ALGEBRACHAPTER 6

Ms. Fisher

OBJECTIVE: EVALUATE EXPRESSIONS CONTAINING ZERO AND INTEGER EXPONENTS.

WARM-UP: HOW WAS YOUR WINTER BREAK?!

GET ANY GOOD PRESENTS?!!!

6.1 Integer Exponent 01/05/2015 Mon

5² = 25

5 ̄ ² = 1 5²

6.1 Integer Exponent (Simplifying Expressions with Zero and Negative Exponents

= 1 = 1 = 1 THE BASE IS NEG (-3)(-3)(-3)(-3) 81= - 1 = - 1 = -1 THE BASE 3 IS POS 3 * 3* 3* 3 81

6.1 Integer Exponent BE CAREFUL**** ORDER OF OPERATIONS

EVALUATE THE EXPRESSION: Aº A=8 B= -2

8º * 1 * 1 = 1* 1 = -1/8 (-2) (-2)(-2)

6.1 Integer Exponent

SIMPLIFY EXPRESSION:

= 3 * =3 *1

6.1 Integer Exponent

= 3

SMALL GROUP WITH MS. FISHER: MADDIE, NIKKI, & CHRISTIAN HW: PG 395 #’S 2-23EXTENSION: ALEX & JAMES HW & #’S 25-42LEO: STUDY ISLAND ON LAPTOP

Independent Work Time…

-GO OVER PARKING LOT QUESTIONS/ HW-TEACH SECTION 6.2 WHOLE GROUP-SMALL GROUP INSTRUCTION TIME

OBJECTIVE: EVALUATE AND SIMPLIFY EXPRESSIONS CONTAINING RATIONAL EXPONENTS.

WARM-UP: WHAT DOES RATIONAL MEAN?

A RATIONAL NUMBER IS A NUMBER THAT CAN BE EXPRESSED AS A FRACTION P/Q WHERE P AND Q ARE INTEGERS AND Q ≠0

6.2 Rational Exponents 01/06/2015 Tuesday

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HW page 395 #’s 2-20

2. 1/36 12. 1/93. 1 13. 1/2564. -1/25 14. 1/325. 1/27 15. -1/326. 1 16. 47. -1/512 17. 3/ 8. 1/100 18. 9. 1 19. 10. -1/27 20. 2/ 11. 1/16

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6.2 Rational Exponents in Radical Form

Rational- means NOT negative

is rational NOT rational

Radical Form

6.2 Rational Exponents 01/06/ Tuesday

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6.2 Rational Exponents 01/06/ Tuesday.

Example: Simplify each expression

Example:

1. 81¼

3*3*3*3 = 81 Answer= 3

Example #2:

216²⁄³ =

¿3√(6³ ) ²= (6)²= 36

**Make sure each student has a calculator and knows how to use it**

6.2 Rational Exponents.

Calculator Skills you need to know: In calculator input: Example: 81

1. 81¼

3*3*3*3 = 81 Answer= 3

4 = You should get the answer 3

2nd key

6.2 Rational Exponents 01/06/ Tuesday.

Example: Simplify each expression

C=72m¾ m=16 = 72(16)¾ =72 =72⁴)³ b/c 2*2*2*2=16 =72 (2)³ =72(8) =576

6.2 Rational Exponents 01/06/ Tuesday.

** In this Chapter the best advice I can give you is…

The more problems you do, the better off you are. You need to practice this skill. This is a very difficult skill. The only way to mastered this skill is by working through problems…

Independent Work Time.

Small group with Ms. Fisher: Maddie, Nikki, & Christian HW: pg 401#’s 2-21Extension: Alex & James HW & #’s 23-50Leo: Study Island on laptop

6.3 Polynomials 01/07/2015 Wed. .

Go over Parking Lot Questions/ Hw-Teach Section 6.3 Whole Group-Small Group Instruction Time

Objective: Evaluate polynomial expressions.

6.3 Polynomials 01/07/2015 Wed. .

HW: pg 401#’s 2-21

2. 8¹⁄³ 2*2*2 = 8 = 23. 44. 0¹⁄6 0*0*0*0*0*0 = 0

5. 27¹⁄³ 3*3*3 = 27 = 36. 910.36½ + 1¹⁄³ 6 +1 = 7

19. 64⁴⁄ ³ How you would input this problem into your calculator to solve…

6.3 Polynomials 01/07/2015 Wed. .

19. 64⁴⁄ ³ How you would input this problem into your calculator to solve…In calculator input:64 64⁴⁄ ³ 4*4*4 = 64 3 Denominator = 4 = 256⁴= = 4*4*4*4=2564 Answer 4 Numerator

=256 Answer

2nd key

6.3 Polynomials 01/07/2015 Wed. .

Page 401

39. 125¹∕³ + 81½

Take your calculator :

125 3 = 5

81 = 9

5 + 9 = 14 Final Answer

2nd

key

6.3 Polynomials 01/07/2015 Wed.

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6.3 Polynomials 01/07/2015 Wed.

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Terms of an

** In this section you will have to take some time to memorize the degree names and term names found in the boxes on page 407 of your textbook** At the end of class grab a partner and quiz each other

6.3 Polynomials 01/07/2015 Wed.

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6.3 Polynomials 01/07/2015 Wed.

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6.3 Polynomials Independent Work Time01/07/2015 Wed.

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Small group with Ms. Fisher: Maddie, Nikki, & Christian HW: pg 409#’s 1-25Extension: Alex & James HW & #’s 27-49Leo: Study Island on laptop

6.4 Adding and Subtracting Polynomials 01/08/2015 Thursday

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Go over Parking Lot Questions/ Hw-Teach Section 6.4 Whole Group-Small Group Instruction Time

Objective: Add and Subtract Polynomials

6.4 Adding and Subtracting Polynomials 01/08/2015 Thursday

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HW: pg 409#’s 1-25

1. 2x³ + 6 name = cubic binomial2. 3x³ + 4x² - 7 name = cubic trinomial3. 5x²-2x + 3x ⁴ -6 name= quartic polynomial

Find the Degree – Remember Looking for GREATEST DEGREE4. 0 8. x²-2x +1 degree= Greatest degree 25. -7xy² = 3 2 1 0 6. 8 9.87. 0 10.3

6.4 Adding and Subtracting Polynomials 01/08/2015 Thursday

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6.4 Polynomials Independent Work Time01/08/2015 Thurs.

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Small group with Ms. Fisher: Maddie, Nikki, & Christian HW: pg 417#’s 1-14Extension: Alex & James HW & #’s 16-32Leo: Study Island on laptop

6.5 Multiplying Polynomials01/09/2015 Friday

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Go over Parking Lot Questions/ Hw-Teach Section 6.5 Whole Group-Small Group Instruction Time

Objective: Multiply Polynomials

6.5 Multiplying Polynomials01/09/2015 Friday

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HW: pg 417#’s 1-14

1. 7a²-10a² +9a = -3a² + 9a2. 13x² + 9y² - 6x²= 7x² +9y²3. .07+ .32 + .19= .26r + .3211. (6 + 8c +6) - (2)= 4+ 8c +612. (16y²-8y+ 9) – (6y²-2y +7y)= 10y² -13y + 9

MONOMIAL EXAMPLES:

13,    3X,    -57,     X²,     4Y²,     -2XY,  OR  520X²Y²

BINOMIAL EXAMPLES:

3X + 1,    X² - 4X,     2X + Y,    OR    Y - Y²

POLYNOMIAL EXAMPLES:

X2 + 2X + 1,      3X² - 4X + 10,       2X + 3Y + 2

6.5 Multiplying Polynomials Page 422

MULTIPLYING MONOMIAL BY MONOMIAL

STEP ONE: GROUP LIKE BASES TOGETHEREX: (-3X³Y²) (4X) = (-3 * 4) (X³ * X) (Y² * )

STEP TWO: ADD EXPONENTSEX: -12

6.5 Multiplying Polynomials Page 422

MULTIPLYING POLYNOMIAL BY A MONOMIAL- USE DISTRIBUTIVE PROPERTY

STEP ONE: DISTRIBUTESTEP TWO: MULTIPLYSTEP THREE: GROUP LIKE BASES

5(2X² + X + 4)

10X² + 5X +20

6.5 Multiplying Polynomials Page 422

MULTIPLYING BINOMIAL BY BINOMIAL- USE FOIL METHOD

1.MULTIPLY THE FIRST TERMS (X + 3) (X + 2) X²

2. MULTIPLY THE OUTER TERMS (X + 3) (X + 2) 2X

3. MULTIPLY THE INNER TERMS (X + 3) (X + 2) 3X

4. MULTIPLY THE LAST TERMS (X + 3) (X + 2) 3 * 2 = 6

(X + 3) (X + 2) = X²+2X +3X +6 = X²+ 5X +6

6.5 Multiplying Polynomials Page 422

MULTIPLYING BINOMIAL BY A POLYNOMIAL(MULTIPLYING POLYNOMIALS)

-USE RECTANGLE MODEL-WRITE THE PRODUCTS OF THE MONOMIALS IN EACH ROW AND COLUMN-TO FIND THE PRODUCT, ADD ALL OF THE TERMS INSIDE THE RECTANGLE BY COMBING THE LIKE TERMS AND SIMPLIFYING.(5X+ 3) (2X²+10X-6) = 10X³+ 6X² + 50X² +30X-30X -18

6.5 Multiplying Polynomials Page 422

10x³ 50x² -30x

6x² 30x -18

2x² 10x

-6

5x

3

Final Answer: 10X³ + 56x² -18