1. SAMPLEKM & PP 1 MENU- click a link AIM Algebra In Motion Fall 2008 On the MENU below please find links to three of the Power Point presentations we have created as part of our AIM Project. Thanks for looking! Kathy Monaghan & Pat Peterson

2. SAMPLEKM & PP 2 Thanks for Looking!

3. SAMPLEKM & PP 3 Getting Started with Algebra What isAlgebra? is a branch of mathematics in which symbols, usually letters, are used to represent quantities that can be replaced by a number or an expression. Algebra

4. SAMPLEKM & PP 4 Getting Started with Algebra Who inventedAlgebra? is a reasoning skill and language that developed and evolved along with civilization. No one person invented Algebra

5. SAMPLEKM & PP 5 Getting Started with Algebra Where did the word Algebra originate ? The word is from Kitab al-Jabr wa-l-Muqabala which was a book written in approximately 820 A.D. by a Persian mathematician. Algebra

6. SAMPLEKM & PP 6 Variables A is variable a letter used to represent various numbers. “x” is frequently used as the variable, but many other letters can be used.

7. SAMPLEKM & PP 7 Variables For example, jean sizes are often given by waist and leg inseam measurements. waist measurement leg inseam measurement

8. SAMPLEKM & PP 8 Define each Variable We must always define what quantity or measurement the letter represents. Here are three examples: = waist measurement = leg inseam measurement = unknown number

9. SAMPLEKM & PP 9 Constants A isconstant a letter used to represent a number that doesn’t change its value in the problem. For example: = the speed of light in Einstein’s equation E = mc 2 = “pi” = 3.1416….

10. SAMPLEKM & PP 10 Algebraic Expressions Analgebraic expression is a mathematical phrase using variables, constants, numerals, & operation signs. An algebraic expression will NOT have any of the following symbols: = > <

11. SAMPLEKM & PP 11 Algebraic Expressions: Examples x is the variable. + is the operation 5 is a numeral and a constant. algebraic expression is the

12. SAMPLEKM & PP 12 Algebraic Expressions: Examples p is the variable.. is the indicated operation 3 is a numeral and a constant. algebraic expression is the

13. SAMPLEKM & PP 13 Algebraic Expressions: Examples z is the variable. - is the operation 9 is a numeral and a constant. algebraic expression is the

14. SAMPLEKM & PP 14 Algebraic Expressions: Examples y is the variable. ÷ is the operation 5 is a numeral and a constant. algebraic expression is the

15. SAMPLEKM & PP 15 Algebraic Expressions: Examples x and y are variables.  and + are operations 2 and 5 are numerals and constants. algebraic expressionis the

16. SAMPLEKM & PP 16 Algebraic Expressions: Examples x and y are variables. + ÷  are operations 5 and 2 are numerals and constants. algebraic expression is the

17. SAMPLEKM & PP 17 Substitution When a variable is replaced with a numerical value, that is called substitution. Sometimes, in higher mathematics, a variable is replaced with an expression. That is also called substitution.

18. SAMPLEKM & PP 18 Evaluate an Algebraic Expression When a numerical value is substituted into an algebraic expression and then simplified, that is called evaluating the expression. Evaluating means you will compute a numerical value.

19. SAMPLEKM & PP 19 Evaluate an Expression: Example 1a Evaluate when

20. SAMPLEKM & PP 20 Evaluate an Expression: Example 1b Evaluate when

21. SAMPLEKM & PP 21 Evaluate an Expression: Example 1c Evaluate when

22. SAMPLEKM & PP 22 Evaluate an Expression: Example 1d Evaluate when

23. SAMPLEKM & PP 23 Evaluate an Expression: Example 2 Evaluate a) when b) when

24. SAMPLEKM & PP 24 Evaluate an Expression: Example 3 when Evaluate

25. SAMPLEKM & PP 25 Evaluate an Expression: Example 4a when Evaluate

26. SAMPLEKM & PP 26 Evaluate an Expression: Example 4b when Evaluate

27. SAMPLEKM & PP 27 Evaluate an Expression: Example 5 When and Evaluate

28. SAMPLEKM & PP 28 Evaluate an Expression: Example 6a Evaluate When and

29. SAMPLEKM & PP 29 Evaluate an Expression: Example 6b Evaluate When and

30. SAMPLEKM & PP 30 Evaluate an Expression: Example 6c Evaluate When and

31. SAMPLEKM & PP 31 Evaluate an Expression: Example 6d Evaluate When and

32. SAMPLEKM & PP 32 Application: Area of a Rectangle The AREA of a Rectangle Area = length x width A=l. w

33. SAMPLEKM & PP 33 Translating: English into Algebra In order to solve problems, English phrases must be translated into the language of algebra. The following slides list keywords which can help us translate.

34. SAMPLEKM & PP 34 English & Algebra ADDITION The following words translate as ADDITION: Plus Sum Add Added to Total More than Increased by

35. SAMPLEKM & PP 35 X + 7 The following phrases would translate to : A number plus seven The sum of a number and seven Add a number and seven Seven added to a number The total of seven and a number Seven more than a number A number increased by seven

36. SAMPLEKM & PP 36 English & Algebra SUBTRACTION The following words translate as SUBTRACTION: Minus Difference Subtract Subtracted From Take away Less Than Decreased by

37. SAMPLEKM & PP 37 X - 7 The following phrases would translate to : A number minus seven The difference of a number and seven Subtract a number and seven Seven subtracted from a number Seven take away a number Seven less than a number A number decreased by seven

38. SAMPLEKM & PP 38 English & Algebra MULTIPLICATION The following words translate as MULTIPLICATION: Multiplied by Multiply Product Times Of

39. SAMPLEKM & PP 39 7x The following phrases would translate to : A number multiplied by seven Multiply seven and a number The product of a number and seven The product of seven and a number Seven times a number

40. SAMPLEKM & PP 40 English & Algebra DIVISION The following words translate as DIVISION: Divided by Divide Quotient

41. SAMPLEKM & PP 41 x/7 The following phrases would translate to : A number divided by seven Divide a number by seven The quotient of a number and seven

42. SAMPLEKM & PP 42 7/x The following phrases would translate to : Seven divided by a number Divide a seven by a number The quotient of seven and a number

43. SAMPLEKM & PP 43 “OF” “Half of a number” would be or

44. SAMPLEKM & PP 44 “OF” “Thirty percent of a number” is: or

45. SAMPLEKM & PP 45 “Twice” or “Double” “Twice a number” is: “Double a number” is:

46. SAMPLEKM & PP 46 Translate a Phrase “Seven more than twice a number” Seven more thantwice a number

47. SAMPLEKM & PP 47 Translate a Phrase “Seven less than twice a number” Seven less thantwice a number

48. SAMPLEKM & PP 48 Translate a Phrase (watch for the comma) “the quotient of seven and a number increased by two” “the quotient of seven and a number, increased by two”

49. SAMPLEKM & PP 49 Salary Increase? Suppose you will get a salary increase of 3%. Let s represent your old salary. The increase is 3% of your current salary, so 0.03s is the increase. Your new salary will be the sum of the old salary and the increase. So, s + 0.03s is your new salary.

50. SAMPLEKM & PP 50 Discount? Suppose the bookstore has all merchandise on sale for 15% off. Let p represent the regular price. The discount is 15% of the regular price, so 0.15p is the discount. The sale price will be the difference of the regular price and the discount So, p - 0.15p is the sale price.

51. SAMPLEKM & PP 51 That’s All for Now!

52. SAMPLEKM & PP 52 Slope

53. SAMPLEKM & PP 53 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The denominator can’t be zero.

54. SAMPLEKM & PP 54 A Slope Triangle P 1 (x 1, y 1 ) RUN x 2 - x 1 RISE y 2 - y 1 P 2 (x 2, y 2 ) RISE y 2 - y 1 x 2 - x 1 RUN

55. SAMPLEKM & PP 55 m

56. SAMPLEKM & PP 56 Compute the Slope (-2, -3) (4, -1) GOING UPWARDS

57. SAMPLEKM & PP 57 Another Slope (-4, -3) (0, 5)

58. SAMPLEKM & PP 58 Compute this Slope (-5, 2) (4, -1) GOING DOWNWARD

59. SAMPLEKM & PP 59 Compute the Slope (-5, -1) (4, -1) HORIZONTAL

60. SAMPLEKM & PP 60 Compute the Slope (-4, -5) (-4, 0) VERTICAL

61. SAMPLEKM & PP 61 SLOPE BASICS  POSITIVE SLOPE  The line rises from left to right.  ZERO SLOPE  The line is HORIZONTAL  NEGATIVE SLOPE  The line falls from left to right.  UNDEFINED SLOPE  The line is VERTICAL.

62. SAMPLEKM & PP 62 That’s All for Now!

63. SAMPLEKM & PP 63 Systems of Equations

64. SAMPLEKM & PP 64 Systems of Equations In order to solve a system of equations by graphing: Graph each of the lines using the best method. Plot Points Plot x and y-intercepts Use Point Slope The point(s) where the lines intersect are in the solution set.

65. SAMPLEKM & PP 65 Where will they meet?

66. SAMPLEKM & PP 66 How about this pair?

67. SAMPLEKM & PP 67 What if?

68. SAMPLEKM & PP 68 How about these lines?

69. SAMPLEKM & PP 69 That’s All for Now!