Download Multiply a Fraction or Mixed Number by a Whole Number

LESSON
8.4
Multiply a Fraction or Mixed
Number by a Whole Number
FOCUS
COHERENCE
RIGOR
LESSON AT A GLANCE
F C R Focus:
Common Core State Standards
4.NF.B.4c Apply and extend previous understandings of multiplication
to multiply a fraction by a whole number. Solve word problems involving
multiplication of a fraction by a whole number, e.g., by using visual
fraction models and equations to represent the problem.
MATHEMATICAL PRACTICES
MP1 Make sense of problems and persevere in solving them. MP4 Model with mathematics.
F C R Coherence:
Standards Across the Grades
Before
Grade 4 After
3.OA.D.8 4.NF.B.4c 5.NF.B.4a
3.NF.A.1
F C R Rigor:
Level 1: Understand Concepts....................Share and Show (
Checked Items)
Level 2: Procedural Skills and Fluency.......On Your Own
Level 3: Applications..................................Think Smarter and Go Deeper
Learning Objective
Multiply a fraction by a whole number to solve
a problem.
Language Objective
Students explain and give examples of how you
can multiply a fraction by a whole number to
solve a problem.
Materials
MathBoard
FC R
For more about how GO Math! fosters Coherence
within the Content Standards and Mathematical Progressions
for this chapter, see page 453H.
About the Math
Professional Development
Teaching for Depth
Students now multiply a mixed number by a whole
number, using what they have learned in previous lessons.
By writing the mixed number as a fraction, students
recognize they are multiplying a fraction by a whole
number, a concept they explored in the last lesson. The
expression 5 × 2 2_3 becomes 5 × 8_3 , when 2 2_3 gets renamed
as 8_3 . Then students can model the multiplication or
simply multiply the numerator by the whole number
__ .
and write the product over the denominator to get 40
3
Students then rename the fraction as a mixed number,
__ is 40 ÷ 3. The
connecting fractions and division. 40
3
quotient is the number of wholes, and the remainder is
the number of thirds left over.
When multiplying a fraction by a whole number, students
reason that if the fraction is less than 1, the product is less
than the whole-number factor. If the fraction is greater
than 1, the product is greater than the whole-number
factor. (Note: 0 and 1 are exceptions.)
Professional Development Videos
475A
Chapter 8
Interactive Student Edition
Personal Math Trainer
Math on the Spot
Animated Math Models
HMH Mega Math
1 ENGAGE
Daily Routines
Common Core
Problem of the Day 8.4
1 _34
Lulu has
loaves of banana bread. She
cuts the loaves into 1_4 pieces. She counts the
number of fourth-size pieces she cuts. Write
1 3_4 as a fraction. 7_4
Vocabulary
™Interactive Student Edition
™Multimedia eGlossary
with the Interactive Student Edition
Essential Question
How can you multiply a fraction by a whole number to
solve a problem?
Making Connections
Ask students to tell what they know about using division to write
improper fractions as mixed numbers.
• What is the quotient when 13 is divided by 5? What is the
remainder? quotient: 2, remainder: 3
___ ? 2
• How many whole units are there in 13
5
__ as a mixed number? 2 3
__
• How do you write 13
5
5
Vocabulary Builder
Materials paper, scissors, glue, old magazines or
newspapers
Wanted: Mixed Numbers Have students
make a Wanted poster for mixed numbers.
Students should describe what a mixed
number is and where mixed numbers might
be found. Then have students look through
old magazines or newspapers to find
examples of mixed numbers to decorate
their poster.
Learning Activity
What is the problem the students are trying to solve? Connect the
story to the problem Ask the following questions.
• Is it possible to multiply two whole numbers and get a product
that is less than each factor? If so, give an example. no
• Is it possible for the product of a whole number and a fraction
to be greater than the whole number? If so, give an example.
Possible answer: yes, if the fraction is a mixed number greater than 1
Literacy and Mathematics
View the lesson opener with the students. Then have the class
participate in the following activity.
• Have students look around the classroom or school and describe
examples of mixed numbers that they see. For example, there
__ full shelves of books in a bookshelf or 44
__ tables filled
might be 23
4
5
with students in the cafeteria. Ask students to give examples of
how they could model these mixed numbers.
How can you multiply
a fraction by a whole
number to solve a
problem?
Lesson 8.4
475B
8.4
2 EXPLORE
4.NF.B.4c Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve
DO
NOTproblems
EDIT--Changes
must
be made through
"File by
info"
word
involving
multiplication
of a fraction
a whole number, e.g., by using visual fraction models and equations
CorrectionKey=B
to represent the problem.
Lesson 8.4
Name
Unlock the Problem Multiply a Fraction or Mixed Number
by a Whole Number
MATHEMATICAL PRACTICES
To introduce the lesson, have students watch
the Real World Video, The Basics of Dancing.
• How many of you like to dance?
• Dancing involves positions and steps. How
does this relate to fractions? Possible answer:
Unlock
Unlock the
the Problem
Problem
Christina is planning a dance routine. At the end of
each measure of music, she will make a 1 1_4 turn. How many
turns will she make after the first 3 measures of music?
some dances involve fractions of a turn.
1
1
1
1
1
1
1
1
1
1
1
15
___
__ + 1
__ + 1
__ + 1
__ + _ + _ + _ + _ + _ + _ + _ + _ + _ + _ + _
=1
4
4
4
4
4
4
4
4
4
4
4
_
_
_
_
_
_
_
_
_
_
_
4
4
4
4
4
1
• In Step 2, how many fourths equal one
whole? 4 fourths
• How many fourths are left over after
making wholes? 3 fourths, or ​ _34 ​
Team students with a mix of language
proficiency to provide language practice.
• Have students practice multiplying mixed
numbers by whole numbers.
• Have team members discuss ways to write
the mixed number as a fraction, multiply
the fraction by the whole number, and then
write the product as a mixed number.
475 Chapter 8
1
+
1
__
4
+
+
1
__
4
1
__
4
+
= 3 + ____ Combine the wholes. Then combine the remaining parts.
4 Possible answer: you can divide to find the number of equal groups. If each
group contains 4 fourth-size parts, then 15 ÷ 4 = 3 r3 tells you that there
3
Write the mixed number. are 3 equal groups of 4 fourth-size parts, with
= 3 ____
4
3 fourth-size parts left over.
Math
Talk
3 3_4
So, Christina will make _
turns.
© Houghton Mifflin Harcourt Publishing Company
MATHEMATICAL PRACTICES 8
Generalize How is writing
the mixed number as a
fraction in Step 2 related
to division?
1. If you multiply 3 × 1_4 , is the product greater than or
less than 3? Explain.
Less than 3; possible explanation: 3 × 1_4 = 3_4 and 3_4 is less than 3. Since 41_ is less than 1,
you know that 3 groups of 1_4 are less than 3 groups of 1 whole, or 3.
2. Explain how you can tell that 3 × 1 41_ is greater than 3
without finding the exact product.
Possible answer: you know that 1 1_4 is greater than 1, so 3 × 1 1_4 must be greater than 3 × 1.
Chapter 8 475
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2
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1
Lesson 8.4
Reteach
Name Lesson 8.4
Enrich
Name
Multiply​a​Fraction​or​Mixed​​
Number​by​a​Whole​Number
Unknown Numbers
Find the unknown number that makes each equation true.
To multiply a fraction by a whole number, multiply the numerators.
Then multiply the denominators.
1.
1
3 5 2__
3 __
4
4
Step​1 Write and solve an equation.
3.
2. Write 21
_ as a fraction.
Write 2 as _
1
4
Multiply the numerators.
Then multiply the denominators.
5.
__​​
Simplify.
5 18
4
Step​2 Write the product as a mixed number.
4
4
4
4
4
4
4
4
4
1
1
​_1​​
​_1​​
2​
4_
4 , or
​​
​​
5 4 + 4 + 4
​​
1
4
4
4
4
4
4
4
1
1
1
1
4
25
3 __
5
1​
1​_
5
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23
2
2
_
9
1 5 62
__
__
3
3
3
1
55 9 __
3 1__
6
6
6.
5
2 5 13 __
3 2__
7
7
8-11
6
Explain how you found the unknown number in
the numerator of the unknown fraction,
4​or​1​_
1​
_​
1​2
1​_
8
2 3. 5 3 __31 5 3
35
3 __
8
3​
6 ​or​2​_
2​
__
6​_
3 2​​ ​​
4. 2 3 1___ 5 10
5 5. 4 3 1__32 5 3
10
Chapter Resources
4.
Possible answer: first, I wrote 7 as 7_1
__ . I rewrote the
and 1 5_9 as the fraction 14
9
__ .
multiplication sentence as 7_1 3 5 14
9
The unknown number must be a fraction,
since the product is a fraction. To find
1 _
1_11
4 4
Combine the wholes. Then combine the remaining parts.
2. 4
5
5 1__
9
Exercise 3.
Multiply.​Write​the​product​as​a​mixed​number.
1. 3
73
7.
4
1​
4_
2
Add. Write the sum as a mixed number.
_​​
41
2 cups of flour.
So, you will need
5
3
4 3 __ 5 1__
5
5
5
18 5 _
11_
11_
111
1​1​
1​1​
1​1​
1​1​
1​1​
1​1​
1​1​
1​1​
1​1​
1​1​
1​1​
1​1​
1​
__
_11
_​​1​_
​ _
​ _
​ _
​ _
​ _
​ _
​ _
​ _
​ _
​ _
​ _
​ _
4
2.
3
A​recipe​for​one​loaf​of​bread​calls​for​2​​_14​​cups​of​flour.​How​many​
cups​of​flour​will​you​need​for​2​loaves​of​bread?
_52
_39
_
2 3 21
4 1 4
39
_____
52
134
Differentiated
Instruction
Enrich 8.4
3
DO NOT EDIT--Changes must be made through "File info"
CorrectionKey=A
5
5
Cooperative Grouping
1
+
3
Math
Talk
ELL
multiplication
STEP 2 Write the product as a mixed number.
Possible answer: multiply the numerator by 3, and
15  ​.
write the product over the denominator: 3 × ​ _45 ​= ​ __
4
to solve the problem?
15
5
__ = 3 × ____ = _____ Write 1 1_ as a fraction. Multiply.
3 × 11
4
4
4
4
• How can you find the product of 3 ∙ ​ _54 ​?
Strategy:
more
• What operation will you use
STEP 1 Write and solve an equation.
1 + ​ _14 ​, or ​ _44 ​+ ​ _14 ​= ​ _54 ​.
The whole numbers 0 and 1 are exceptions
to the rule. If students notice, explain that 0
and 1 are special cases.
or less than 1 1_4 turns in
3 measures of music?
Example
• In Step 1, how can you write 1​ _14 ​ as a
fraction? Possible answer: you can write 1​ _41 ​as
whole number and a fraction less than 1 is always less
than the whole-number factor. The product of a whole
number and a fraction greater than 1 is always greater
than the whole-number factor.
• Will Christina make more
You can multiply a mixed number by a whole number.
Example
Use Math Talk to focus on students’
relating the writing of a fraction as
a mixed number to division.
In Exercises 1 and 2, students examine the
relationships of products and factors.
MP8 Look for and express regularity in
repeated reasoning. • How is the product of a whole number and
a fraction less than 1 different from the
product of a whole number and a fraction
greater than 1? Possible answer: the product of a
Number and Operations—
Fractions—4.NF.B.4c
MATHEMATICAL PRACTICES
MP1, MP7, MP8
Essential Question How can you multiply a fraction by a whole number
to solve a problem?
5
5
LESSON
I divided 14 by 7 to get 2. To find the
denominator of the unknown fraction, I
divided 9 by 1 to get 9. So the unknown
number is 2_9 .
1
_
1 8​ ​
6. 7 3 1__ 5 6
6
Reteach
Chapter Resources
© Houghton Mifflin Harcourt Publishing Company
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4_MNLEAN343139_C08E04.indd 12
8-12
Enrich
18/02/14 6:06 PM
Rename Mixed Numbers
and Fractions
Rename Mixed Numbers and Fractions You can
use multiplication and division to rename fractions and
mixed numbers.
5
The Identity Property of
Multiplication states that the
product of any number and
1 is that number.
32 as a mixed number.
Write __
5
Write 8 1_5 as a fraction.
__ = 8 + 1
__
81
Students use multiplication and division to
rename fractions and mixed numbers.
Direct students’ attention to writing the
mixed number 8 1_5 as a fraction.
• Why can you rewrite 8 as 8 × 1? Possible
__ .
Find how many groups of 5_5 are in 32
5
5
= (8 × _
1 ) + 1__ Use the Identity Property
5
of Multiplication.
( )
5
__
= 8 × ____ + 1
5
5
40
1
= _____ + ____
5
5
Rename 1.
• The quotient is the
__ .
number of wholes in 32
5
• The remainder is the
number of fifths left over.
Multiply.
41
= _____
5
• Divide 32 by 5.
Add.
•
6 r2
5)‾
32
30
–____
2
5
answer: so the denominator is the same as _15
• How can you find the product of
8 × 5_5 ? Possible answer: multiply the numerator by
There are 6 groups of 5_5 , or 6 wholes.
There are 2 fifths, or 2_5 left over.
2
32
___
= 6 ____
5
•
5
the whole number, and write the product over the
__ .
denominator: 8 × 5_5 = 40
5
__ + 1_ ?
How can you find the sum of 40
5
5
Possible answer: add the numerators, and write the
__ + 1_ = 41
__ .
sum over the denominator: 40
5
5
5
Try This! Find 5 × 2 2_3 . Write the product as a mixed number.
8
_
5 × 2 _2 = 5 × _
3
3
40
__
=
3
_
_
131
=_
3
answer: the Identity Property of Multiplication
states that the product of any number and 1 is that
number, so 8 × 1 = 8.
Why do you rename 1 as _5 ? Possible
Direct students’ attention to the
right column.
Write 2 2_3 as a fraction.
• Why is dividing by 5 the same as finding
__ ? Possible
how many groups of 5_5 are in 32
5
Multiply.
Divide the numerator by 3.
answer: both are finding how many wholes there
are and how many fifths are left over.
3. Explain why your solution to 5 × 2 2_3 = 13 1_3 is reasonable.
5 × 2 = 10. Since 13 1_3 is greater than 10, my solution is reasonable.
4. Sense or Nonsense? To find 5 × 2 2_3 , Dylan says he can find
(5 × 2) + ( 5 × 2_3 ). Does this make sense? Explain.
Yes. Possible explanation: Dylan can think of 2 2_3 as 2 + 2_3 . Then he can use the Distributive
Property to write 5 × ( 2 + 2_3 ) as (5 × 2) + ( 5 × 2_3 ).
476
Try This!
© Houghton Mifflin Harcourt Publishing Company
Possible explanation: since 2 2_3 is greater than 2, you know that 5 × 2 2_3 is greater than
Discuss how to write 2 2_3 as a fraction.
• Will the product be greater or less than 5?
Explain. greater than 5; possible explanation:
the whole-number factor is multiplied by a fraction
greater than 1, so the product will be greater than
the whole-number factor.
DEEPER
Advanced Learners
Mathematical / Logical
Partners
Materials recipes, number cubes
• Have students practice multiplying a fraction
or a mixed number by a whole number.
• Pair students and give each pair a copy of a simple
recipe that includes fractions of amounts.
• Have partners take turns rolling a number cube
labeled 1–6 to find how many times to multiply
the recipe. If a student rolls a 3, for example, the
student would multiply all the measurements for the
ingredients by 3 to find the new measurements.
• Students can rewrite the ingredients using the new
measurements. Have partners check each other’s
work.
MP7 Look for and make use of
structure.
• How can you use the Distributive
Property to find 2 × 3 5_6 ? Possible answer:
__ = 6 +
2 × 3 5_6 = (2 × 3) + (2 × 5_6 ) = 6 + 10
6
1 4_6 = 7 4_6 .
COMMON ERRORS
Error Students may incorrectly multiply only
the fraction part of the mixed number by the
whole number.
_=4
_ , or 1 _1
Example 2 × 2 2
3
3
3
Springboard to Learning Remind students
to rename the mixed number as a fraction
before multiplying.
Lesson 8.4
476
DO NOT EDIT--Changes must be made through "File info"
CorrectionKey=A
Name
3 EXPLAIN
Share
Share and
and Show
Show
MATH
BOARD
11
__
1. 2 × 32_ = 2 ×
3
_
3
Share and Show
MATH
22
__
=_
3
BOARD
Use the checked exercises for Quick Check.
=
_
71
3
_
Multiply. Write the product as a mixed number.
Quick Check
If
Then
3
2
1
Rt I
2
_
2. 6 × 2_ = 25
5 _
Math Talk: Possible answer: 3 × 2 = 6; 2 3_4 is greater than 2;
so, 3 × 2 3_4 is greater than 6. My answer of 8 1_4 is greater
than 6, so it is reasonable.
a student misses the checked
exercises
Math
Talk
4
_
5. 4 × 5_ = 28
8 _
6
__
5
6. 6 × __
= 212
12 _
1
_
7. 3 × 2_1 = 72
2 _
1
_
8. 2 × 22_ = 53
3 _
2
_
9. 5 × 12_ = 74
4 _
3
_
10. 4 × 2_2 = 95
5 _
MATHEMATICAL
PRACTICE
On Your Own If students complete the check exercises
correctly, they may continue with the
remaining exercises.
MP7 Look for and make use of structure. Exercises 11–13 require students to use higher
order thinking skills to find an unknown
number in a multiplication sentence involving
multiplication of a mixed number by a whole
number.
• Explain how you found the answer to
Exercise 11. Possible explanation: I renamed 2​ _13 ​ as the
11.
7
Look for a Pattern Algebra Write the unknown number.
4 × 21_ = 91_
3
3
2
2 = 7_
12. 3 × 2____
4
4
13. 3 × 1 _3 = 4_1
8
8
14. Describe two different ways to write 7_3 as a mixed number.
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
Use Math Talk to focus on students’
understanding of how to check
the reasonableness of the product of a whole
number and a mixed number.
• What is the product of 3 ∙ 2? 6
• How does 2​ _34 ​ compare to 2? 2 _34 ​ > 2
• Would you expect the product of 3 ∙ 2​ _34 ​ to
be greater than or less than 6? greater than 6
MATHEMATICAL PRACTICES 1
Evaluate Reasonableness
How do you know your
answer to Exercise 3 is
reasonable?
Multiply. Write the product as a mixed number.
Math
Talk
477 Chapter 8
4
_
4. 2 × 15_ = 36
6 _
On
On Your
Your Own
Own
Differentiate Instruction with
• Reteach 8.4
• Personal Math Trainer 4.NF.B.4c
• RtI Tier 1 Activity (online)
28  ​ to get ? × ​ _
7 ​ = ​ __
28  ​.
fraction ​ _73 ​ and 9​ _13 ​ as the fraction ​ __
3
3
3
Then I thought what whole number times 7 is 28?  
4 × 7 = 28, so 4 × 2​ _13 ​ = 9​ _13 ​.
1
_
3. 3 × 23_ = 84
4 _
Possible description: one way: divide 7 by 3. Write the whole number part of the quotient
as the whole number part of the mixed number. Write the remainder as the numerator of
the fraction with the denominator of 3; another way: write 7_3 as a sum of unit fractions.
Combine fractions that make wholes, and write that amount as the whole number part of
the mixed number. Then write the remaining fraction.
Chapter 8 • Lesson 4
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477
01/03/14 12:45 PM
MATHEMATICAL PRACTICES
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4 ELABORATE
Use the recipe for 15–18.
15. Otis plans to make 3 batches of sidewalk chalk. How much
plaster of Paris does he need?
Problem Solving • Applications
4 1_2 cups
MATHEMATICAL PRACTICES
__ .
16. What’s the Question? The answer is 32
3
MP4 Model with mathematics. Students
use information in a recipe to solve
Exercises 15–18.
Possible question: How many tablespoons of
powdered paint are needed for 4 batches of chalk?
Sidewalk Chalk Recipe
_3
4
SMARTER
Patty has 2 cups of
warm water. Is that enough water to
make 4 batches of sidewalk chalk?
Explain how you know without finding
the exact product.
cup warm water
1 _12
2 _23
tablespoons powdered
paint
No; possible explanation: 4 × _12 is 2 and _34 is greater
than 1_2 , so 4 × 3_4 is greater than 2.
DEEPER
Rita makes sidewalk chalk 2 days a week.
Each of those days, she spends 11_ hours making the chalk.
18.
4
How much time does Rita spend making sidewalk chalk
in 3 weeks?
_ hours
71
2
Personal Math Trainer
SMARTER
Oliver has music lessons Monday,
Wednesday, and Friday. Each lesson is __34 of an hour. Oliver
says he will have lessons for 3__12 hours this week. Without
multiplying, explain how you know Oliver is incorrect.
19.
SMARTER
cups plaster of Paris
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (cr) ©Kent Knudson/PhotoLink/Getty Images, (br), (tr) ©Houghton Mifflin Harcourt
17.
Possible explanation: I know 3_4 is less than 1, and
I know 1 × 3 = 3. So 3_4 × 3 will also be less than 3.
Oliver's answer, 3 1_2 , is greater than 3, so it is incorrect.
478
DIFFERENTIATED INSTRUCTION
D
INDEPENDENT ACTIVITIES
For Exercise 17, students need to find the
total amount of water Patty needs to make
4 batches of chalk and compare that to the
amount of water she has.
Math on the Spot
Video Tutor
Use this video to help students model and
solve this type of Think Smarter problem.
Math on the Spot videos are in the Interactive
Student Edition and at www.thinkcentral.com.
SMARTER
Personal Math Trainer
Be sure to assign the problem in Exercise 19
to students in the Personal Math Trainer. It
features a video to help them model and
answer the problem. This problem requires
students to use numerical reasoning to
determine that Oliver’s answer is greater
than the actual product.
5 EVALUATE Formative
Assessment
Essential Question
Using the Language Objective
Differentiated Centers Kit
Activities
Fraction Bingo!
Students
complete
purple
Activity Card
6 by creating
pictorial models of fractions
and finding equivalent
fractions.
Literature
A Melody in Fractions
Students read
the book and
learn how
fractions and
equivalent
fractions are
used to read music.
Reflect Have students explain and give
examples to answer the Essential Question.
How can you multiply a fraction by a whole
number to solve a problem? Possible answer:
rename the mixed number as a fraction. Then multiply
the numerator in the fraction by the whole number, and
write the product over the denominator. Rename the
product as a mixed number.
Math Journal
WRITE
Math
Write a word problem that you can solve
by multiplying a mixed number by a whole
number. Include a solution.
Lesson 8.4
478
Practice and Homework
Lesson 8.4
Name
Multiply a Fraction or Mixed Number by
a Whole Number
COMMON CORE STANDARD—4.NF.B.4c
Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers.
Multiply. Write the product as a mixed number.
Practice and Homework
Use the Practice and Homework pages to
provide students with more practice of the
concepts and skills presented in this lesson.
Students master their understanding as they
complete practice items and then challenge
their critical thinking skills with Problem
Solving. Use the Write Math section to
determine student’s understanding of content
for this lesson. Encourage students to use their
Math Journals to record their answers.
3 =
1. 5 × ___
5
1__
10
_
_
2. 3 × __ =
__ =
4. 4 × 11
4
4_
5
_
_
__ =
5. 2 × 21
10
5
3
5
_
14
5
_
_
3
2
4_
3
_
_
3
4
3. 5 × __ =
_
33
4
_
_
__ =
6. 5 × 11
6
_
55
6
_
_
Problem
Problem Solving
Solving
7. Brielle exercises for 3_4 hour each day for
8. A recipe for quinoa calls for 2 2_3 cups of milk.
6 days in a row. Altogether, how many hours
does she exercise during the 6 days?
Conner wants to make 4 batches of quinoa.
How much milk does he need?
© Houghton Mifflin Harcourt Publishing Company
2 hours
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9.
2 cups
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Math Write a word problem that you can solve by
WRITE
multiplying a mixed number by a whole number. Include a
solution.
Check students’ work.
Chapter 8
PROFESSIONAL
DEVELOPMENT
Mathematical Practices in Your Classroom
CCSS.Math.Practice.MP7 Look for and make use of
structure.
As students multiply fractions and mixed numbers by whole numbers,
they begin to reason about the size of the products. Students
understand that when a fraction is greater than 1, the product will be
greater than the whole-number factor because it must be greater than
the whole number times 1. Then students use their understanding of
fractions and operations to reason that a product can be less than the
whole-number factor when multiplying by a fraction less than 1.
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Help students understand how a product can be less than the wholenumber factor when multiplying by a fraction less than 1:
•
•
•
•
What does 6 3 1_2 mean? Possible answer: 6 groups of 1_2
How many halves are there in 6 groups of 1_2 ? 6 halves, or 6_2
How can we rename 6_2 ? 3 Write 6 3 1_2 5 6_2 5 3 on the board.
Is 3 less than or greater than 6? 3 , 6
Repeat using other examples until students seem to grasp the idea.
Lesson Check (4.NF.B.4c)
1. A mother is 1 3_4 times as tall as her son. Her
son is 3 feet tall. How tall is the mother?
1 feet
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2. The cheerleaders are making a banner that
is 8 feet wide. The length of the banner is
1 1_3 times the width of the banner. How long
is the banner?
Continue concepts and skills practice with
Lesson Check. Use Spiral Review to engage
students in previously taught concepts and
to promote content retention. Common Core
standards are correlated to each section.
2 feet
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Spiral Review (4.NF.B.3c, 4.NF.B.4a, 4.NF.B.4b)
3. Karleigh walks 5_8 mile to school every day.
4. Write a fraction that is a multiple of 4_5 .
How far does she walk to school in 5 days?
5. Jo cut a key lime pie into 8 equal-size slices.
The next day, 7_8 of the pie is left. Jo puts each
slice on its own plate. How many plates
does she need?
7 plates
12
Possible answer: __
5
6. Over the weekend, Ed spent 1 1_4 hours
doing his math homework and 1 3_4 hours
doing his science project. Altogether,
how much time did Ed spend doing
homework over the weekend?
3 hours
© Houghton Mifflin Harcourt Publishing Company
25
__ miles
8
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Personal Math Trainer
Lesson 8.4
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