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Junior Additional Basic Qualifications May, 2005 Mike McCabe Nipissing University

IT’S NOT MAGIC. IT’S MATH. Junior Additional Basic Qualifications May, 2005 Mike McCabe Nipissing University. IT’S NOT MAGIC. IT'S NUMERATION. THE MATH WIZARD. http://www.cyberglass.net/. PERFECT SQUARES. Area of a square = side x side (or s 2 )

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Junior Additional Basic Qualifications May, 2005 Mike McCabe Nipissing University

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  1. IT’S NOT MAGIC... IT’S MATH Junior Additional Basic Qualifications May, 2005 Mike McCabe Nipissing University

  2. IT’S NOT MAGIC... IT'S NUMERATION

  3. THE MATH WIZARD http://www.cyberglass.net/

  4. PERFECT SQUARES • Area of a square = side x side (or s2) • What if the sides end in a 5 (i.e., 15, 25, 35) S S 1 x 2 2 x 3 3 x 4 4 x 5

  5. SIMPLE MULTIPLICATION • 4 x 4 = 16 -1 3 x 5 = 15 • 8 x 8 = 64 -1 7 x 9 = 63 • TRY ONE • 11 x 13 = 19 x 21 =

  6. WHAT IF…? 5 x 5 = 9 x 9 = 7 x 3 = 7 x 11 = 6 x 6 = try one… 3 x 9 = 2 2 2 2 3 3

  7. What if you own a lawn care company and a rectangular field, 54m X 56m, has to be mowed? You charge by the size of the lot (area). What is the area? 56m 54m

  8. 34 34 PAINT MY HOW MUCH HOUSE PAINT? 34 36 7 9 7 9

  9. CHARACTERISTICS OF A GOOD (RICH) LESSON:(see: Flewelling (2002). Realizing a Vision of Tomorrow’s Classroom, Rich Tasks) • Curriculum relevance • Student relevance • Authentic content and structure • Flexible- for different levels • Problem solving and question posing • Inquiry/exploration/investigation/experimentation • Communication • Reflect on learning • Creative Go to: http://math.unipa.it/~grim/AFlewelling70-72

  10. SUBTRACTION

  11. NIFTY 9’s • THE MATH WIZARD: http://www.cyberglass.net/

  12. 2 1 4 7 8 9 3 10 6 5 3 x 9 =

  13. 2 7

  14. MAGICFINGERS FOR MULTIPLES OF 6x6 OR GREATER. THUMBS ARE 6, INDEX FINGERS 7… PUT DIGITS TOGETHER FOR QUESTION (i.e. 7 x 8) ADD TOUCHING FINGERS AND LOWER FOR TENS COLUMN MULTIPLY OTHERS FOR ONES COLUMN.

  15. MULTIPLYING FINGERS 10 10 9 9 8 8 7 7 6 6

  16. MULTIPLYING FINGERS 8 7

  17. 7 X 8 For the 10’s column: Count all fingers touching and below. 5 tens For the 1’s column: Multiply the fingers above touching fingers on left hand with fingers above touching fingers on right hand . 2 X 3 = 6 ones = 56

  18. STRATEGIES FOR MULTIPLICATION COMPLETE NUMBER STRATEGIES PARTITIONING STRATEGIES COMPENSATION STRATEGIES USING MULTIPLES OF 10 AND 100 TWO DIGIT MULTIPLIERS (The area model) MATRIX MODEL

  19. COMPLETE NUMBER STRATEGIES Repeated addition: 73 X 4 = 73 + 73 73 146 73 146 + 73 73 219 73 146 292 + 73 292

  20. PARTITIONING STRATEGIES • Breaking numbers up in a variety of ways that reflect an understanding of base 10. 27 X 4 268 X 6 20 X 4 = 80 200 X 6 = 1200 7 X 4 = 28 60 X 6 = 360 108 8 X 6 = 48 1608

  21. COMPENSATION STRATEGIES Looking for strategies to manipulate numbers so the calculations are easier (more familiar). Double/Half: 27 X 4 3 X 18 30 X 4 = 120 (3 X 2) X (18 / 2) - 3 X 4 = 12 6 X 9 108

  22. MATRIX MODEL 36 X 42 1200 240 + 60 12 1512

  23. Any number x 11 • 435216 x 11 • 6 • Add last two digits (6 + 1) = 7 • Add 1 + 2 = 3 • 2 + 5 = 7 • 5 + 3 = 8 • 3 + 4 = 7 • Write down the 4 • Answer = 4 787 376

  24. Try • 4251432 x 11

  25. Multiplying 2 two-digit numbers with the same tens digit • 73 x 72 • 3 x 2 = 6 keep the 3 • (3 + 2) x 7 = 35 • 7 x 7 + 3 = 52 • Answer = 5256

  26. TRY ONE: 86 x 83 =

  27. PATTERNING WITH DIVISION(THE USE OF A CALCULATOR. HMMMMMM) • 1/1 = 1.00 • 1/2 = 0.50 • 1/3 = 0.33 • 1/4 = 0.25 • 1/5 = 0.20 • 1/6 = 0.167 • 1/7 = 0.1428 TRY 2/7 AND 3/7 AND 4/7… • 1/8 = 0.125 • 1/9 = 0.111 TRY 2/9 AND 3/9 AND 4/9… • 1/10= 0.10 • 1/11= 0.0909 TRY 2/11 AND 3/11 AND 4/11 • TRY FOR ALL NUMBERS FROM 12- 19 ON A CHART

  28. MYSTERIOUS 7’S 1/7 = 0.142857 2/7 = 0.285714 3/7 = 0.428571 Based upon the pattern above, determine: 4/7 = 5/7 = 6/7 =

  29. 7 UP? http://digicc.com/fido/

  30. MULTIPLYING FRACTIONS USING PAPER ½ x ¼ = FOLD THE PAPER HORIZINTALLY INTO FOURTHS. NOW, FOLD THE PAPER VERTICALLY INTO HALVES. SHADE ON SECTION TRY 2/3 X 3/4 =

  31. IT’S NOT MAGIC... IT'S GEOMETRY

  32. WALKING THROUGH PAPER http://www.themathlab.com/geometry/section10/paperhole.gif

  33. TEMPLATE

  34. LOOPS

  35. MOBIUS STRIPS

  36. TESSELLATIONS

  37. CUBES There are 11 different ‘nets’ that will fold up into a cube. Using the ‘polydrons’, create as many as you can Copy the ‘net’ for each onto the chart paper

  38. SPONGE BOBSQUARE PANTS?

  39. SPONGE BOBRECTANGULAR PRISM PANTS

  40. IT’S NOT MAGIC... IT'S DATA MANAGEMENT

  41. MY BATH Write a story about my bath.

  42. Weighing Coins You are provided with eight (8) identical looking coins. Seven (7) have the identical mass. The remaining one is lighter. You can use the standard balance scale only twice. How will you determine which coin is the light one? http://matti.usu.edu/nlvm/nav/frames_asid_139_g_3_t_2.html http://matti.usu.edu/nlvm/nav/vlibrary.html

  43. THE PEARL KEEPER http://www.ebaumsworld.com/pearl.shtml

  44. IT’S NOT MAGIC... PATTERNING

  45. Cee Cee, MY PLAYMATE Cee Cee, MY PLAY MATE, COME OUT AND PLAY WITH ME AND BRING YOUR DOLLY’S THREE, CLIMB UP MY APPLE TREE. SLIDE DOWN MY RAINBOW INTO MY CELLAR DOOR AND WE’LL BE JOLLY FRIENDS FOR EVERMORE, MORE, MORE, MORE, MORE MORE!

  46. The Clapping • Self clap • Right hands clap • Self clap • Left hands clap • Self clap (x2) • Back clap • Front clap • repeat

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