M&M® Distributing Property
Lesson Plan
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Standard 6.EE.3: Apply the properties of operations to generate equivalent expressions. For example,
apply the distributive property to the expression 3(2  x) to produce the equivalent expression 6  3x ;
apply the distributive property to the expression 24 x 18y to produce the equivalent expression
6(4 x  3y) ; apply properties of operations to y  y  y to produce the equivalent expression 3y .
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Objective: Given M&Ms, exploratory resource sheets, and practice resource sheets, students will
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demonstrate an understanding of the use of the distributive property by simplifying expressions and
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finding perimeter of rectangles.
Time Table: This lesson is designed for a 50-minute class period.
Materials:
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M&Ms per class: 15 baggies of 6 red, 3 yellow, 2 green, 10 blue, 6 brown, 9 orange.(If
you do not want to use M&Ms, you can revise all of the problems to use x and use
algebra tiles or just draw and color the M&Ms.)
Copies of “M&M® Distributing: Distributive Property Activity” (Student Resource 1)
“M&M® Distributing: Distributive Property Activity” (Student Resource 1 Key)
Copies of “M&M® Distributing: Distributive Property Practice” (Student Resource 2)
“M&M® Distributing: Distributive Property Practice” (Student Resource 2 Key)
Copies of “M&M® Distributing: Distributive Property Homework” (Student Resource 3)
“M&M® Distributing: Distributive Property Homework” (Student Resource 3 Key)
Lesson Overview: This lesson is a review of the definition of multiplication as repeated addition in an
effort to provide the conceptual base for introducing the distributive property. The lesson uses visual
representations to model the distributive property and then provides the students with time to practice
these skills.
Grouping: The M&M activity can be completed in pairs, and the practice problems can be completed in
pairs or individually.
Procedure:
1. Review Multiplication defined as repeated addition (Parentheses mean to multiply).
a. 3(4)  4  4  4
b. 7(2)  2  2  2  2  2  2  2
c. 4(2  6)  2  6  2  6  2  6  2  6
d. 2( x  3)  x  3  x  3
2. Distribute and complete as a class problem #1 on “M&M® Distributing: Distributive Property
Activity.”
a. Read the word problem.
b. Set up the M&Ms.
c. Write the algebraic expression.
d. Write out the repeated addition.
e. Add the expressions.
3. Have students complete “M&M® Distributing: Distributive Property Activity” problems #2, 3, 4,
and 5 in pairs. Stop between each problem to discuss results.
4. Problem #5 will be impossible for the students to complete because they will not have enough
M&Ms. Ask, “Do you see a pattern or a shortcut we could take instead of using repeated
addition?” The answer you are looking for is “We could use multiplication instead.”
5. Thus, on #5, show them how to multiply one of the following two ways (or both).
12(6 g  8 y )
12(6 g  8 y )
6g  8 y
12(6 g )  12(8 y )

12
72 g  96 y
72 g  96 y
6. Have students complete the 10 practice problems from “M&M® Distributing: Distributive
Property Practice” in class either individually or in pairs (at the teacher’s discretion).
7. Check the 10 problems and go over questions.
8. Distribute “M&M® Distributing: Distributive Property Homework.”
Homework: “M&M® Distributing: Distributive Property Homework”
Extensions:
More problems that use geometry (Perimeter and Area) could be added to the practice problems and
the homework for a geometry review.
Algebra 1
Student Resource Sheet 1 Key
NAME: __________________________________ PER: __________ DATE: ____________
M&M® Distributing
Distributive Property Activity
Represent each of the following situations using M&Ms. Then write each as an algebraic expression.
1.
three groups of 2 red and 1 yellow
Algebraic Expression: 3(2r +1 y)
Repeated Addition:
2r + 1y
2.
two groups of 1 green and 5 blue
Algebraic Expression: 2(1g + 5b)
Repeated Addition:
2r + 1y
+ 2r + 1y
Total:
6r + 3y
1g + 5b
+ 1g + 5b
Total:
2g + 10b
3.
three groups of 2 brown and 3 orange
Algebraic Expression: 3(2b + 3o)
Repeated Addition:
2b + 3o
4.
two groups of 5 blue and 3 red
Algebraic Expression:
Repeated Addition:
2b + 3o
2(5b + 3r)
5b + 3r
+ 5b + 3r
+ 2b + 3o
Total:
Total:
5.
10b + 6r
6b + 9o
twelve groups of 6 green and 8 yellow
Algebraic Expression: 12(6g + 8y)
12(6g + 8y)
6g + 8y
12(6g) + 12(8y)
x
72g + 96y
12(6g) + 12(8y) = 72g + 96y
Total:
Algebra 1
12
72g + 96y
Student Resource 2 Key
NAME: _________________________________ PERIOD: _________ DATE: _____________
M&M® Distributing
Distributive Property Practice Key
The Distributive Property
Let a, b, c be real numbers.
Algebra
Examples
The product of a and (b + c)
a(b  c)  ab  ac
(b  c)a  ba  ca
3(4  2)  3(4)  3(2)
(3  5)2  3(2)  5(2)
The product of a and (b – c)
a(b  c)  ab  ac
(b  c)a  ba  ca
5(6  4)  5(6)  5(4)
(8  6)4  8(4)  6(4)
Words
Directions: Please simplify the following expressions by using the distributive property.
1. 3(2 y  5)
3(2) y  3(5)
6 y  15
4. 7(5 x  10)
7(5) x  7(10)
35 x  70
7.
2( x  4)  3
2 x  2(4)  3
2x  8  3
2x  5
10.
5(c  3a  5t )  8(d  2o  g )
2. 2(8  h)
2(8)  2h
16  2h
5. ( y  x)
1( y)  1( x)
y  x
3. (3  3x)(5)
3(5)  3(5) x
15  15 x
6. (5  6 x)(2)
5(2)  6(2) x
10  12 x
8. 4( z  8)  3 z  2
4 z  4(8)  3 z  2
4 z  32  3 z  2
7 z  30
9. 11(2 x  1)  4(7  3 x)
11(2) x  11(1)  4(7)  4( 3) x
22 x  11  28  12 x
34 x  39
11. A square has sides of
length 3x 10.
12. Find the area of the rectangle.
5c  3(5)a  5(5)t  8d  8(2)o  8 g
7x – 4
3
5c  15a  25t  8d  16o  8 g
What is the perimeter
of the square?
p  4(3x  10)
p  12 x  40
A = 21x – 12
Algebra 1
NAME:
Student Resource 3 Key
DATE:
PERIOD:
M&M® Distributing
Distributive Property Homework Key
The Distributive Property
Let a, b, c represent real numbers.
Algebra
Examples
The product of a and (b + c)
a(b  c)  ab  ac
(b  c)a  ba  ca
3(4  2)  3(4)  3(2)
(3  5)2  3(2)  5(2)
The product of a and (b – c)
a(b  c)  ab  ac
(b  c)a  ba  ca
5(6  4)  5(6)  5(4)
(8  6)4  8(4)  6(4)
Words
Use the distributive property to write an equivalent expression.
2. 9(a  b)
b+7
Find
the
area
.
1.
2
2b  14
9a  9b
3. 8( y  2)
4.  3(2w  7)
8 y  16
6w  21
5.  4(e  4)
6. (8  j)3
4e  16
24  3 j
7. (7  l )9
8. 4(a  b  c)
63  9l
4a  4b  4c
9. Find the perimeter .
3x  3
3x  3
10. Find the perimeter .
4x  4
9x  9
2x  2
3x  3
12 x  12
11. Find the area.
5x + 15
x+3
5
2x  2
4x  4
12. Find the perimeter of the regular octagon.
16x + 56
2x + 7
Algebra 1
Student Resource 1
NAME: _____________________________ PER: __________ DATE: ____________
M&M® Distributing
Distributive Property Activity
Represent each of the following situations using M&Ms. Then write each as an algebraic
expression.
1.
three groups of 2 red and 1 yellow
Algebraic Expression: ________________
Repeated Addition:
2. two groups of 1 green and 5 blue
Algebraic Expression: ________________
Repeated Addition:
+
Total:
+
Total:
3. three groups of 2 brown and 3 orange
Algebraic Expression: ________________
Repeated Addition:
4.
two groups of 5 blue and 3 red
Algebraic Expression: ________________
Repeated Addition:
+
Total:
+
Total:
5. twelve groups of 6 green and 8 yellow
Algebraic Expression: ________________
Total:
ALGEBRA 1
Student Resource 2
NAME: _________________________________ PERIOD: _________ DATE: _____________
M&M® Distributing
Distributive Property Practice
The Distributive Property
Let a, b, c be real numbers.
Algebra
Examples
The product of a and (b + c)
a(b  c)  ab  ac
(b  c)a  ba  ca
3(4  2)  3(4)  3(2)
(3  5)2  3(2)  5(2)
The product of a and (b – c)
a(b  c)  ab  ac
(b  c)a  ba  ca
5(6  4)  5(6)  5(4)
(8  6)4  8(4)  6(4)
Words
Directions: Please simplify the following expressions by using the distributive property.
1. 3(2 y  5)
2. 2(8  h)
3. (3  3x)(5)
4. 7(5x 10)
5. ( y  x)
6. (5  6 x)( 2)
8. 4(z  8)  3z  2
9. 11(2 x  1)  4(7  3 x)
11. A square has sides of
length 3x 10.
What is the perimeter
of the square?
12. Find the area of the
rectangle
7.
2( x  4)  3
9. 5(c  3a  5t )  8(d  2o  g )
7x – 4
3
3x 10
Algebra 1
Student Resource 3
NAME:
PERIOD:
DATE:
M&M® Distributing
Distributive Property Homework
The Distributive Property
Let a, b, c represent real numbers.
Algebra
Examples
The product of a and (b + c)
a(b  c)  ab  ac
(b  c)a  ba  ca
3(4  2)  3(4)  3(2)
(3  5)2  3(2)  5(2)
The product of a and (b – c)
a(b  c)  ab  ac
(b  c)a  ba  ca
5(6  4)  5(6)  5(4)
(8  6)4  8(4)  6(4)
Words
Use the distributive property to write an equivalent expression.
2. 9(a  b)
b+7
1. Find the area.
2
3. 8( y  2)
4.  3(2w  7)
5.  4(e  4)
6. (8  j)3
7. (7  l )9
8. 4(a  b  c)
9. Find the perimeter .
10. Find the perimeter .
3x  3
3x  3
11. Find the area.
x+3
5
3x  3
4x  4
2x  2
2x  2
4x  4
12. Find the perimeter of the regular octagon.
2x + 7