9.1
Use the
Distributive Property
PROBLEM SOLVING •
?
Essential Question How can you use the strategy draw a diagram to multiply
with multiples of 10?
Texas Essential
Knowledge and Skills
How can you use the
strategy draw a diagram
to multiply with multiples
of 10?
Number and Operations—3.4.G
Use strategies and algorithms, including the standard
algorithm, to multiply a two-digit number by a one-digit
number. Strategies may include mental math, partial
products, and the commutative, associative, and distributive
properties Also 3.4.E, 3.4.K
MATHEMATICAL PROCESSES
3.1.A Apply mathematics to problems
3.1.B Use a problem-solving model
3.1.E Create and use representations
Are You Ready?
Access Prior Knowledge
Use the Are You Ready? 9.1 in the
Assessment Guide to assess students’
understanding of the prerequisite skills
for this lesson.
Lesson Opener
Making Connections
Invite students to tell you what they know about multiples of 10.
Vocabulary
Go to Multimedia eGlossary at
thinkcentral.com
What is a multiple of 10? (A number that has 10 as a factor.) What pattern do you see
in multiples of 10? (Possible answer: They end in 0.) What digit does 30 end in? (0)
Using the Digital Lesson
You may want to discuss how multiples of ten can be represented by tens bars, tens
cubes, or tens lines.
Learning Task
What is the problem the students are trying to solve? Connect the story to the problem.
• How many boxes are there? (3 boxes)
• How many golf balls are in each box? (30 golf balls)
• What operations could you use to find the total number of golf balls?
(multiplication, addition)
• What equations could you use to find the total number of golf balls? (3 × 30,
30 + 30 + 30)
Literacy and Mathematics
Choose one or more of the following activities.
• Ask students to clarify the story and the problem by asking them to pick out the
important information from the lesson opener.
• Have students think of reasons a golfer might hit so many golf balls. Why did he
want to practice?
Resources
For the student
For the teacher
Interactive
Student Edition
provides students
with an interactive learning
environment!
Digital Management
Center organizes program
resources by TEKS!
eTeacher
Edition
Math on the Spot
Video Tutor
Online Assessment
System
iTools Virtual
Manipulatives
Soar to Success Math
Online Intervention
Lesson 9.1 275A
Name
9.1
?
Unlock the Problem
Essential Question
An area model helps students visualize multiplication
and how the Distributive Property can be used to
multiply with greater numbers.
How can you use the strategy draw a diagram
to multiply with multiples of 10?
Unlock
Unlock the
the Problem
Problem
The school assembly room has 10 rows of chairs with
20 chairs in each row. If the third-grade classes fill 3 rows
of chairs, how many third graders are at the assembly?
Make sure students understand that they need to
find the number of third graders at the assembly.
Discuss with students how the graphic organizer
helps to organize their problem solving.
Read
• Why are you using the Distributive Property?
Solve
What do I need to find?
Possible answer: if I break apart the factor 20 into smaller
numbers, I can multiply using facts I know.
third
graders
I need to find how many _
_
_
are at the assembly.
Discuss with students that drawing a model on grid
paper is like making an array. It shows rows and
columns but there is no space between the rows and
columns. This model is called an area model.
3
The third graders fill _
rows of
chairs.
© Houghton Mifflin Harcourt Publishing Company
• Why do you add the products of the smaller
rectangles to find the total product? Possible
English Language Learners
What is my plan or strategy?
30
3 × 10 = _
The Distributive Property tells me
30 = _
60
30 + _
_
break apart
the factor 20
I can ___
to multiply.
60
3 × 20 = _
10 )
3 × 20 = 3 × (10 + _
60 third graders are at
So, _
the assembly.
1.
30
3 × 10 = _
Explain how breaking apart the factor 20 makes finding
Possible explanation: I can use facts I know to find the product.
the product easier. ___________
Module 9 275
Visual
Small Group
ELL Language Support
ELPS
Beginning: Activity 8
2.1.4, 3.G.1, 3.H.3
Intermediate: Activity 40
4.F.6, 4.G.2, 4.G.4
Strategy: Draw
Advanced: Activity 57
2.C.4, 3.D.2, 3.E
Materials: Base-Ten Grid Paper (see eTeacher Resources)
Advanced High: Activity 30
1.F, 2.I.3, 3.H.3
275 Module 9
30
30
Leveled Activities
Go to thinkcentral.com for the ELL Activity
Guide containing these leveled activities.
10
I can use the sum of the products
of the smaller rectangles to find how
many third graders are at the assembly.
Plan
• Could you break apart the factors in a different
way? Explain. Yes; possible explanation: I could break
apart the 3 into a 1 and a 2. Multiply 2 × 20 = 40 and
1 × 20 = 20. Add 40 + 20 = 60.
1
20 chairs in each row.
There are _
Help students work through the steps of finding
and adding the products of the smaller rectangles to
solve.
Possible answer: It is easy to multiply with 10.
10
What information am I given?
to another 3 rows of 10.
• Why is it helpful to break apart 20 into 10 + 10?
Draw a diagram. Finish the shading to
show 3 rows of 20 chairs.
3
• How does the diagram show the Distributive
Property? Possible answer: it shows 3 rows of 10 added
answer: the products of the two smaller rectangles
combined equal the total number of third graders at the
assembly.
Number and
Operations—3.4.G
Also 3.4.E, 3.4.K
MATHEMATICAL PROCESSES
3.1.A, 3.1.B, 3.1.E
Use the
Distributive Property
PROBLEM SOLVING •
ELPS 1.A.2, 1.D, 3.H.3
• Have students draw to break
apart a larger rectangle into
smaller ones. Students can
use their drawings to help
explain how to use the
Distributive Property.
• Have students use their
models to explain how they
arrived at their answers.
4 x 30 = 4 x (10 + 10 + 10)
10
4
+
30
10
+
10
Try
Try Another
Another Problem
Problem
Megan is watching a marching band practice.
The band marches by with 4 rows of people playing
instruments. She counts 30 people in each row. How
many people are marching in the band?
Read
Try Another Problem
For this problem, make sure students understand that
they need to find the number of people marching
in the band. Have students answer the questions in
the graphic organizer and solve the problem. Invite
students to share their diagrams by sketching them
on the board. Ask them to communicate the steps
they used.
Solve
What do I need to find?
I need to find how many
people are marching in
the band.
Record the steps you used to solve
the problem.
10
4
1
40
10
1
40
10
• What strategy and steps did you use to solve the
problem? Possible answer: I broke apart the factor 30 into
10 + 10 + 10. I shaded 4 rows of 10 three times. I used
40
What information am I
given?
The band has 4 rows of
people playing instruments.
There are 30 people in
each row.
Plan
What is my plan or
strategy?
I will draw a diagram and
break apart the factor 30
into 10 + 10 + 10 to use
facts I know.
2.
the diagram to find the products of the smaller rectangles.
Then I added the products.
• Why do you add the products of the smaller
rectangles to find the total product? Possible answer:
First, I shade 4 rows of 30, or 10 + 10 + 10.
Next, I find the products of the three
smaller rectangles.
4 × 10 = 40 4 × 10 = 40 4 × 10 = 40
Then, I find the sum of the three products.
40 + 40 + 40 = 120
4 × 30 = 120
each smaller product is part of the total product. I add the
parts together to find the whole product.
• How could you break apart the factor 30 into three
addends? Possible answer: I could break apart 30 into
10 + 10 + 10.
So, 120 people are marching in the band.
• What is another way you can break apart the
factor 30? Possible answer: 10 + 20
Explain how you can use the Distributive Property to
help you find a product.
add the products to find the total product.
Math Talk
Possible explanation: there are 4 rows with
30 people in each row; 30 + 30 + 30 + 30 = 120.
So, my answer of 120 people is reasonable.
Mathematical Processes
Explain how you can check
to see if your answer is
reasonable.
276
© Houghton Mifflin Harcourt Publishing Company
Possible explanation: I can break apart the greater factor to use facts I know. Then I can
Math Talk
Mathematical Processes
Use Math Talk to help students understand the
reasonableness of their answer.
COMMON ERRORS
C
E
Error
Students may use addition instead of
multiplication when using an area model to solve a
problem.
Example Students write:
4 + 10 = 14
Enrich
Visual / Kinesthetic
Individual / Partners
Materials: Base-Ten Grid Paper (see eTeacher Resources)
• Have students find all the possible
10 + 10 + 10 + 10 + 10 + 10
4 40
40
40
40
40
40
ways to break apart a factor into
multiples of 10 for 4 × 60 = ■.
4 x 60 = 4 x (10 + 10 + 10 + 10 + 10 + 10)
Students should break apart 60 into
addends that are multiples of 10. Let students know that they may use
any number of addends.
• Have students show each example on grid paper with an equation that
shows the Distributive Property. One possible way is shown.
• Have students write an explanation for how they found all the ways to
break apart the factor.
Go to Go to thinkcentral.com for additional enrichment
activities in the Enrich Activity Guide.
4 + 10 = 14
4 + 10 = 14
14 + 14 + 14 = 42
4 × 30 = 42
Springboard to Learning Remind students that
an area model shows equal groups. Help students
recognize that these groups are shown by rows,
which each have the same number of squares. Point
out that the number of rows and the number of
squares in each row represent factors.
Lesson 9.1
276
Name
Unlock
Unlock the
the Problem
Problem
Share
Share and
and Show
Show
Share and Show
1.
The first problem connects to the learning model.
Have students use the MathBoard to explain their
thinking.
Problem 2 requires students to reinterpret Problem 1
given different information.
The front section of a theater has 6 rows
with 40 seats in each row. In the front section,
24 seats are reserved. How many seats in the front
section of the theater are not reserved?
1
10
6
Use the checked exercises for Quick Check. Students
should show their answers for the Quick Check on the
MathBoard.
1
10
1
10
60
60
Choose a strategy you know.
60
10
60
Find the products of the smaller rectangles.
× 10
60
=_
6 ×_
10 = _
60
_
60
6 ×_
10 = _
_
6 ×_
60
10 = _
_
6
3
60 + _
60 + _
60 = __
60 + _
240
Find the sum of the products. _
Quick Check
IF
Underline important facts.
Draw and label a diagram to break apart the problem.
Have students compare their models in Problems
1 and 2 and discuss different ways to break apart the
factors.
1
Use the Problem Solving MathBoard.
6 × 40
Step 1, Write the problem you need to solve. __
Go Deeper
2
√
√
√
Tips
240
There are __
seats in the front section of the theater.
24 = __
216
Step 2, Find the difference. 240 − _
a student misses the checked exercises
216
So, there are __
seats in the front section that are not reserved.
THEN
Differentiate Instruction with
RtI Tier 1 Lesson 41
2.
What if seats are added to the front section of the theater so
that there are 6 rows with 50 seats in each row? How many seats
are in the front section?
300 seats
Problem Solving
In Problem 3, students need to multiply to find the
lengths of the blue ribbons and the red ribbons and
then compare the two products.
© Houghton Mifflin Harcourt Publishing Company
Problem
Problem
Problem Solving
Solving
3.
Multi-Step Tova sewed 60 pieces of blue ribbon
together to make a costume. Each piece of ribbon was 2 meters long.
She also sewed 40 pieces of red ribbon together that were each 3
meters long. Did Tova use more blue ribbon or red ribbon? Explain.
She used the same amount. 60 × 2 = 120; 40 × 3 = 120
Module 9 • Lesson 1 277
M
Math
on the Spot
Video Tutor
V
Through the Math on the Spot Video Tutor,
students will be guided through an interactive
solving of this type of H.O.T. problem. Use this
video to also help students solve the H.O.T.
problem in the Interactive Student Edition. With
these videos and the H.O.T. problems, students
will build skills needed in the TEXAS assessment.
3
RtI Tier 1 Lesson 41
2
1
Name
Name
LESSON
41
3.4.G
OBJECTIVE Solve multiplication problems by using the strategy draw a diagram.
Read
Math on the Spot videos are in the
Interactive Student Edition and at
thinkcentral.com.
Solve
10
+
60
6
1.
10
6
rows of singers.
20
singers.
Plan
© Houghton Mifflin Harcourt Publishing Company
What is my plan or strategy?
I can draw a diagram and use the
Distributive Property to break apart
the factor 20 into 10 + 10 to use
facts I know.
Use this problem for 4–6.
An artist sells 4 paintings for
$20 each, 4 sculptures for
$60 each, and 4 photographs for
$10 each at her art show.
Lee has 6 sheets of stickers with
30 stickers on each sheet. She has
8 sheets with 20 stickers each and
9 sheets with 10 stickers each.
60
6
rows of
20
The artist sells 2 more paintings
and 4 more sculptures at the same
prices. What is the total amount of
money the artist has made so far?
3.
How many more paintings,
sculptures, and photographs would
the artist need to sell to make
another $500?
singers.
Next, I break apart 20 into 10 + 10
and find the products of the two
smaller rectangles.
6 × 10 =
60
6 × 10 =
+ 60
160 players
Number and Operations
5.
Lee gives 4 sheets with 20 stickers
and 3 sheets with 10 stickers to her
sister. How many stickers does Lee
have left?
6.
Now Lee gives some stickers to
her friend Myla. What sheets does
Lee give to Myla if she has 200
stickers left?
320 stickers
= 120
6 × 20 = 120
Possible answer: 5 paintings,
Possible answer: 2 sheets with
5 sculptures, 10 photographs
30 stickers and 3 sheets with
So, there are 120 singers.
1. Eight teams play in a Little
League series. Each team has
20 players. How many players
are in the series?
How many stickers does Lee have in
all?
$640
60
Then, I find the sum of the two
products.
60
4.
430 stickers
2.
First, I draw and label a diagram to
show
How much money does the artist
make on these sales in all?
$360
What information am I given?
There are
Use this problem for 1–3.
Record the steps you used to solve
the problem.
are in the performance
Each row has
Apply the Distributive Property
Use the Distributive Property to help solve each problem.
There are 6 rows of singers in a performance. There
are 20 singers in each row. How many singers are in
the performance?
What do I need to find?
Enrich 42
1
Problem Solving • Use the
Distributive Property
I need to find how many singers
277 Module 9
Enrich 42
20 stickers
7.
2. The assembly room has 6 rows
with 30 chairs in each row.
If third graders fill 3 rows,
how many third graders are
in the room?
How did the Distributive Property help
you solve the problems?
Possible answer: I used the Distributive Property to break apart
greater numbers into lesser numbers that are easier to work with.
90 third graders
81
Enrich
© Houghton Mifflin Harcourt Publishing Company
E42
Mathematical Processes
Model ¥ Reason ¥ Communicate
Daily
Daily Assessment
Assessment Task
Task
3
Fill in the bubble for the correct answer choice.
4.
5.
6.
Daily Assessment Task
Apply A zoo gives 8 tubs of food to the male gorillas. Each
tub has 40 pounds of food. How much food do the male
gorillas eat each day?
A
270 pounds
B
180 pounds
C
320 pounds
D
90 pounds
THEN
IF
NO
•
Soar to Success Math
Warm-Up 12.51
A
23
C
60
B
17
D
50
YES
•
•
Enrich 42
Homework and Practice
Lesson 9.1
Multi-Step Shania makes a scrapbook about her trip to
the state capitol. She makes 2 sections about the history and
4 sections about what she saw. Each history section has
30 pages and each section about what she saw has 20 pages.
How many pages does Shania’s scrapbook have?
B
1
Can students use the strategy draw a diagram
to multiply with multiples of 10?
Marcus will make 20 omelets. Each omelet takes 3 eggs.
How many eggs will Marcus use?
A
2
TEXAS Test Prep Coach
140
C
80
Test Prep Coach helps teachers to identify common
errors that students can make.
300
D
60
In the Test Prep exercise, if students selected:
A They may have added 5 to the tens place.
B They may have broken $20 into $10 + $10 and
added $5 to each $10.
TEXAS Test Prep
Stefan orders theater tickets for each of the 5 members
in his family. If each ticket costs $20, what is the total
cost for the tickets?
A
$70
B
$30
C
$25
D
$100
C They added $5 to $20.
© Houghton Mifflin Harcourt Publishing Company
7.
278
?
Essential Question
Write
Math
How can you use the strategy draw a diagram to
multiply with multiples of 10? Possible answer: I can
draw and shade a rectangle on grid paper to show the
problem. Then I can break apart a factor to make smaller
rectangles for facts I know.
Differentiated Centers Kit
Games
Games
Multiplication
Bingo
Students practice
multiplication
facts through 10.
Literature
Party Plans by the
Numbers!
Students read the book
and use multiplication
facts and strategies to
plan a party.
Activities
Multiplication Dash
Students complete
orange Activity
Card 17 by using
models to apply
multiplication facts
through 12 by 12.
Lesson 9.1
278
5
Number and Operations—3.4.G
Also 3.4.E, 3.4.K
MATHEMATICAL PROCESSES 3.1.A, 3.1.B, 3.1.E
9.1
Name
Fill in the bubble completely to show your answer.
• Use the Distributive
PROBLEM SOLVING
Property
4.
Draw and label the diagram to solve.
1.
The Morgan family buys 7 booklets of tickets at the carnival.
Each booklet has 30 tickets. Of all the tickets bought, 21 tickets
are for rides. How many tickets are not for rides?
Step 1
+
10
10
10
+
1
10
1
10
10
7
6.
Find the products of the smaller rectangles.
7
7
×
10
×
10
=
70
=
70
×
7
=
10
70
Find the sum of the products.
70
+
70
+
70
7
×
30
=
210
=
8.
21
=
189
© Houghton Mifflin Harcourt Publishing Company
189
tickets that are not for rides.
So, there are __
Problem
Problem Solving
Solving
2.
The roller coaster ride costs 8 tickets.
If 30 people ride the roller coaster,
how many tickets are collected?
30
×
8
=
240
3.
50
×
6
=
At the town picnic, there are 7 stacks
of paper cups on a shelf. Each stack
holds 60 cups. How many cups are
on the shelf?
160
A
490
B
28
B
420
C
16
C
670
D
140
D
67
Mr. Franz buys 4 bags of forks. There
are 30 forks in each bag. Which
number sentence shows how many
forks are there in all?
7.
Valerie buys 5 sticker books. Each
book has 80 stickers. Which number
sentence shows how many stickers
Valerie buys?
A
4 + 30 = 34
A
5 × 80 = 40
B
4 × 30 = 120
B
8 + 50 = 58
C
4 + 30 = 120
C
5 × 80 = 400
D
40 + 30 = 70
D
5 × 80 = 450
Use the Homework and Practice pages to provide
students with more practice on the concepts and
skills of this lesson.
279
Multi-Step A farm stand has
4 bushels of apples. Each bushel
has 40 red apples. There are also
7 bushels of 30 green apples. How
many apples are there in all?
A
490
B
370
D
300
Module 9 • Lesson 1
Module 9
5.
A
C
The giant swing ride costs 6 tickets.
If 50 people ride the giant swing ride,
how many tickets are collected?
Homework and Practice
279-280
Ari has a rock collection. He puts
20 rocks into each of 8 boxes. How
many rocks does Ari have in his
collection?
210
210
tickets.
They have __
Step 2 Find the difference. 210 −
TEXAS Test Prep
Lesson
Lesson Check
Check
280
280
160
9.
Multi-Step Marcel buys 3 large
boxes of cherries. Each box holds
40 cherries. He also buys 8 small
boxes. Each small box holds
20 cherries. How many cherries
does Marcel buy?
A
280
B
120
C
480
D
160
© Houghton Mifflin Harcourt Publishing Company
Ho mewo rk
and Practice