# 214089199 the distributive property

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The distributive property

Van Siclen Community Middle SchoolMr. E Grade 6 MathClass 603/604/605Monday March 24, 2014

The Distributive Property

Lesson OverviewLast Weeks LessonsLast week, we learned about writing expressions in the fewest terms possible (shortening expressions). For example, the expression 103BC can be written as 30BC. We also learned about expanding expressions (making them larger). For example, the expression 12D can be broken down into its factors, written as 12D or 34D or even 62D.We also learned bout finding the product of terms. For example the product of 7B and 6D = 42BD.Lastly, we practiced combining like terms. Example: In the expression 3a + 3a + 2b, we can only combine as with as and bs with bs.Todays LessonToday we will learn about another mathematical property mathematicians call The distributive property. We will also continue to practice combining like terms.Complete todays do now.

HomeworkTodays homework will focus on combining like terms and using the distributive property.

Do NowQuestion # 1Evaluate the following expressions using the distributive property:A) b(12 + 2)B) c(4 + 3)C) 4(6 2)Question # 2Combine like terms for the following expressions:10b 6b + 2a + 10 + 552 + 2x 7 + 3x 2b6a + 7b + 2j

Look at the model on the right. How many 2s are in the model?How many 3s are in the model?What expression can we write to represent this model?------------------------------------------------Look at the model on the right. How many 2s are in the model? How many 3s are in the model?What expression can we write to represent this model?The Distributive Property

2 x 22 x 3

2 + 32 + 3Are these two models equivalent? How do you know?

The distributive property says that instead of representing this expression as (2 x 2) + (2 x 3) or (2 + 3) + (2 + 3), we can use 2(2 + 3). Take a look on the right.The distributive property is done by multiplying the outside of the parenthesis by whats on the inside of the parenthesis. 2 x 2 = 4 , 2 x 3 = 6. 6+4 = 10.The Distributive Property Part II

2(2 + 3)(2 x 2) + (2 x 3)

4 + 6

10

Evaluate the following expressions using the distributive property.A) 2(7 - 4) B) 5(4 1)C) 17(6 + 2)D) 7(5 + 3)E) 5(6 + 4)Practice!

Look at the model on the right. How many As are in the model?How many Bs are in the model?What expression can we write to represent this model?------------------------------------------------Look at the model on the right. How many As are in the model? How many Bs are in the model?What expression can we write to represent this model?The Distributive Property VariablesAB2 x A2 x B

A + BA + BAre these two models equivalent?

How can we re-write this expression using the distributive property?BAAABB

Rewrite the following expressions using the distributive property.3(z - b)5(2 + d)A(a + c)X(10 + 6)M(7 + 3)Practice!

Using the greatest common factor & the distributive property to write equivalent expressions:A) 6x + 9yFind the greatest common factor. What is the GCF of 6 and 9?What times the greatest common factor will give me 6x?What times the greatest common factor will give me 9y?Key questionsWe can write equivalent expressions using the distributive property by using the greatest common factor (GCF). For example, in the expression 3a + 3b, 3 is the common factor. How can we re-write this expression to create an equivalent expression? (Hint: Outside of the parenthesis will be the greatest common factor) Common FactorsCommon Factors and the Distributive Property

Use the greatest common factor & the distributive property to write equivalent expressions:15x + 10y6x + 6y11b + 2b

Practice!

Using the greatest common factor & the distributive property to write equivalent expressions:A) 24x + 6Find the greatest common factor. What is the GCF of 6 and 24?What times the greatest common factor will give me 24x?What times the greatest common factor will give me 6?Key questionsFor example, in the expression 3d + 5d, d is the common factor. How can we re-write this expression to create an equivalent expression? (Hint: Outside of the parenthesis will be the greatest common factor) Common FactorsAnother Example.

Todays ClassworkFind the missing value to make the expressions equivalent!12x + 2y _______(6x + y)32b + 8 _______(4b + c)55x + 50n _______(11x+10n)100n + 50x ________(2n + x)75d + 50x _______(3d + 2x)17c + 15c ______(17 + 15)4d + 7d ________ (4 + 7)Use GCF & Distributive Property to write an equivalent expression60y + 10y30 15y18 + 6b16 2p100b 4m35c 14dCombine Like Terms4a + 5b 2a + 2b -2a6x + 2n n + 8 - 3xThe number of shoes Mr. E has can be represented as 3x + 4b 2n + x - b. Combine like terms to show the amount of shoes Mr. E has.

Combine Like Terms:4a + 5b 2a + 5b + a - b5x + 10 + 5 2n 8 + 3x - 42a + 2b 2a + 2b5d + 5n +8 - 3d 3

Use GCF & Distributive Property to write an equivalent expression:70n + 7x15b + 15b (can this be done in more than one way?)42c + 21b10d + 5c

Math Homework March 25, 2014

Combine Like Terms:5b + 2c + 8 4b c + 2

Use the GCF and distributive property to write an equivalent expression: 36n + 12y

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