Ms Math Summit Day 2 V4


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  • Speed Math inequalities: Inequality Game:
  • Refer to File Transfer for Scantron Score information
  • or the ‘unknown’ was originally referred to as ‘thing’ or ‘object’ of couple of derivatives of translation you end with a shortened version ‘x’. Also noted that the Greek word ‘xenos’ is the word for unknown or stranger also shortened to x.
  • Checkor X if you would like me to work through or skip the next three slides. You can use these slides as a starting point for your direct instruction and family support.
  • One variable (kind) = one dimension
  • Open or ClosedLeft or Right
  • Point out inequalities have more than one solution Call out open dot on graph
  • You can review this slide on your own time, however it explains the math behind ‘Flipping the Sign’
  • Error Analysis
  • Solve or write the inequality
  • Ms Math Summit Day 2 V4

    1. 1. MS Math SummitDecember 2009<br />
    2. 2. Math Challenge<br />
    3. 3. Scantron Reflection<br />On the whiteboard: share your thoughts about taking the Scantron Performance Series Math assessment<br />
    4. 4. Personal Needs Reflection <br />Did you come to any conclusion about your own personal development needs in Mathematics?<br />List your thoughts in the chat window. <br />
    5. 5. Scantron Data<br />
    6. 6. Math is a Journey<br /><ul><li>Build your Toolbox
    7. 7. Connect what you like
    8. 8. Connect what you know
    9. 9. Embrace how you learn
    10. 10. Practice
    11. 11. Share</li></li></ul><li>Rules of the Road<br /><ul><li>Stay on the Road </li></ul> (don’t create your own path or make up math as you go) <br /><ul><li>Obey the Law (don’t break any math rules)
    12. 12. Arrive on Time (leave early if you take the long way)
    13. 13. Travel Comfortable</li></ul> (use the tools you’re comfortable and confident)<br /><ul><li>Check Your Location</li></ul> (check your work – is your answer reasonable and accurate? Did you answer the question?) <br />
    14. 14. Building Your Toolbox<br /><ul><li>Your math toolbox includes the tools, resources, formulas, rules, strategies and tricks, you learn and collect, during your journey. </li></ul>Patterns<br />Tables<br />Vocabulary<br />Projects<br />Symbols<br />Stories<br />Letters<br />Puzzles<br />Graphs<br />Formulas<br />
    15. 15. Lesson Objective<br />Solve and Graph single variable equations and inequalities<br />Toolbox Vocabulary: Toolbox Rules:<br />Equation/Inequality Addition Property of Equality<br />Equivalent Equations Multiplication Property of Equality<br />Transformations Reciprocal<br />Simplify Product Rules<br />Replacement Set<br />Reverse or ‘flip’ inequality signs<br />Open Dot or Closed Dot<br />
    16. 16. Getting Started<br />Why X?<br />
    17. 17. Solving Equations – the same but different<br />Which tool do you grab from your toolbox?<br /><ul><li>Do you guess and check?
    18. 18. Do you use Transformations of Addition and Subtraction to isolate the fraction?
    19. 19. Do you convert your fraction to a decimal?
    20. 20. Do you use Transformations of Multiplication and Division to remove the fraction?
    21. 21. Do you graph or use a table of values?</li></ul>From this:<br />To this:<br />
    22. 22. Solving Equations – Mel’s Route<br />Steps:<br /><ul><li>Given
    23. 23. Transformation by Multiplication
    24. 24. Simplify
    25. 25. Transformation by Subtraction
    26. 26. Simplify
    27. 27. Transformation by Multiplication
    28. 28. Solution</li></ul>Is the equation true when <br />x = – 14?<br />
    29. 29. Solving Equations – Mel’s Route Graphed<br />Only one solution satisfies this equation. <br />Is the equation true when <br />x = – 14?<br />
    30. 30. Solving Equations – Checking Mel’s Route<br />Is the equation true when x = – 14?<br />Steps:<br /><ul><li>Given
    31. 31. Substitute (replace) x with – 14
    32. 32. Divide with Product Rule
    33. 33. Simplify with Product Rule
    34. 34. Simplify by addition
    35. 35. Solution</li></ul>Is the equation true when x = –14? YES  <br />
    36. 36. No Really! Inequalities - the same but different <br />From this:<br />What is the same?<br />What is different?<br />How will the solution change?<br />What might trip us up?<br />To this:<br />
    37. 37. Solving Inequalities – Mel’s Route <br />Steps:<br /><ul><li>Given
    38. 38. Transformation by Multiplication
    39. 39. Simplify
    40. 40. Transformation by Subtraction
    41. 41. Simplify
    42. 42. Transformation by Multiplication – flip the sign
    43. 43. Solution</li></ul>Is the inequality true when <br />x &lt; – 14?<br />
    44. 44. Solving Inequalities – Mel’s Route Graphed<br />Is the inequality true when <br />x &lt; –14? Are their one, none or many solutions? Is –14 included in the solution?<br />
    45. 45. Solving Inequalities – Checking Mel’s Route <br />We already know –14 is not included, so now choose an easy number left of –14 and substitute (replace) and solve.<br />By selecting –20 and solving, we learn numbers left or smaller than –14 are true solutions of this inequality. <br />Many solutions satisfy this inequality. Values less than but NOT including -14 are all solutions.<br />
    46. 46. Why Flip the Sign?<br />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:<br />This shows when an inequality is multiplied by –1, the inequality is reversed. <br />Therefore: <br /> is the same as: <br />
    47. 47. Breakout Rooms<br />
    48. 48. Now What’s Wrong?<br />Look at the problems below. Indicate if the problem is algebraically correct, explain your answer.<br />Look at the problems below. Select points on number line to check the solution and accuracy of the graph. Explain your findings.<br />
    49. 49. Inequalities – Your Route <br />
    50. 50. Let’s Play<br />Solutions<br />Why did the surfer dude cross the ocean?<br />
    51. 51. Teacher Toolbox<br /><ul><li>OLS Curriculum: Pre-Algebra A </li></ul> U2 L2: Writing Inequalities<br /> U2 L3 & L4: Writing Inequalities Part 1 & 2<br /> U2 L6 & L7: Solving Other Equalities and Inequalities<br /><ul><li>OLS Curriculum: Pre-Algebra B </li></ul> U1 L4: Inequalities<br /> U1 L9: Equalities & Inequalities for Word Sentences<br /> U5 L8: Equivalent Inequalities<br /> U5 L9 & L10: Solving Inequalities by Several Transformations Part 1 & 2<br /> OLS Curriculum: Algebra I: Unit 14: Inequalities<br /><ul><li>Mathematics Structure and Methods Course 2 Chapter 5
    52. 52. Speed Math inequalities:
    53. 53. Inequality Game:
    54. 54. Why is a negative times a negative a positive?
    55. 55. Why x?</li></li></ul><li>Quiz and Session Survey<br />Quick Inequality Quiz:<br /><br />Session Survey:<br /><br />Pick up File Transfer Documents<br />Scantron Survey:<br /><br />Scantron Performance Series FAQ’s:<br /><br />
    56. 56. Any Questions?<br />