Junior Additional Basic Qualifications

1
ITS NOT MAGIC...
ITS MATH

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

2
ITS 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

• PAINT MY HOW MUCH
• HOUSE PAINT?
• 34
• 36

34
7 9
7 9
9
CHARACTERISTICS OF A GOOD (RICH) LESSON(see
Flewelling (2002). Realizing a Vision of
Tomorrows 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/AFlewelling70-7
  2

10
SUBTRACTION
11
NIFTY 9s

• 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
MAGIC FINGERS

• 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 10s column
• Count all fingers touching and below.
• 5 tens
• For the 1s 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 7S

• 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
ITS NOT MAGIC...
IT'S GEOMETRY
32
WALKING THROUGH PAPER

• http//www.themathlab.com/geometry/section10/paper
  hole.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
ITS 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
ITS NOT MAGIC...
PATTERNING
45
Cee Cee, MY PLAYMATE

• Cee Cee, MY PLAY MATE,
• COME OUT AND PLAY WITH ME
• AND BRING YOUR DOLLYS THREE,
• CLIMB UP MY APPLE TREE.
• SLIDE DOWN MY RAINBOW
• INTO MY CELLAR DOOR
• AND WELL 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