4.3
Use Properties to Add
ALGEBRA
?
Essential Question How can you add more than two addends?
Texas Essential
Knowledge and Skills
Number and Operation—3.4.A
Solve with fluency one-step and two-step problems involving
addition and subtraction within 1,000 using strategies based
on place value, properties of operations, and the relationship
between addition and subtraction Also 3.5.A
MATHEMATICAL PROCESSES
3.1.D Communicate mathematical ideas and reasoning
3.1.F Analyze mathematical relationships
How can you add more
than t wo addends?
Are You Ready?
Access Prior Knowledge
Use the Are You Ready? 4.3 in the
Assessment Guide to assess students’
understanding of the prerequisite skills
for this lesson.
Vocabulary
Lesson Opener
Making Connections
Invite students to talk about adding whole numbers.
How do you add whole numbers? (Line up the digits in each number by their place
value, starting with the ones place.) What do you do when the sum of the digits in a
place is greater than 9? (You regroup in the next place to the left.) How can you check
that your sum is reasonable? (Estimate by using rounding or compatible numbers.)
Commutative Property of Addition,
Associative Property of Addition
Go to Multimedia eGlossary at
thinkcentral.com
Using the Digital Lesson
Write the numbers 4, 7, and 3 on the board. Have students describe the different ways
the numbers can be added to get the same sum. Discuss the advantage of adding 7 + 3
first to make a ten before adding 4.
Learning Task
• What information are you given in this problem? (Friends are counting prairie
dog holes.)
• How many prairie dog holes did each of the friends count? (34, 16, 29)
Literacy and Mathematics
You may choose one or both of the following activities.
• Have students write a story problem in which they find the sum of three addends.
Have them illustrate their story using pictures, and then ask them to share their
stories and pictures with one another.
• Have students explain whether it makes any difference in the solution of the
problem if Calypso counted sixteen holes and Elya counted thirty-four holes.
Resources
For the student
For the teacher
Interactive
Student Edition
provides students
with an interactive learning
environment!
Digital Management
Center organizes program
resources by TEKS!
eTeacher
Edition
Math on the Spot
Video Tutor
Online Assessment
System
iTools Virtual
Manipulatives
Soar to Success Math
Online Intervention
Lesson 4.3 113A
Name
4.3
ALGEBRA
Unlock the Problem
?
Tell students that they will learn different strategies
to add more than two addends.
Number and
Operations—3.4.A
Also 3.5.A
MATHEMATICAL PROCESSES
3.1.D, 3.1.F
Use Properties to Add
Essential Question
How can you add more than two addends?
The Commutative Property of Addition states
that you can add two or more numbers in any order
and get the same sum.
Discuss the Commutative Property and Associative
Property of Addition. Help students see that they
can add two or more numbers in any order to get
the same sum. They may also group the addends,
including just the ones digits or just the tens digits, in
any way to add.
16 + 9 = 9 + 16
The Associative Property of Addition states that
you can group addends in different ways and still
get the same sum. It is also called the Grouping Property.
Point out the parentheses in the example under the
definition of the Associative Property. Tell students
that the parentheses show the grouping of addends,
and that those numbers within the parentheses
should be added first.
Math Idea
You can change the
order or the grouping
of the addends to make
combinations that are
easier to add.
(16 + 7) + 23 = 16 + (7 + 23)
Unlock
Unlock the
the Problem
Problem
Mrs. Gomez sold 36 cucumbers, 37 tomatoes, and
51 peppers at the Farmers’ Market. How many
vegetables did she sell?
Have student read the problem and discuss the
properties that they may use to solve the problem.
• Will the sum be closer
to 120 or 150?
closer to 120
• In Step 2, why are 37 and 51 easy to add? Possible
answer: you can just count on by tens and ones to add
the number; there is no regrouping.
Use properties to find 36 + 37 + 51.
STEP 1 Line up the numbers
• Why does the Associative Property of Addition
help you add? Possible answer: I can change the
by place value.
grouping of addends to make them easier to add.
© Houghton Mifflin Harcourt Publishing Company
36
37
+
51
_
English Language Learners
Leveled Activities
ELPS
Beginning: Activity 36
2.E.3, 3.D.2, 3.F.2
Intermediate: Activity 40
4.F.6, 4.G.2, 4.G.4
Advanced: Activity 41
4.F.3, 4.F.8
Advanced High: Activity 43
4.F.8, 4.G.2, 4.G.4
Go to thinkcentral.com for the ELL Activity
Guide containing these leveled activities.
113 Module 4
STEP 2 Change the grouping.
STEP 3 Add.
Think: Adding 37 + 51 first
would be easy because there is
no regrouping needed.
36
37
+
51
_
1
88
36
+
88
_
124
124 vegetables .
So, Mrs. Gomez sold ___
ELL Language Support
Module 4 113
Verbal / Linguistic
Small Group
ELPS 1.F, 2.C.4, 3.D.2
Strategy: Rephrase
• Students can demonstrate understanding
of the Associative Property of Addition
(16 + 29) + 21 =
by rephrasing the definition in their own
16 + (29 + 21)
words.
• Read the definition of the Associative
Property of Addition. Have students
rephrase it in their own words, either
verbally or in drawings.
• If students need help verbalizing the
definition, provide this sentence starter: The Associative Property says
that (5 + 9) + 11 = ___________
Try This!
Subtraction is not commutative or associative. Perform
operations in parentheses first.
Share and Show
Then subtract from left to right.
A
B
44
(88 − 34) − 10 = _
64
88 − (34 − 10) = _
Tell students that they can choose any property that is
easy for them and efficient. Point out the parentheses
in the problem in Exercise 2.
• In Exercise 2, why is it possible to change the order
you add the addends even though the parentheses
show two of the addends grouped together?
• Explain how you can use your answers to show that
subtraction is not associative. Possible explanation:
I know subtraction is not associative since I cannot group the numbers differently and get
the same answer.
Possible answer: the Associative Property of Addition says
that I can group the addends in any order, and the sum
stays the same.
Share
Share and
and Show
Show
Find the sum. Write the addition property you used.
1.
STEP 1
STEP 2
STEP 3
46
55
+_
24
55
46
+_
24
55
46
+_
24
Commutative
___
Property of Addition
Problem 3 connects to the learning model. Have
students use the MathBoard to explain their thinking.
STEP 4
55
+_
70
125
70
Math Talk
Use Math Talk to focus on students’ understanding
of the similarities and differences between the
Commutative and Associative Properties of
Addition.
Associative
___
Property of Addition
Strategies will vary. Check students' work.
Use addition properties and strategies to find the sum.
2.
93
13 + 26 + 54 = _
3.
218
57 + 62 + 56 + 43 = _
Use the checked exercises for Quick Check. Students
should show their answers for the Quick Check on the
MathBoard.
Math Talk
Mathematical Processes
Change the order and the grouping of the addends
so that you can use mental math to find the sum.
Then find the sum.
Explain how the Commutative
and Associative Properties of
Addition are alike and how
they are different.
136
43 + 39 + 43 + 11 = _
Possible explanation: the Commutative
Property changes the order of two
addends. The Associative Property changes the grouping of three addends. They are alike
because you get the same sum if you reorder or regroup.
136
43 + _
43 + _
39 + _
11 = _
_
114
3
© Houghton Mifflin Harcourt Publishing Company
4.
Mathematical Processes
2
Quick Check
1
a student misses the checked exercises
IF
THEN
Differentiate Instruction with
RtI Tier 1 Lesson 16
COMMON ERRORS
C
Enrich
E
Error
Students may change the order of addends,
without finding an easier way to add.
Logical / Mathematical
Individual / Partners
Example Students f ind 14 + 49 + 36 using
(36 + 49) + 14
• Have students find one way to use the Associative Property to find the
sum for the problem below, and then a way to use the Commutative
Property to find the sum in a different way:
36 + 34 + 3 + 27 + 14 = __________.
Associative Property
(36 + 34) + (3 + 27) + 14
70 + 30 + 14 = 114
Commutative Property
36
14 > 50
3 30
27 >
+ 34
114
Springboard to Learning Remind students that
the goal of using properties to add is to help make
adding easier. Have them write each addend on
a separate index card. Have them move the cards
around until they notice two addends that are easy
to add mentally.
• Have students share their strategies with a partner. Have them discuss
whether the groupings they used are similar or different.
Go to Go to thinkcentral.com for additional enrichment
activities in the Enrich Activity Guide.
Lesson 4.3
114
Name
Problem
Problem Solving
Solving
Problem Solving
5.
In Problems 7–10, students may choose and apply
any property or strategy to help find each sum. Tell
students that if at first they do not find a different
grouping or order to add the numbers, they should
try to look at the ones digits, or the numbers as a
whole, to find whether a different order helps.
Apply Mr. Arnez bought 32 potatoes,
29 onions, 31 tomatoes and 28 peppers
to make salads for his deli. How many
vegetables did he buy?
6.
Problem 10 requires students to use higher order
thinking skills and communicate what property
they used.
Multi-Step Ms. Chang is baking pies
and cakes for the school bake sale. She
bought 16 apples, 29 peaches, and
11 bananas at the Farmers’ Market.
How many pieces of fruit did she buy?
56 pieces of fruit
7.
Problem 11 requires students to use both higher
order thinking skills and multiple steps to solve the
problem. Remind students to think of the strategies
they have been using to add.
Multi-Step Mr. Staples bought 48 paper
plates, 22 paper cups, and 50 paper
napkins for the picnic. How many paper
products did he buy?
120 paper products
8.
Communicate What is the
unknown number? Which property did
you use?
M
Math
on the Spot
Video Tutor
V
(■ + 8) + 32 = 49
9; Associative Property of Addition
9.
Multi-Step Change the
order or grouping to find the sum.
Explain how you used properties to
find the sum.
63 + 86 + 77
© Houghton Mifflin Harcourt Publishing Company
Math on the Spot videos are in the
Interactive Student Edition and at
thinkcentral.com.
Possible explanation: first, I used the Commutative Property of
Addition to change the order of 63 and 86 to get 86 + 63 + 77. Then
I added 63 and 77 to get 140. Then I added 86 and 140 to get 226.
Module 4 • Lesson 3 115
3
RtI Tier 1 Lesson 16
2
1
Enrich 18
Name
Name
LESSON
16
3.4.A
The Associative Property of
Addition states that you can group
addends in different ways and get
the same sum.
Step 1 Look for numbers that are
easy to add.
Think: Make doubles.
3 + 1 = 4 and 4 + 4 = 8
Step 1 Look for numbers that are
easy to add.
Think: Make a ten.
7 + 3 = 10
Step 2 Use the Commutative
Property to change the order.
3 + 14 + 21 = 3 + 21 + 14
Step 2 Use the Associative Property
to change the grouping.
7 + (3 + 22) = (7 + 3) + 22
Step 3 Add.
Step 3 Add.
So, 3 + 14 + 21 = 38.
© Houghton Mifflin Harcourt Publishing Company
1.
Find 7 + (3 + 22).
The Commutative Property of
Addition states that you can add
numbers in any order and get the
same sum.
24 + 14 = 30 + 8
Properties on Parade
Use addition properties to find the unknown numbers.
Write the property that you used.
Find 3 + 14 + 21.
3 + 21 + 14 = 24 + 14
3. 25 + 44 + 5 =
5. 23 + 14 + 23 =
Number and Operations
74
60
4.
Property of Addition
(96 1 7) 1 73 5 ■ 1 (■ 1 73)
5.
96, 7; Commutative
(7 + 3) + 22 = 10 + 22
10 + 22 = 32
(9 1 17) 1 ■ 5 59
33; Associative Property
Property of Addition
3.
(44 1 8) 1 52 5 ■ 1 (■ 1 52)
44, 8; Commutative
of Addition
2.
of Addition
(■ 1 3) 1 75 5 98
6.
(■ 1 5) 1 65 5 89
20; Associative Property
19; Commutative
of Addition
Property of Addition
So, 7 + (3 + 22) = 32.
7.
Strategies will vary. Check students’ work.
25
(■ 1 7) 1 30 5 47
10; Associative Property
Use addition properties and strategies to find the sum.
1. 2 + 15 + 8 =
Enrich 18
1
Algebra • Use Properties to Add
OBJECTIVE Use the Commutative and Associative Properties of Addition to add more than two addends.
You can use addition properties and strategies
to help you add.
115 Module 4
Show Your Work
120 vegetables
Problems
Through the Math on the Spot Video Tutor,
students will be guided through an interactive
solving of this type of H.O.T. problem. Use this
video to also help students solve the H.O.T.
problem in the Interactive Student Edition. With
these videos and the H.O.T. problems, students
will build skills needed in the TEXAS assessment.
Write Math
2. 19 + 36 + 1 =
Explain how using addition properties can
make adding easier.
Possible explanation: you can use the addition
56
properties to regroup or reorder numbers so that
4. 12 + 36 + 18 + 14 =
80
6. 11 + 15 + 19 + 14 =
59
numbers that are easy to add mentally are next to one
another.
31
Enrich
© Houghton Mifflin Harcourt Publishing Company
E18
Mathematical Processes
Model ¥ Reason ¥ Communicate
Daily
Daily Assessment
Assessment Task
Task
3
Fill in the bubble for the correct answer choice.
Use properties to solve.
10.
11.
12.
Daily Assessment Task
154
C
124
B
144
D
164
He regrouped the numbers as 97 − (22 − 5).
B
He subtracted the numbers in parentheses first.
C
He did not subtract all the numbers.
D
He subtracted from left to right.
NO
•
Soar to Success Math
Warm-Up 10.42
YES
•
•
Enrich 18
Homework and Practice
Lesson 4.3
TEXAS Test Prep Coach
Multi-Step A travel company offers rafting trips for families.
The fees for the trip are $54 for adults and $46 for children.
The Kirk family of two adults and two children want to go on
the trip. How much will they pay for their rafting trip?
In the Test Prep exercise if students selected:
B They chose the Commutative Property of Addition.
A
$200
C
$220
C They chose the Identity Property of Addition.
B
$300
D
$320
D They chose the expanded form.
?
TEXAS Test Prep
Communicate Which shows the Associative Property
of Addition?
A
(86 + 7) + 93 = 86 + (7 + 93)
B
86 + 7 = 7 + 86
C
86 + 0 = 86
D
86 = 80 + 6
116
Essential Question
Write
Math
How can you add more than two addends?
© Houghton Mifflin Harcourt Publishing Company
13.
THEN
IF
Tim got the answer 80 to the problem (97 − 22) − 5.
Which statement shows the error he made?
A
1
Can students add more than two addends?
Josephine took photos of three canyons during the rafting
trip. In the first canyon, she took 64 photos. She took
31 photos of the second canyon. In the third canyon, she
took 49 photos. How many photos did Josephine take in all?
A
2
Possible answer: use the Associative Property of Addition
to group the addends to make them easier to add, group
the ones or the tens to make them easier to add, or use the
Commutative Property to change the order of the addends.
Differentiated Centers Kit
Games
Games
Auto Addition
Students practice
2-digit addition
to move along
the game path.
Literature
So Many Seashells
Students read about how
to use addition to find
the number of seashells
collected.
Activities
Roll to 100!
Students complete
orange Activity Card 1
by finding the sum of
three numbers.
Lesson 4.3
116
5
Ho mewo rk
and Practice
Fill in the bubble completely to show your answer.
Use Properties to Add
9.
Find the sum. Write the addition property you used.
1.
99
28 + 29 + 42 = _
2.
Associative
___
Property of Addition
3.
198
25 + 48 + 125 = _
136
23 + 36 + 77 = _
Associative
___
Property of Addition
4.
Associative
___
Property of Addition
150
34 + 22 + 46 + 48 = _
Commutative
___
Property of Addition
11.
5.
160
21 + 55 + 39 + 45 = _
6.
Commutative
___
Property of Addition
137
62 + 27 + 48 = _
Associative
___
Property of Addition
Problem
Problem Solving
Solving
The Smoothie Stop sold 35 banana
smoothies, 48 strawberry smoothies,
and 25 orange smoothies. How many
smoothies were sold in all?
© Houghton Mifflin Harcourt Publishing Company
7.
8.
Max spent 28 minutes on math
homework, 27 minutes on science
homework, and 22 minutes on
English homework. How much time
did he spend on homework?
108 smoothies
Module 4 • Lesson 3
Use the Homework and Practice pages to provide
students with more practice on the concepts and
skills of this lesson.
Module 4
12.
77 minutes
Homework and Practice
117-118
TEXAS Test Prep
Lesson
Lesson Check
Check
Name
117
118
Students collected used books to
sell at the school fair. On Wednesday,
74 books were donated. On Thursday,
62 books were collected. On Friday,
students brought in 36 books. How
many books were collected on all
three days?
A
162
B
182
C
172
D
170
Mrs. Jackson is in charge of the food
booth. She made a supply list. How
many packages of paper goods are on
the supply list?
A
92
B
82
C
72
D
50
Multi-Step There was a food drive
at the school fair. Two local grocery
stores each donated the number of
food packages shown in the table.
How many packages of food did
both stores donate altogether?
A
105
C
210
B
135
D
150
10.
Local farmers had a booth at the
school fair. Farmers sold 53 pounds
of squash, 58 pounds of tomatoes,
and 37 pounds of zucchini. How
many pounds of vegetables were
sold in all?
A
148 pounds
B
90 pounds
C
158 pounds
D
138 pounds
Supply List
25 packages of cups
32 packages of plates
25 packages of napkins
Item
Donation Amount
boxes of pasta
75 boxes
cans of soup
30 cans
© Houghton Mifflin Harcourt Publishing Company
4.3
Number and Operations—3.4.A
Also 3.5.A
MATHEMATICAL PROCESSES 3.1.D, 3.1.F