Lesson
8 Multiplying Mixed Numbers
Problem Solving:
Floor Plans
Lesson8 SkillsMaintenance
Lesson Planner
Name
Skills Maintenance
SkillsMaintenance
ConvertingFractions
Converting Fractions, Transformations
Activity1
Convertthemixednumbersintoimproperfractionsandviceversa.
Building Number Concepts:
Multiplying Mixed Numbers
Students learn how to multiply mixed
numbers. LAPS helps us keep our work
organized when we are working problems
with a lot of steps to remember.
Date
1.
32
3
3.
23
8
5.
7
3
11
3
19
8
21
3
2.
41
2
4.
11
4
6.
11
2
9
2
23
4
51
2
Transformations
Activity2
Identifythetransformationthatistakingplacebetweeneachpairof
shapes.Circlethecorrectanswer.
Converting from mixed numbers to improper
fractions is an important part of the process
of multiplying mixed numbers that takes
place in the alter step.
Simplifying is another important step
because the numbers we get when we
multiply can be quite large. Students should
remember to use their knowledge of number
theory to help with this step.
1.
slide or reflection
2.
slide or reflection
3.
slide or reflection
4.
slide or reflection
5.
slide or reflection
6.
slide or reflection
Objective
Students will multiply mixed numbers.
Problem Solving:
110
Unit3•Lesson8
Floor Plans
In this lesson, students continue to look at
real-world situations where they can apply
the concepts they learn. This time, they look
at floor plans as a real-world context where
we multiply mixed numbers.
Objective
Students will multiply mixed numbers in the
real-world context of floor plans.
Homework
Students convert mixed numbers to improper
fractions, multiply mixed numbers, and find
the area of two shapes in a simple tessellation.
In Distributed Practice, students solve a
mix of problems involving operations with
fractions.
352 Unit 3 • Lesson 8
Skills Maintenance
Converting Fractions, Transformations
(Interactive Text, page 110)
Activity 1
Students convert mixed numbers to improper
fractions, and vice versa.
Activity 2
Students tell if a transformation is a slide or a
reflection.
Lesson
Building Number Concepts:
Then, add the answer to
the numerator.
Connect to Prior Knowledge
Begin by discussing the algorithm for converting
mixed numbers to improper fractions. Remind
students that when we multiply fractions, we
multiply across. Explain that we use the same
steps to multiply mixed numbers, but first we
change them into improper fractions.
Multiply the whole
number by the
denominator:
7 · 9 = 63
•Show the mixed number 9 37 on the
board. ​
•Elicit from students the steps for converting
93
7 to an improper fraction. Write out the
steps of the conversion according to student
responses. Guide students as needed. Make
sure to hit the following points:
63 + 3 66
93
7= 7 = 7
When we multiply fractions, we multiply across. When multiplication
problems include mixed numbers, we follow the same steps, but first
wechangemixednumbersintoimproperfractions.LAPShelpsus
remember what to do.
Let’ssolveaproblemusingLAPS.
Example 1
1
Multiply 3 2
3 · 2.
Link to Today’s Concept
In today’s lesson, we multiply mixed numbers
and use LAPS to help us.
Board: Show the mixed number on
the board, and modify as discussed.
Floor Plans
We know that before we multiply mixed numbers, we convert them
into improper fractions. Let’s use 9 3
7 toreviewthestepsforconverting
mixed numbers into improper fractions.
(Student Text, pages 214–216)
Overhead Projector: Display the
mixed number on a transparency,
and modify as discussed.
Problem Solving:
How do we multiply mixed numbers?
How do we multiply mixed numbers?
: Use the mBook Teacher
Edition for pages 214–215 of the
Student Text. ​
Multiplying Mixed Numbers
Multiplying Mixed Numbers
Multiplying Mixed Numbers
Demonstrate
Engagement Strategy: Teacher Modeling
Demonstrate how to convert mixed numbers to
improper fractions in one of the following ways:
8
L—LOOK at the problem carefully.
• Makesurethenumbersarelinedupcorrectly.
• Decidewhatoperationissupposedtobeperformed.
1
32
3·2
Inthisproblem,wewillusemultiplication.Thereisamixednumberwe
will need to convert into an improper fraction.
214
214
Unit 3 • Lesson 8
Listen for:
•First you multiply the denominator by the whole
number. So 7 · 9 = 63. ​
•Next you have to add 63 to the numerator. So
63 + 3. This goes above the denominator, 7. ​
•When we add the numbers in the numerator, we
get 66. The improper fraction is 66
7 . ​
•Show the problem 3 23 · 12 from Example 1 .
L—LOOK
•Remind students that the first step is to check
that the numbers are lined up correctly and to
decide what operation we are going to perform.
In this case, we are multiplying. ​
Unit 3 • Lesson 8 353
Lesson 8
How do we multiply mixed numbers?
(continued)
Demonstrate
•Continue through the LAPS process.
A—ALTER
•Pay particular attention to this step, where
Lesson 8
A—ALTER the problem if necessary.
Nowwechangethemixednumberintoan
improper fraction.
11
32
3= 3
11 1
3 ·2
The problem is now set up for the next step.
P—PERFORM the operation.
This part is easy. We multiply across.
S—SIMPLIFY the answer.
The answer is not in its simplest form.
We need to convert to a mixed number.
We divide the denominator into the
numerator.
Remember, we multiply
3 · 3 = 9. Then we add
9 + 2 = 11. This is the
new numerator. We put
it over 3 to create the
improper fraction 11
3 .
11 1 11
3 ·2= 6
1 R5
11
6 = 6q11
= 15
6
11
we convert 3 2
3 to an improper fraction, 3 .
Answer: 1 5
6
Remind students about multiplying the
denominator, 3, and the whole number,
3, and adding the sum to the numerator,
2. ​
Now that we know the steps, we can also solve a multiplication problem
with two mixed numbers.
P—PERFORM
•Point out that once we create the improper
fraction, we can multiply across to get the
answer, 161 . ​
S—SIMPLIFY
•Note to students that the answer is not
in its simplest form. We can see that the
product is an improper fraction, with a
value greater than 1. So we divide the
denominator into the numerator to get the
mixed number 1 5
6 . ​
•Explain that we can use these steps to
multiply two mixed numbers.
354 Unit 3 • Lesson 8
Unit 3 • Lesson 8
215
215
Lesson 8
Example 2
Demonstrate
•Have students look at Example 2 on page
216 of the Student Text, where we
Multiply 2 15 · 4 3
4.
L—LOOK at the problem carefully.
3
21
• Makesurethenumbersarelinedupcorrectly.
5 · 44
• Decidewhatoperationissupposedtobeperformed.
Inthisproblem,wewillusemultiplication.Therearetwomixednumbers
we will need to convert into improper fractions.
multiply 2 15 by 4 3
4 . Again, go through
all the LAPS steps, paying particular
attention to the alter step.
L—Look
•Point out that the numbers are lined up
correctly.
A—ALTER the problem if necessary.
Wechangebothmixednumbersintoimproperfractions.
Wechangethefirstmixednumber:
11
21
5= 5
Nowwechangethesecondmixednumber:
19
43
4= 4
The problem is now set up for the next step.
11 19
5 · 4
P—PERFORM the operation.
This part is easy. We multiply across. We’ll use a
calculator if we need to.
•Explain that we look at the problem
S—SIMPLIFY the answer.
The answer is not in its simplest form.
We need to convert it into a mixed
number. To do this, we divide the
denominator into the numerator.
and decide which operation should be
performed. In this case, we are multiplying.
10 R9
209
20 = 20q209
9
= 10 20
Multiplyingmixed
numbers is easy if
wechangethemixed
numbers into improper
fractions first. Then we
can multiply across.
A–Alter
•Make sure students understand the
algorithm for converting mixed numbers
2 · 5 = 10 and add 10 + 1 = 11 to get the
3
improper fraction 11
5 . For 4 4 , we multiply
4 · 4 = 16 and add 16 + 3 = 19 to get the
improper fraction 19
4 .
P–PERFORM
•Note that the process for multiplying
mixed numbers is the same as multiplying
fractions as long as we remember to
convert the mixed numbers to improper
fractions: 151 · 149 = 209
20
S–Simplify
•Check to see if the answer is in its simplest
form. It is not, so we divide the denominator
into the numerator to get 10 R9. The
9
answer is 10 20
.
216
216
Remember, we multiply
4 · 4 = 16. Then we add
16 + 3 = 19. This is the
new numerator. We put it
over 4 to create 19
4 .
11 19 209
5 · 4 = 20
9
Answer: 10 20
into improper fractions. For 2 1
5 , we multiply
Remember, we multiply
2 · 5 = 10. Then we add
10 + 1 = 11. This is the
new numerator. We put it
over 5 to create 11
5 .
Apply Skills
Reinforce Understanding
Turn to Interactive Text,
page111.
Use the mBook Study Guide
to review lesson concepts.
Unit 3 • Lesson 8
Check for Understanding
Engagement Strategy: Pair/Share
Have students work in pairs to multiply two mixed
numbers together. Have them use the problem
3
1 14 · 3 12 Q 45 · 27 = 35
8 = 4 8 R . Ask them to write the
letters LAPS vertically on the page and write each step
out for the problem. Have students use Example 2 as a
model, if necessary. When pairs finish, have volunteers
share their steps and solutions with the class.
Discuss
Call students’
attention to the Power
Concept, and point out
that it will be helpful
as they complete the
activity.
Multiplying mixed
numbers is easy if
we change the mixed
numbers into improper
fractions first. Then we
can multiply across.
Unit 3 • Lesson 8 355
Lesson 8
Lesson8 ApplySkills
Name
Apply Skills
ApplySkills
MultiplyingMixedNumbers
(Interactive Text, page 111)
Activity1
MultiplythemixednumbersusingLAPS.Changeallthemixednumbers
intoimproperfractionsintheA—alterstep.Thenmultiply.Inthe
S—simplifystep,changethefractionbackintoamixednumber.
Have students turn to page 111 in the Interactive
Text, which provides students an opportunity to
practice multiplying mixed numbers.
1.
Activity 1
Students multiply mixed numbers using LAPS.
Monitor students’ work as they complete the
activity.
2.
Watch for:
3.
•Do students know to convert the mixed
numbers to improper fractions in the
alter step?
•Can students perform the operation?
•Can students simplify the answer?
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
356 Unit 3 • Lesson 8
4.
71
2
L The problem is aligned and it is multiplication.
1 10 and 2 1 = 9
A 3 =
3 3
4 4
P 10 · 9 = 90
3 4 12
S 90 = 7 6 = 7 1
12
12
2
3
1 6
11
·
5
16
8
2
L The problem is aligned and it is multiplication.
1 9
1 11
A 1 = and 5 =
8 8
2 2
P 9 · 11 = 99
8 2 16
S 99 = 6 3
16
16
48
2
11
·
3
9
3
3
L The problem is aligned and it is multiplication.
1 4
2 11
A 1 = and 3 =
3 3
3 3
P 4 · 11 = 44
3 3
9
S 44 = 4 8
9
9
3
21 · 11
1
31
3 · 24
2
Unit 3
Date
5
L The problem is aligned and it is multiplication.
1 5
1 6
A 2 = and 1 =
2 2
5 5
P 5 · 6 = 30
2 5 10
S 30 = 3
10
Unit3•Lesson8
111
Lesson 8
Problem Solving: Floor Plans
What are floor plans?
Problem Solving:
Floor Plans
What are floor plans?
(Student Text, page 217)
Floorplansaredrawingsthatbuildersusetoconstructhomes.The
builderknowshowmuchmaterialtobuybasedonthesedrawings.
Let’s look at the parts of this floor plan.
5"
1 38 "
1
2"
2 12 "
2"
Connect to Prior Knowledge
Remind students about the house project we
discussed previously.
Link to Today’s Concept
In today’s lesson, we compute area by using
information from a floor plan.
Demonstrate
•Have students look at page 217 of the
Student Text. Introduce the idea of a floor
plan. The measurements on floor plans,
or blueprints, are often mixed numbers.
We need to know the area of pictured
rectangles. The area formula involves
multiplication. Remind students that the
area of a rectangle = length · width.
1"
2
32"
1
1 18 "
2"
3"
We see that:
• Thedimensionsoftheroomsarelabeledonthefloorplansandare
used to compute the area.
key
1 in. = 6 ft.
• Theroomsarerectangular.
• Theareaiscomputedbymultiplyingthelengthoftheroombythe
width of the room.
• Thedesignisdrawninsmallerunits,suchasinches,andakeyis
givenforcomputingtheactualareaoftheroom.Forinstance,one
inchontherulercouldbeequaltooneyard.Inthiscase,oneinch
equals six feet.
Problem-Solving Activity
Reinforce Understanding
Turn to Interactive Text,
page112.
Use the mBook Study Guide
to review lesson concepts.
Unit 3 • Lesson 8
217
217
•Read the text at the bottom of the page,
and point out that plans are drawn in
smaller units than the actual measurements
of the room. For example, an inch in a
drawing might be equal to a yard in the true
measurement of the room.
Unit 3 • Lesson 8 357
Lesson 8
Lesson8 Problem-SolvingActivity
Name
Problem-Solving Activity
Date
Problem-SolvingActivity
FloorPlans
(Interactive Text, page 112)
LookatthefloorplanforTodd’ssummercabin.Toddwantstocarpetthe
entirelowerfloorexceptfortheporch.Usethedimensionsgivenforeach
roomtocomputehowmuchcarpetwillbeneeded.Remember,tofindthe
areaofarectangleyoumultiplylength·width.
Have students turn to page 112 in the Interactive
Text, which provides students an opportunity to
practice calculating area.
Todd’sSummerCabin
bathroom
BathroomDimensions
1
21
3 yards × 4 2 yards
KitchenDimensions
Explain that Todd’s summer cabin needs new
carpeting. Students figure out how much carpet
is needed by computing the area. Have students
compute the area by multiplying length times
width.
1
82
3 yards × 4 2 yards
kitchen
living room
PorchDimensions
1 yard × 11 yards
porch
Carpet needed:
Monitor students’ work as they complete this
activity.
Bathroom
10 1 square yards
2
39 square yards
49 1 square yards
2
Living Room
Kitchen
Watch for:
•Can students determine the amount of
Total
99 square yards
carpet needed for each of the rooms using
the area formula?
•Can students multiply the mixed numbers
correctly?
•Do students remember to convert the mixed
numbers to improper fractions?
•Can students add up all the areas at the end
and come up with a total?
Once students complete the activity, discuss
their answers together in class.
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
358 Unit 3 • Lesson 8
LivingRoomDimensions
11 yards × 4 1
2 yards
ReinforceUnderstanding
Use the mBook Study Guide to review lesson concepts.
112
Unit3•Lesson8
Lesson 8
Homework
Activity 1
Convert the mixed numbers into improper fractions.
Homework
11
4
21
5
3
1. 2 4
3.
Go over the instructions on page 218 of the
Student Text for each part of the homework.
4 15
4
2. 3 5
4.
5 23
19
5
17
3
Activity 2
Multiply the mixed numbers using LAPS. Remember to change the mixed
numbers into improper fractions in the “A—Alter” step, and then change the
answer back into a mixed number in the “S—Simplify” step.
Activity 1
1. 1 3 · 2 4
2
1
2. 2 5 · 3 2
1
1
4. 3 3 · 2 3
3. 4 2 · 1 16
Students convert mixed numbers into improper
fractions.
See Additional Answers below.
1
1
1
2
Activity 3
Shape A and Shape B are
used in a simple tessellation.
The length and the width
of each rectangle is
shown at right.
Activity 2
Shape A
Students multiply mixed numbers using LAPS.
Shape B
Activity 3
3
1
13
3 4 inches
inches
Students find the area of two shapes in a simple
tessellation.
1
13
inches
1.
Activity 4 • Distributed Practice
3
What is the area of Shape A? 9
8
1
2 2 inches
2. What is the area of Shape B?
17
9
Activity 4 • Distributed Practice
Solve.
Students solve a mix of problems involving
operations with fractions.
218
218
1.
2
3
4.
6
10
· 48
−
1
3
2
5
6
1
2. 9 ÷ 3
1
5
5.
8
9
·
7
8
2
7
9
3.
4
5
6.
1
3
7
+ 23 1 15
−
1
5
2
15
Unit 3 • Lesson 8
(Additional Answers continue on Appendix, pages A5–A6.)
Unit 3 • Lesson 8 359