Lesson
7 Regrouping in Expanded Addition
Problem Solving:
Finding Information in Tables
Regrouping in Expanded Addition
Vocabulary
When do we have to regroup to add?
regroup
We know that we can model numbers with place-value coins.
The number 57 is 5 tens coins and 7 ones coins as shown in the
coin model below.
If we want to add 5 to 57,
we add 5 ones coins
to the ones column.
Tens
Ones
10
10
1
1
1
10
10
1
1
1
1
1
1
1
1
10
57
1
+5
50 + 7 + 5
When we find the sum, we see
that 5 ones coins and 7 ones
coins combine to make 12
ones coins.
Tens
Tens
Ones
10
10
1
1
1
10
10
1
1
1
10
10
1
1
1
10
10
1
1
1
1
1
1
10
10
1
1
1
1
1
1
1
1
1
10
When we have ten ones coins,
we can regroup them into
1 tens coin.
We use this model to learn
how to regroup ones into
tens when we have more
than 9 coins in an addition
problem.
Ones
Regrouping
50 + 12
Tens
10
10
10
10
10
10
Ones
1
1
60 + 2 = 62
Unit 1 • Lesson 7 29
Lesson 7
We have been adding numbers using expanded addition. Now, we will
try some problems that need regrouping. We have to regroup ones to
tens when the sum of the ones is greater than 9.
Example 1
Find the sum of 57 and 28 using expanded addition.
Step 1
Add the ones.
50
+ 20
7
8
15
Step 2
Write the sum in expanded form. Because 15 is greater than 9, we have to
regroup. Rewrite 15 as 1 ten and 5 ones.
50
+ 20
7
8
10 + 5
Step 3
Regroup.
Regroup 1 ten from the ones column to
the tens column.
50
+ 20
Step 4
Add the tens.
Step 5
Write the sum in standard form.
The sum is 85.
30 57
+ 28
Unit 1 • Lesson 7
10
7
8
10 + 5
10
50 7
+ 20 8
80 5
10
50 7
+ 20 8
80 5 S 85
Lesson 7
Example 2
Find the sum of 315 and 238 using expanded addition.
Step 1
Add the ones.
Step 2
Write the sum in expanded form. Because 13 is greater than 9, we have to
regroup. Rewrite 13 as 1 ten and 3 ones.
Step 3
Regroup.
Regroup 1 ten from the ones column to
the tens column.
Step 4
Add the tens.
STEP 5
Add the hundreds. Step 6
Write the sum in standard form.
The sum is 553.
Apply Skills
Turn to Interactive Text,
page 21.
315
+ 238
300 10
+ 200 30
5
8
13
300 10
+ 200 30
5
8
10 + 3
10
300 10
+ 200 30
5 8
10 + 3
10
300 1 0 5
+200 30 8
50 3
10
300 10 5
+200 30 8
500 50 3
10
300 10 5
+200 30 8
500 50 3 S 553
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 7 31
Lesson 7
Problem Solving: Finding Information in Tables
How do we find information in a table?
Sometimes the information we need to solve a word problem
is in a table . A table is another way to show information.
This table shows CD sales for five bands on Hipster Records.
Hipster Records
CD Sales
January–April
Band
The Hammerheads
One Later
4 Floors Up
The Scatter Plots
Three Ears
CD Sales
$30,000
$24,000
$19,000
$12,000
$6,000
The column on the left shows the names of each different band.
The column on the right shows how much money each band made
selling CDs during the four-month period from January through April.
To read the table, we find the name of the band on the left, and read
across to the right to find out how much money it made selling CDs
from January through April.
Problem-Solving Activity
Turn to Interactive Text,
page 22.
32 Unit 1 • Lesson 7
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Vocabulary
table
Lesson 7
Homework
Activity 1
Complete the following basic and extended facts.
1. 7 +
= 16
2. 90 + 70 =
4. 7 + 8 =
5. 80 +
7. 60 + 70 =
8.
3. 700 + 900 =
= 150
+ 600 = 1,300
+ 800 = 1,500
6.
9. 6 +
= 13
Activity 2
Rewrite the problem in expanded form. Do not find the sum.
Model
1.
432
+ 161
400 30
+ 100 60
327
+ 21
2.
220
+ 100
3.
500
+ 102
2
1
Activity 3
Add using expanded addition. Regroup when necessary.
Then write the answer in standard form.
Model
1.
327
+ 21
2.
220
+ 100
3.
54
+ 29
4.
78
+ 13
37
+ 46
30 7
+ 40 6
70 13
10
30 7
+ 40 6
80 3
80 + 3
Answer: 83
Unit 1 • Lesson 7 33
Lesson 7
Homework
Activity 4
Use the bar graph to answer the following questions.
The Scatter Plots CD Sales
January–April
Number of CDs Sold
500
400
300
200
100
0
January
February
March
April
Month
1.
Suppose the Scatter Plots CD sales continue the same trend over the next
three months. How many CDs will they sell in July? 2.
If you were going to make a graph to show the CD sales from January to July,
what scale and interval would you choose? What does the first graph show?
3.
How would you change the scale and interval if the Scatter Plots CD sales
had only increased by 50 each month over the next three months?
Activity 5 • Distributed Practice
Add.
34 1.
7+9
2.
40 + 40
3.
600 + 600
4.
70 + 60
5.
80 + 20
6.
400 + 500
Unit 1 • Lesson 7