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.