Multiplying Fractions and Mixed Numbers
Making Muffins
ACTIVITY
ACTIVITY 2.3 Investigative
2.3
Multiplying Fractions
and Mixed Numbers
SUGGESTED LEARNING STRATEGIES: Create Representations,
Quickwrite, Look for a Pattern
My Notes
Activity Focus
Jack wants to use this recipe to make some muffins, but he has only
2 cups of flour. He thinks he can change the amounts of all the
other ingredients so that the recipe uses 2 cups of flour.
Blueberry Cinnamon Muffins
8 cups whole-wheat flour
2 cups honey
1 tsp. cinnamon
1 tbs. baking powder
4 __
1 __
2
2
3
1
__ tsp salt
2 __ cups applesauce
3
8
1 cups blueberries
3 __
4 cups milk
2
Makes 48 muffins
• Multiplying fractions
• Multiplying mixed numbers
CONNECT TO MEASURES
Materials
1 cup = 16 tablespoons (tbs)
1 cup = 4 tbs
__
4
1 tbs = 3 teaspoons (tsp)
• Measuring cups (optional)
• Measuring spoons (optional)
• Sand (or some other suitable
matter for measuring)
Chunking the Activity
Think about how 2 cups of flour is related to 8 cups of flour.
#1–2
#3
1. How many 2-cup amounts are there in 8 cups? Make a drawing
to show your answer.
#4–6
#7–8
#9–Try These A
#10–11
4 2-cup-amounts
1 Create Representations This
question introduces the focus on
multiplying fractions by scaling
down a recipe.
2. What fraction of 8 is 2? Show how you found your answer.
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1 ; I said that the whole was
Answers may vary. Sample answer: __
4
8 and the part was 2, and since a fraction is a part to the whole,
2 and it simplifies to __
1.
the fraction is __
8
4
2 Students find what fraction 2 is
of 8 and support their answers.
3 Look for a Pattern,
3. Help Jack figure out how to change his recipe so he can use the
2 cups of flour that he has.
Debriefing Be sure to debrief
after Question 3 so that all students understand that all recipe
amounts must be multiplied by _14_.
You may also want to use measuring tools and sand to model the
measuring tasks in the questions
in this activity.
a. How will he use the fraction to adjust the recipe?
1 of each ingredient or he can divide the amount
He can use __
4
of each ingredient by 4.
b. How much milk will he use?
1 cup
c. How much honey will he use?
__1 cup
2
d. How many muffins will he make?
12
Unit 2 • Operations with Numbers
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Unit 2 • Operations with Numbers
83
ACTIVITY 2.3 Continued
4 Students use a drawing to
show _13_ of 6.
ACTIVITY 2.3
continued
Multiplying Fractions and Mixed Numbers
Making Muffins
SUGGESTED LEARNING STRATEGIES: Create Representations,
Look for a Pattern, Quickwrite
My Notes
56 Create Representations,
4. Joy wants to use one-third of this recipe to make some muffins.
She is wondering how much cornmeal she should use.
Look for a Pattern, Debriefing
Students now discover how
to multiply by a unit fraction,
and then, by extension, how to
multiply by any fraction.
Cornmeal Muffins
1 tbs. salt
6 cups cornmeal
1 __
2
3
1
__ cups flour
7 __ tsp. baking powder
4
2
1 cups milk
1 cup sugar
__
4 __
4
2
1 cup corn oil
__
6 eggs
2
Makes 36 muffins
Suggested Assignment
CHECK YOUR UNDERSTANDING
p. 86, #1–3
1 of 6 cups.
a. Make a drawing to show __
3
UNIT 2 PRACTICE
p. 134, #12–15
b. How much cornmeal will Joy use? 2 cups
1 of 6 is by multiplying fractions. Each step
5. Another way to find __
3
is shown below. Explain what was done in each step.
Explanation
Wrote 6 as a fraction with 1 as the denominator.
Multiplied the numerators and the denominators.
© 2010 College Board. All rights reserved.
Remember that a fraction shows
a division problem.
1=1÷4
__
4
6=6÷4
__
4
A whole number can always be
represented as fraction with a
denominator of 1.
3
3 = __
1
Steps
6
1 × __
__
3 1
1×6
_____
3×1
6
__
3
2
Simplified the numerator and the denominator.
Simplified the fraction.
2 of 6? Find the answer two ways. Show your work for
6. What is __
3
each method.
1 of 6
Answers may vary. Sample answer: One way is to find __
1 × 6 × 2 = 4. Another way is to 3multiply
and multiply that by 2: __
3
1 of that:
1 = 4.
6 by 2 and find __
6 × 2 × __
3
3
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Multiplying Fractions and Mixed Numbers
ACTIVITY 2.3
Making Muffins
ACTIVITY 2.3 Continued
continued
79 Create Representations
SUGGESTED LEARNING STRATEGIES: Create Representations
These questions build on each
other and begin a process that
motivates students understanding
of multiplication of fractions.
They build understanding by
progressing from drawings to
algorithms.
My Notes
Now look at the amounts of some other ingredients in Joy’s recipe.
7. This grid is a model for 1 cup of
sugar.
1 cup
a. Shade the grid to show __
4
of sugar.
EXAMPLE 1 Create Representations, Debriefing Students
now apply their understanding
of expressing mixed numbers as
improper fractions to be able to
extend multiplying fractions to
multiplying fractions and mixed
numbers.
1 of __
1.
b. Use an X to show what part of the drawing represents __
3 4
1 of __
1 cup?
c. What fraction of the whole cup represents __
3 4
1
___
It is
12
of the whole cup.
1 . Write and evaluate an expression
1 of __
d. Your model shows __
3 4
1
1.
to show multiplying __ × __
3 4
1
1 1 1×1
__ × __ = _____ = ___
3
3×4
4
12
1.
2 of __
8. Write and evaluate an expression to find __
3 4
Differentiating Instruction
2 × 1 = ___
2 = __
1
__2 × __1 = _____
3
3×4
4
12
6
Work one-on-one with struggling
students to be sure that they
understand the drawings before
moving to the algorithms. Point
out that the product (or answer)
when multiplying with proper
fractions will not be greater than
either factor.
1 squares
9. Make a drawing in the My Notes space to represent 1 __
© 2010 College Board. All rights reserved.
1 of that amount2 is.
of baking chocolate. Then show what __
3
EXAMPLE 1
1 × 1 __
1.
Find __
3
2
When you write an expression for multiplication with a mixed
number, change the mixed number to an improper fraction.
3 = _____
1 × 3 = __
3 = __
1
1 = __
1 × __
1 × 1__
__
3
2
3
2
3×2
6
2
TRY THESE A
Write and evaluate an expression to find each product.
2
3 × 2 __
2
1
__
b. 1 __
a. __
3 × 12
4
3
2 × 3 = __
6=1
__2 × 1__1 = __2 × __3 = _____
3
2
3
2
3×2
6
3 × 2 __
8 = ___
56 = ___
2 = __
7 × __
14 = 4 __
2
1 __
4
3 4 3 12
3
3
Unit 2 • Operations with Numbers
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Unit 2 • Operations with Numbers
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ACTIVITY 2.3
continued
0a Think/Pair/Share Consider
guiding students through
Question 10 and let them do
Question 11 independently.
Multiplying Fractions and Mixed Numbers
Making Muffins
SUGGESTED LEARNING STRATEGIES: Think/Pair/Share
My Notes
10. Rewrite the amounts of all the ingredients so that Joy can
1 of the original recipe.
make __
3
Suggested Assignment
Cornmeal Muffins
CHECK YOUR UNDERSTANDING
p. 86, #4–6
2
__1
UNIT 2 PRACTICE
p. 134, #16–18
4
1
___
12
__1
6
2. _12_
2
1
2 __
cups flour
2
1
1 __
cup sugar
cup corn oil
Makes
1.
__1
cups cornmeal
12
tbs. salt
tsp. baking powder
2
cups milk
2
eggs
muffins.
11. Rewrite the amounts of all the ingredients in Jack’s recipe so
that he can make 12 Blueberry Cinnamon muffins.
3. 1_13_
4. 8_13_
Blueberry Cinnamon Muffins
33
11 = 2_3_
5. _13_ × 8_14_ = _13_ × ___
= ___
4
4
4
2
6. Answers may vary. Sample
answer: The operation signs
are different but the result is
the same. _51_ × 25 is the same
as 25 ÷ 5—both have 5 as the
answer.
__3
8
7
___
12
__7
8
cups whole-wheat flour
2
1
1 __
tsp baking powder
8
3
___
cups applesauce
cups blueberries
Makes
_1_
12
cups honey
tsp cinnamon
32
teaspoon salt
1
cups milk
© 2010 College Board. All rights reserved.
ACTIVITY 2.3 Continued
muffins.
CHECK YOUR UNDERSTANDING
Write your answers on notebook paper.
Show your work.
1 × 9.
1. Make a drawing to show __
3
Find each product.
1×2
2. __
4
2×6
3. __
9
2×5
4. 1 __
3
1 of 8 __
1 yards. Write and
5. Joe wants to find __
4
3
solve an equation to find the answer.
6. MATHEMATICAL Compare multiplying
1 and dividing by 5.
R E F L E C T I O N by __
5
Include diagrams with your explanation.
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