1. Distributive Property

2. 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 can be found by doing the following work.
Do you think this is correct? Explain.
Yes, this method can be used because 27 is still being multiplied by 8.
27 is just split into 20 and 7 first before it is multiplied by 8.

3. 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
A = 4200

4. College Basketball Court
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 Basketball Court
Can you think of a method to find the area of the college basketball court?

5. Launch- High School Vs. College B-ball
84 ft
50 ft
10 ft
Can you think of a method to find the area of the college basketball court?
Why parenthesis?
Method 1
Method 2
50(84+10)
84+10
84 50  +
10 50  94  50
4200 +
500
A = 4700
A = 4700
What can we say about these two expressions? 5

6. 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
120 yds
30 yds
50 yds
120 yds
50 yds
80 yds
40 yds

7. Explore- Splitting Athletic Fields
1. Find the area of this field near Ambria’s house.
50 yds
120 yds
2. This field is divided into two parts.
20 yds
120 yds
30 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?
=240  +
=360 

8. Explore- Splitting Athletic Fields
20 yds
120 yds
30 yds 
=240  
=360 
b. Write one numerical expression that will calculate the area based on the work you did in part a.
c. Find a different way to calculate the area of the entire field and write it as one numerical expression.
20 yds
120 yds
30 yds +

9. Explore- Splitting Athletic Fields
3. The field is divided into two parts.
a. Write 2 different numerical expressions that will calculate the area of the entire field.
40 yds
80 yds
50 yds
4. The field below is split into two parts but are missing the dimensions.
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.

10. Summary- The Distributive Property
50 yds
80 yds
40 yds
20 yds
120 yds
30 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

11. 400 600 200 600 The Distributive Property
Summary- The Distributive Property
The Distributive Property 50 80 40
50 yds
80 yds
40 yds
400
600
200 50
120 50 80 40
600 50 80 40 50 80 40 50 +

12. The Distributive Property
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 2 3 5 +
Examples
Formal definition

13. Explore- Splitting Athletic Fields
5. An algebraic expression to represent the area of the rectangle below is 8 x
a. Write two different expressions to represent the area of each rectangle below. 5 x 2 3 x 4

14. 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) = ___________
b) 7(x + 3)=________________
c) x( )= ___________
d) a(10 + 9)= _______________
e) -2(x + 10)=_______
f) 3x(x + 10)= ______________

15. Provide evidence to support your answer.
Assessment- Exit Slip
Who correctly used the distributive property to write an equivalent expression?
Provide evidence to support your answer.
Riley
Michael
Michael did because he correctly distributed the 7 to all terms inside the parenthesis.