SWBAT… compute problems involving zero & negative exponents Mon, 4/4

Agenda 1. WU (5 min)

2. Midterms Results/ Calendar / Reminders / Expectations (10 min)

3. Get Ready for Chapter 8 / Exponents quick review (20 min)

4. Lesson on monomials and exponents (10 min) Zero Exponents Negative Exponents

WARM-UP1. Take out Get Ready for Chapter 7

2. Write your hw in your planners for the week

3. Set-up Cornell Notes: Topic is “Simplifying Monomials – Zero & Negative Exponent Property”

HW1: Zero and negative exponents (back of agenda)

Monday, 4/4 Tuesday, 4/5 Wednesday, 4/6 Thursday, 4/7 Friday, 4/8

Exponents Overview

Zero Exponent Property (1)

Negative Exponent Property (2)

Zero Exponent Property (1)

Negative Exponent Property (2)

(cont’d)

Quiz: Zero and negative monomials

(1, 2)

Multiplying Monomials

Product of Powers (3)Power of a Power (4)

Power of a Product (5)

No Classes:Report Card

Pick-up/ Parent-Teacher

Conferences

Multiplying Monomials

(cont’d)

Quiz: multiplying monomials

(3, 4, 5)

Monday, 4/11 Tuesday, 4/12 Wednesday, 4/13 Thursday, 4/14 Friday, 4/15

Dividing Monomials

Power of a Quotient (6)

Quotient of Powers (7)

Dividing Monomials(cont’d)

Quiz: dividing monomials (6, 7)

All 7 rules of exponents

Exponent Posters

Quiz on the 7 exponent rules (1 - 7)

Adding and subtracting polynomials

Monday, 4/25 Tuesday, 4/26 Wednesday, 4/27 Thursday, 4/28 Friday, 4/29

Multiplying a monomial by a

polynomial

No ClassesPSAE Testing:

Day 1-ACT

No ClassesPSAE Testing:

Day 2-WorkKeys

Multiplying two binomials: FOIL method

Multiplying two binomials: FOIL method

Reminders / Expectations1. Warm-up will be started as soon as you get to class

1. Come prepared with pencils & notebook & planner

2. Come on time (10 points off for each tardy)

2. Homework will be completed in it’s entirety before class

3. I will be checking homework on your way in to class – so please have it out before entering class

4. After 3 days, you will not be given credit for homework

5. If you miss a test/quiz – it is your responsibility to arrange a time with me to make up the test/quiz

6. Check assignment detail on Grade Book for “0”

7. BE RESPECTFUL – When a teacher or classmate is talking – you shouldn’t be talking!

Office Hours - Reminder

Monday – Friday8:15AM – 8:45AM in Room 208

Tuesdays3:30PM – 5:30PM in Room 208

Questions?Comments?Concerns?

New unit on Polynomials & Exponents SWBAT…1. Apply and explain the rules of exponents (7rules)

2. Identify the difference between monomials, binomials and trinomials and the degree of each.

3. Add and subtract polynomials.

4. Multiply a monomial by a polynomial.

5. Solve equations with polynomials.

6. Multiply two binomials using the FOIL method.

Test is on Friday, May 18

Exponent Review

Ms. Sophia Papaefthimiou

Infinity HS

Definition of an exponent

An exponent tells how many times a number is multiplied by itself.

34

= (3)(3)(3)(3) = 81

34

BaseExponent

How to read an exponent

Three to the fourth power

34

How to read an exponent (cont’d)

Three to the 2nd power or Three squared

32

How to read an exponent (cont’d)

Three to the 3rd power or Three cubed

33

Exponents are often used in area problems to show the units are squared

Area = (length)(width) Length = 30 ftWidth = 15 ft

Area = (30 ft)(15 ft) = 450 ft 2

15ft

30ft

A = π(8cm)2

A = 64π cm2

Exponents are often used in volume problems to show the units are cubed

Volume = (length)(width)(height) Length = 10 cmWidth = 10 cmHeight = 20 cm

Volume = (20cm)(10cm)(10cm) = 2,000 cm3

10

10

20

What is the exponent?

(5)(5)(5)(5) = 54

What is the answer?

53

= 125

What is the base and the exponent?

(7)(7)(7)(7)(7) = 7 5

What is the base and the exponent?

(x)(x)(x)(x)(x)(x) =x 6

What the base and the exponent?

(a)(a)(a)(b)(b)(c) =a 3b2c

Compute: (-4)2

Answer: (-4)(-4) = 16

Calculate: -42

Answer: -(4)(4) = -16

PEMDAS

Simplify: n2 when n = -5

Answer: (-5)2 = (-5)(-5) = 25

Simplify: -n2 when n = -5

Answer: -(-5)2 = -(-5)(-5) = -25

Compute: (-6)2

Answer: (-6)(-6) = 36

Compute: -62

Answer: -(6)(6) = -36

Compute: -(-6)2

Answer: -(-6)(-6) = -36

Simplify: (x + 3)2

Answer: (x + 3)(x + 3) x2 + 6x + 9

Compute: 02

Answer: (0)(0) = 0

Compute: 20

Answer: 1Yes, it’s 1…explanation will follow

WHY is anything to the power zero "1"

36 = 72935 = 243 34 = 81 33 = 27 32 = 9 31 = 3

30 = 1

Laws of Exponents

nmn

m

m

mm

mmm

mnnmnmnm

nnn

n

xx

x

y

x

y

xyxxy

xxxxx

xx

orx

xx

.7

.6.5

.4.3

11.21.1 0

A monomial is an algebraic expression consisting of only one term.

A term may be a number, a variable, or a product or quotient of numbers and variables (separated by a + or –)

Examples of monomials: 3, s, 3s, 3sp, 3s2p

Open Ended: Write 3 different examples of monomials

Determine whether each expression is a monomial. Say yes or no. Explain your reasoning.

1.) 101.) Yes, this is a constant, so it is a monomial.

2.) f + 242.) No, this expression has addition, so it has more than one

term.

3.) 3ab5

3.) Yes, this expression is a product of a coefficient and variables.

4.) j4.) Yes, single variables are monomials.

Zero Exponent Property (1)Words: Any nonzero number raised to the zero

power is equal to 1.

Symbols: For any nonzero number a, a0 = 1.

Examples:

1.) 120 = 1

2.)

3.)1

0

c

b

17

20

Open Ended: Create a problem that satisfies this property!

Let’s practice

Simplify each expression:

1. (-4)0

2. -40 (Recall PEMDAS - Exponents first!)

3. (5x)0 5x0

4. -(-4.9)0 (Recall PEMDAS – Exponents first!)

5. [(3x4y7z12)5 (–5x9y3z4)2]0

SWBAT… compute problems involving zero & negative exponents Wed, 4/6

Agenda 1. Review problems Zero & Negative Exponent Property (20 min)

2. Practice – hw#1 (15 min)

3. Quiz (10 min)

WARM-UP

1. (5x)0

2. 5x0

3.4.

HW: Quiz corrections

0)( iouPapaefthimSophia3)2(

SWBAT… compute problems involving zero & negative exponents Wed, 4/6

Agenda 1. Lesson on monomials and exponents w/ many examples (20 min)

Zero Exponent Property Negative Exponent Property

2. Practice – hw#1 (15 min)

3. Quiz (10 min)

WARM-UP

1. (5x)0

2. 5x0

3.

HW: Quiz corrections

0)( iouPapaefthimSophia

Negative Exponent Property (2)

Words: For any nonzero number a and any integer n,

a-n is the reciprocal of an.

Also, the reciprocal of a-n = an.

Symbols: For any nonzero number a and any integer n,

Examples:

nnn

n aa

anda

a 11

25

1

5

15

22 3

3

1m

m

Open Ended: Create a problem that satisfies this property!Use any number for a and n.

52

152 32

Examples

24

1

24 16

112

12

1

4848

1

4096

1

3)2(

1

3)2( )2)(2)(2(

1

8

1

22

1

1

8

4

1

1

8 2228

Examples (cont’d)

24

4 24

1

1

4 244 164 64

0)6(9 )1(9 9

2

2

8

2

2

2

8

1

1

2

22

82

1 64

4

1 16

228

2

2

7

2

24

4

06 yx