Lesson
9 More Methods of Regrouping
Problem Solving:
Posing Questions From a Graph
More Methods of Regrouping
How do we regroup to the hundreds place?
We have been adding two-digit numbers that need regrouping. Now
we will work on problems that include three-digit numbers and need
regrouping.
The number 168 can be shown as 1 hundreds
coin, 6 tens coins, and 8 ones coins.
Hundreds
Tens
100
To add 54 more, we add 5 tens coins
and 4 ones coins.
10
10
10
10
10
10
10
10
Ones
10
10
1
1
1
1
1
1
1
1
1
1
1
1
+ 54
10
There are more than 9 ones coins, so we
must regroup.
There are more than 9 tens coins, so we
must regroup again.
Hundreds
Tens
100
10
10
10
1
1
1
1
10
10
10
10
1
1
1
1
10
10
10
10
1
1
1
1
100
Hundreds
10
10
10
10
10
10
10
10
10
10
10
10
1
1
Ones
Tens
10
100 100
200
Ones
Tens
100
The sum is 222.
Ones
10
Hundreds
+
168
10
20
1
+
1
2
= 222
In this problem, we regrouped coins from the tens place to the hundreds
place the same way we regrouped from the ones place to the tens place.
Unit 1 • Lesson 9 39
Lesson 9
Let’s use this thinking with a problem in expanded addition.
Example 1
Find the sum of 197 and 35 using expanded addition.
Step 1
Add the ones.
Step 2
Write the sum in expanded form.
Step 3
Regroup.
Regroup 1 ten from the ones column to
the tens column.
100 90
+
30
7
5
12
100 90
+
30
7
5
10 + 2
10
100 90
+
30
Step 4
Add the tens.
10
100
+
STEP 5
Regroup.
Regroup 1 hundred from the tens
column to the hundreds column.
Step 6
Add the hundreds.
Step 7
Write the sum in standard form.
The sum is 232.
40 Unit 1 • Lesson 9
7
5
10 + 2
90 7
30 5
1 30 2
100
100
+
100
10
90 7
30 5
1 00 + 30 2
10
1 00 90 7
+
30 5
200 30 2
100
10
100 90 7
+
30 5
200 30 2 S 232
Lesson 9
Here is the same problem using traditional addition.
Example 2
Find the sum of 197 and 35 using traditional addition.
Step 1
Add the ones.
197
+ 35
2
Step 2
Regroup.
1
197
+ 35
2
Step 3
Add the tens.
Think: 1 ten + 9 tens + 3 tens = 13 tens.
Step 4
Regroup.
Each addition algorithm
has advantages.
Expanded addition more
clearly shows how to
regroup. Traditional
addition is faster, but we
are more likely to make a
regrouping mistake.
1
197
+ 35
32
1 1
197
+ 35
32
Step 5
Add the hundreds.
Think: 1 hundred + 1 hundred = 2 hundreds.
1 1
1 97
+ 35
232
The sum is 232.
Apply Skills
Turn to Interactive Text,
page 27.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 9 41
Lesson 9
Problem Solving: Posing Questions From a Graph
How can we pose a question from a graph?
Look at the bar graph.
The Scatter Plots Weekly CD Sales
700
600
Number of CDs Sold
Most people use graphs to
answer a particular question
they are interested in. It is
important that we become
good at answering questions,
based on the data in a graph.
One way to practice this skill
is to pose our own question
about the data and then
answer it.
500
400
300
200
100
0
Week 1
Week 2
Week 3
Example 1 shows questions
that can be answered by the
graph.
Week 4
Week
Example 1
The Scatter Plots manager, Ana, noticed that sometimes their CD sales
drop from one week to the next. Pose a question about this situation and
answer it.
Some possible questions are:
• When was the largest drop in sales?
• How many CDs were sold the week before the big drop?
• How many CDs were sold the week after the big drop?
We would answer these questions by looking at the bar graph for
the biggest difference between two of the bars.
• The largest drop in sales occurred from Week 3 to Week 4.
• The week before the big drop, 450 CDs were sold.
• The week after the big drop, 550 CDs were sold.
Problem-Solving Activity
Turn to Interactive Text,
page 28.
42 Unit 1 • Lesson 9
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Week 5
Week 6
Lesson 9
Homework
Activity 1
Add using expanded addition. Write the answer in standard form.
Model
585 + 127
S
500 80
+ 100 20
5
7
12
10
500 80
+ 100 20
100
142
+ 684
2.
493
+ 278
3.
286
+ 423
4.
216
+ 596
5
7
10 + 2
10
500 80 2
+ 100 20 7
10 2
100
1.
10
500 80 2
+ 100 20 7
700 10 2
Answer: 712
Unit 1 • Lesson 9 43
Lesson 9
Homework
Activity 2
Add using traditional addition.
Model
1.
566
+ 259
1
566
+ 259
5
782
+ 135
2.
917
4.
395
+ 176
237
+ 23
3.
260
5.
571
495
+ 156
651
148
+ 26
6.
174
273
+ 508
781
1 1
566
+ 259
25
1 1
566
+ 259
825
Answer: 825
Activity 3 • Distributed Practice
Add.
44 1.
8+9
2.
40 + 60
3.
200 + 700
4.
80 + 20
5.
600 + 300
6.
900 + 900
Unit 1 • Lesson 9