1. (Real World Connection, Lesson and Practice) 7.EE.A.1

2.  We are going to learn about the “ Distributive Property ”.  We’ll learn:  The definition of the Distributive Property and how to recognize it when you see it.  How to apply the Distributive Property.  How to “undo” distribution by using common factors.

3. Defining and Recognizing the Distributive Property

4. Jeremy… Will you take the bowl of lollipops and distribute them?

5.  Do you think that Jeremy’s teacher wants him to hand a lollipop to one student… or … to pass them out to every student in the classroom?

6. Distribute means...  To give or deliver something in shares.  To deal out.  To scatter or spread over an area. So... Jeremy’s teacher wants him to give every student in the classroom a lollipop. If he gave just one student a lollipop, then he would not be “distributing” them as he should. You would see some pretty upset kids if they were not given a lollipop!

7. See if you can figure out why it is called the “Distributive Property”.

8. The Distributive Property involves the operations of… multiplication and addition or multiplication and subtraction. Example 1Example 2 5(4 + 6)2(8 – 3) The multiplication must be located directly outside the parentheses. The addition or subtraction must be on the inside of the parentheses. SubtractionMultiplication MultiplicationAddition

9. Which of the following can the distributive property be applied? Check all that apply.  2(4 + 6)  5(10 – 3)  7(2 ∙ 8)  (9 + 4)∙2  7 + (8 ∙ 1) How do you recognize the distributi ve property? 1)Combination of multiplication with either addition or subtraction. 2)Multiplication… outside of ( ). 3)Addition or subtraction… inside of ( ).

10. Applying/Distributive Property

11.  Example 1 5(4 + 6) = (5 ∙ 4) + (5 ∙ 6) = 20 + 30 = 50  Example 2 2(8 – 3) = (2 ∙ 8) – (2 ∙ 3) = 16 - 6 = 10 When applying the Distributive Property… You want to take the number on the outside of the parentheses and multiply it with every number located inside the parentheses.

12. Think of Jeremy and to whom he was to distribute the lollipops! Everyone, right? 5(4 + 6) = (5 ∙ 4) + (5 ∙ 6) = 20 + 30 = 50

13. Apply the distributive property to evaluate the following. Show all steps. 9(5 + 2) = (9 ∙ 5) + (9 ∙ 2) = 45 + 18 = 63

14. Example 6(n + 5) =(6 ∙ n) + (6 ∙ 5) = 6n + 30 The distributive property can be applied even when variables are involved. REMINDER A variable is just a letter that stands for an unknown number. nx

15. Apply the distributive property to create an equivalent expression. Show all steps. 11(a - 4) =(11 ∙ a) - (11 ∙ 4) = 11a - 44 Equivalent means… EQUAL Equivalent expression

16. Apply the distributive property to create an equivalent expression. Show all steps. 6(7 + k) =(6 ∙ 7) + (6 ∙ k) = 42 + 6k or…6k + 42 utilizing the commutative property!

17. Apply the distributive property to create an equivalent expression. Show all steps. (x + 3)∙9 = (9 ∙ 3) + (9 ∙ x) =27 + 9x or… 9x + 27

18. Apply the distributive property to create an equivalent expression. Show all steps. 3(x – y + 4) = (3 ∙ x ) - (3 ∙ y) + (3 ∙ 4) = 3x - 3y + 12

19. Use the distributive property to express the area of the below garden. 4 (x + 3) = (4 ∙ x) + (4 ∙ 3) = 4x + 12 x 4 3 AREA of a Rectangle Length times Width Length = x + 3 Width = 4

20. Apply the distributive property to create an equivalent expression. Show all steps. -3(-10 - x) =(-3 ∙ -10) - (-3 ∙ x) = 30 - (-3x) = 30 + 3x

21. Undoing the Distributive Property by Factoring

22.  What if… You have an expression that has already been distributed and you wish to put it back in its original form? Given 36x + 84(9x + 2)  Well, you have to undo the distribution.  Some call this process of “undoing”… reverse distribution (Because basically you are going backwards.)

23. Given 36x + 8 4(9x + 2)  You use a common factor to reverse distribute.  A common factor is just a number that divides evenly into both terms. Notice… 4 goes into both 36 and 8 evenly.

24. Given 36x + 8 4(9x + 2)  Even though you can use any common factor to reverse distribute… This lesson will focus on using the Greatest Common Factor.  The Greatest Common Factor (GCF) is the largest number that divides evenly into both terms.

25. Use factoring to rewrite the following distributed expression: 36x + 8 Step 1 Find the GCF of the terms. Step 2 Pull out the GCF and write it on the outside of the ( ). Step 3 Think… What number times the GCF will give me the original distributed terms? 4 Because… 4 times 9x… gives you the 36x 4 times 2….. gives you the 8 4( ? + ? )4( + ) 4(9x + 2 )

26. Factor the following expression. Use the GCF. 12 + 144x GCF = 12 12( ? + ? ) 12(1 + 12x)  Answer

27. Factor the following expression. Use the GCF. 56x - 24 GCF = 8 8( ? + ? ) 8(7x - 3)  Answer

28. Factor the following expression. Use the GCF. 9x + 18x + 27 GCF = 9 9( ? + ? + ? ) 9(x + 2x + 3)  Answer

29. Factor the following expression. Use the GCF. 6x – 33x GCF = 3x 3x( ? - ? ) 3x(2 - 11)  Answer

30. Factor the following expression. 17x + 7 Just leave the answer as 17x + 7 since the GCF = 1.

31. Factor the following expression. Use the GCF. – 25b - 5 GCF = -5 -5( ? - ? ) -5(5b + 1)  Answer

32. 1)What does “distribute” mean? 2)The distributive property always involves a combination of which operations? 3)When applying the distributive property… y ou want to take the number on the outside of the parentheses and ___________ with every number located inside the parentheses. 4)How can you use the distributive property to make multiplying larger numbers easier? Example: 5 x 14 5)To “undo” something that has been distributed you use __________?