GOAL STATEMENT: -will use the Distributive Property to solve various types of math problems Copy anything in purple

CAMPING PROBLEM You and a friend are going on a camping trip. You each buy a backpack that costs $90 and a sleeping bag that costs $60. What is the total cost of the camping equipment? CAN YOU SOLVE THIS PROBLEM IN TWO WAYS? SHARE YOUR WAYS WITH A PARTNER.

CAMPING PROBLEM You and a friend are going on a camping trip. You each buy a backpack that costs $90 and a sleeping bag that costs $60. What is the total cost of the camping equipment? METHOD 1: Find the cost of one backpack and one sleeping bag. Then multiply the result by 2 (the number of each bought item). Total Cost: 2( )

CAMPING PROBLEM You and a friend are going on a camping trip. You each buy a backpack that costs $90 and a sleeping bag that costs $60. What is the total cost of the camping equipment? METHOD 2: Find the cost of two backpacks and the cost of two sleeping bags. Then add the costs. Total Cost: 2(90) + 2(60)

Distributive Property The expressions 2( ) and 2(90) + 2(60) are called equivalent numerical expressions- expressions that have the same value (the same final answer). In this case, they both equal $300. The distributive property is when you distribute the number outside the ( ) to each term inside the ( ) using multiplication. Let’s look at some examples…

Example #1: At an electronics store, you purchase 3 DVDs. Each DVD costs $5.95. Use the distributive property and estimation to find the total cost of the DVDs. CAN YOU FIND TWO DIFFERENT WAYS TO DETERMINE THE COST?

At an electronics store, you purchase 3 DVDs. Each DVD costs $5.95. Use the distributive property and estimation to find the total cost of the DVDs. The expression for estimation and total cost: = 3(6 – 0.05) = 3(6 – 0.05) = 3(5.95) = 3(5.95) = = 17.85

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

At an electronics store, you purchase 3 DVDs. Each DVD costs $5.95. Use the distributive property and estimation to find the total cost of the DVDs. The Distributive Property for solving: = 3(6 – 0.05)

At an electronics store, you purchase 3 DVDs. Each DVD costs $5.95. Use the distributive property and estimation to find the total cost of the DVDs. The Distributive Property for solving: = 3(6 – 0.05) = 3(6) - 3(0.05)

At an electronics store, you purchase 3 DVDs. Each DVD costs $5.95. Use the distributive property and estimation to find the total cost of the DVDs. The Distributive Property for solving: = 3(6 – 0.05) = 3(6) - 3(0.05) =

At an electronics store, you purchase 3 DVDs. Each DVD costs $5.95. Use the distributive property and estimation to find the total cost of the DVDs. The Distributive Property for solving: = 3(6 – 0.05) = 3(6) - 3(0.05) = = Notice how they rounded up to 6 and then subtracted the extra They then distributed the 3 to each term inside the ( ). To get the final answer, they subtracted the two values.

Complete Checkpoint on page 72 (lesson 2.2) # 1 – 8. Check your answers on the next slide.

Checkpoint Solutions 1) 392) 223) 424) 55 5) 4(100+5) = 4(100) + 4(5) = 420 6) 3(100-1) = 3(100) – 3(1) = 97 7) 5(3 – 0.1) = 5(3) – 5(0.1) = ) 8( ) = 8(7) + 8(0.2) = **If you missed any of these, check with a neighbor for some help or raise your hand**

Ex #2: Use the distributive property to write an equivalent variable expression. 3(y + 7)

Use the distributive property to write an equivalent variable expression. 3(y + 7) 3(y) + 3(7)

Use the distributive property to write an equivalent variable expression. 3(y + 7) 3(y) + 3(7) 3y y + 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)

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

(-2)n + (-2)4

(n + 4)(-2) (-2)n + (-2)4 -2n + (-8) Notice how the number you are distributing is BEHIND the ( ). The process is the same.

-5(2y – 3)

-5(2y)

Ex #3 -5(2y – 3) Ex #3 -5(2y – 3) -5(2y) - (-5)(3)

-5(2y – 3) -5(2y) - (-5)(3) -10y - (-15)

-5(2y – 3) -5(2y) - (-5)(3) -10y - (-15) -10y + 15

OYO: Complete checkpoint problems on page 72 Check your solutions on the next slide.

Checkpoint Solutions 9) 8x ) t 11) 27m ) -12y + 8 If you missed any, check with a neighbor for help or raise your hand

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

Ex# 4 Use the distributive property to find the area of the rectangle below. (draw the rectangle and label the units) b

4 A = lw

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

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

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

Green Homework Pages 73 – 74: 2 – 11all, 13 – 35 odd, 36, 37, 38 Blue/Black Challenge: one more slide…

Ex # 5 Use the distributive property to find the area of the triangle below. (copy if necessary) 3 + a 10 10

3 + a 3 + a A = ½ bh

3 + a 3 + a A = ½ bh = ½(10) = ½(10)

3 + a 3 + a A = ½ bh = ½(10)(3 + a) = ½(10)(3 + a)

3 + a 3 + a A = ½ bh = ½(10)(3 + a) = ½(10)(3 + a) = 5(3 + a) = 5(3 + a)

3 + a 3 + a A = ½ bh = ½(10)(3 + a) = ½(10)(3 + a) = 5(3 + a) = 5(3 + a) = 5(3) + 5a = 5(3) + 5a

3 + a 3 + a A = ½ bh = ½(10)(3 + a) = ½(10)(3 + a) = 5(3 + a) = 5(3 + a) = 5(3) + 5a = 5(3) + 5a = a = a

Blue/Black HW Pgs 73-75: 11, 21-27odd, 44, Blue/Black WS