GOAL STATEME

NT:

-will use the

Distributive

Property to so

lve various ty

pes

of math proble

ms

Copy anything in purple

CAMPING PROBLEM

You and a friend are going on a camping You and a friend are going on a camping trip. You each buy a backpack that costs trip. You each buy a backpack that costs $90 and a sleeping bag that costs $60. $90 and a sleeping bag that costs $60. What is the total cost of the camping What is the total cost of the camping equipment?equipment?

CAN YOU SOLVE THIS PROBLEM IN TWO WAYS? CAN YOU SOLVE THIS PROBLEM IN TWO WAYS? SHARE YOUR WAYS WITH A PARTNER.SHARE YOUR WAYS WITH A PARTNER.

CAMPING PROBLEM

You and a friend are going on a camping trip. You and a friend are going on a camping trip. You each buy a backpack that costs $90 and a You each buy a backpack that costs $90 and a sleeping bag that costs $60. What is the total sleeping bag that costs $60. What is the total cost of the camping equipment?cost of the camping equipment?

METHOD 1: Find the cost of one backpack and METHOD 1: Find the cost of one backpack and one sleeping bag. Then multiply the result by one sleeping bag. Then multiply the result by 2 (the number of each bought item). 2 (the number of each bought item).

Total Cost: 2(90 + 60)Total Cost: 2(90 + 60)

CAMPING PROBLEM

You and a friend are going on a camping trip. You and a friend are going on a camping trip. You each buy a backpack that costs $90 and a You each buy a backpack that costs $90 and a sleeping bag that costs $60. What is the total sleeping bag that costs $60. What is the total cost of the camping equipment?cost of the camping equipment?

METHOD 2: Find the cost of two backpacks and METHOD 2: Find the cost of two backpacks and the cost of two sleeping bags. Then add the the cost of two sleeping bags. Then add the costs.costs.

Total Cost: 2(90) + 2(60)Total Cost: 2(90) + 2(60)

Distributive PropertyThe expressions 2(90 + 60) and 2(90) + The expressions 2(90 + 60) and 2(90) + 2(60) are called 2(60) are called equivalent numerical equivalent numerical expressions-expressions-expressions that have the same expressions that have the same value (the same final answer). value (the same final answer). In this In this case, they both equal $300. case, they both equal $300.

The The distributive property is when you distributive property is when you distribute the number outside the ( ) to distribute the number outside the ( ) to each term inside the ( ) using each term inside the ( ) using multiplication.multiplication.

Let’s look at some examples…Let’s look at some examples…

Example #1: At an electronics Example #1: At an electronics store, you purchase 3 DVDs. Each store, you purchase 3 DVDs. Each DVD costs $5.95. Use the DVD costs $5.95. Use the distributive property and distributive property and estimation to find the total cost estimation to find the total cost of the DVDs.of the DVDs.

CAN YOU FIND TWO DIFFERENT WAYS TO CAN YOU FIND TWO DIFFERENT WAYS TO DETERMINE THE COST?DETERMINE THE COST?

At an electronics store, you purchase 3 At an electronics store, you purchase 3 DVDs. Each DVD costs $5.95. Use the DVDs. Each DVD costs $5.95. Use the distributive property and estimation to distributive property and estimation to find the total cost of the DVDs.find the total cost of the DVDs.

The expression for estimation and total The expression for estimation and total cost: cost:

= 3(6 – = 3(6 – 0.05)0.05)

= 3(5.95)= 3(5.95)

= 17.85= 17.85

At an electronics store, you At an electronics store, you purchase 3 DVDs. Each DVD costs purchase 3 DVDs. Each DVD costs $5.95. Use the distributive $5.95. Use the distributive property and estimation to find the property and estimation to find the total cost of the DVDs.total cost of the DVDs.

The Distributive Property for The Distributive Property for solving:solving:

At an electronics store, you At an electronics store, you purchase 3 DVDs. Each DVD costs purchase 3 DVDs. Each DVD costs $5.95. Use the distributive $5.95. Use the distributive property and estimation to find the property and estimation to find the total cost of the DVDs.total cost of the DVDs.

The Distributive Property for The Distributive Property for solving:solving:

= 3(6 – 0.05)= 3(6 – 0.05)

At an electronics store, you At an electronics store, you purchase 3 DVDs. Each DVD costs purchase 3 DVDs. Each DVD costs $5.95. Use the distributive $5.95. Use the distributive property and estimation to find the property and estimation to find the total cost of the DVDs.total cost of the DVDs.

The Distributive Property for The Distributive Property for solving:solving:

= 3(6 – 0.05)= 3(6 – 0.05)

= 3(6) - 3(0.05)= 3(6) - 3(0.05)

At an electronics store, you At an electronics store, you purchase 3 DVDs. Each DVD costs purchase 3 DVDs. Each DVD costs $5.95. Use the distributive property $5.95. Use the distributive property and estimation to find the total and estimation to find the total cost of the DVDs.cost of the DVDs.

The Distributive Property for The Distributive Property for solving:solving:

= 3(6 – 0.05)= 3(6 – 0.05)

= 3(6) - 3(0.05)= 3(6) - 3(0.05)

= 18 - 0.15= 18 - 0.15

At an electronics store, you purchase At an electronics store, you purchase 3 DVDs. Each DVD costs $5.95. Use the 3 DVDs. Each DVD costs $5.95. Use the distributive property and estimation distributive property and estimation to find the total cost of the DVDs.to find the total cost of the DVDs.

The Distributive Property for The Distributive Property for solving:solving:

= 3(6 – 0.05)= 3(6 – 0.05)

= 3(6) - 3(0.05)= 3(6) - 3(0.05)

= 18 - 0.15= 18 - 0.15

= 17.85= 17.85

Notice how they rounded up to 6 and then subtracted the extra 0.05. They then distributed the 3 to each term inside the ( ). To get the final answer, they subtracted the two values.

Complete Checkpoint on Complete Checkpoint on page 72 (lesson 2.2) # page 72 (lesson 2.2) # 1 – 8.1 – 8.

Check your answers on Check your answers on the next slide.the next slide.

Checkpoint Solutions

1) 391) 39 2) 222) 22 3) 423) 42 4) 554) 55

5) 4(100+5) = 4(100) + 4(5) = 4205) 4(100+5) = 4(100) + 4(5) = 420

6) 3(100-1) = 3(100) – 3(1) = 976) 3(100-1) = 3(100) – 3(1) = 97

7) 5(3 – 0.1) = 5(3) – 5(0.1) = 14.57) 5(3 – 0.1) = 5(3) – 5(0.1) = 14.5

8) 8(7 + 0.2) = 8(7) + 8(0.2) = 56.168) 8(7 + 0.2) = 8(7) + 8(0.2) = 56.16

**If you missed any of these, check with a **If you missed any of these, check with a neighbor for some help or raise your neighbor for some help or raise your hand**hand**

Ex #2: Use the distributive

property to write an

equivalent variable

expression.3(y + 7)3(y + 7)

Use the distributive

property to write an

equivalent variable

expression.3(y + 7)3(y + 7)

3(y) + 3(7)3(y) + 3(7)

Use the distributive

property to write an

equivalent variable

expression.3(y + 7)3(y + 7)

3(y) + 3(7)3(y) + 3(7)

3y + 213y + 21

3y + 21 is your final answer since you cannot combine unlike terms. The first term has a “y” and the second term does not.

Ex #2: (n + 4)(-2)Ex #2: (n + 4)(-2)

(n + 4)(-2)(n + 4)(-2)

(-2)n(-2)n

(n + 4)(-2)(n + 4)(-2)

(-2)n + (-2)4 (-2)n + (-2)4

(n + 4)(-2)(n + 4)(-2)

(-2)n + (-2)4 (-2)n + (-2)4

-2n + (-8)-2n + (-8)Notice how the number you are distributing is BEHIND the ( ). The process is the same.

-5(2y – 3)-5(2y – 3)

-5(2y – 3)-5(2y – 3)

-5(2y)-5(2y)

Ex #3 Ex #3 -5(2y – 3)-5(2y – 3)

-5(2y) - (-5)-5(2y) - (-5)(3)(3)

-5(2y – 3)-5(2y – 3)

-5(2y) - (-5)-5(2y) - (-5)(3)(3)

-10y - (-15)-10y - (-15)

-5(2y – 3)-5(2y – 3)

-5(2y) - (-5)-5(2y) - (-5)(3)(3)

-10y - (-15)-10y - (-15)

-10y + 15-10y + 15

OYO: Complete OYO: Complete checkpoint problems checkpoint problems 9-12 on page 729-12 on page 72

Check your solutions Check your solutions on the next slide.on the next slide.

Checkpoint Solutions

9) 8x + 169) 8x + 16

10) -28 + 4t10) -28 + 4t

11) 27m + 4511) 27m + 45

12) -12y + 812) -12y + 8

If you missed any, check with a If you missed any, check with a neighbor for help or raise your handneighbor for help or raise your hand

Read through the Read through the example 4 on page 73 example 4 on page 73 to understand how to to understand how to find the areas of find the areas of geometric figures.geometric figures.

Ex# 4 Use the distributive

property to find the area

of the rectangle below. (draw

the rectangle and label the units)

44

8 + 7b8 + 7b

44

8 + 7b8 + 7b

A = lwA = lw

44

8 + 7b8 + 7b

A = lwA = lw

= (8 + 7b)(4)= (8 + 7b)(4)

44

8 + 7b8 + 7b

A = lwA = lw

= (8 + 7b)(4)= (8 + 7b)(4)

= (4)(8) + = (4)(8) + (4)(7b)(4)(7b)

44

8 + 7b8 + 7b

A = lwA = lw

= (8 + 7b)(4)= (8 + 7b)(4)

= (4)(8) + = (4)(8) + (4)(7b)(4)(7b)

= 32 + 28b= 32 + 28b

Green Homework

Pages 73 – 74:

2 – 11all, 13 – 35 odd, 36, 37, 38

Blue/Black Challenge: one more slide…

Ex # 5 Use the distributive Ex # 5 Use the distributive property to find the area property to find the area of the triangle below. of the triangle below. (copy (copy if necessary)if necessary)

3 + a3 + a

1010

3 + a3 + a

1010

A = ½ bhA = ½ bh

3 + a3 + a

1010

A = ½ bhA = ½ bh

= ½(10)= ½(10)

3 + a3 + a

1010

A = ½ bhA = ½ bh

= ½(10)(3 + = ½(10)(3 + a)a)

3 + a3 + a

1010

A = ½ bhA = ½ bh

= ½(10)(3 + = ½(10)(3 + a)a)

= 5(3 + a)= 5(3 + a)

3 + a3 + a

1010

A = ½ bhA = ½ bh

= ½(10)(3 + a)= ½(10)(3 + a)

= 5(3 + a)= 5(3 + a)

= 5(3) + 5a= 5(3) + 5a

3 + a3 + a

1010

A = ½ bhA = ½ bh

= ½(10)(3 + a)= ½(10)(3 + a)

= 5(3 + a)= 5(3 + a)

= 5(3) + 5a= 5(3) + 5a

= 15 + 5a= 15 + 5a

Blue/Black HW

Pgs 73-75: 11, 21-27odd, 44, 45Pgs 73-75: 11, 21-27odd, 44, 45

2.2 Blue/Black WS2.2 Blue/Black WS