Name: ______________________________

Date: November 28, 2016

Homeroom:

7th Grade Math:

Unit: Rational Numbers

Packet 49: Simplifying Expressions

Objectives: Scholars will be able to define and identify the parts of a variable expression. Scholars will be able to simplify variable expressions (without parentheses).

Agenda:

1. Review Do Now 6. Simplifying Algebraic Expressions2. Parts of an Algebraic Expression 7. Independent Practice3. Variables, Constants and

Coefficients8. Exit Ticket

4. Special Examples 9. Homework Overview5. Combining Like Terms Homework 49: Simplifying

ExpressionsDo Now: Madeline wants to create a scale drawing of a room. The room is rectangular with a length of 24 feet and a width of 18 feet. Using a scale of 1 inch: 3 feet, create the scale drawing.

Parts of an Algebraic Expression

Terms: When addition or subtraction signs separate an algebraic expression into

parts, each part is called a ________________________.

Examples:

If an expression does not have any addition or subtraction signs, then the entire expression is a ____________________ _______________________.

Examples:

3x + 5

Check it out!How many terms are in the expression 3x + 5 ?

There are __________ terms.

List the terms: _____________ and ____________

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Variables, Constants and Coefficients: A variable is a _______________ or _______________ that stands for a value you

don’t know.

A term without a variable (so all it has is a number) is called a _________________________.

The number that is being multiplied by the variable is called the ________________________.

Label the parts of the expressions below:

3x + 5

Don’t be fooled!

All variables have coefficients. When you see a variable that seems to have no coefficient, it actually has a coefficient of ________.

For example, in the expression 5x + y, the x has a coefficient of ________, and y has a coefficient of _______.

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Fractions and Decimals ________________________ and ____________________ can be fractions and

decimals, too

Example: 23x+0 .09

List the constants and coefficients:

Constants: _______________

Coefficients: _______________

Negative Constants and Coefficients Constants and coefficients can be negative numbers, too.

Example:

4y – 5x – 2Change the entire expression to addition!

Constant: _______________

Coefficients: _______________ and _______________

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Combining like Terms:Here you cannot combine any terms!

We can think of x as a bag that holds some unknown number of M&Ms. Let’s look at a few expressions to see what they mean:

5 + 2x 5 loose M&Ms 2 bags of

M&Ms

We can’t combine or simplify this anymore than it already is. It is two bags of M&Ms and 5 loose M&Ms.

Here you can combine like terms!3x + 2x

3 bags of M&Ms 2 bags of M&Ms

Now we could add those 3 bags to the 2 bags and get a total of ____________ bags of M&Ms.

3x + 2x = ______

5x

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Let’s look at another example: Read the passage below and try to fill in the blanks. We will go over this in a few minutes.

In the same way, if we have 8x – 2, then we’re saying that we have ________ bags of M&Ms minus ________ loose M&Ms. There’s nothing else we can do to simplify that expression. But, if we instead had:

8x – 2x

…then we could subtract 2 bags from the 8 bags and end up with ________ bags of M&Ms. And _______ is a much simpler way of saying 8x – 2x, which is why we can say we’ve simplified it.

If you want to add or subtract two terms that have the exact same variable part, then you can simply add and subtract their ____________________________. Just remember to keep the variable stuck to the answer!

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Simplifying Algebraic Expressions:

Simplify the expression: 5 – 2x – 3 + x

Step One: Write the expression as a sum

______________________________________________________________________________

Step Two: Identify your like terms by boxing/circling/underlining, etc.

Step Three: Combine your variable like terms by adding/subtracting the coefficients. Combine your constants by adding/subtracting their values.

Simplified Expression: _______________________________________________________

Directions: Using the three steps from above, simplify the expressions below.

4y + 6 – y k + m – 2k – 9m

Answer: ___________________________ Answer: _______________________

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Independent PracticeDirections: For the given expressions, use the steps from page 7 to simplify. First, rewrite each expression as addition on the line to the right.

1.) 3x + 2 + 5x – 4x = _______________________________________

Answer: ____________________________

2.) –7b + 3 + b – 10 = _______________________________________

Answer: ____________________________

3.) 5 + 8w – 6 – w = _______________________________________

Answer: ____________________________

4.) 6x + x + 2 + 4 = _______________________________________

Answer: ____________________________

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5.) –2s – 8t + 9t – 6s = _______________________________________

Answer: ____________________________

6.) 5n + 1 – n – 8 = _______________________________________

Answer: ____________________________

7.) 5m + 8 – 3m – 7 = _______________________________________

Answer: ____________________________

8.) 8c + 3d – 2c + 5d = _______________________________________

Answer: ____________________________

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9.) –8q + 6 + 5q – 3 10.) f – 3f + 2 – 1

Answer: ______________________________ Answer: ________________________________

11.) 4x – 2x – x 12.) 5h – 3g + 2g – h

Answer: ______________________________ Answer: ________________________________

13.) 3c + 4d – c + 2 14.) m + 4m + 2m + 5

Answer: ______________________________ Answer: ________________________________

15.) 9c – 4c + 2c 16.) 10x + 7 + 3x – 4

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Answer: ______________________________ Answer: _______________________________

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Practice beyond Perfection-Turn in for Dollars!

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Directions: Answer the following questions. Circle your final answer.

1. What are terms that have a number but no variable called? _________________________________________

2. What is the constant in the expression 4x + 5? ___________________________

3. What is the coefficient of x in the expression 3 + 42x – 7? _________________

4. What is the coefficient of y in the expression 8 – 3y + 1? __________________

5. What are the variables in the expression -7j + 2j – 3k + 27 -17k? ____________ and _____________

Simplify each expression. Show all of your work and circle your answer.

6. 2x + 5x 7. 7b + 2b 8. y + 10y – 7

9. 5j + j 10. 2a + 3 + 5a 11. 6x + 4 – 4x

12. Which of the following terms are not like terms?

8y and -4y

2f and -3f

-4g – 1g

4t and 4tf

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Name: ______________________________

Date:

Homeroom:

Ms. Petrozzi: (614) 725-9693

7th Grade Math:

Unit: Rational Numbers

Packet 49: Simplifying Expressions

Redo: Score: ________/5 _________% DNG A B C D F

Simplify the expression below. Begin by writing each expression as an addition expression.

13. 7x + x – 3 + 7 = ___________________________________________

Answer: _____________________________________________________________________

14. 6n + 1 – n – 6 = ____________________________________________

Answer: _____________________________________________________________________

15. 3y + 18 – y – 4 = ____________________________________________

Answer: _____________________________________________________________________

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Directions: Answer the following questions. Once you finish your exit ticket, place it face down on your desk and work on your advanced work!

Directions: Look at the following algebraic expression. Answer the questions that follow.

7x + 2y + 10

1. What is your constant? _____________________

2. What are your variables? _______________ and ________________

3. What is the coefficient of x? __________________

4. What is the coefficient of y? __________________

Directions: Combine like terms to simplify each expression.

5.) 7x + 5x

_____________________________________________________________________________

6.) 4y + 3 - 2y

_____________________________________________________________________________

7.) 2n + 5 – 4 + 10n

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Name: ______________________________

Date:

Homeroom:

7th Grade Math:

Unit: Rational Numbers

Packet 49: Simplifying Expressions

_____________________________________________________________________________

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Self-Assessment: _______ Test-Ready _______ More Practice ________ Help!

Mastery: Mastered Progressing Not-Mastered