Algebra
7
Objective
Model and identify the
Associative Property of
Addition.
Skills
• Adding
• Applying the Associative
Property of Addition
• Understanding sums
NCTM Expectations
Algebra
• Identify such properties as
commutativity, associativity,
and distributivity and use
them to compute with
whole numbers.
• Represent the idea of a
variable as an unknown
quantity using a letter or
a symbol.
The Associative Property of Addition allows you to group and regroup
addends without changing the sum: (a  b)  c  a  (b  c) for any three
values, a, b, and c. Students will find that the Associative Property allows them
to add compatible numbers more easily by regrouping a series of addends
when finding the sum.
Talk About It
Discuss the Try It! activity.
. Say: A train of purple, green, and red Cuisenaire®
Rods shows 4  3  2. A blue Rod shows the sum. Ask: What is the sum?
■ Display 4  3  2 
■ Display (4  3)  2 
. Remind students that they should do the
work inside the parentheses first. Ask: What train did we use to show that
we added the 4 and 3 first? (the black Rod and the red Rod) Ask: When we
added the 4 and the 3 first, did we still get 9 as the sum?
■ Display 4  (3  2) 
. Ask: What train did we use to show that
we added the 3 and the 2 first? (the yellow Rod and the purple Rod)
Ask: When we added the 3 and the 2 first, did we still get 9 as the sum?
Solve It
With students, reread the problem. Ask students to explain in writing how
they used the Associative Property to write two addition sentences to show
the total weight of Tricia’s books.
More Ideas
For other ways to teach about the Associative Property of Addition—
■ Have students work in pairs to represent number sentences using Three
Bear Family® Counters. Students should draw large parentheses lengthwise
on index cards and pick one size of Bear. Then one student should write a
pair of number sentences, and the other student should place groups of
Bears inside the parentheses to show the different groupings of addends.
■ Have students use Centimeter Cubes to model two number sentences, such
as (7  9)  6 
and 7  (9  6) 
color for each numerical value.
. They should use a different
Standardized Practice
Have students try the following problem.
What is another way to write 8  (9  4)  21 using the Associative Property?
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ETAM_G3-4_106-131_F.indd 118
A. 4  8  9  21
B. (8  9)  4  21
C. (8  4)  9  21
D. 8  (9  4)  21
12/19/05 2:03:15 PM
Try It!
20 minutes | Pairs
Here is a problem about the Associative Property of Addition.
Tricia’s math book weighs 4 pounds. Her science book weighs 3 pounds, and
her reading book weighs 2 pounds. Write two addition sentences that can be
used to find the total weight of her books. Then solve to find the total weight.
1. Ask students to model the addition number
sentence 4  3  2 using a train of Rods to
show the addends and find the Rod that shows
the sum (blue). Have students complete the
first section on their worksheets by writing the
number sentence and sketching the Rods.
3. Have students make another purple, light
green, and red train. Write the number
sentence 4  (3  2) 
on the board.
Ask students to model this number sentence
with Rods and fill in the third section on their
worksheets.
ETAM_G3-4_106-131_F.indd 119
Algebra
Introduce the problem. Then have students
Materials
do the activity to solve the problem.
• Cuisenaire® Rods (1 each of blue, black, yellow;
Distribute materials to students. Review
2 each of purple, light green; 3 red per pair)
the meanings of addend and sum. Explain
• Associative Property Worksheet (BLM 13; 1 per pair)
that each Rod represents a number. Have
students count how many white Rods each
Rod is made out of to find the number it represents.
2. Have students make another purple, light
green, and red train. Write the number sentence
on the board. Explain that
(4  3)  2 
the numbers in parentheses must be added first.
Have students find a Rod the same length as
the purple and green Rods combined (black) to
show that these Rods are being added first. They
should then combine the black Rod with the red
Rod. Have students complete the second section
on their worksheets.
Students may confuse the Commutative
Property of Addition with the Associative
Property of Addition. Emphasize that the
use of parentheses tells students that they
are grouping numbers together using the
Associative Property; whereas the Commutative
Property involves the order of numbers.
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13
Name
Associative Property Worksheet
BL M
1.
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2.
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© ETA/Cuisenaire®
188 188
BLM 13 Associative Property Worksheet
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This hands-on lesson was provided by ETA/Cuisenaire®. Hands-on materials help
students learn faster! They help students deepen their understanding of important
mathematical concepts and foster the transition of student understanding from concrete to
representational to abstract.
FAQ
Q: Where can I find and buy the manipulatives identified in the lesson for my students
to use?
A: Go to www.etacuisenaire.com. Type the name of the manipulative in the Search box
at the top of the ETA Web page.
Q: Can I use virtual manipulatives to teach the lesson?
A: Yes! We recommend you use ETA/Cuisenaire certified manipulatives available from
Promethean® Planet or from www.etacuisenaire.com. If possible, use the virtual
manipulatives for whole-class instruction and the physical manipulatives for small group
and independent student work.
Q: Where can I get more lessons like this one?
A: Two great resources for lessons focused on hands-on materials available from
ETA/Cuisenaire are The Super Source® books and Hands-On Standards®, Deluxe
Edition.
Q: What is the difference between lessons in The Super Source books and Hands-On
Standards, Deluxe Edition?
A: Hands-On Standards, Deluxe Edition provides scripting and support for the teacher
who is beginning to introduce the use of manipulatives into the math classroom. The
Super Source provides a wide range of topics and lessons that can be taught with a
specific manipulative.