1. PRE-ALGEBRA&MathLine Pre-Algebra

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

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

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

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

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

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

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

9. 1

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12. 4

13. 5

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

15. If X + 4 = 9 Then X = 5 45

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

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

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

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

20. So subtract 4 from 9 … Pre-Algebra

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

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

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

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

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

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

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

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

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

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

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

32. So subtract 5 from 17… Pre-Algebra

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

34. We now know… Pre-Algebra 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.. 12 3456

38. Pre-Algebra Or divide 12 into two GROUPS… 66

39. Pre-Algebra Either way X = 6 66

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

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

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

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

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

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

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

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