Bell Ringer Write an English sentence for the mathematical expression Write an algebraic expression for the statement Ten monkeys plus seventeen bananas.

Bell Ringer

Write an English sentence for the mathematical expression

Write an algebraic expression for the statementTen monkeys plus seventeen bananas

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Bell Ringer!

Pull out notes, write down as many English words as you can for each sign:

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Homework

5 minutes to complete

Correct. Out of 32!

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Add and Subtract Polynomials

Review

x + x2x

x·xx2

2x + 3x

5x

2x·3x

6x2

4x2 + 4xNOT LIKE

TERMS!

4x2·4x

16x3

5x2 + x2

6x2

5x2·x2

5x4

Adding/Subtracting Polynomials

• We will discuss three methods– Algebra Tiles– Vertical Method– Horizontal Method

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Algebra Tiles

Algebra tiles can be used to model operations involving integers.

Let the small green square represent +1 and the small pink square represent -1.

The green and pink squares are additive inverses of each other.

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Algebra Tiles

Algebra tiles can be used to model operations involving variables.

Let the green rectangle represent +1x or x and the pink rectangle represent -1 x or -x .

The green and red rods are additive inverses of each other.

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Algebra Tiles

Let the green square represent x2. The pink square represents -x2.

As with integers, the green squares and the pink squares form a zero pair.

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Modeling with Algebra Tiles

2x + 3

4x – 2

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Zero Pairs

Called zero pairs because they are additive inverses of each other.

When put together, they model zero.

Practice with Integers

Algebra tiles can be use to model adding, subtracting, multiplying, and dividing real numbers.

Remember, if you don’t have enough of something, you can add “zero pairs”

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Modeling Addition/Subtraction -2 – 3 Start with -2

Take away positive 3. But wait, I don’t have 3 so I must add zero pairs!

Now remove positive 3 You are left with -5

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Adding Polynomials

(2x + 4) + (x + 1)

Combine like terms to get three x’s and five positive ones

= 3x + 5

Activity Sheet

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Find question 4

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Work through the worksheet as partners

We will discuss two other ways to think about adding/subtracting next.

Every group needs to answer questions 1-6 completely.

Attempt Question 7.

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Adding and Subtracting Polynomials

(3x4 – 5x2 + 1) + (6x4 + 2x2 – 7)

Combine Like TERMS!

9x4 – 3x2 – 6

(r2 + 2r – 3) + (3r2 – r – 1)

Combine Like TERMS!

4r2 + r – 4

(-2a5 – 2a4 + 7a) + (6a4 + 2a2 – 2a)

Combine Like TERMS!

-2a5 + 4a4 + 5a+ 2a2

(-c5 + 8c + 2) – (-2c5 + 6c – 1)

Distribute the Negative!

c5 + 3+ 2c(-c5 + 8c + 2) + (2c5 – 6c + 1)

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If you haven’t already finished question 7, finish it then turn it in.

Bulls Eye

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Homework: Worksheet

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