Lesson
1
Addition and Subtraction Fact Families
Problem Solving:
Answering the Right Question
Addition and Subtraction Fact Families
How are addition and subtraction related?
Vocabulary
fact family
There is a special relationship between addition and subtraction
facts. This relationship can be seen in fact families. A fact family is a set of facts with the same three numbers.
In the following fact family, all four facts have the numbers 2, 8, and 10.
Fact Family for 2, 8, and 10
8 + 2 = 10
2 + 8 = 10
10  2 = 8
10  8 = 2
Subtraction facts and addition facts are opposites. The answer at the
end of an addition fact is at the beginning of a subtraction fact in
its fact family. Look at the facts to see how the numbers move around.
Example 1
Write the fact family for 7, 8, and 15.
Fact Family
Addition Facts: 7 + 8 = 15
8 + 7 = 15
Subtraction Facts: 15 − 8 = 7
15 − 7 = 8
Notice that the same three numbers are used, but in a different order. It is
important to remember this difference when solving subtraction problems.
Example 2
Complete the subtraction fact using a related addition fact.
15 − 6 =
Think: 15 − 6 =
and 6 +
= 15 are in the same fact family.
Because we know 6 + 9 = 15, we also know 15 − 6 = 9.
The complete subtraction fact is 15 − 6 = 9.
We can figure out
the missing numbers
in a subtraction fact
by thinking about an
addition fact in the
same fact family.
Unit 2 • Lesson 1 73
Lesson 1
What is the relationship between basic and
extended subtraction facts?
We learned that once we know a basic addition fact, we can create
extended addition facts. The same is true for subtraction.
Remember
that extended
facts are just
basic facts
multiplied by
a power of 10.
Basic Fact
17 − 8 = 9
× 100
× 10
× 1,000
170 − 80 = 90
1,700 − 800 = 900
17,000 − 8,000 = 9,000
Extended Fact
Extended Fact
Extended Fact
We also write fact families for extended facts. Look at the number of
zeros in each of the extended facts. In the fact 170 − 80 = 90, each of
the numbers has one zero. Notice the pattern in the other extended facts.
Example 1
Write the fact family for 70, 80, and 150.
70 + 80 = 150
80 + 70 = 150
150 − 80 = 70
150 − 70 = 80
Apply Skills
Turn to Interactive Text,
page 51.
74 Unit 2 • Lesson 1
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Lesson 1
Problem Solving: Answering the Right Question
How do we answer the right question?
We learned how to be good problem solvers by identifying what a
problem asks and finding the important information needed to solve it.
Now we will learn that a good problem solver always checks the answer
by asking, “Did I answer the question asked in the problem?”
Let’s look at an example that shows how a student made the correct
calculations but did not answer the question that was being asked.
Example 1
Problem:
Taylor has a gift card to the music store. She heard the
Scatter Plots on the radio and wants to buy one of its
CDs. If the difference between the costs of the group’s
newest CD and its first CD is less than $5, then Taylor
will buy the newest CD. She also wants to buy a button
and a poster. Which CD will she buy?
The Scatter Plots’
Merchandise
Newest CD
First CD
Poster
Button
Cost
$9
$7
$4
$2
Your friend solved the problem:
$2 + $4 = $6
Taylor can buy a button and a poster because it would only cost $6.
Is her answer correct?
Your friend didn’t answer the question the problem was asking.
The problem wants to know, “Which CD will she buy?”
Your friend’s calculations are correct, but she did not answer the
right question.
The right question is, “Which CD will Taylor buy?” We need to know the
difference in price between the two CDs. Because $7 is $2 less than $9,
Taylor will buy the newest CD.
The correct answer is Taylor will buy the newest CD.
Problem-Solving Activity
Turn to Interactive Text, page 52.
After solving a word
problem, check
to make sure you
answered the question
that was asked.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 2 • Lesson 1 75
Lesson 1
Homework
Activity 1
Write the fact family for the group of numbers.
Model7, 8, and 15
7 + 8 = 15 15 − 8 = 7
8 + 7 = 15 15 − 7 = 8
1. 3, 9, and 12
2. 6, 7, and 13
3. 8, 6, and 14
4. 9, 8, and 17
Activity 2
Use a related addition fact to solve the subtraction fact.
Model13 − 4 =
4 + 9 = 13
So 13 − 4 = 9.
1. 15 − 7
2. 11 − 6
3. 120 − 40
4. 140 − 90
Activity 3
Write the extended fact family for the group of numbers.
Model20, 60, and 80
20 + 60 = 80 80 − 60 = 20
60 + 20 = 80 80 − 20 = 60
1. 40, 50, and 90
2. 60, 80, and 140
3. 70, 90, and 160
4. 30, 90, and 120
Activity 4
Complete the table of basic and extended subtraction facts.
Basic Fact
Extended Fact (× 10)
Extended Fact (× 100)
17 − 8 = 9
170 − 80 = 90
120 − 60 = 60
1,700 − 800 = 900
13 − 5 = 8
1,100 − 400 = 700
1,500 − 900 = 600
14 − 6 = 8
160 − 90 = 70
Activity 5 • Distributed Practice
Add.
1.
77
+ 91
168
76 Unit 2 • Lesson 1
2.
26
+ 66
92
3.
378
+ 16
394
4.
426
+ 14
440