Transcript Math Is Magic

Junior Additional Basic Qualifications
May, 2005
Mike McCabe
Nipissing University
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
Sides
Area(s2)
5
25
1x2
15
225
2x3
25
S
625
3x4
35
1225
4x5
45
2025
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…?
5x5=
2
2
9x9=
2
2
7x3=
7 x 11 =
6x6=
try one…
3
3
3x9=
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
PAINT MY
HOUSE
HOW MUCH
PAINT?
34
34
7
34
7
9
9
36
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
SUBTRACTION
STANDARD
ADD TO EACH
AUSTRIAN
357
- 263
357
- 263
357
- 263
When we have Left to Right
to trade, simply
357
add to each
- 263
number
Ex) 3(15)7
- 3 6 3
NIFTY 9’s
• THE MATH WIZARD:
http://www.cyberglass.net/
1
2
4
7
8
9
3
10
6
5
3x9=
2
7
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.
MULTIPLYING FINGERS
10
10
9
9
8 8
7
6
7
6
MULTIPLYING FINGERS
8
7
7X8
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
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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
+ 73
146
+ 73
219
+ 73
292
73 X 4 =
73
73
73
73
146
146
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:
3 X 18
(3 X 2) X (18 / 2)
6 X 9
27 X 4
30 X 4 = 120
- 3 X 4 = 12
108
MATRIX MODEL
36 X 42
1200
240
+
60
12
1512
x
40
2
30
6
1200 240
60
12
Any number x 11
• 435216 x 11
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•
•
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•
•
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
A.
B.
C.
D.
3x2=6
(3 + 2) x 7 = 35
7 x 7 + 3 = 52
Answer = 5256
keep the 3
TRY ONE:
86 x 83 =
PATTERNING WITH DIVISION
(THE USE OF A CALCULATOR. HMMMMMM)
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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
½x¼=
FOLD THE PAPER HORIZINTALLY INTO
FOURTHS.
NOW, FOLD THE PAPER VERTICALLY INTO
HALVES.
SHADE ON SECTION
TRY 2/3 X 3/4 =
WALKING THROUGH PAPER
http://www.themathlab.com/geometry/section
10/paperhole.gif
TEMPLATE
LOOPS
MOBIUS STRIPS
TESSELLATIONS
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
SPONGE BOB
SQUARE PANTS?
SPONGE BOB
RECTANGULAR PRISM PANTS
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
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
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•
Self clap
Right hands clap
Self clap
Left hands clap
Self clap (x2)
Back clap
Front clap
• repeat