ✎
In each of these problems, assume that people divide the food evenly. Write your answer as a division problem in fraction form:
If two people share one soda, how much of the soda should each person get?
If two people share three hamburgers, how much should each person get?
If three people share a large box of fries, what part is each person’s share?
Three people share seven brownies. How many brownies should each person get?
Two people share five apple turnovers. How many turnovers should each person get?
If five people share three cartons of chow mein, what is each person’s share?
Complete the web shown below to represent the portion
as a fraction, a decimal, and with words. Homework Help ✎