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

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

3. 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(90 + 60)

4. 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)

5. Distributive Property The expressions 2(90 + 60) 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…

6. 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?

7. 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 = 17.85

8. 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:

9. 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)

10. 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)

11. 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) = 18 - 0.15

12. 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) = 18 - 0.15 = 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.

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

14. 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) = 14.5 8) 8(7 + 0.2) = 8(7) + 8(0.2) = 56.16 **If you missed any of these, check with a neighbor for some help or raise your hand**

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

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

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

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

19. (n + 4)(-2) (-2)n

20. (-2)n + (-2)4

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

22. -5(2y – 3)

23. -5(2y)

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

25. -5(2y – 3) -5(2y) - (-5)(3) -10y - (-15)

26. -5(2y – 3) -5(2y) - (-5)(3) -10y - (-15) -10y + 15

27. OYO: Complete checkpoint problems 9- 12 on page 72 Check your solutions on the next slide.

28. Checkpoint Solutions 9) 8x + 16 10) -28 + 4t 11) 27m + 45 12) -12y + 8 If you missed any, check with a neighbor for help or raise your hand

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

30. Ex# 4 Use the distributive property to find the area of the rectangle below. (draw the rectangle and label the units) 4 8 + 7b

31. 4 A = lw

32. 4 8 + 7b A = lw = (8 + 7b)(4) = (8 + 7b)(4)

33. 4 8 + 7b A = lw = (8 + 7b)(4) = (8 + 7b)(4) = (4)(8) + (4)(7b) = (4)(8) + (4)(7b)

34. 4 8 + 7b A = lw = (8 + 7b)(4) = (8 + 7b)(4) = (4)(8) + (4)(7b) = (4)(8) + (4)(7b) = 32 + 28b = 32 + 28b

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

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

37. 3 + a 3 + a 10 10 A = ½ bh

38. 3 + a 3 + a 10 10 A = ½ bh = ½(10) = ½(10)

39. 3 + a 3 + a 10 10 A = ½ bh = ½(10)(3 + a) = ½(10)(3 + a)

40. 3 + a 3 + a 10 10 A = ½ bh = ½(10)(3 + a) = ½(10)(3 + a) = 5(3 + a) = 5(3 + a)

41. 3 + a 3 + a 10 10 A = ½ bh = ½(10)(3 + a) = ½(10)(3 + a) = 5(3 + a) = 5(3 + a) = 5(3) + 5a = 5(3) + 5a

42. 3 + a 3 + a 10 10 A = 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

43. Blue/Black HW Pgs 73-75: 11, 21-27odd, 44, 45 2.2 Blue/Black WS