21st Century Lessons
Distributive Property
1
Warm UpObjective: Students will be able to apply the distributive property to write equivalent expressions.
Agenda
2
Ronisha and Kalyn are arguing whether the answer to can be found by doing the following work.
Do you think this is correct? Explain.
8(27)
820
87
160
216
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.
Language Objective: Students will be able explain how to use the distributive property verbally and in writing.
56
Agenda:
1) Warm Up
2) Launch
3) Explore
4) Summary
5) Explore
6) Assessment
3
Objective: Students will be able to apply the distributive property to write equivalent expressions.
Individual
High School Vs. College B-ball- Whole Class, Pairs
Splitting Athletic Fields– Groups
Exit Slip- Individual
Splitting Athletic Fields- Groups
The Distributive Property- Whole Class
Language Objective: Students will be able explain how to use the distributive property verbally and in writing.
4 minutes
13 minutes
17 minutes
10 minutes
4 minutes
12 minutes
Launch- High School Vs. College B-ball
Agenda
4
84 ft
50 ft
To find the area of the court you can use the formula of A=l w
A standard size high school basketball court is 84ft long and 50ft wide in the shape of a rectangle.
A = 84 ft 50ftA = 4200
ft 2
5
Agenda
Can you think of a method to find the area of the college basketball court?
Did you know that a college basketball court is usually 10ft longer than a high school basketball court? 84 ft
50 ft
10 ft
College Basketball Court
Launch- High School Vs. College B-ball
66
Agenda
Can you think of a method to find the area of the college basketball court?
84 ft
50 ft
10 ft
84+1094 50
A = 4700
ft 2 4200
A = 4700
ft 2 500+
+50(84+10)
What can we say about these two expressions?
Why parenthesis?
Launch- High School Vs. College B-ball
84 50 10 50
Method 1 Method 2
Explore- Splitting Athletic Fields
7
Agenda
50 yds
120 yds
50 yds
80 yds 40 yds
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
8
Agenda
50 yds120 yds
20 yds
120 yds30 yds
1. Find the area of this field near Ambria’s house.
2. This field is divided into two parts.
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?
240yds2
360yds2+
600yds2
600yds2
Explore- Splitting Athletic Fields
20 120=240
30 120=360
9
Agenda
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
20120 30120
120(20 30)
Explore- Splitting Athletic Fields
20 120=240
30 120=360
20 120
30 120
20 yds
120 yds30 yds+
10
Agenda
3. The field is divided into two parts.
40 yds80 yds
50 ydsa. Write 2 different numerical expressions that will calculate the area of the entire field.
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.
_______________
______
50(80 40)
50805040
50
100 20
501005020
Explore- Splitting Athletic Fields
Summary- The Distributive Property
11
Agenda
20 yds
120 yds
30 yds50 yds
80 yds 40 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
12
Agenda
50
80 40
50805040
The Distributive Property
50
80 40
50
120+
50(80 40)50
80 40
50
80 40
50
Summary- The Distributive Property
50 yds
80 yds 40 yds
600 400 200600
13
Agenda
The Distributive Property
2(35)
23
The Distributive Property is a property in mathematics which helps to multiply a single term and two or more terms inside parenthesis.
Lets use the distributive property to write an equal expression.
252
3 5+
2
Check it out!
8(3 x)
83
8x
a(3 5)
a3 a5
Examples
Summary- The Distributive Property
Formal definition
15
Agenda
8x
5
x2
3
x 4
a. Write two different expressions to represent the area of each rectangle below.
5. An algebraic expression to represent the area of the rectangle below is .
8x 8x
x(52)
5x 2x
3(x 4)
3x 34
x5 x2
Explore- Splitting Athletic Fields
3x 12
16
Agenda
6. Use the distributive property to re-write each expression. You may want to draw a rectangle to represent the area.
Explore- Splitting Athletic Fields
a) 10( a + 7) = ___________
c) x( 3 + 10)= ___________
b) 7(x + 3)=________________
d) a(10 + 9)= _______________
e) -2(x + 10)=_______ f) 3x(x + 10)= ______________
10a107
7x 73
x3 x10
a10 a9
3xx 3x101022 x
Assessment- Exit Slip
17
Agenda
Who correctly used the distributive property to write an equivalent expression? Provide evidence to support your answer.
7(4 10 y)
74 710 y
7(4 10 y)
74 710 7y
Riley
Michael
Michael did because he correctly distributed the 7 to all terms inside the parenthesis.