1. MS Math SummitDecember 2009

2. Math Challenge

3. Scantron Reflection On the whiteboard: share your thoughts about taking the Scantron Performance Series Math assessment

4. Personal Needs Reflection Did you come to any conclusion about your own personal development needs in Mathematics? List your thoughts in the chat window.

5. Scantron Data

7. Connect what you like

8. Connect what you know

9. Embrace how you learn

10. Practice

12. Arrive on Time (leave early if you take the long way)

15. Lesson Objective Solve and Graph single variable equations and inequalities Toolbox Vocabulary: Toolbox Rules: Equation/Inequality Addition Property of Equality Equivalent Equations Multiplication Property of Equality Transformations Reciprocal Simplify Product Rules Replacement Set Reverse or ‘flip’ inequality signs Open Dot or Closed Dot

16. Getting Started Why X?

18. Do you use Transformations of Addition and Subtraction to isolate the fraction?

19. Do you convert your fraction to a decimal?

20. Do you use Transformations of Multiplication and Division to remove the fraction?

21. Do you graph or use a table of values?From this: To this:

23. Transformation by Multiplication

24. Simplify

25. Transformation by Subtraction

26. Simplify

27. Transformation by Multiplication

28. SolutionIs the equation true when x = – 14?

29. Solving Equations – Mel’s Route Graphed Only one solution satisfies this equation. Is the equation true when x = – 14?

31. Substitute (replace) x with – 14

32. Divide with Product Rule

33. Simplify with Product Rule

34. Simplify by addition

35. SolutionIs the equation true when x = –14? YES 

36. No Really! Inequalities - the same but different From this: What is the same? What is different? How will the solution change? What might trip us up? To this:

38. Transformation by Multiplication

39. Simplify

40. Transformation by Subtraction

41. Simplify

42. Transformation by Multiplication – flip the sign

43. SolutionIs the inequality true when x < – 14?

44. Solving Inequalities – Mel’s Route Graphed Is the inequality true when x < –14? Are their one, none or many solutions? Is –14 included in the solution?

45. Solving Inequalities – Checking Mel’s Route We already know –14 is not included, so now choose an easy number left of –14 and substitute (replace) and solve. By selecting –20 and solving, we learn numbers left or smaller than –14 are true solutions of this inequality. Many solutions satisfy this inequality. Values less than but NOT including -14 are all solutions.

46. Why Flip the Sign? This example requires Transformation of Multiplication and Division. When working with inequalities, and using this transformation we’re instructed to ‘Flip the Sign’. Here’s the math behind the request: This shows when an inequality is multiplied by –1, the inequality is reversed. Therefore: is the same as:

47. Breakout Rooms

48. Now What’s Wrong? Look at the problems below. Indicate if the problem is algebraically correct, explain your answer. Look at the problems below. Select points on number line to check the solution and accuracy of the graph. Explain your findings.

49. Inequalities – Your Route

50. Let’s Play Solutions Why did the surfer dude cross the ocean?

52. Speed Math inequalities: http://education.jlab.org/sminequality/index.html

53. Inequality Game: http://www.math-play.com/Inequality-Game.html

54. Why is a negative times a negative a positive?

56. Any Questions?