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-UP 1. 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, 4/4Tuesday, 4/5Wednesday, 4/6Thursday, 4/7Friday, 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, 4/11Tuesday, 4/12Wednesday, 4/13Thursday, 4/14Friday, 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, 4/25Tuesday, 4/26Wednesday, 4/27Thursday, 4/28Friday, 4/29 Multiplying a monomial by a polynomial No Classes PSAE Testing: Day 1-ACT No Classes PSAE Testing: Day 2-WorkKeys Multiplying two binomials: FOIL method

Reminders / Expectations 1. 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 – Friday  8:15AM – 8:45AM in Room 208 Tuesdays  3:30PM – 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. 3 4 = (3)(3)(3)(3) = Base Exponent

How to read an exponent Three to the fourth power 3 4

How to read an exponent (cont’d) Three to the 2 nd power or Three squared 3 2

How to read an exponent (cont’d) Three to the 3rd power or Three cubed 3 3

Exponents are often used in area problems to show the units are squared Area = (length)(width) Length = 30 ft Width = 15 ft Area = (30 ft)(15 ft) = 450 ft 2 15ft 30ft

A = π(8cm) 2 A = 64π cm 2

Exponents are often used in volume problems to show the units are cubed Volume = (length)(width)(height) Length = 10 cm Width = 10 cm Height = 20 cm Volume = (20cm)(10cm)(10cm) = 2,000 cm

What is the exponent? (5)(5)(5)(5) =5 4

What is the answer? 5 3 = 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 3 b 2 c

Compute: (-4) 2 Answer: (-4)(-4) = 16

Calculate: -4 2 Answer: -(4)(4) = -16 PEMDAS

Simplify: n 2 when n = -5 Answer: (-5) 2 = (-5)(-5) = 25

Simplify: -n 2 when n = -5 Answer: -(-5) 2 = -(-5)(-5) = -25

Compute: (-6) 2 Answer: (-6)(-6) = 36

Compute: -6 2 Answer: -(6)(6) = -36

Compute: -(-6) 2 Answer: -(-6)(-6) = -36

Simplify: (x + 3) 2 Answer: (x + 3)(x + 3) x 2 + 6x + 9

Compute: 0 2 Answer: (0)(0) = 0

Compute: 2 0 Answer: 1 Yes, it’s 1…explanation will follow

WHY is anything to the power zero "1" 3 6 = = = = = = = 1

Laws of Exponents

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, 3s 2 p Open Ended: Write 3 different examples of monomials

Determine whether each expression is a monomial. Say yes or no. Explain your reasoning. 1.) 10 1.) Yes, this is a constant, so it is a monomial. 2.) f ) No, this expression has addition, so it has more than one term. 3.) 3ab 5 3.) Yes, this expression is a product of a coefficient and variables. 4.) j 4.) 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, a 0 = 1. Examples: 1.) 12 0 = 1 2.) 3.) Open Ended: Create a problem that satisfies this property!

Let’s practice Simplify each expression: 1. (-4) (Recall PEMDAS - Exponents first!) 3. (5x) 0 5x (-4.9) 0 (Recall PEMDAS – Exponents first!) 5. [(3x 4 y 7 z 12 ) 5 (–5x 9 y 3 z 4 ) 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) x HW: Quiz corrections

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) x 0 3. HW: Quiz corrections

Negative Exponent Property (2) Words: For any nonzero number a and any integer n, a -n is the reciprocal of a n. Also, the reciprocal of a -n = a n. Symbols: For any nonzero number a and any integer n, Examples: Open Ended: Create a problem that satisfies this property! Use any number for a and n.

Examples

Examples (cont’d)