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Quick Check - Laws of Exponents9/4/19

1. 94 x 98 =

2. 24-5 x 248

3.b2 x c3 x b3 =

4. 108 104 =

5. 911

93

6. 563 x 566=

7.

Write all answers as exponential expressions

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Topics to Review for Quiz on Thursday:

1. Simplifying Algebraic Expressions

2. Evaluating Algebraic Expressions

3. Interpreting Algebraic Expressions

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HW Reviews 9/4/19

Day 1

3.

Simplifying

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HW Reviews 9/4/19

Day 2

2.

Simplifying & Evaluating

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Day 2 HW: Interpreting

• 2 represents the cost of skating per hour• 2y represents amount paid for skating

for h number of hours.• 3 represents the cost of skate rental• 3 + 2y represents the total cost of skate

rental and skating.

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HW Reviews 9/4/19

Day 3

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Review Interpreting Algebraic Expressions (Study pages 11 & 12 in your notes)

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9/4/19 Module 2Day 6  Pythagorean Theorem

Essential Question

How can I use the Pythagorean Theorem to solve real world problems?

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Mini-Lesson

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On Your Boards, Set, Go!

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Notes Page 16

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Attachments

Exponent Properties  Practice 82416.ksipa

CombineLikeTerms.ppt

SMART Notebook

Combine Like Terms

I can simplify expressions with several variables by combining like terms.

Vocabulary

Constant

A number with nothing else attached to it.

Examples: 1, 2, 47, 925

Vocabulary

Variable

A letter that represents an unknown number.

Examples: a, b, x, y

Vocabulary

Coefficient

The number in front of the variable.

Examples: 3x 3 is the coefficient

2x 2 is the coefficient

Like Terms:

In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents).

Examples: 4x and -3x or 2y2 and –y2

Like terms because each term consists of a single variable, x, and a numeric coefficient:

2x, 45x, x, 0x, -26x, -x

Like terms because they are all constants:

15, -2, 27, 9043, 0.6

Like terms because they are all y² with a coefficient: 3y², y², -y², 26y²

What are unlike terms?

The following two terms both have a single variable, but the terms are not alike since different variables are used: 17x, 17z

Each y variable in the terms below has a different exponent, therefore these are unlike terms: 15y, 19y², 31y5

Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either: 19x, 14xy

Combine Like Terms

I can simplify expressions with several variables by combining like terms.

Like Terms – same variable with same exponent

6x + 2x =

When combining like terms, only use the coefficients.

6x + 2x =

8x

4x + 3y – 2x + 4y =

Simplify

2x + 7y

Simplify

Never, NEVER, combine x’s and y’s or constant terms with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a.

Key Skills

5 cats + 3 cats

8 cats

5a + 3a

8a

5 apples + 3 oranges

5 apples + 3 oranges

5 cats + 3 dogs

5 cats + 3 dogs

You Try

3y + 2 + 3x – y + 5x

x + x

Distribute by multiplication:

15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem.

The Distributive Property

Expressions with variables:

Simplify 5(3n + 4).

No symbol between the 5 and the parenthesis indicates a multiplication problem.

The constant terms 8 and 6 can be combined to form the constant number 14. The answer 28n + 14 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem.

The Distributive Property

Simplify 4(7n + 2) + 6.

No symbol between the 4 and the parenthesis indicates a multiplication problem.

Step 1) Use the Distributive Property 3 (2x – 5) - 2x

Step 2) Combine Like Terms6x – 15 – 2x

*** 6x and 2x are like terms!!!!

Step 3) Simplified Expression4x – 15

Distributive Property

Distributive Property

Example:

6(a + 3)Use the Distributive Property

(6a) + (6 x 3)Multiply

6a + 18Simplified

***CAN NOT add 6a + 18 together because they are not like terms.

Solve: 2x + 6(x + 1)

Explain how each of the below answers are wrong and why.

2x + 6x + 1

9x

Practice Problems

=

+

)

4

3

(

5

n

)

3

(

5

n

+

)

4

(

5

=

n

15

20

=

+

+

6

)

2

7

(

4

n

)

7

(

4

n

)

2

(

4

n

28

8

6

14

SMART Notebook

Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8Page 9: Sep 3-5:20 PMPage 10: Sep 3-6:02 PMPage 11: Sep 3-6:03 PMPage 12Page 13: Sep 3-6:15 PMPage 14: Sep 3-6:18 PMPage 15: Sep 3-6:19 PMPage 16: Sep 3-6:45 PMPage 17Attachments Page 1