Equivalent Expressions February 20th, 2018Launch (3 min) Learning

Target

I can develop a method to write equivalent expressions.

1.) What are three expectations for group conversations?

2.) Identify the inverse operations in the following equations:

a.) 3X = 126b.) T - 15.12 = 23.65c.) C/4 = 3.25

3.) Describe the direction of the arrow when graphing the following inequalities:

a.) X < 34b.) “Kyle has more than 23 animals”c.) 45 > Y

Master Note Takers (30 sec)

Use your graphic organizer to take notes on…

Distributive Property & Combining Like Terms

Glue your graphic organizer in your notebook.

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Distributive Property- Mini Lesson(5 min)

What is Distributive Property?What does it sound like?

Shmoop Video

After the video what do you know about Distributive Property? Talk to you group using good math conversations. (1 ½min)

The Distributive Property says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.

Example: 3(5G + D) = 3(5G) + 3D = 15G + 3D

So the "3" can be "distributed" across the "5G + D" into 3 times 5G and 3 times D.

Distributive Property

NOTE: 3(5G + D) says “3 multiplied by the sum of 5G and D”

Why Distributive Property?So you may be asking why can’t you always use order of operations to solve?

What would happen if you have 3(4x+2)?

Can you still use order of operations?Can you add 4x and 2?

You can not combine things that are not the same. So we use Distributive Property to simplify.

Simplify Expressions NotesMethod 1: Distributive Property Method 2: Combining Like Terms

Definition:The distributive property says

You _____________ things that

Definition:Like terms are

When combining like terms,

Example:

3(5G + D) = _________ + _________

= ____________

Example: 2A + 3B + A + B - 2A

Practice:

3(4X+ 2) =Practice: 3a + 4b + 4a + 2b + 6 + 2 - 6b

that multiplying a number by a group of numbers added together is the same as doing each multiplication separately

cannot combine

are not the same.

3(5G) 3(D)

15G + 3D

3(4x) + 3(2) = 12x + 64x + 24x + 24x + 2

Combining Like TermsCombining like terms is like combining fruit.

This is the expression: 2A + 3B + A + B

This simplifies to 3A + 4B

Combining Like TermsLike terms are terms that contain the same variables raised to the same power.

When combining like terms, you add or subtract the coefficients of the like terms.

For example: 2A + 3B + A + B - 2A is…2A + A - 2A = A

3B + B = 4B

A + 4B

3a + 4b + 4a + 2b + 6 + 2 - 6b

Practice: (5min)Simplify the expression by combining like terms

3a+4a

4b+2b-6b

6+2

Whiteboard Races

Your goal is for you and/or your team to create equivalent expressions by simplifying the given expressions.

Each person at your group must find a correct, but different possible solution

Once you have an answer, raise a fist

Create an equivalent expression for…..

Whiteboard Races

Y+5+Y+5+Y+5

Create an equivalent expression for…..

Whiteboard Races

6(X+3)

Create an equivalent expression for…..

Whiteboard Races

(Z+4) + (Z+4)

Create an equivalent expression for…..

Whiteboard Races

3(X+3)

Create an equivalent expression for…..

Whiteboard Races

2x + 5x + 7y + 3x + 4y

Create an equivalent expression for…..

Whiteboard Races

2(Y+10) + 2Y

Create an equivalent expression for…..

Whiteboard Races

3w + 7y - 3y + 4 - 3

Create an equivalent expression for…..

Whiteboard Races

3(x+y) + 3x + y +4x

Create an equivalent expression for…..

Whiteboard Races

5y + x + 7(x+y)

Mini Lesson: Finding MistakesITT (1min) Table Talk (2min)

Jonny D. was trying to solve the equation 3y = 4.2. He showed his work below.

3y = 4.2 ÷3 ÷3

y = 14

“Well I know the inverse of multiplication is division so...”

What did Jonny do well?What was Jonny´s beautiful mistake?What can Jonny do to correct his mistake?

Work Time Work with your team to identify common errors.

Start with what you agree with about the work.

Write what you disagree with about the work.

Provide feedback to correct the error.

Write your work in your graphic organizer today!

Station 1: Distributive Property

Simplify the following expression using distributive property.

1.) 2(3X + 2)

2.) 2(3X + 2)

3.) 4(X -3)

Station 2: Combining Like TermsSimplify the following expression by combining like terms.

1.) 3y + 2X - 2y + 5

2.) 3X + 2X - X

3.) 3X + 5 - 2

Station 3: Equations and InequalitiesSolve the following equations and inequalities by using inverse operations.

1.) 2X = 71

2.) 20.75 = B - 15.50

3.) 20 < 2X

Catch (5min)What does distributive property tell us to do?

What terms can we combine in the expression: 3y + 2x -2y + 5?

What are the inverse operations for…?addition

subtraction

multiplication

division

Closure (5 min)What were the mistakes in the following?

2(3X + 2) is equivalent to 5X + 4

3y + 2X - 2y + 5 is equivalent to 8X

20.75 = B - 15.50, -15.50 5.25 = B

Reflection (3min)

1.) What helped you to find the common errors?

2.) How did finding these errors help you to grow in your understanding?

Catch (5min)What does distributive property tell us to do?

What terms can we combine in the expression: 3y + 2x -2y + 5?

What are the inverse operations for…?addition

subtraction

multiplication

division

Closure (10 min)What were the mistakes in the following?

2(3X + 2) is equivalent to 5X + 4

3y + 2X - 2y + 5 is equivalent to 6X

20.75 = B - 15.50, -15.50 5.25 = B

Reflection (5min)

1.) What helped you to find the common errors?

2.) How did finding these errors help you to grow in your understanding?