Lesson
1
Addition and Subtraction Fact Families
Problem Solving:
Answering the Right Question
Lesson1 SkillsMaintenance
Lesson Planner
Name
Vocabulary Development
Date
SkillsMaintenance
BasicandExtendedAdditionFacts
fact family
Activity1
Completethesetsofbasicandextendedadditionfacts.
Skills Maintenance
1.
7+2=
Basic and Extended Addition Facts
2.
3+
3.
9+3=
12
90 + 30 =
120
900 + 300 = 1,200
4.
4+7=
11
40 + 70 =
110
700 + 400 = 1,100
5.
8+1=
9
80 + 10 =
90
800 + 100 =
Building Number Concepts:
ddition and Subtraction Fact
A
Families
9
6
20 + 70 =
=9
60
90
+ 30 = 90
700 + 200 =
30 +
60
900
= 90
900
In this lesson, students are introduced to fact
families. Students learn that a fact family
consists of addition and subtraction facts
that use the same numbers. Students explore
the properties of different kinds of families,
including families with only two facts.
Objective
Students will identify and explain the
relationship between addition and subtraction.
Problem Solving:
Answering the Right Question
Students learn the importance of checking
their answers to ensure they answered the
question asked in the problem. In today’s
activity, students use their knowledge of fact
families to solve three word problems.
Objective
Students will solve word problems using
addition and subtraction.
Homework
Students write basic fact families for given
sets of numbers, use related addition facts to
solve subtraction facts, write extended fact
families, and complete a table of basic and
extended subtraction facts. In Distributed
Practice, students practice multidigit addition.
140 Unit 2 • Lesson 1
50
Unit2•Lesson1
Skills Maintenance
Basic and Extended Addition Facts
(Interactive Text, page 50)
Activity 1
Students complete basic and extended addition facts
by filling in the missing numbers.
Lesson
Building Number Concepts:
ddition and Subtraction Fact
A
Families
How are addition and subtraction
related?
1
Problem Solving:
Answering the Right Question
Addition and Subtraction Fact Families
Vocabulary
How are addition and subtraction related?
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
(Student Text, page 73)
Build Vocabulary
Use the model to demonstrate that a fact family is a set of facts with the same three numbers.
Addition and Subtraction Fact Families
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
Demonstrate
Engagement Strategy: Teacher Modeling
Demonstrate how to write a fact family using
one of the following ways:
: Use the mbook Teacher Edition
for page 73 in the Student Text. ​
Overhead Projector: Reproduce
the blank fact family table on
a transparency, and modify as
discussed.
Board: Draw the blank fact family
table on the board, and modify as
discussed.
•Display the addition facts. Explain that they
include the numbers 2, 8, and 10. Note that
the positions of 2 and 8 can change without
changing the sum. Show that the 10 is alone
on one side of the equal sign. ​
•Next display the subtraction fact 10 − 2 =
8. Note that 8 and 2 are now on different
sides of the equal sign. Explain that the
difference is alone on one side of the equal
sign. Show that 10 is no longer alone, and 8
is the difference when we subtract 2 from
10. Repeat for the second subtraction fact
10 − 8 = 2. Point out that the 2 is now the
difference when we subtract 8 from 10. ​
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
73
•Tell students that addition and subtraction facts
are related. Note that a subtraction fact is the
opposite of the corresponding addition fact in the
same fact family. In the addition facts, the sum
of 10 is alone on one side of the equal sign, and
the numbers 2 and 8 are on the other side with
an addition sign. In the subtraction facts, the
sum of 10 from the addition facts is the number
from which we subtract the other numbers.
•Discuss the fact family for 7, 8, and 15
in Example 1 . Explain that two addition and
two subtraction facts can be written from this
fact family.
•Have students look at the addition and
subtraction facts. Mention how the same three
numbers are used, just in a different order. Point
out that the four number sentences make up the
fact family for 7, 8, and 15.
Unit 2 • Lesson 1 141
Lesson 1
Lesson 1
What is the relationship between basic and
extended subtraction facts?
How are addition and subtraction
related? (continued)
We learned that once we know a basic addition fact, we can create
extended addition facts. The same is true for subtraction.
Basic Fact
17 − 8 = 9
Demonstrate
•Direct students’ attention to Example 2 on
page 73. Look at the subtraction fact 15 −
6= . Have students think about the
facts in this fact family.
× 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.
•Tell students that because 6 + 9 = 15, the
Example 1
missing number in the subtraction fact must
be 9. Explain that because we know this
related addition fact, we can find missing
numbers in a subtraction fact from the
same fact family. Fact families can be used
to find or check answers to addition and
subtraction problems.
Check for Understanding
Engagement Strategy: Think Tank
Have students take out a strip of paper and
write their names on it. On the strip of paper,
have them write down an addition fact for the
numbers 3, 7, and 10. On the other side of the
paper, have them write a subtraction fact for the
same fact family. Put the strips of paper into a
container, and draw an answer. Read the answer
aloud. If correct, congratulate the student. If
incorrect, elicit a correct answer from the class.
Remember
that extended
facts are just
basic facts
multiplied by
a power of 10.
Write the fact family for 70, 80, and 150.
70 + 80 = 150
80 + 70 = 150
150 − 80 = 70
150 − 70 = 80
What is the relationship between
basic and extended subtraction facts?
(Student Text, page 74)
Explain
Direct students to the basic and extended fact
illustration on page 74 of the Student Text. Point
out that writing an extended fact family follows
the same process as writing a basic fact family,
except the numbers are greater because they
have been multiplied by a power of 10. Help
students notice that the number of zeros is the
same in each number in the fact.
142 Unit 2 • Lesson 1
Apply Skills
Turn to Interactive Text,
page 51.
74
74
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 2 • Lesson 1
Demonstrate
•Remind students of the fact family 7, 8, and
15. Use Example 1 to show how we write an
extended fact family for 70, 80, and 150. Note
that creating an extended fact family is just like
creating a basic fact family.
Check for Understanding
Engagement Strategy: Pair/Share
Have students work with a partner to write the fact
families for the following numbers:
40, 50, and 90 60, 70, and 130
Have partners discuss how they arrived at their
answers. At the end of the activity, have students
volunteer to explain their thinking.
Lesson1 ApplySkills
Name
Apply Skills
ApplySkills
AdditionandSubtractionFactFamilies
(Interactive Text, page 51)
Activity1
Unit 2
Date
Writethebasicfactfamiliesforthegroupsofnumbers.
Have students turn to Interactive Text, page 51,
where they practice writing fact families.
1.
Activity 1
Students write fact families for two groups of
numbers.
7, 8, and 15
7
6, 7, and 13
2.
+
8
=
15
6
+
7
=
13
8
+
7
=
15
7
+
6
=
13
15
−
8
=
7
13
−
7
=
6
15
−
7
=
8
13
−
6
=
7
Activity2
Completethesubtractionfactsusingrelatedadditionfacts.
Activity 2
Students complete subtraction facts using
related addition facts.
8
2.
11 − 5 =
6
3.
8−3=
5
4.
10 − 7 =
3
5.
17 − 8 =
9
6.
9−6=
3
Activity3
1.
Students write extended fact families for two
groups of numbers.
Monitor students’ work as they complete these
activities.
•Can students write fact families for basic and
14 − 6 =
Writetheextendedfactfamiliesforthegroupsofnumbers.
Activity 3
Watch for:
1.
70, 80, and 150
70
80
2.
20, 90, and 110
+
80
= 150
20
+
90
=
110
+
70
=
150
90
+
20
=
110
150 −
80
=
70
110 −
90
=
20
150 −
70
=
80
110 −
20
=
90
Unit2•Lesson1
51
extended addition and subtraction facts?
•Do students use addition facts to solve
subtraction facts?
•Do students calculate correct sums and
differences for both basic and extended
facts?
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
Unit 2 • Lesson 1 143
Lesson 1
Lesson 1
Problem Solving: Answering the Right Question
How do we answer the right question?
Problem Solving:
Answering the Right Question
How do we answer the right question?
(Student Text, page 75)
Explain
Turn to Student Text, page 75. Discuss the first
paragraph. Tell students that a good problem
solver always checks an answer by asking, “Did I
answer the question asked in the problem?”
Demonstrate
•Use Example 1 to demonstrate answering
the correct question in a word problem.
There is extra information in this problem.
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.
After solving a word
problem, check
to make sure you
answered the question
that was asked.
•Read the word problem aloud, and look at
the table. Make sure students understand
all the vocabulary. Point out that generally
the correct question comes at the end of the
word problem.
•Stop after each sentence, and ask students
if the sentence helps us decide what the
problem is asking for.
•Read the problem again. Have students
focus on the question that is asked, “Which
CD will she buy?”
•Find phrases in the problem that help
answer the question; for example “wants to
buy one of its CDs” and “If the difference
between the costs of the group’s newest CD
and its first CD is $5 or less, Taylor will buy
the newest CD.”
•Remind students that Taylor also wants
to buy a button and a poster. Ask if this
information helps us answer the question,
“Which CD will she buy?”
•Look at the solution. Point out that although
the calculation of $2 + $4 = $6 is correct, it
does not answer the question being asked.
144 Unit 2 • Lesson 1
Problem-Solving Activity
Turn to Interactive Text, page 52.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 2 • Lesson 1
75
75
•Explain that the sentence “She also wants to buy
a button and a poster” is extra information that
does not help us.
•Read through the last two paragraphs of the
example. Point out the correct information in the
table, and refer students to the word problem
to check that the answer relates to the question
being asked.
•Reinforce the importance of going back to the
problem to check that the answer relates to the
question being asked.
•Explain that correct calculations can produce
an incorrect answer if they do not relate to the
question being asked.
Lesson1 Problem-SolvingActivity
Name
Problem-Solving Activity
Problem-SolvingActivity
AnsweringtheRightQuestion
(Interactive Text, page 52)
TheCivicAuditoriumhiredtheScatterPlotstoplayaconcertlastFriday.
Thetableliststhecostforeachconcertexpense.Usethedatatosolve
theproblems.Showallyourwork.Remembertocheckyouranswerby
askingyourself,“DidIanswerthequestionaskedintheproblem?”
Direct students to Interactive Text, page 52.
Review the directions and table of data shown.
Discuss concerts and the costs and terms
associated with them.
To assist students in completing the activity:
1.
•Read through the problems one at a time
to ensure that students understand all the
vocabulary.
Expense
Cost
Security
$200
Stage crew
$300
Lighting and sound
$100
Concessions (food and drink)
$120
Standard employees
$700
Total
$1,420
It was expensive to put on the concert. The Civic Auditorium had to
pay for security, a stage crew, lighting and sound, concessions, and
the standard employees who take tickets and clean up. How much
more did the standard employees cost than security for the concert?
$700 − $200 = $500;
Standard employees cost $500 more than security.
2.
•Prompt students to use extended facts to
solve the problems.
The owners of the Civic Auditorium had to figure out how much to
pay the Scatter Plots. They decided to pay them $900. How much
more did they pay the Scatter Plots than the stage crew?
$900 − $300 = $600; They paid
the Scatter Plots $600 more than the crew.
Monitor students’ work as they complete the
activity.
3.
Watch for:
•Do students understand all the vocabulary?
Auditorium owners make money at a concert through concession
sales—selling food and drinks. The Civic Auditorium bought food
and drinks to sell at the concert. The concession sales for the
Scatter Plots’ concert were $240. How much profit did the owners
make on concessions? The profit is the difference between how
much money was spent buying the food and drinks and how much
money was made selling the food and drinks.
$240 − $120 = $120; The owners
Are students having trouble with any terms?
•Are students using extended facts to solve
Date
made a profit of $120 on concessions.
52
Unit2•Lesson1
the problems?
•As students finish a problem, do they
monitor their work by asking, “Did I answer
the question asked in the problem? Is this
really what the problem is asking for?”
•Can students separate the question from
the problem?
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
Unit 2 • Lesson 1 145
Lesson 1
Lesson 1
Homework
Activity 1
Write the fact family for the group of numbers.
Homework
Model 7, 8, and 15
7 + 8 = 15 15 − 8 = 7
8 + 7 = 15 15 − 7 = 8
Go over the instructions on page 76 in the
Student Text for each part of the homework.
1. 3, 9, and 12
2. 6, 7, and 13
3. 8, 6, and 14
4. 9, 8, and 17
See Additional Answers below.
Activity 2
Use a related addition fact to solve the subtraction fact.
Model 13 − 4 =
4 + 9 = 13
So 13 − 4 = 9.
Activity 1
Students write basic fact families for given sets
of numbers.
1. 15 − 7
8
3. 120 − 40
2. 11 − 6
80
5
4. 140 − 90
50
Activity 3
Write the extended fact family for the group of numbers.
Model 20, 60, and 80
20 + 60 = 80 80 − 60 = 20
60 + 20 = 80 80 − 20 = 60
Activity 2
1. 40, 50, and 90
2. 60, 80, and 140
3. 70, 90, and 160
4. 30, 90, and 120
See Additional Answers below.
Activity 4
Students use related addition facts to solve
subtraction facts.
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
12 − 6 = 6
Activity 3
14 − 6 = 8
16 − 9 = 7
160 − 90 = 70
11 − 4 = 7
15 − 9 = 6
Students write extended fact families for given
sets of numbers.
1,700 − 800 = 900
130 − 50 = 80
110 − 40 = 70
150 − 90 = 60
140 − 60 = 80
13 − 5 = 8
1,200 − 600 = 600
1,300 − 500 = 800
1,100 − 400 = 700
1,500 − 900 = 600
1,400 − 600 = 800
1,600 − 900 = 700
Activity 5 • Distributed Practice
Add.
1.
Activity 4
168
Students complete a table of basic and extended
subtraction facts.
Activity 5 • Distributed Practice
Students practice multidigit addition.
Additional Answers
Activity 1
1. 3 + 9 = 12
9 + 3 = 12
2. 6 + 7 = 13
7 + 6 = 13
3. 8 + 6 = 14
6 + 8 = 14
4. 9 + 8 = 17
8 + 9 = 17
146 Unit 2 • Lesson 1
12 − 9 = 3
12 − 3 = 9
13 − 7 = 6
13 − 6 = 7
14 − 6 = 8
14 − 8 = 6
17 − 8 = 9
17 − 9 = 8
77
+ 91
76
76
2.
26
+ 66
92
3.
378
+ 16
394
4.
426
+ 14
440
Unit 2 • Lesson 1
Activity 3
1. 40 + 50 = 90
50 + 40 = 90
2. 60 + 80 = 140
80 + 60 = 140
3. 70 + 90 = 160
90 + 70 = 160
4. 30 + 90 = 120
90 + 30 = 120
90 − 50 = 40
90 − 40 = 50
140 − 80 = 60
140 − 60 = 80
160 − 90 = 70
160 − 70 = 90
120 − 90 = 30
120 − 30 = 90