Lesson
3 Addition Problems in Expanded Form
Problem Solving:
Finding What the Problem Is Asking For
Addition Problems in Expanded Form
How do we use expanded form in addition?
Vocabulary
place-value coins
We know that coins have different values. A penny is worth 1 cent,
and a dime is worth 10 cents. We can use place-value coins to help
show place value. Place-value coins are worth 1, 10, or 100.
We can show the number 32 as 3 tens coins and 2 ones coins.
Tens
10
10
Ones
10
1
32
1
When we add 3 to 32, we add 3 ones coins.
Tens
10
10
Ones
10
1
1
1
1
32
1
+3
The coins help us see the answer to 32 + 3 because they show place
value. We use the same thinking when we do addition in expanded form.
Unit 1 • Lesson 3 15
Lesson 3
In Lesson 2, we wrote numbers as a sum of the value of their digits. This
is called expanded form. Now, we will learn to write addition problems in
expanded form.
Sometimes it is easier to see what is happening in addition when we
write a problem in expanded form. Writing an addition problem in
expanded form helps us clearly see that we add ones to ones
and tens to tens.
Example 1
42
Write the addition problem + 35 in expanded form.
�
The expanded form of 42 is 40 + 2.
The expanded form of 35 is 30 + 5.
The expanded form of
�
Apply Skills
Turn to Interactive Text,
page 10.
16 Unit 1 • Lesson 3
40 2
42
+ 35 is + 30 5 .
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Writing an addition
problem in expanded form
helps us keep track of
place value when we add.
Lesson 3
Problem Solving: Finding What the Problem Is Asking For
How do we know if we answered the question
being asked?
When we solve a word problem, we must decide what the problem is
asking. One common error when solving word problems is answering a
question that is not asked.
Let’s show how a student did the calculation correctly, but found the
answer to a question that was not asked. Following the problem-solving
steps is a good way to avoid making this common mistake.
Example 1
Solve the word problem.
Problem:
Michael has two brothers. One brother is 3 years
older than Michael, and the other is 3 years younger.
If the youngest brother is 12 years old, how old is the oldest brother?
Samantha solved the problem and wrote her solution on the board:
12 + 3 = 15
Michael is 15 years old.
Steps for Solving
a Word Problem:
STEP 1
Figure out what the
problem is asking, and
rewrite what you find.
Is Samantha’s answer correct?
No, because the problem did not ask for Michael’s age. The problem
asked, “How old is the oldest brother?”
STEP 2
Decide what information
you need to find the
answer.
The correct solution is:
Youngest brother’s age: 12
Michael’s age: 12 + 3 = 15
Oldest brother’s age: 15 + 3 = 18
STEP 3
Find the important
information in the
problem.
The oldest brother is 18 years old.
Problem-Solving Activity
Turn to Interactive Text,
page 11.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 3 17
Lesson 3
Homework
Activity 1
Write the number in expanded form.
Model293 Answer: 200 + 90 + 3
85
1.
387
2.
3.
175
Activity 2
Rewrite the problem in expanded form. Do not find the sum.
Model Answer:
37
30 7
​
+ 49 S + 40 9
1.
35
+ 28
2.
47
+ 80
3.
47
+ 65
4.
95
+ 62
5.
38
+ 51
6.
90
+ 20
7.
60
+ 72
8.
82
+ 12
Activity 3
Write what the problem is asking for. Do not solve.
Model A
CD store sells about 200 CDs each day. The store manager wants to
know about how many CDs the store sells in a week. The 20 best-selling
CDs are in the rock/pop category. The store also sells a lot of movie
soundtracks.
Q: What is the problem asking for?
A: About how many CDs does the store sell in a week?
1.
The human heart beats about 72 times per minute. It pumps blood at a
rate of about 5 liters per minute. How many times does the heart beat in
an hour? 2.
The world population increases by 240,000 people daily. Population experts
want to know how much the world’s population grows in a week. Half the
world’s population lives in just 6 countries. Many of these countries are very
poor. How much does the world’s population grow in a week? Activity 4 • Distributed Practice
Add.
1.
18 7+9
Unit 1 • Lesson 3
2.
90 + 10
3.
900 + 700
4.
300 + 400