LESSON PLAN (Linda Bolin) - Granite School District

LESSON PLAN (Linda Bolin)
Lesson Title: The Distributive Property For Numerical and Variable Expressions
Course: Pre-Algebra Date: Sept Lesson 2
Utah State Core Content and Process Standards: 1.2c
Recognize and use the distributive property of multiplication over addition
Lesson Objective(s): Apply the distributive property in simplifying algebraic expressions
Enduring Understanding (Big
Ideas):
Properties can be used to
simplify mathematical
expressions
Skill Focus: Identify and use
the distributive property
Essential Questions:
• How can I use the distributive property to multiply
factors with two or more digits?
• How can the distributive property be modeled using
manipulatives?
Vocabulary Focus:
distributive property, factors, terms
Materials:
• Journal page: “Distributive Property Examples”
• Algeblocks (units and x’s)
• “Distributive Property With Algeblocks”
Assessment (Traditional/Authentic): Performance tasks, observing
Ways to Gain/Maintain Attention (Primacy): comparing, seeing patterns, manipulatives,
story, sketching
Written Assignment:
• Journal page: “Distributive Property Examples” and examples from the Cookie Monster
story
• “The Distributive Property With Algeblocks” (worksheet)
• p73/1-11; p74 # 38-39 (McDougall Littell Pre-Algebra)
List the vocabulary on the board
Content Chunks
Starter: For each problem tell which way is easiest for you to do mentally.
Explain why the one you chose was easier for you than the other.
1. Which is easiest to do mentally for you?
A. 2 • 50 + 2 • 9 OR 2 • 59
B. 3 • 436 OR 3 • 400 + 3 • 30 + 3 • 6
1 8
C. x 9_ OR 9 x 10 + 9 x 8
2. Use you calculator to do both problems for each above. Are the two
expressions equivalent in each? What is the product?

Lesson Segment 1: How can I use the distributive property to multiply factors
with one, two or more digits?
Connect the problems in the Starter to the distributive property by asking them if 50 +
9 is the same as 59, and if 400 + 30 + 6 is the same as 436, etc. Multiplying each of
the place value parts of a number individually then adding the products together gives
you the same answer as multiplying the entire number. The algorithm for
multiplication is an example of how you have used the distributive property in your life.
Use the journal page “Distributive Property Examples” to guide class and cooperative
discussion in this manner:
1. Look at one example and discuss the example making sure you USE THE
VOCABULARY words in the last column.
2. Have students work in pairs to try to place the words correctly in the blanks
3. Have each pair share with another to see if they agree. Correct with whole class to
make sure all words have been placed correctly in the blanks.
4. Ask each pair to then make up an example and write it on their papers.
5. Have each person share with another from another pair to explain why their
example shows the use of the distributive property. If the partner doesn’t agree, they
can work together to make corrections.
Lesson Segment 2: How can the distributive property be modeled using
manipulatives?
Model and represent: Give each team a package of Algeblocks. Have them take out
several green squares and several yellow bars. On the back of the journal have
students sketch, and represent the models from “The Real Cookie Monster” as you go
over the story with them. Ask one person to be the model builder, while a partner
coaches. Both sketch the models and write the variable expression as you go through
the story. Work with the students to represent each piece. The green represents
exactly one cookie. The yellow bar is X and represents an undetermined number of
cookies.
Using the attached worksheet, “Distributive Property With Algeblocks”, as a guide, help
students understand and apply the distributive property. Work together to complete #
1-9. Have students take turns modeling as team members sketch and represent the
questions.
Lesson Segment 3: Practice
Assign students to complete # 10-16 of the “Distributive Property With Algeblocks”
worksheet. Go over any additional practice you select from a text book.

Distributive Property Examples Date______ Name__________________
Example My own example My words
1. 3(20 + 4) = 3 · 20 + 3 · 4
3 (24) = 60 + 12
72 = 72
Use these words:
parentheses, distribute,
terms
To __________ means to
multiply both _______ in
parentheses by the same
factor. The factor is
outside the __________.
3 7
2. x 5 5(30 + 7)
3 5 5 · 30 + 5 · 7
1 5 0 150 + 35
1 8 5 = 1 8 5
+
3 x 4 + 3 x 2
= 12 + 6
= 18
Use these words:
multiplying, property,
factor
I can apply the distributive
__________ when I am
__________ each number
by the same __________.
Use these words: rows,
add, factor, distributive
property, multiply
Since both tables have 3
_______, we can _____
the columns in both tables,
then __________ that
sum by 3. This is an
example of the _________
______________.
OR
= 3(4 + 2)
= 3(6)
= 18
5”
4” 4”
5”
P = 2l + 2w or
P = 2(l + w)
P = 2 x 4 + 2 x5
P = 2(4 + 5)
P = 2(9)
P = 18”
Use these words: length,
width, perimeter,
distribute, factor
Since the formula for
___________ asks for 2
times the ________
added to 2 times the
_________, we can
____________ a
common _________
of 2 to find perimeter.

The Real Cookie Monster
Lets say the green square represents exactly one unit. If I were talking about candy
bars, the green piece would represent one candy bar. If I were talking about the
minutes I usually get to talk on the phone, the green piece would represent one
minute. If I were talking about dollars, the green piece would represent 1 dollar.
AJ says he can eat 3 cookies. Model, sketch use a math symbol to represent the
number of cookies AJ can eat.
3 units represents the number of cookies AJ can eat.
Falesiu says she’s not sure how many she can eat, but she knows she can eat several
cookies. Now, we don’t know the exact unit, so we will use the yellow bar to represent
an undetermined number of cookies. We’ll call this yellow bar, X.
X represents the number of cookies Falesiu can eat.
Now, you know how some people don’t like to be outdone. Well, Tyson says he can eat
twice as many cookies as AJ can eat. Represent the number of cookies Tyson can eat.
2 • 3 or 6 represents the number of cookies Tyson can eat
Krista, does not want to be outdone, so she brags that she can eat twice as many cookies as Falesiu
can eat. How would we represent that?
2X represents the number of cookies Krista can eat
Now, Jayden gets involved. She says she can eat twice as many cookies as Krista and Tyson
combined. Model, sketch and represent the number of cookies Jayden claims she can eat.
4X + 12 represents Jayden’s claim.
OR
2(2x +6) represents Jayden’s
claim

Distributive Property With
Algeblocks
Name _________
1. Arrange 5X’s and 10 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 5X and 10 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’s 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’s 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.
10. 2x + 14 11. 21 + 14x 12. 5x + 15
Use the distributive property to write the problems below without the parentheses
13. 4(2x + 9) 14. 2(4 + x) 15. (w + 6)2
16. The problems above have demonstrated the distributive property of multiplication
over addition. In your own words, write a definition or explanation for what it means
to distribute and how the distributive property works.