Lesson
12 Horizontal Expanded Addition
Problem Solving:
Horizontal Bar Graphs
Horizontal Expanded Addition
Vocabulary
What is horizontal expanded addition, and
why do we learn about it?
In previous lessons, we solved addition problems vertically using the
traditional and expanded algorithms.
Traditional
65 + 31
Expanded
60 5
+ 30 1
Another way to add is to use horizontal expanded addition . In
horizontal expanded addition, we write the problems across the page on
one line. Then we write a new line each time we do a step.
Steps for Using Horizontal Expanded Addition:
Step 1
Rewrite the problem by putting addition signs in place of the vertical bars.
Step 2
Move everything to one line.
Group the numbers together by place value. When the four numbers are
written horizontally, the easiest way to add
is to first add the tens, then add the ones.
60 + 30 + 5 + 1
Step 3
Combine the place values to find the sum.
90 + 6 = 96
The sum is 96.
56 60 5 60 + 5
+ 30 1
+ 30 + 1
Unit 1 • Lesson 12
60 + 5 + 30 + 1
60 + 5 + 30 + 1
Tens
Ones
horizontal expanded
addition
commutative property
Lesson 12
Special rules, called properties, help us through each step of addition.
The property that allows us to change the order of the numbers without
changing the sum is called the commutative property .
3+7
10
=
=
7+3
10
We can write the problem as 3 + 7 or 7 + 3. The sum does not change.
Example 1
Find the sum of 57 and 11 using horizontal expanded addition.
STEP 1
Write the numbers in expanded form using an addition sign.
57 + 11 = 50 + 7 + 1 0 + 1
STEP 2
Group the numbers together by
57 + 11 = 50 + 7 + 1 0 + 1
Tens
Ones
place value.
50 + 1 0 + 7 + 1
We use the commutative property
to change the order of the numbers
being added.
STEP 3
Combine the place values to find
the answer.
The sum is 68.
57 + 11 =
=
=
=
50 + 7 + 1 0 + 1
50 + 1 0 + 7 + 1
60 + 8
68
Horizontal expanded addition helps us understand place value
in a different way and prepares us for algebra.
Apply Skills
Turn to Interactive Text,
page 37.
When we add numbers,
the commutative
property allows us to add
the numbers in any order
we want.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 12 57
Lesson 12
Problem Solving: Horizontal Bar Graphs
What are horizontal bar graphs?
We have been studying vertical bar graphs. On these graphs, the bars
are drawn from bottom to top. Horizontal bar graphs are very much like
vertical bar graphs. The difference is that bars are drawn from left to
right. The scale is numbered on the horizontal axis, and the data labels
are placed on the vertical axis.
Look at the horizontal bar graph below. It shows the CD sales for four
different record companies.
CD Sales
Record Company
▲
Hipster Records
Expressions
Hitz
Revolution Records
▲
Data labeled on
vertical axis.
0 100 200 300 400 500 600 700 800
Sales (in thousands)
Scale numbered on
horizontal axis.
We can read a horizontal bar graph and use estimation to make
conclusions about the data. For example:
• Revolution Records sold more than 700,000 CDs.
• Hitz sold the least number of CDs.
• Expressions sold more than 550,000 CDs but less than
600,000 CDs.
Problem-Solving Activity
Turn to Interactive Text,
page 38.
58 Unit 1 • Lesson 12
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Lesson 12
Homework
Activity 1
Add using horizontal expanded addition. Write the answer in standard form.
Model
70 + 21 =70 + 0 + 20 + 1
70 + 20 + 0 + 1
90 + 1 = 91
Answer: 91
1.
4.
22 + 35
71 + 13
2.
5.
43 + 36
25 + 40
3.
6.
12 + 56
30 + 59
Activity 2
Add using vertical expanded addition. Write the answer in standard form.
2.
364
+ 326
1.
607
+ 205
3.
293
+ 222
3.
904
+ 47
Activity 3
Add using traditional addition.
2.
129
+ 96
1.
225
399
+ 187
586
951
Activity 4 • Distributed Practice
Add. Try to find the sum mentally.
1.
70 + 60
2.
100 + 800
3.
8,000 + 6,000
4.
90 + 30
5.
700 + 700
6.
10,000 + 20,000
Unit 1 • Lesson 12 59