LESSON PLAN (Linda Bolin) - Granite School District

LESSON PLAN (Linda Bolin)
Lesson Title: Simplifying Algebraic Expressions Using Properties
Course: Math 7 Date: December Lesson 3
Utah State Core Content and Process Standards:
1.3c Apply the identity, commutative and associative properties of addition and multiplication
and the distributive property of multiplication over addition in simplifying algebraic
expressions
3.1c Evaluate algebraic expressions for a given value including fraction and decimal values
Lesson Objective(s): Students will simplify algebraic expressions using the identity
properties of addition and multiplication, the commutative and associative properties of
addition and multiplication, and the distributive property of multiplication over addition.
Enduring
Understanding (Big
Ideas):
Properties apply in both
numeric and algebraic
situations. Properties can
expedite simplifying
expressions
Essential Questions:
• What is the product of any number and 1? What is the sum of
any number and 0?
• How does applying the commutative or associative properties
affect the sum or product?
• How can I demonstrate the use of the distributive property of
multiplication over addition?
• How do properties help me simplify algebraic expressions?
Skill Focus:
Apply properties in
simplifying algebraic
expressions
Vocabulary Focus:
Commutative property, Associative property, Multiplicative
Identity Property, Additive Identity Property, distributive
property, algebraic expression, simplify
Materials:
• Ti-73’ and view screen
• Paper for foldable
• Algeblocks
• Worksheets: Using the TI-73: Simplifying Algebraic Expressions, Distributive Property With
Algeblocks
Assessment (Traditional/Authentic): observation, questioning, writing, mental math,
student response cards
Ways to Gain/Maintain Attention (Primacy): Contest, predicting, music, technology,
stories, analogy, manipulative, writing, movement, cooperative discussion, journaling
Written Assignment:
Contest: Properties Guess activity record, Properties Foldable, Worksheets: Using the TI-73:
Simplifying Algebraic Expressions, Distributive Property With Algeblocks
Post vocabulary
Starter: Accessing prior knowledge
1. Which of these representations does not tell us to multiply?
a) 3(4) b) 2m c) _r_ d) 6 • 7 c) 8 x 10
5
2. Use Mental Math to compute.
a) 3 + (17 + 138) b) 1( ½ + 4 + ½ ) c) 5 x 26 x 2
d) 2(13) + 2(7) e) 5(2 + 10) f) 231 • 8 • 0

• Lesson Segment 1: (Accessing prior knowledge) What is the product of any
number and 1? What is the sum of any number and 0? How does applying
the commutative or associative properties affect the sum or product? How
can I demonstrate the use of the distributive property of multiplication over
addition?
Team Contest: Use the #1 question on the starter to review properties by asking
students to look at property words on the board. Tell them you can compute much
faster and easier by using these properties. Have students take out a paper for an
assignment activity called “Properties Guess”, and number the paper a-f. As you
mentally compute each starter problem, have students quietly discuss with their team
and write which property or properties they think you applied. Ask students to respond
after they have written the property they think you applied. Any team who correctly
identified the property(s) earns a point. You may need correct their thinking as you go
over each problem. After discussing an expression, have students write the correct
property and how it was applied to simplify each expression on their paper.
a) 3 + (17 + 138) Use associative property to regroup adding 3 and 17 first.
b) 1( ½ + 4 + ½ ) Use the commutative property to reorder ½ + ½ + 4 in
the parentheses, and then multiply by 1 using the identity property.
c) 5 x 26 x 2 Use the commutative property to reorder 5 x 2 x 26.
d) 2(13) + 2(7) Use the distributive property to multiply the sum of 13 and 7
(20) by 2.
e) 5(2 + 10) Use the distributive property to multiply 5 x 2 (10) and 5 x 10
(50). Add 10 and 50.
f) 231 • 8 • 0
Tell students these properties work for addition and multiplication with variables too.
If they have their properties foldable from September Lesson 7, they could use it to
compare. Make this foldable for properties
with variables. Fold both edges toward the
center. Clip on the dotted line to the fold to
make four shutters. Inside students should
Commutative Associative
write examples of the application of these
Properties Properties
properties using variables. Work with
students to write simple algebraic examples
such as:
Cut here
Cut here
a + b = b + a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
1a = a
a(b+c) = ab + ac
Identity
Properties
Distributive
Property

Lesson Segment 2: How do properties help me simplify algebraic
expressions?
Sing or say the Properties Song to review (attached).
Accessing and building background knowledge:
Tell the students when they were finding a simple answer for the operations in the
contest, they were “simplifying the expression”. Give a brief explanation for the word,
simplify such as, “What we mean by “simplifying an expression” is to make the
expression more simple to understand or look at without changing the value of the
expression.
In our language we often simplify expressions. For example, we could say, “Hi there.
How are you doing? Or, we could say, “Hey, Sup?” The meaning is the same, but the
second expression is much shorter and simpler than the original expression.
In mathematics we want to write expressions as simply as possible, but do not want to
change their meaning or value. We want the simplified expression to be equivalent to
the original, longer expression.
Ask the following questions and have students record the examples on their Team
Contest record paper.
Q. When we say two expressions are equivalent what does that mean? For example
when we say 3 + 1 is equivalent to 4 (or 3 + 1 = 4), what does that mean?
The equal sign tells us one expression is equivalent to the other or in other words, the
expressions have the same value.
Q. If two expressions are equivalent, must they always look exactly the same? What
makes you think so?
Show examples: 2 • 6 = 3 • 4 3(2 • 5) = (3 • 2)5 3(5 + 6) = 3 • 5 + 3 • 6
Q. How can we know whether two expressions are equivalent if they don’t look alike?
One way to verify that two expressions are equivalent, is to simplify each expression.
Example 1: 2 • 6 = 3 • 4
2 • 6 simplified is 12
3 • 4 simplified is 12
12 = 12.
So, 2 • 6 = 3 • 4
Example 2: 3(2 • 5) = (3 • 2)5
3(2 • 5) is 3(10) =30
(3 • 2)5 is (6)5 = 30
30 – 30
So, 3(2 • 5) = (3 • 2)5

Example 3: 3(5 + 6) = 3 • 5 + 3 • 6
3(11) = 33
3 • 5 + 3 • 6 is 15 + 18 = 33
33 = 33
So, 3(5 + 6) = 3 • 5 + 3 • 6
Tell students these ideas about equivalency and simplifying apply with variables as well
as numbers. We use properties to simplify algebraic expressions. When we simplify an
algebraic expression using properties, we can compare the original expression with the
simplified expression to make sure they are equivalent. A simplified expression is
always equivalent to the original. Students will be simplifying algebraic expressions,
and then substituting values in the expressions to verify equivalency.
Work with the class to complete the Simplifying Algebraic Expressions worksheet.
Lesson Segment 3: How can the distributive property be applied to algebraic
expressions?
Using Algeblocks, work through the attached Distributive Property Using Algeblocks
investigation (attached). This is a powerful visualization for applying the distributive
property with variables. Make sure students build, draw and represent as instructed.
Discuss their models.
Assign text practice as needed.

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 the Distributive Property
Says factors should be shared,
All numbers in parentheses,
With the same factor paired.
So 5 times 2 plus five times one
Is the same as five times three.
Multiplying will be easier with
Distributive Property!
Chorus
Oh, with these properties
computing can be fun
Making operations easier to be
done!

Using The TI-73:
Simplifying Algebraic Expressions
Name _____________
Look at the original expression and the simplified expression. Tell which property was
used to simplify the expression. Then, substitute the given value for the variable using
the TI-73 to check.
To compare the original and the simplified expressions, first substitute a value. Type
a value and press X I b.
To compare the two expression, first press -1. Type the original expression.
Then, curser to the = sign and press b. Now, type the simplified expression on
the right of the equal sign. Curser to Done and press b b. If a 0 appears, the
expressions are NOT equivalent. If a 1 appears, the expressions are equivalent.
1. 3 + x + 7 2. 2(3x)
= 3 + 7 + x = (2 • 3)x
= 10 + x = 6x
Property used to simplify?
Substitute 2 for x and prove equivalency.
Property used to simplify?
Substitute 5 for x and prove equivalency.
3. 1x 4. 8 + (2 + r)
= x = (8 + 2) + r
= 10 + r
Property used to simplify?
Substitute 7.3 for x and prove equivalency.
Property used to simplify?
Substitute 6 for x and prove equivalency.
5. 4w • 5 6. 5b + 3b
= 4 • 5 • w = (5 + 3)b
= 20w = 8b
Property used to simplify?
Substitute -1 for x and prove equivalency.
Property used to simplify?
Substitute ½ for x and prove equivalency.

Distributive Property With
Algeblocks
Name _________
Use the yellow piece to represent x and the green piece to represent one unit.
1. Arrange 4X’s and 8 units into groups so that each group is identical to the other
groups. Sketch your work. Write a variable expression using parentheses to represent
your groups.
2. Find another way to group 4X and 8 units so that each group is identical. Sketch
your work. Write a variable expression using parentheses to represent your grouping.
3. Arrange 8X’s and 12 units into groups so that each group is identical to the other
groups. Sketch your work. Write a variable expression using parentheses to represent
your groups.
4. Find another way to group 8X and 12 units so that each group is identical. Sketch
your work. Write a variable expression using parentheses to represent your grouping.
5. Arrange 6X and 6 units into groups so that each group is identical to the other
groups. Sketch your work. Write a variable expression using parentheses to represent
your groups.
6. Find another way to group 6X and 6 units so that each group is identical. Sketch
your work. Write a variable expression using parentheses to represent your grouping.
7. Make up a problem of your own. Show the X’s and units in your sketch and write
the algebraic expression for your problem.

8. Build and sketch 3(x + 3).
Now rearrange the Algeblocks so all X’s are grouped together and all units are grouped
together. Sketch your new arrangement.
Write a variable expression for the rearranged Algeblocks.
9. Build and Sketch 2(3x + 4).
Now rearrange the Algeblocks so all X’s are grouped together and all units are grouped
together. Sketch your new arrangement.
Write a variable expression for the rearranged Algeblocks.
Use the distributive property to write the problems below using parentheses.
Substitute a value for the variable to check your new expression with the original.
10. 2x + 14 11. 5x + 15
Use the distributive property to write the problems below without the parentheses
Substitute a value for the variable to check your new expression with the original.
12. 4(2x + 9) 13. (W + 6)2
10. The problems above have demonstrated the distributive property of multiplication
over addition and over subtraction. In your own words, explain the distributive
property.