LESSON PLAN (Linda Bolin)
Lesson Title: Properties: Commutative, Associative, Identity, Properties of 0
Course: Pre-Algebra
Date: Sept Lesson 1
Utah State Core Standards: 1.2c
Recognize and use the identity property of addition and multiplication, the multiplication
property of 0, the commutative and the associative properties of addition and multiplication
Lesson Objective(s): Identify and apply properties of addition and multiplication
Enduring Understanding
(Big Ideas):
Properties of Operations
exist. Properties expedite
computation.
Essential Questions:
 How are the outcomes of multiplying by 1 and of adding 0 to
an expression similar? Different?
 What is the product of any number and 0
 Why is division by zero undefined?
 How can commutative and associative properties be used to
simplify numerical expressions?
 Do the commutative and associative properties apply to all
operations?
Skill Focus:
Vocabulary Focus:
Identify properties
Identity property, undefined, commutative property,
Simplify expressions using
associative property
properties
Materials:
 scissors and colored paper for foldable
 graphing calculators
 Color Tiles
 Linker Cubes
 Worksheet: Linker Cube Properties
 8 large charts and 8 markers for Round The Room Writing
Assessment (Traditional/Authentic): Performance, Stand-Up-If, Game, manipulatives
Ways to Gain/Maintain Attention (Primacy): Game, calculators, manipulatives, graphic
organizer
Written Assignment:
Foldable
Properties Examples (on student’s own paper)
Linker Cube Properties
Content Chunks
Post vocabulary on Word Wall
Starter:
Compute using mental math-no calculator
1. 42 • 33 • 0
2. 4.9 + 6.8 + 3.2
3. 2 • 29 • 5
4. 2,900,145 x 1
Lesson Segment 1: Identify Commutative, Associative and Identity Properties
Q. How did you do the problem in the Starter? Did anyone do it differently? Is there
another way to work the problem that would make it easier to do?
Go over the essential questions with the students telling them they will need to be able
to answer them at the end of the lesson.
A property is simply a true characteristic or attribute of something. Do “Stand Up If”
where you as students to stand up if you name a property that is true for them,
personally.
Stand up if…
a. Brown hair is a property for you
b. Being a good pet owner is a property for you
c. Texting is a property for you
d. Being over five foot tall is a property for you
Operations have properties, or true characteristics, too. Addition is an example of an
operation. Think of three other operations.
Have students make a foldable where flaps open in the center to make four sections
like this
Have students use the
graphing calculator to
review commutative,
associative and identity
properties as explained in the
TI-73 Equivalency attachment.
After discussing a property, and
Trying several examples, have
students write three examples of
that property and an explanation
for how that property works under
the appropriate flap of the foldable.
Commutative
Property
Cut here
Identity
Properties
Associative
Property
Cut here
Properties of
Zero
Lesson Segment 2: Properties of 0
Multiplication by 0
Ask each student to write a LONG multiplication problem that has a product of 0. Have
student share around their team in a Round Robin. Have a few share with the class.
Q. If I want a product of numbers to be 0, what must one of the factors be? Q. Can I
ever get a product of 0 if none of the factors is 0? Q. Can I ever get a product other
than 0 if one of the factors is 0?
Division by 0
Give students several color tiles. Tell them they will be making various groups using
12 color tiles. They should sketch and record each of the tasks on their own Properties
Examples assignment paper. Have them separate the color tiles into groups by:
1. First dividing the tiles into 12 equal groups. Ask, “How many tiles in each group?”
Have them sketch the groups and write 12/12 = 1 tile in the group.
2. Next, have them divide the color tiles 6 equal groups. Ask, “How many tiles in each
group?” Sketch the groups, and write 12/6 = 2 tiles in each group.
3. Next, have them divide the color tiles into 4 groups. Ask, “How many tiles in each
group?” Sketch the groups, and write 12/4 = 3 tiles in each group.
Q. As we divide the 12 into fewer groups, what is happening to the number of tiles in
each group? Predict: Will that pattern continue?
4. Next, have them divide the color tiles into 3 groups. Ask, “How many tiles in each
group?” Sketch the groups, and write 12/3 = 4 tiles in each group.
5. Next, have them divide the color tiles into 2 groups. Ask, “How many tiles in each
group?” Sketch the groups, and write 12/2 = 6 tiles in each group.
6. Next, have them divide the color tiles into 1 group. Ask, “How many tiles in each
group?” Sketch the groups, and write 12/1 = 12 tiles in the group.
Q. Has your prediction proven to be true so far?
7. Last, have them divide the color tiles into 0 groups. As they look for ways to form
no groups, they will try to form one group or they will say they will use no tiles. But,
that is not what they are being asked to do. Guide their discussion to the fact that
there is no way to identify what a no groups look like. So, there is no way to make no
groups when you have any number of items. Thus, dividing by 0 is undefined or
impossible. Have them try 12/0 on their calculator. Have them try dividing several
numbers by 0. Show them this is different from when we have no tiles and try to make
12 groups. Have them try this on their calculator.
Have them write examples for multiplying by 0 and for dividing by 0 and write in their
own words what happens when multiplying by 0 and when dividing by 0 under the
properties of 0 flap of the foldable.
Lesson Segment 3: Modeling, Applying and Recognizing Properties
Linker Cubes can be used to model properties. Give each pair several linker cubes and
work with them to model the properties listed on the attached worksheet, “Linker Cube
Properties”. Have students work with a partner taking turns being the builder to build,
and sketch two examples for each of the properties on the paper.
Sing the attached Properties Song with the students a couple of times.
Do Stand-Up-If where students stand up if the statement is true. As they stand or
remain sitting, ask them which property helped them to know this.
1. 15 x 1 = 1,
2.
32 +8 + 14 = 54
4. 0/7 is undefined or impossible
5. 7/0 = 0
3.
14/2 = 2/14
6. 3 + 28 + 7 = 38
Round The Room Writing Properties
Objective: Students will identify and write examples of properties
Materials: Eight Large papers with name of property and variable example on top, eight
markers. Papers will be titled thus
1. Additive Identity
2. Multiplicative Identity
3. Multiplication by 0
4. 0 as a dividend
5. 0 as a divisor
6. Commutative Property for addition
7. Commutative property for multiplication
7. Associative Property for addition
8. Associative Property for multiplication
Assign rotating roles: Scribe, Editor, Encourager, and Coach(es). The scribe writes
only what the coaches suggest. The editor makes sure the expression looks correct
and is large enough to be read across the room. As students move to each successive
chart, the roles should be rotated giving each a chance to perform all the roles.
Procedure:
Student teams will revolve around the room as directed by the teacher stopping
at one of the 8 charts each time they move. When they stop at a chart, they should
read any expressions shown and put a small smiley face by the expressions they
believe are correct. Then, they will write one or two example on the paper. You may
want to instruct them to write an example using fractions or decimals and an example
using whole number. When each team has visited all the papers, have the teams
return to their first chart where they will decide which of the expressions are correct.
They will then explain to the class why the expressions are correct or incorrect and the
class members write all corrected expressions.
Lesson segment 4: Practice
Game: Play Concentration (see attached game) by dividing the class in half and having
them take turns choosing two squares to be a match. If they choose two that match,
their team gets a point. Students write the numbers and examples from the game on
their paper.
Cooperative Activity: Do Round The Room Writing (instructions attached)
Assign any additional text practice as needed.
Using the TI-73 to Verify Equivalency
The graphing calculator may be used whenever checking for equivalency in
numerical or algebraic expressions is important such as checking the solution
to an equation, checking for proof when using properties, or checking
accuracy when simplifying algebraic expressions
To validate a property, press . Type the expression on the left of the equal
sign. Then, curser to the = sign. and press . Type the expression on the right of
the equal sign. Curser to Done and press  . If a 0 appears, the expressions are
NOT equivalent. If a 1 appears, the expressions are equivalent.
Try several examples of properties to check for equivalency. Give the students
some non examples using subtraction and division. Students should record the
expressions on their paper and indicate whether they are equivalent or not.
Properties Song
(to “Macnamara’s Band”)
The Commutative Properties
Are like an order game
Whether first is last or last is
first,
The answer will be the same.
So one plus two is two plus one,
And either sum is three.
And, five times eight is eight
times five.
Commutative Property!
Chorus
Oh with these properties
computing can be fun,
Making operations easier to be
done!
The Identity Property
Makes numbers stay the same.
How can you add or multiply
And not change the number’s
name?
When adding, add a zero,
Multiplying, times by one.
The answer will be identical to
The number where you’ve
begun.
Chorus
Oh with these properties
computing can be fun,
Making operations easier to be
done!
The Associative Properties
Say grouping can be fun!
And, the little parentheses
Show how the grouping’s done.
Often, answers can be found
More quick or easily by
Moving parentheses around.
Associative Property!
Chorus
Oh, with these properties
computing can be fun
Making operations easier to be
done!
Now Zero has some properties
Though Zero’s nothing at all.
You can’t divide by zero,
Whether the number is large or
small.
And Zero wants all products
To be nothing, you can bet.
So, if you multiply by Zero,
Then, Zero is all you get!
Chorus
Oh, with these properties
computing can be fun
Making operations easier to be
done!
Linker Cube Properties
(
+
Name _____________________
)+
=
+(
+
)
Build 2 models using Linker to show examples for each property listed below. Sketch
and label each model. Write the numerical expressions to represent your models
Commutative Property for Addition
Commutative Property for Multiplication
Associative Property for Addition
Associative Property for Multiplication
Identity Property for Addition
Identity Property for Multiplication
Properties Concentration
1
2
3
4
Commutative
Property
For Addition
297 • 1 =
297
44.6 + 0 =
44.6
Division
Property
of 0
5
6
7
8
Associative
Property for
Addition
17 + 18 +3 =
17 + 3 +18
8 ÷ 0 is
undefined
9
11
3•bc = 3b•c
10
Commutative
Property
For
Multiplication
2.7(0) =0
Identity
Property
For
Multiplication
12
Associative
Property for
Multiplication
13
14
15
2 • 38 • 5 =
2 • 5 • 38
Multiplication (31+9)+28=
Property
31+ (9+28)
of 0
16
Identity
Property
For Addition
Put the game on a transparency. Put small post-its over the squares. Have
students select the number of a square. Lift the flap post-it. Have the student
select a number for a square they think may be a match. Lift that. When
students find a match, the post-its are removed from the two squares and a
point is given to that team.
Answers:
1-6, 2-8, 3-16, 4-7, 5-15, 9-12, 11-14, 13-10,