Lesson
2 Expanded Subtraction
Problem Solving:
Analyzing Data Using Subtraction
Lesson2 SkillsMaintenance
Lesson Planner
Name
Vocabulary Development
Date
SkillsMaintenance
BasicandExtendedFactFamilies
expanded subtraction
difference
Unit 2
Activity1
Findthemissingvaluesforthebasicfactfamilies.
1.
Skills Maintenance
7+8=
15
8+7=
15
2.
6+9=
15
9+6=
15
7
3.
+ 6 = 13
7
6+
Basic and Extended Fact Families
15
−7=8
15
−6=9
13 − 6 =
Building Number Concepts:
15
−8=7
15
−9=6
13 −
Expanded Subtraction
= 13
7
7
=6
Activity2
Writetheextendedfactfamiliesforthegroupsofnumbers.
In this lesson, students learn how to write and
solve subtraction problems in expanded form.
They solve problems with numbers that are up
to three digits long.
1.
70, 80, and 150
2.
200, 900, and 1,100
70
+
80
=
150
200 + 900 = 1,100
80
+
70
=
150
900 + 200 = 1,100
Objective
150 −
80
=
70
1,100 − 900 = 200
Students will write and solve expanded
subtraction problems.
150 −
70
=
80
1,100 − 200 = 900
Problem Solving:
nalyzing Data Using
A
Subtraction
Students read and analyze data in bar
graphs. They use extended addition and
subtraction facts to make observations about
data in bar graphs.
Objective
Skills Maintenance
Students will analyze data in bar graphs.
Basic and Extended Fact Families
(Interactive Text, page 53)
Homework
Students solve problems using expanded
subtraction and use data in a bar graph
to solve problems. In Distributed Practice,
students practice multidigit addition.
Unit2•Lesson2
53
Activity 1
Students fill in the missing numbers in fact families.
Activity 2
Students write extended fact families for each group
of numbers.
Unit 2 • Lesson 2 147
Lesson 2
Building Number Concepts:
Expanded Subtraction
How do we write and solve subtraction
problems in expanded form?
(Student Text, pages 77–79)
Lesson
2
Expanded Subtraction
Problem Solving:
Analyzing Data Using Subtraction
Expanded Subtraction
Vocabulary
How do we write and solve subtraction
problems in expanded form?
expanded subtraction
difference
We learned how to use expanded addition to solve problems in
Unit 1, Lesson 3. The expanded form is also used to solve subtraction
problems. This is called expanded subtraction .
Look at how we model the subtraction problem 98 − 65.
Steps for Using Expanded Subtraction:
Connect to Prior Knowledge
Remind students how to use expanded addition
to solve problems. Write the problem 47 + 21 on
the board. Have students identify the steps to
complete the problem. Illustrate the steps as the
students discuss them with you.
•Write the numbers in expanded form.
•Add the ones column. Write 8 in the ones
STEP 1
Write the numbers in expanded form.
Step 2
Subtract the ones column.
Write 3 in the ones column.
Step 3
Subtract the tens column.
Write 30 in the tens column.
Step 4
Combine and write the answer in standard form.
column: 7 + 1 = 8.
•Add the tens column. Write 60 in the tens
column: 40 + 20 = 60.
98
90 8
 65 S − 60 5
90 8
− 60 5
3
90 8
− 60 5
30 3
90 8
− 60 5
30 3
30 + 3 = 33
The sum is 30 + 3 = 33.
Remembering the steps of expanded addition will help us complete
expanded subtraction problems. We write problems in expanded form
to see the value of each digit in the problem.
•Combine and write the answer in standard
Unit 2 • Lesson 2
form: 60 + 8 = 68.
Link to Today’s Concept
Explain that like expanded addition, expanded
subtraction is a way to solve problems using the
expanded form of numbers.
Demonstrate
Engagement Strategy: Teacher Modeling
Demonstrate expanded subtraction in one of the
following ways:
: Use the mBook Teacher
Edition for Student Text, page 77. ​
Overhead Projector: Reproduce each
step from page 77 of the Student
Text, and modify as discussed.
Board: Write out each step from page
77 of the Student Text on the board,
and modify as discussed.
148 Unit 2 • Lesson 2
Step 1
•Display 98 − 65, and help students note how to
write the numbers in expanded form. Mention
that like expanded addition, we write the
problems by separating place value. ​
Step 2
•Subtract the ones column. ​
Step 3
•Then subtract the tens column. ​
Step 4
•Combine the values in the tens and ones
columns to write the answer in standard
form, just as we do in expanded addition. ​
77
77
Lesson 2
Let’s try solving a problem using expanded subtraction. As in addition,
we combine the parts of our answer to write it in standard form. The
answer in subtraction is called the difference .
Build Vocabulary
Have students look at Student Text, page 78.
Explain that expanded form can be used to
subtract, or find the difference, between two
numbers. Mention that the answer in subtraction
is called the difference .
Example 1
Find the difference between
85 and 23 using expanded form.
80 5
− 20 3
60 2
Demonstrate
•Review these key points with students:
The difference is 62.
80 5
− 20 3
60 2 S 62
We can also use expanded form to subtract three-digit numbers.
Expanded form helps you understand
the numbers in a problem.
■
Example 2
Find the difference between
589 and 262 using expanded form.
Expanded form shows the value of each
digit. For example, 7 − 2 = 5 in the tens
place represents 70 − 20 = 50.
■
589
500 80 9
 262 S − 200 60 2
500 80 9
− 200 60 2
300 20 7
•Draw students’ attention to Example 1 .
Demonstrate expanded subtraction for 85 −
23. Point out that we write the numbers 85
and 23 in expanded form in the same way
as we write them in expanded addition—by
separating place value.
85
80 5
 23 S − 20 3
The difference is 327.
78
78
500 80 9
− 200 60 2
300 20 7 S 327
Unit 2 • Lesson 2
•Remind students that we still solve problems
beginning with the ones and then the tens.
However, we are subtracting the numbers
in each column to find the difference, as
indicated by the minus sign.
•Show students how to combine the values
to write the standard form answer of 62.
Remind them that 62 is the difference.
•Tell students that we also use expanded
form to subtract three-digit numbers. Walk
through Example 2 with students. Point
out how the numbers 589 and 262 are
written in expanded form.
•Have students identify the value of each
Check for Understanding
Engagement Strategy: Look About
After reviewing Example 2, tell students they will use
expanded subtraction to find the difference with the
help of the whole class. Write the problem 58 − 12 (46)
on the board. Students should write their solutions in
large writing on a piece of paper or a dry erase board.
When they finish, ask them to hold up their solutions
for everyone to see.
If students are not sure about their answers, prompt
them to look about at the other students’ solutions
to help them with their thinking. Review the answers
after all students hold up their solutions.
digit in the numbers 589 and 262. Then
find the difference between the numbers in
each place value, and combine to write the
answer in standard form. Explain that 327
is the difference.
Unit 2 • Lesson 2 149
Lesson 2
How do we write and solve subtraction
problems in expanded form? (continued)
Demonstrate
•Direct students’ attention to page 79. Tell
students that if there are zero ones, tens,
hundreds, etc., in a number, we write a zero
as a placeholder for that particular place
value. Have students look at Example 3 .
Point out that there are zero tens in 204.
•Guide students through the example.
Emphasize the importance of writing zero
as a placeholder in the expanded form of
the number. Tell students they will not get
the correct answer if they ignore the zero.
Lesson 2
Sometimes a number has digits that are zeros. When this happens
in expanded subtraction, we need to use a placeholder.
Example 3
Find the difference between 479 and 204 using expanded form.
479
400 70 9
 204 S − 200 0 4
400 70 9
− 200 0 4
200 70 5 S 275
Notice that there are 0 tens in 204. The 0 is written as a placeholder,
and we subtract 70 − 0 in the tens place. The other digits are
subtracted as usual.
The difference is 275.
Sometimes when we subtract, the amount of digits in each number
is not the same. For example, we can subtract a two-digit number from
a three-digit number.
Example 4
Find the difference between 586 and 61 using expanded form.
586
500 80 6
 61 S −
60 1
−
500 80 6
60 1
500 20 5 S 525
There are no hundreds in 61, so we do not need to write a 0 in the
hundreds place. The other digits are subtracted as usual.
The difference is 525.
•Walk the students through the subtraction
in each place value, emphasizing how
the zero is handled. Have them help you
combine the values to write the answer in
standard form.
Expanded subtractions
helps us see place value.
Apply Skills
Turn to Interactive Text,
page 54.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 2 • Lesson 2
•Tell students that sometimes in subtraction
problems, the number of digits in each
number is not the same. Show them
how to work through a problem like this
in Example 4 .
•Show how the problem is written in
expanded form. Tell students that even
though there are no hundreds in 61, there
is no need to write 0 as a placeholder, as
in Example 3, because tens is the greatest
place value in the number.
•Tell students they can write a zero in this case
if they find it helpful, but it is not necessary.
Remind them to think of subtracting 500 − 0
for the hundreds column.
Check for Understanding
Engagement Strategy: Pair/Share
Put students into pairs, and ask each member to
solve two of the following subtraction problems
using expanded form:
150 Unit 2 • Lesson 2
95 − 42 (53)
877 − 603 (274)
186 − 51 (135)
542 − 211 (331)
When finished, have partners share their answers,
and explain how they used expanded subtraction.
Listen for:
•The identification of different digit values
•Zero as a placeholder in the tens place in 603
•Standard form answers
Have students volunteer to present their work and
explain how they used expanded subtraction to solve
their problems.
Reinforce Understanding
If students need more practice solving expanded
subtraction problems, use these examples.
74 − 21 (53)
399 − 102 (297)
79
79
Lesson2 ApplySkills
Name
Apply Skills
Date
ApplySkills
ExpandedSubtraction
(Interactive Text, page 54)
Activity1
Writethesubtractionproblemsinexpandedformandsolve.
Have students turn to Interactive Text, page 54,
where they practice expanded subtraction.
1.
Activity 1
2.
Students practice expanded subtraction. Monitor
students’ work as they complete the activity.
3.
Watch for:
4.
•Are students lining up the digits in their
correct place-value columns?
5.
•Are students writing the expanded form of
69
 27
60 9
− 20 7
40 2
Answer
42
57
 36
50 7
30 6
20 1
Answer
21
96
 32
90 6
30 2
60 4
Answer
64
597
 175
500 90 7
100 70 5
400 20 2
Answer
422
358
 142
300 50 8
100 40 2
200 10 6
Answer
216
each number correctly?
•Are students performing the subtraction
correctly?
•Are students able to combine the answers
and write the answer in standard form?
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
54
Unit2•Lesson2
Unit 2 • Lesson 2 151
Lesson 2
Lesson 2
Problem Solving: Analyzing Data Using Subtraction
How do we find differences in data?
We used bar graphs to display data. Now we will use subtraction to
analyze data in a bar graph. We use subtraction to find the difference
between two pieces of data. The difference represents an increase or
a decrease.
Problem Solving:
Analyzing Data Using Subtraction
Look at the bar graph below. The graph displays the CD sales for
the Scatter Plots from January through April.
How do we find differences in data?
Hipster Records–The Scatter Plots
CDs Sold January–April
Number of CDs Sold
(Student Text, page 80)
Explain
Direct students’ attention to the bar graph on
Student Text, page 80. Ask them to describe the
data displayed.
5,000
4,000
3,000
2,000
1,000
0
January
February
March
April
Month
Suppose the Scatter Plots’ manager wants to know how many more
CDs were sold in April than in January. We subtract the data in the
graph to determine the difference in sales between the months.
Listen for:
The graph shows that 1,000 CDs were sold in January.
It also shows that 4,000 CDs were sold in April.
We solve an extended subtraction fact to find the difference:
4,000 − 1,000 = 3,000.
•The bar graph uses vertical bars.
•The data are about CD sales for the Scatter
When we analyze data
in a graph, it helps us to
compare information
by finding differences.
The differences show an
increase or decrease.
The Scatter Plots sold 3,000 more CDs in April than January.
Plots.
•The scale has an interval of 1,000.
Demonstrate
•Explain to students that they can apply
their knowledge of subtraction to find
differences in data. Read the text below the
graph with students. Make sure students
know that the problem is asking for the
difference in the number of CDs sold in
January and April.
•Have students identify the CD sales in
January and in April. Tell students that we
use an extended subtraction fact to find the
difference.
Check for Understanding
Engagement Strategy: Think, Think
Have students answer the following questions
about the graph. Remember to give students
adequate time to think of each answer before you
call on them to respond.
Problem-Solving Activity
Turn to Interactive Text, page 55.
80
80
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 2 • Lesson 2
3,000 CDs because there were more CDs sold in
April than in January.)
Suppose sales for January were 4,000 CDs, and
sales for April were 1,000 CDs. Would sales have
increased or decreased by 3,000 CDs? How do
you know? (Sales would have decreased by 3,000
CDs because there would be more CDs sold in
January than April.)
Ask:
What is 4,000 minus 1,000? (3,000)
Did sales increase or decrease by 3,000
CDs? How do you know? (Sales increased by
152 Unit 2 • Lesson 2
Discuss
Call students’ attention to
the Power Concept, and
point out that it will be
helpful as they complete
the Problem-Solving
Activity.
When we analyze data
in a graph, it helps us to
compare information
by finding differences.
The differences show an
increase or decrease.
Lesson2 Problem-SolvingActivity
Name
Problem-Solving Activity
Problem-SolvingActivity
AnalyzingDataUsingSubtraction
(Interactive Text, page 55)
Usethebargraphtoanswerthequestions.Writeanextendedfactto
solveeachproblem.
NumberofCDsSold
Have students complete the activity on
Interactive Text, page 55. Students answer a
series of questions about a bar graph that
shows sales.
TheScatterPlots
CDsSoldJanuary–April
5,000
4,000
3,000
2,000
1,000
0
To assist students in completing the activity:
January
February
March
April
Month
•Read through the problems one at a time
1.
to ensure that students understand all the
vocabulary.
What is the difference between the number of CDs the Scatter
Plots sold in March and the number they sold in April?
4,000 − 3,000 = 1,000; The difference between the number
of CDs the Scatter Plots sold in March and April is 1,000 CDs.
2.
•Prompt students to write the extended
What is the difference in sales between January and February?
2,000 − 1,000 = 1,000; The difference in sales between
January and February is 1,000 CDs.
subtraction facts and the answer in a
complete sentence on their papers.
3.
What is the difference in sales between February and April?
4,000 − 2,000 = 2,000; The difference in sales between
February and April is 2,000 CDs.
Monitor students’ work as they complete
the activity.
4.
If this pattern of sales continues, how many CDs would be sold in
the month of May?
4,000 + 1,000 = 5,000; There would be 5,000 CDs sold
Watch for:
in May.
ReinforceUnderstanding
•Do students know to subtract when the
problem asks about the difference?
Unit 2
Date
Use the mBook Study Guide to review lesson concepts.
Unit2•Lesson2
55
•Are students able to write and solve the
correct extended fact?
Ask different students to share their answers when
they complete the activity. Have students explain
how they decided to add or subtract to solve each
problem. In the subtraction problems, ask students
to indicate if it is an increase or a decrease.
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
Unit 2 • Lesson 2 153
Lesson 2
Lesson 2
Homework
Activity 1
Find the difference using expanded form. Then write the answer in standard form.
Homework
Model
76
70 6
 53 S − 50 3
20 3
Go over the instructions on page 81 in the
Student Text for each part of the homework.
S 20 + 3 = 23
1.
98
 64
2.
77
 15
3.
275
 53
4.
353
 31
5.
436
 125
6.
397
 265
See Additional Answers below.
Activity 2
Activity 1
Use the bar graph to solve the problem.
Hipster Records—The Scatter Plots
CDs Sold May–August
Students solve problems using expanded
subtraction. Tell students to use the model
provided as a guide to set up each problem.
Month
August
July
June
May
0
Activity 2
100
200
300
Number of CDs Sold
400
500
1. How many CDs did the Scatter Plots sell between May and August? The Scatter Plots sold
1,000 CDs. 100 + 200 + 300 + 400 = 1,000
2. Compare the CD sales for May and June. What is the difference? You subtract the CD sales
Students answer questions about the data in a
bar graph. Students are to identify monthly sales
figures and find differences and totals for
the data.
for May from the CD sales for June: 200 − 100 = 100. The difference is 100 CDs.
3. Compare the CD sales for July and August. What is the difference? You subtract the CD sales
for July from the CD sales for August: 400 − 300 = 100. The difference is 100 CDs.
4. What were the total CD sales for May and June? July and August? Total CD sales for May
and June were 300. Total CD sales for July and August were 700.
Activity 3 • Distributed Practice
Add.
1.
Activity 3 • Distributed Practice
365
+ 29
2.
394
4.
In Distributed Practice, students practice
multidigit addition.
446
+ 172
618
400
+ 30
3.
430
5.
24
+ 85
109
446
+ 501
947
6.
677
+ 196
873
Additional Answers
Activity 1
90 8
1.
− 60 4
30 4 ​S ​30 + 4 = 34
2.
70 7
− 10 5
60 2 ​S ​60 + 2 = 62
3.
200 70 5
−
50 3
200 20 2 ​S ​200 + 20 + 2 = 222
4.
300 50 3
−
30 1
300 20 2 ​S ​300 + 20 + 2 = 322
5.
400 30 6
− 100 20 5
300 10 1 ​S ​300 + 10 + 1 = 311
154 Unit 2 • Lesson 2
Unit 2 • Lesson 2
6.
300 90 7
− 200 60 5
100 30 2 ​S ​100 + 30 + 2 = 132
81
81