Download MM_Distributive Property

TEACHER NOTES – M&M® Distributing
Topic: This lesson is designed to explore the concept behind and practice the distributive property.
Objective: Given M&M’s, exploratory worksheets, and practice worksheets, students will demonstrate
an understanding of the use of the distributive property by simplifying expressions and finding perimeter
of rectangles.
Time Table: This lesson is designed for a 50 minute class period.
TEKS Focus: A.4.B Use the commutative, associative, and distributive properties to simplify algebraic
expressions
Additional TEKS: A.4.A
Materials:
M&M’s (Per Class: 15 baggies of 6 red, 3 yellow, 2 green, 10 blue, 6 brown, 9 orange)
Worksheets provided
Transparencies of all worksheets.
Lesson Overview: This lesson is a review of the definition of multiplication as repeated addition in
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 (NOTE: Parentheses mean 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. Walk through the M&M® Distributing: Distributive Property Activity problem #1 as a class.
a. Read word problem.
b. Set up M&M’s.
c. Write Algebraic Expression.
d. Write out the repeated addition.
e. Add the expressions.
3. 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&M’s. 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. 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. Pass out the homework.
Homework: M&M® Distributing: Distributive Property Homework
Extensions:
1. If you do not want to use M&M’s, you can change all of the problems to x’s and use algebra tiles
or just draw and color the M&M’s.
2. More problems over Geometry (Perimeter and Area) could be added to the practice problems and
the homework for a geometry review.
ALGEBRA 1
STUDENT NOTES KEY
NAME: __________________________________ PER: __________ DATE: ____________
M&M® DISTRIBUTING
Distributive Property Activity
Represent each of the following situations using M&M’s. Then write 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
12(6g) + 12(8y) = 72g + 96y
Total:
72g + 96y
ALGEBRA 1
IN-CLASS PRACTICE KEY
NAME: _________________________________ PERIOD: _________ DATE: _____________
M&M® DISTRIBUTING
Distributive Property Practice Key
The Distributive Property
Words
The product of a and (b + c)
The product of a and (b – c)
Let a, b, c be real numbers.
Algebra
Examples
a(b  c)  ab  ac
3(4  2)  3(4)  3(2)
(b  c)a  ba  ca
(3  5)2  3(2)  5(2)
a(b  c)  ab  ac
5(6  4)  5(6)  5(4)
(b  c)a  ba  ca
(8  6)4  8(4)  6(4)
Directions: Please simplify the following expressions by using the distributive property.
1. 3(2 y  5)
3(2) y  3(5)
6 y  15
2. 2(8  h)
4. 7(5 x  10)
5. ( y  x)
1( y )  1( x)
y  x
7(5) x  7(10)
35 x  70
7.
2( x  4)  3
2 x  2(4)  3
2x  8  3
2x  5
3. (3  3x)(5)
2(8)  2h
3(5)  3(5) x
16  2h
15  15 x
8. 4( z  8)  3 z  2
4 z  4(8)  3 z  2
4 z  32  3 z  2
7 z  30
10.
11. A square has sides of
length 3x 10.
5(c  3a  5t )  8(d  2o  g )
5c  3(5)a  5(5)t  8d  8(2)o  8 g
3x 10
5c  15a  25t  8d  16o  8 g
What is the perimeter
of the square?
p  4(3 x  10)
p  12 x  40
6. (5  6 x)(2)
5(2)  6(2) x
10  12 x
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
12. Find the area of the rectangle.
7x – 4
3
A = 21x – 12
ALGEBRA I
NAME:
HOMEWORK KEY
DATE:
PERIOD:
M&M® Distributing
Distributive Property Homework
The Distributive Property
Words
Let a, b, c represent real numbers.
Algebra
Examples
a(b  c)  ab  ac
3(4  2)  3(4)  3(2)
(b  c)a  ba  ca
(3  5)2  3(2)  5(2)
a(b  c)  ab  ac
5(6  4)  5(6)  5(4)
(b  c)a  ba  ca
(8  6)4  8(4)  6(4)
The product of a and (b + c)
The product of a and (b – c)
Use the distributive property to write equivalent expression.
2. 9(a  b)
1. Find the area.
b+7
2
2b  14
9a  9b
3. 8( y  2)
4.  3(2 w  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
10. Find the perimeter.
4x  4
9x  9
3x  3
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 NOTES
NAME: _____________________________ PER: __________ DATE: ____________
M&M® DISTRIBUTING
Distributive Property Activity
Represent each of the following situations using M&M’s. Then write as an algebraic
expression.
1.
three groups of 2 red and 1 yellow
Algebraic Expression: ________________
Repeated Addition:
3. 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:
5.
two groups of 5 blue and 3 red
Algebraic Expression: ________________
Repeated Addition:
+
Total:
5.
+
Total:
twelve groups of 6 green and 8 yellow
Algebraic Expression: ________________
Total:
ALGEBRA 1
IN-CLASS PRACTICE
NAME: _________________________________ PERIOD: _________ DATE: _____________
M&M® DISTRIBUTING
Distributive Property Practice
The Distributive Property
Words
The product of a and (b + c)
The product of a and (b – c)
Let a, b, c be real numbers.
Algebra
Examples
a(b  c)  ab  ac
3(4  2)  3(4)  3(2)
(b  c)a  ba  ca
(3  5)2  3(2)  5(2)
a(b  c)  ab  ac
5(6  4)  5(6)  5(4)
(b  c)a  ba  ca
(8  6)4  8(4)  6(4)
Directions: Please simplify the following expressions by using the distributive property.
1. 3(2 y  5)
2. 2(8  h)
3. (3  3 x)(5)
4. 7(5 x  10)
5. ( y  x)
6. (5  6 x)(2)
8. 4( z  8)  3z  2
9. 11(2 x  1)  4(7  3x)
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 )
3x 10
7x – 4
3
ALGEBRA I
NAME:
PERIOD:
HOMEWORK
DATE:
M&M® Distributing
Distributive Property Homework
The Distributive Property
Words
Let a, b, c represent real numbers.
Algebra
Examples
a(b  c)  ab  ac
3(4  2)  3(4)  3(2)
(b  c)a  ba  ca
(3  5)2  3(2)  5(2)
a(b  c)  ab  ac
5(6  4)  5(6)  5(4)
(b  c)a  ba  ca
(8  6)4  8(4)  6(4)
The product of a and (b + c)
The product of a and (b – c)
Use the distributive property to write equivalent expression.
2. 9(a  b)
1. Find the area.
b+7
2
3. 8( y  2)
4.  3(2 w  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