junior additional basic qualifications may, 2005 mike mccabe nipissing university
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Junior Additional Basic QualificationsMay, 2005
Mike McCabeNipissing University
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
Sides Area(s2)
5 25
15 225
25 625
35 1225
45 2025
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 =
22 22
33
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
PAINT MY HOW MUCH HOUSE PAINT?
34
36
34
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
SUBTRACTION
STANDARD ADD TO EACH AUSTRIAN
357
- 263
357
- 263
357
- 263
When we have to trade, simply add to each number
Ex) 3(15)7
- 3 6 3
Left to Right
357- 263
1
3
4
56
7 89
10
2
3 x 9 =
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
6
7
8
9
10 10
9
8
7
6
MULTIPLYING FINGERS
8 7
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 manipulatenumbers so the calculations are easier(more familiar).
Double/Half: 27 X 43 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
x 30 6
40 1200 240
2 60 12
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
A. 3 x 2 = 6 keep the 3
B. (3 + 2) x 7 = 35
C. 7 x 7 + 3 = 52
D. 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 = 0.1428572/7 = 0.2857143/7 = 0.428571
Based upon the pattern above, determine:4/7 =5/7 =6/7 =
MULTIPLYING FRACTIONSUSING PAPER
½ x ¼ =
FOLD THE PAPER HORIZINTALLY INTOFOURTHS.
NOW, FOLD THE PAPER VERTICALLY INTOHALVES.
SHADE ON SECTION
TRY 2/3 X 3/4 =
WALKING THROUGH PAPER
http://www.themathlab.com/geometry/section10/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 BOBSQUARE PANTS?
SPONGE BOBRECTANGULAR 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
Cee Cee, MY PLAYMATE
Cee Cee, MY PLAY MATE,COME OUT AND PLAY WITH MEAND BRING YOUR DOLLY’S THREE,CLIMB UP MY APPLE TREE.SLIDE DOWN MY RAINBOWINTO MY CELLAR DOORAND WE’LL BE JOLLY FRIENDSFOR EVERMORE, MORE, MORE, MORE, MOREMORE!
The Clapping
• Self clap• Right hands clap• Self clap• Left hands clap• Self clap (x2)• Back clap• Front clap
• repeat