### Distributive Property

```21st Century Lessons
Distributive Property
1
Warm Up
Objective: Students will be able to apply the distributive property to
write equivalent expressions.
Language Objective: Students will be able explain how to use the
distributive property verbally and in writing.
Ronisha and Kalyn are arguing whether the answer
to 8(27 ) can be found by doing the following work.
8 20  160
8 7  56
216
Do you think this is correct? Explain.


2

 

Agenda
Agenda:
Objective: Students will be able to apply the distributive property to
write equivalent expressions.
Language Objective: Students will be able explain how to use the
distributive property verbally and in writing.
1) Warm Up
Individual
4 minutes
2) Launch
13 minutes
3) Explore
High School Vs. College B-ballWhole Class, Pairs
Splitting Athletic Fields- Groups
4) Summary
The Distributive Property- Whole Class
10 minutes
5) Explore
Splitting Athletic Fields– Groups
12 minutes
6) Assessment Exit Slip- Individual
3
17 minutes
4 minutes
Launch- High School Vs. College B-ball
A standard size high school basketball court is 84ft
long and 50ft wide in the shape of a rectangle.
84 ft
50 ft
To find the area of the court you can
use the formula of A=l  w
A = 84 ft  50ft
2
A = 4200 ft
Agenda
4
Launch- High School Vs. College B-ball
Did you know that a college basketball court is
usually 10ft longer than a high school basketball
court?
84 ft
10 ft
50 ft
College
Can you think of a method to find the
area of the college basketball court?
Agenda
5
Launch- High School Vs. College B-ball
84 ft
10 ft
50 ft
Why parenthesis?
Method 1
Method 2
50(84+10)
84+10
94  50
A = 4700 ft
Can you think of a
method to find the area
court?
84  50 + 10  50
4200 + 500
2
A = 4700
ft
2
What can we say about these two expressions?
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66
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Agenda
Explore- Splitting Athletic Fields
Ambria lives in a neighborhood with three rectangular fields
that all have the same area. The fields are split into different
sections for different sports.
20 yds
50 yds
30 yds
120 yds
120 yds
50 yds
80 yds
40 yds
Agenda
7
Explore- Splitting Athletic Fields
1. Find the area of this field near Ambria’s house.
50 yds
120 yds
600 yds
2
2. This field is divided into two parts.
20 yds
30 yds
120 
yds
a. Find the area of each part and record your steps as you go.
Prove the area is the same as in the first field?
20  120=240
2
240 yds + 360 yds 2  600 yds
30  120=360
Agenda
8
2
Explore- Splitting Athletic Fields
20 yds
20  120
20  120=240
30 yds
30  120
120 yds
30  120=360
b. Write one numerical expression that will calculate the
area based on the work you did in part a.
20  120  30  120
c. Find a different way to calculate the area of the entire field
and write it as one numerical expression.
120 (20  30 )
20 yds
+
30 yds
120 yds
Agenda
9
Explore- Splitting Athletic Fields
3. The field is divided into two parts.
50 yds
80 yds 40 yds
a. Write 2 different numerical
expressions that will calculate
the area of the entire field.
50 (80  40 )
50  80  50  40
4. The field below is split into two parts but are missing the dimensions.
50
______
100 20
_________
______

a. Fill in the missing dimensions of
the rectangular field whose area can
be calculated using the expression.
50(100  20 )
b. Write a different numerical expression to calculate the area of the field.
50  100  50  20

10
Agenda
Summary- The Distributive Property
20 yds
50 yds
30 yds
80 yds
40 yds
120 yds
Let’s look at the two equivalent ways of finding the area and
connect it to an important property in math.
The Distributive Property
Agenda
11
Summary- The Distributive Property
The Distributive Property
50 yds
80 yds 40 yds
50  (80  40 )  50  80  50  40

50
80 120+ 40
50
80
40
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12
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Agenda
Summary- The Distributive Property
The Distributive Property
The Distributive Property is a property in mathematics which
helps to multiply a single term and two or more terms inside
parenthesis.
Check it out!
Lets use the distributive property to write an equal expression.
2(3  5) 
Examples
8(3  x ) 
8  3  8 x
a(3  5) 
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 
Formal
a 3  a 5
definition
13
2 3  2 5
2
3 + 5
Agenda
Explore- Splitting Athletic Fields
5. An algebraic expression to represent the area of
the rectangle below is 8 x  8 x .
8
x
a. Write two
 different expressions to represent the area
of each rectangle below.
5
2
3
x
x(5  2)
x 5  x 2
5x  2x
x
4
3( x  4)
3 x  3 4
3 x  12
Agenda
15
Explore- Splitting Athletic Fields
6. Use the distributive property to re-write each expression.
You may want to draw a rectangle to represent the area.
a) 10( a + 7) = 10
___________
 a  10  7 b) 7(x + 3)=________________
7 x  7 3
c) x( 3 + 10)= ___________
x  3  x  10 d) a(10 + 9)= _______________
a 10  a 9

e) -2(x + 10)=_______
 2  x   2  10


f) 3x(x + 10)= 3______________
x  x  3 x  10
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Agenda
16
Assessment- Exit Slip
Who correctly used the distributive property to
write an equivalent expression?