2. Where We’ve Been……. Properties, Part I…….. If I say “order,” you say……… If I say “grouping,” you say……… If I say “identity,” you say……… If I keep saying “properties,” you are probably thinking ……. commutative associative Value stays the same

3. Where We Are Going……. Today, we are going to investigate one of the most important properties you will use this year and in future classes. Distributive Property Algebra Just listen. Associative PropertiesCommutative Properties Identity Properties Order of Operations Translating Expressions

4. The Distributive Property 2.4 p. 40 The Big Dog of Properties !!!

5. Naming What You Know Once again, you already use this property. Let’s say you bought 23 CD’s for $6.00 each. $6 each Is there a way you could mentally rearrange these values to find your total without a pencil and paper? Notes.

6. Many of you would mentally multiply the $6 by 20, multiply the $6 by 3, and add the products. 6(20 + 3) $6 each Let’s try this mentally…. 6(20) 120 + 6(3) 18 = 138 If you have ever tried this mental math, you have used the distributive property!!

7. What Is Our Objective? Use the distributive property to rewrite and simplify multiplication problems What property will we use? What will we do with this property? Distributive Property We will simplify multiplication problems with this property! Notes.

8. To Your Notes……… Vocabulary: This is given in your notes…… The Distributive Property states that multiplying a sum (or difference) by a number gives the same result as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. Now let’s use real words to understand the official definition. Just listen.

9. What does this mean? Let’s take a basic multiplication problem: 6 x 23 We will rewrite 23 as an addition problem. 6 x (20 + 3) Now we will multiply the 6 by EACH of the values that add up to 23. 6 x 20 + 6 x 3 120 + 18 138

10. What it looks like……. Algebraically, the distributive property is defined with variables. a(b + c) = a(b) + a(c) or a(b - c) = a(b) – a(c) Think about our CD example. In expanded form, how would we write 23? 20 + 3 Now, let’s use our price of 6 6(20 + 3) = 6(20) + 6(3) = 120 + 18 = 138 Notes.

11. Guided Practice: 5 x 27 Let’s take the larger factor and write it in expanded form. 5 (20 + 7) Remember, no sign means to multiply! Let’s “ distribute “ the 5. It is the factor used on both the 20 and the 7. (5 x 20)+(5 x 7) = (100) + (35) = 135

12. 4 x 28 Take the larger factor and write it in expanded form. 4 (20 + 8) Let’s “ distribute “ the 4. It is the value used on both the 20 and the 8. (4 x 20)+(4 x 8) = (80) + (32) =112 7 x 108 =7 (100 + 8 ) (7 x 100) + (7 x 8) =700 + 56 = 756

13. What Is Our Objective? Use the distributive property to rewrite and simplify multiplication problems What property will we use? What will we do with this property? Distributive Property We will simplify multiplication problems with this property!

14. Small Group Work With your partners, use the pattern we started in your notes to simplify these examples using the distributive property. First rewrite the problem, breaking up the larger value. Next, show how the single multiplier is “distributed” to both parts of the expanded number. WE ARE ONLY BREAKING UP THE LARGER VALUE AND “DISTRIBUTING “ THE SINGLE-MULTIPLIER! After completing the first four problems, move on to the next three. Try to find a value (evaluate) the expression after you rewrite it! I will check as you work to make sure you are progressing accurately. You will have about 10 minutes.

15. 1) 8(43) = 2) 5(67) = 3) 9(42) = 4) 3(53 ) = 403 9 9 50 3 Give me a sign when you finish this section. 8( 40 + 3) 5( 60 + 7) 8( ) + 8 ( ) 5( ) + 5 ( )60 7 9( 40 + 2) ___(40) + __ (2) 3( 50 + 3) 3( ) + 3 ( ) 344 335 378 159

16. 5) 7(52) = 7( ) 6) 9(107) = ___ ( ) 50 + 2 7(50) + 7(2) 350 + 14 =364 9 100 + 7 9 (100) + 9(7)= 900 + 63 = 963

17. Application FoodCost Organic Chili$6.00 Chicken Tacos$4.00 Fruit Salad$5.00 Organic Salad$5.00 Veggie Plate$6.00 Big Group Menu Discuss with your group…….. The 6 th graders ordered from the Big Group Menu. They ordered 22 organic chilis and 8 veggie plates. Create a problem using the distributive property to represent this situation.

18. Take a moment to reread your definition of the distributive property. Did we leave something out?????? We rewrote all problems as addition. Let’s look at two problems and change them to subtraction.

19. Our first problem in the Guided Practice was 5 x 27 Could we use a subtraction problem to create a value of 27???? 30 – 3 = 27 5 x 27 = 5 ( )30 - 3 5(30)- 5(3) 150 - 15 = 135

20. Could we use a subtraction problem to create a value of 8(78)???? 80 – 2 = 78 8 x 78 = 8 ( )80 - 2 8(80)- 8(2) 640 - 16 = 624

21. Think Critically Look at the expressions represented by the properties we have studied….. 14x 3 = 3 x 14 14 + 4 = 3 + 14 (4 x 5) x 12 = 4 x (5 x 12) (4 + 5) + 12 = 4 + (5 + 12) 12 X 6 = (6 x 10) + (6 x 2) What is the one distinct difference that separates the distributive property from the commutative and associative properties?

22. Let’s Summarize What was the goal of our lesson? Have we accomplished our lesson’s objective?

23. Distributive Property Extension You can apply the Distributive Property to unknown values (models). = 1 = x You are looking at a model that represents 2x + 5 that is written three times. Instead of writing 2x + 5 + 2x + 5 + 2x + 5, we could write 3(2x + 5) We have to use the distributive property to “pull” the values out of the parentheses…… 3(2x) + 3(5) We use the associative property to multiply 3(2)x = 6x and we multiply 3(5). 6x + 15 represents our simplified value. We can do no more.

24. ( + ) 3 2x 5 6x + 15 Use your imagination! What just happened here? (3 ∙ 2x) + ( 3 ∙ 5 ) = 6x + 15

26. What is our common factor? Which number is used twice in multiplication? What do we have left?

27. You can apply the Distributive Property to unknown values (models). = 1 = x What expression represents this model? We have 3x + 7 that is written two times. 2(3x + 7) = 2(3)x 6x + 2(7) + 14

28. Let’s add one more value to this process……..

29. What have we done? We have used the distributive property to solve multiplication problems. We have written problems with variables using the distributive property.