1. SWBAT… review exponents Tues, 4/9 Agenda 1. WU (10 min) 2. Exponent review (25 min) Warm-Up: 1. Write your HW in your planner for the week 2. Write the formula for the area of a rectangle 3. Write the formula for the area of a triangle 4. Write the formula for the area of a circle 5. Write the formula for the circumference of a circle 6. Write the formula for the volume of a rectangular prism See agenda

2. New unit on Polynomials & Exponents SWBAT… 1. Identify the difference between monomials, binomials and trinomials. 2. Apply and explain the rules of exponents (7rules) 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.

3. 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

4. Polynomials A polynomial is a monomial or the sum or difference of monomials Some polynomials have special names:  A monomial has one term  A binomial is the sum or difference of two monomials  A trinomial is the sum or difference of three monomials

5. ExpressionIs it a polynomial? Explain Monomial, binomial, or trinomial? 4y – 5xz -6.5 6x 3 + 4x + x + 3 3ab 5 Fill out the chart above!

6. ExpressionIs it a polynomial? Explain Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5 6x 3 + 4x + x + 3 3ab 5

7. ExpressionIs it a polynomial? Explain Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3 3ab 5

8. ExpressionIs it a polynomial? Explain Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3 3ab 5

9. ExpressionIs it a polynomial? Explain Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3 Yes; 6x 3 + 4x + x + 3 = 6x 3 + 5x + 3, the sum of three monomials Trinomial 3ab 5

10. ExpressionIs it a polynomial? Explain Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3 Yes; 6x 3 + 4x + x + 3 = 6x 3 + 5x + 3, the sum of three monomials Trinomial 3ab 5 Yes; one term with the product of a coefficient and variables. Monomial

11. Exponent Review Ms. Sophia Papaefthimiou Infinity HS

12. Definition of an exponent An exponent tells how many times a number is multiplied by itself. 3 4 = (3)(3)(3)(3) = 81 3 4 Base Exponent

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

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

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

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

17. A = π(8cm) 2 A = 64π cm 2

18. Exponents are often used in volume problems to show the units are cubed Volume = (length)(width)(height) Volume = (20cm)(10cm)(10cm) = 2,000 cm 3 10 20

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

20. What is the answer? 5 3 = 125

21. What is the base and the exponent? (7)(7)(7)(7)(7) =7 5

22. What is the base and the exponent? (x)(x)(x)(x)(x)(x) =x 6

23. What the base and the exponent? (a)(a)(a)(b)(b)(c) = a 3 b 2 c

24. What the base and the exponent? aaabbc = a 3 b 2 c

25. What the base and the exponent? (4)(x)(x)(y) = 4 x 2 y

26. What the base and the exponent? (4xxyyyy)(8xxy) = 32 x 4 y 5

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

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

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

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

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

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

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

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

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

36. Compute: 2 0 Answer: 1 Yes, it’s 1; explanation will follow

37. WHY is anything to the power zero "1" 3 6 = 729 3 5 = 243 3 4 = 81 3 3 = 27 3 2 = 9 3 1 = 3 3 0 = 1

38. Laws of Exponents

39. 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!

40. Let’s practice Simplify each expression: 1. (-4) 0 2. -4 0 (Recall PEMDAS - Exponents first!) 3. (5x) 0 5x 0 4. -(-4.9) 0 (Recall PEMDAS – Exponents first!) 5. [(3x 4 y 7 z 12 ) 5 (–5x 9 y 3 z 4 ) 2 ] 0

41. 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.

42. Examples

44. SWBAT… compute problems involving zero & negative exponents Fri, 4/27 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. 5x 0 3. 4. HW: Quiz corrections

45. Examples (cont’d)

46. SWBAT… simplify problems using the first 5 exponent laws Wed, 5/2 Agenda 1. WU (5 min) 2. Review HW#1 (15 min) and Review HW#2 (20 min) 3. Exit slip (5 min ) Warm-Up: Simplify: