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PRE-ALGEBRA & MathLine

Pre-Algebra. PRE-ALGEBRA & MathLine. Pre-Algebra. Pre-algebra is intimidating! Equality Principle Balancing an Equation Definition of a Variable, etc. Pre-Algebra. MathLine makes Algebraic concepts EASY TO UNDERSTAND!. Pre-Algebra. MathLine makes Algebraic concepts

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PRE-ALGEBRA & MathLine

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  1. Pre-Algebra PRE-ALGEBRA & MathLine

  2. Pre-Algebra • Pre-algebra is intimidating! • Equality Principle • Balancing an Equation • Definition of a Variable, etc.

  3. Pre-Algebra MathLine makes Algebraic concepts EASY TO UNDERSTAND!

  4. Pre-Algebra MathLine makes Algebraic concepts EASY TO UNDERSTAND! By introducing abstract ideas with simple language

  5. Pre-Algebra Take for example X + 4 = 9

  6. Pre-Algebra Students can solve by the “add up” approach

  7. Pre-Algebra For X + 4 = 9, we know we are adding 4, so put 4 on MathLine

  8. Pre-Algebra Then add up till we get to sum

  9. Pre-Algebra 1

  10. Pre-Algebra 2

  11. Pre-Algebra 3

  12. Pre-Algebra 4

  13. Pre-Algebra 5

  14. Pre-Algebra So we add 5 to the 4 and get… 9

  15. Pre-Algebra If X + 4 = 9 Then X = 5 4 5

  16. Pre-Algebra The “add up” approach is correct, but ideally we want students solving for X.

  17. Pre-Algebra So ask the student, what do we know in this sentence: X + 4 = ? 9 We know our sum is9 So put 9 on MathLine

  18. Pre-Algebra Next ask, “If we added 4 to get 9, can we subtract 4 from 9?”

  19. Pre-Algebra So if we added 4 to get 9 Can we subtract 4?

  20. Pre-Algebra So subtract 4 from 9 …

  21. Pre-Algebra To get X by itself X = 5

  22. Pre-Algebra On paper the Algebra looks like this…

  23. Pre-Algebra To get X by itself subtract 4 from both sides of the equation. X + 4 = 9 – 4 –4 This is exercising the Equality Principle

  24. Pre-Algebra What is done to one side of the equation… must be done to the other side to keep it equal.

  25. Pre-Algebra 4’s cancel out X + 4 = 9 – 4 –4

  26. Pre-Algebra 4’s cancel out and 9 – 4 equals 5 X = 9 –4

  27. Pre-Algebra 4’s cancel out and 9 – 4 equals 5 X = 5

  28. Pre-Algebra Another example 2X + 5 = 17

  29. Pre-Algebra So ask the student, what do we know in this sentence: 2X + 5 = ? 17 So put 17 on MathLine We know our sum is17

  30. Pre-Algebra Next ask, “If we added 5 to get 17, can we subtract 5 from 17?”

  31. Pre-Algebra So if we added 5 to get 17 Can we subtract 5?

  32. Pre-Algebra So subtract 5 from 17…

  33. Pre-Algebra To get 2X by itself 2X = 17 - 5

  34. Pre-Algebra We now know… 2X = 12

  35. Pre-Algebra For 2 X = 12 Ask – What number times 2 equals 12?

  36. Pre-Algebra There are two ways of finding X for 2X = 12 On MathLine

  37. Pre-Algebra Divide by 12 by two’s.. 2 1 6 5 4 3

  38. Pre-Algebra Or divide 12 into two GROUPS… 6 6

  39. Pre-Algebra Either way X = 6 6 6

  40. Pre-Algebra On paper the Algebra looks like this…

  41. Pre-Algebra To get X by itself subtract 5 from both sides of the equation. 2X + 5 = 17 – 5 –5 This is exercising the Equality Principle

  42. Pre-Algebra What is done to one side of the equation… must be done to the other side to keep it equal.

  43. Pre-Algebra 5’s cancel out 2X + 5 = 17 – 5 –5

  44. Pre-Algebra 5’s cancel out and 17 – 5 equals 12 2X = 17 –5

  45. Pre-Algebra 5’s cancel out and 17 – 5 equals 12 2X = 12

  46. Pre-Algebra 2X = 12 So divide by 2 on each side 2 X12 2 2 = Or 2 X ÷ 2 = 12÷ 2

  47. Pre-Algebra So, X = 12÷ 2 Or X = 6

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