2. Algebra 1 Unit 1 Expressions and Introduction to Polynomials Resources: VDOE & Henrico County Schools -Algebra 1 Modules

3. SOL A.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. Representing and Evaluating Expressions 2

4. 7 + 4 3. Is your answer 33 or 19? You can get 2 different answers depending on which operation you did first. We want everyone to get the same answer so we must follow the order of operations.

5. 20 - 3 6 + 10 2 + (6 + 1) 4

6. Remember the phrase “Please Excuse My Dear Aunt Sally” or PEMDAS. ORDER OF OPERATIONS 1. Parentheses - ( ) or [ ] 2. Exponents or Powers 3. Multiply and Divide (from left to right) 4. Add and Subtract (from left to right)

7. Example 1 20 - 3 6 + 10 2 + (6 + 1) 4 = 20 - 3 6 + 10 2 + (7) 4(parentheses) = 20 - 3 6 + 100 + (7) 4(exponents) = 20 - 18 + 100 + (7) 4 (Multiply l/r.) = 20 - 18 + 100 + 28 (Multiply l/r.) = 2 + 100 + 28 (Subtract l/r.) = 102 + 28 (Add l/r.) = 130(Add.)

8. What is the area of a rectangle? Length times Width If the length is 3 meters and the width is 2 meters, what is the area? A = L x W A = 3 x 2 = 6 meters 2 A, L and W are the variables. It is any letter that represents an unknown number.

9. An algebraic expression contains: 1) one or more numbers or variables, and 2) one or more arithmetic operations. Examples: x - 3 3 2n

10. In expressions, there are many different ways to write multiplication. 1)ab 2)a b 3)a(b) or (a)b 4)(a)(b) 5)a x b We are not going to use the multiplication symbol any more. Why?

11. Division, on the other hand, is written as: 1) 2) x ÷ 3

12. Throughout this year, you will hear many words that mean addition, subtraction, multiplication, and division. Complete the table with as many as you know.

13. Here are some phrases you may have listed. Addition Subtraction MultiplicationDivisionExponents sumdifference productquotientpower of ___ increase decreasetimesdivided squared plus minusmultiplied ratiocubed add subtract more than less than total

14. Writing Algebraic Expressions Steps for Writing Algebraic Expressions: 1.Read for understanding 2.Define the variable 3.Translate the words into numbers/variables/operations 4.Write as an expression

15. Define a variable and write an algebraic expression for each phrase. two timesa number plus 5 This can be whatever you want it to be Let x = “a number” two timesa number plus 5

16. 7 less than three times a number 7 less than3 timesa number Let x = “a number” 7 less than3 timesa number

17. The absolute value of the sum of a number and 5 the absolute value ofthe sum ofa number and 5 Let x = “a number” the absolute value ofthe sum ofa number and 5

18. The quotient of a number cubed and 12. quotient ofa numbercubed and 12 Let x = “a number” quotient ofa numbercubed and 12

19. The square root of the product of 6 and a number squared. square root of the product of 6 and a number squared Let x = “a number” square root of the product of 6 and a number squared

20. Students need additional practice translating expressions. Select each phrase that verbally translates this algebraic expression: Suggested Practice for SOL A.1 One fourth times the cube root of x less five. One fourth times the cube root of x less than five. Five subtract one fourth times the cube root of x. Five less than one fourth times the cube root of x. 3

21. Write an algebraic expression for 1) m increased by 5. m + 5 2) 7 times the product of x and t. 7xt or 7(x)(t) or 7 x t

22. 3) 11 less than 4 times a number. 4n - 11 4) two more than 6 times a number. 6n + 2 5) the quotient of a number and 12.

23. Which of the following expressions represents 7 times a number decreased by 13? 1.7x + 13 2.7x - 13 3.13 - 7x 4.13 + 7x Answer Now

24. Which one of the following expressions represents 28 less than three times a number? 1.28 - 3x 2.3x - 28 3.28 + 3x 4.3x + 28 Answer Now

25. Write a verbal expression for: 1) 8 + a. The ratio of m to r Do you have a different way of writing these? The sum of 8 and a 2)

26. Which of the following verbal expressions represents 2x + 9? 1.twice a number plus nine 2.a number increased by nine 3.twice a number decreased by 9 4.9 less than twice a number Answer Now

27. Which of the following expressions represents the sum of 16 and five times a number? 1.5x - 16 2.16x + 5 3.16 + 5x 4.16 - 5x Answer Now

28. Which of the following expressions represents the sum of 16 and five times a number? 1.5x - 16 2.16x + 5 3.16 + 5x 4.16 - 5x Answer Now

29. Write an verbal expression for each algebraic expression

31. When looking at the expression 10 3, 10 is called the base and 3 is called the exponent or power. 10 3 means 10 10 10 10 3 = 1000

32. Which of the following verbal expressions represents x 2 + 2x? 1.the sum of a number squared and twice a number 2.the sum of a number and twice the number 3.twice a number less than the number squared 4.the sum of a number and twice the number squared Answer Now

33. Which of the following expressions represents four less than the cube of a number? 1.4 – x 3 2.4 – 3x 3.3x – 4 4.x 3 – 4 Answer Now

34. Evaluate. 2 1 22 2 2 = 4 2323 2 2 2 = 8 2n 7 We can’t evaluate because we don’t know what n equals to!!

35. Is 3 5 the same as 5 3 ? Evaluate each and find out! 3 5 = 3 3 3 3 3 = 243 5 3 = 5 5 5 = 125 243 ≠ 125 They are not the same!

36. What is the value of if n = -8, m = 4, and t = 2 ? 1.10 2.-10 3.-6 4.6 Answer Now

37. Students need additional practice evaluating expressions that contain an absolute value. Evaluate the following expressions: a. b. Suggested Practice for SOL A.1 5

38. Students need additional practice evaluating expressions with cube roots, square roots, and the square of a number, particularly when the replacement variable has a negative value. Evaluate the following expressions: a. b. c. Suggested Practice for SOL A.1 4

39. Students need additional practice translating expressions with square and cube roots. Translate into an algebraic expression: a)The quotient of the square root of x and five b)The cube root of the product of x and y, less twelve c)The sum of the square root of sixteen and the product of four and the cube root of eight Translate into a verbal expression: d) e) Five times the cube root of the product of 4 and x less the square root of y A number y plus the cube root of a number x 38

40. Objectives The student will be able to: 1. add and subtract polynomials. SOL: A.2b Designed by Skip Tyler, Varina High School

41. 1. Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a) Group your like terms. 9y - 3y - 7x + 8x + 15a - 8a 6y + x + 7a

42. 2. Add the following polynomials : (3a 2 + 3ab - b 2 ) + (4ab + 6b 2 ) Combine your like terms. 3a 2 + 3ab + 4ab - b 2 + 6b 2 3a 2 + 7ab + 5b 2

43. 3. Add the polynomials. + 1.x 2 + 3x + 7y + xy + 8 2.x 2 + 4y + 2x + 3 3.3x + 7y + 8 4.x 2 + 11xy + 8 X2X2 11 X X XY Y Y Y Y 111 X Y Y Y 1 11

44. 4. Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a) Rewrite subtraction as adding the opposite. (9y - 7x + 15a) + (+ 3y - 8x + 8a) Group the like terms. 9y + 3y - 7x - 8x + 15a + 8a 12y - 15x + 23a

45. 5. Subtract the following polynomials: (7a - 10b) - (3a + 4b) Rewrite subtraction as adding the opposite. (7a - 10b) + (- 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b

46. 6. Subtract the following polynomials using column form: (4x 2 - 2xy + 3y 2 ) - (-3x 2 - xy + 2y 2 ) Line up your like terms and add the opposite. 4x 2 - 2xy + 3y 2 + (+ 3x 2 + xy - 2y 2 ) -------------------------------------- 7x 2 - xy + y 2

47. Find the sum or difference. (5a – 3b) + (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 3b

48. Find the sum or difference. (5a – 3b) – (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 9b