VAN SICLEN COMMUNITY MIDDLE SCHOOLMR. E – GRADE 6 MATHCLASS 603/604/605MONDAY MARCH 24, 2014

The Distributive Property

Today’s Lesson Link:www.tinyurl.com/vscmath13

Lesson OverviewLast Week’s

Lessons Last 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 “a’s” with “a’s” and “b’s” with “b’s”.

Today’s Lesson Today we will learn about

another mathematical property mathematicians call “The distributive property”. We will also continue to practice combining like terms.

Complete today’s do now.

Homework Today’s homework will

focus on combining like terms and using the distributive property.

Do NowQuestion # 1

Evaluate 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 + 5 52 + 2x – 7 + 3x – 2b 6a + 7b + 2j

• Look at the model on the right. How many 2’s are in the model?

• How many 3’s are in the model?• What expression can we write to

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

represent this model?

The Distributive Property2 x 2 2 x 3

2 + 3 2 + 3

Are 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 what’s 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 A’s are in the model?

• How many B’s are in the model?• What expression can we write to

represent this model?• ------------------------------------------------• Look at the model on the right.• How many A’s are in the model?• How many B’s are in the model?• What expression can we write to

represent this model?

The Distributive Property – Variables

A B2 x A 2 x B

A + B A + B Are these two models equivalent?

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

BA

A AB B

• 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 + 9y• Find 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 QUESTIONS• We 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 FACTORS

Common Factors and the Distributive Property

• Use the greatest common factor & the distributive property to write equivalent expressions:• 15x + 10y• 6x + 6y• 11b + 2b

Practice!

• Using the greatest common factor & the distributive property to write equivalent expressions:• A) 24x + 6• Find 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 QUESTIONS• For 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 FACTORS

Another Example….

Today’s 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 – 2p

100b – 4m35c – 14d

Combine Like Terms

4a + 5b – 2a + 2b -2a 6x + 2n – n + 8 - 3x

The 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 - b 5x + 10 + 5 – 2n – 8 + 3x - 4 2a + 2b – 2a + 2b 5d + 5n +8 - 3d – 3

Use GCF & Distributive Property to write an equivalent expression: 70n + 7x 15b + 15b (can this be done in more than one way?) 42c + 21b 10d + 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

Exit Ticket Question!