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Junior Additional Basic Qualifications May, 2005 Mike McCabe Nipissing University

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## Junior Additional Basic Qualifications May, 2005 Mike McCabe Nipissing University

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**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 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**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 =**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**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**34**34 PAINT MY HOW MUCH HOUSE PAINT? 34 36 7 9 7 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**NIFTY 9’s**• THE MATH WIZARD: http://www.cyberglass.net/**2**1 4 7 8 9 3 10 6 5 3 x 9 =**2**7**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.**MULTIPLYING FINGERS**10 10 9 9 8 8 7 7 6 6**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**STRATEGIES FOR MULTIPLICATION**COMPLETE NUMBER STRATEGIES PARTITIONING STRATEGIES COMPENSATION STRATEGIES USING MULTIPLES OF 10 AND 100 TWO DIGIT MULTIPLIERS (The area model) MATRIX MODEL**COMPLETE NUMBER STRATEGIES**Repeated addition: 73 X 4 = 73 + 73 73 146 73 146 + 73 73 219 73 146 292 + 73 292**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**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**MATRIX MODEL**36 X 42 1200 240 + 60 12 1512**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**Try**• 4251432 x 11**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**TRY ONE:**86 x 83 =**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**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 =**7 UP?**http://digicc.com/fido/**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 =**IT’S NOT MAGIC...**IT'S GEOMETRY**WALKING THROUGH PAPER**http://www.themathlab.com/geometry/section10/paperhole.gif**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**IT’S NOT MAGIC...**IT'S DATA MANAGEMENT**MY BATH**Write a story about my bath.**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**THE PEARL KEEPER**http://www.ebaumsworld.com/pearl.shtml**IT’S NOT MAGIC...**PATTERNING**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!**The Clapping**• Self clap • Right hands clap • Self clap • Left hands clap • Self clap (x2) • Back clap • Front clap • repeat