goals for the session learn how the philosophical shift in the way we teach math affects the way we...
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Goals for the session
• Learn how the philosophical shift in the way we teach math affects the way we teach basic facts
• Learn some effective strategies for teaching basic facts to students
Alberta Program of Studies2007
By decreasing emphasis on rote calculation, drill and practice, and the size of numbers
used in paper and pencil calculations, more time is available for concept development.
Philosophical shift
• Focus on number sense
• Focus on mental math and estimation
What do you think?
Are basic facts important?
Should we be having our students memorize them?
• committing isolated facts to memory one after another
• drill and practice
• relies on thinking, using relationships among the facts
• focusing on relationships
The Nature of MathematicsNumber Sense
Why is this a topic of interest?
• The pendulum goes back and forth• The discussion about memorizing versus
fluency
What are the basic facts?
The Alberta Program of Studies defines them as:
• Addition and Subtraction to 18• Multiplication and Division to 81
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The Power of Thinking Strategies
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Count On
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Count On
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Count On
Doubles
Near Doubles
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Count On
Doubles
Near Doubles
Names of 10
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Count On
Doubles
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Names of 10
Names of 5
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Doubles
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Names of 10
Nine strategies
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Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10
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7 7+1
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Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10
Skip count by 2
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1 1+1
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1+8
1+9
2 2+1
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2+5
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2+7
2+8
2+9
3 3+1
3+2
3+3
3+4
3+5
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3+7
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4 4+1
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4+5
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4+9
5 5+1
5+2
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5+5
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5+8
5+9
6 6+1
6+2
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7 7+1
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8 8+1
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9 9+1
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Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10
Skip count by 2
Number in Middle
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1 1+1
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2 2+1
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2+5
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2+7
2+8
2+9
3 3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4 4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5 5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6 6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7 7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8 8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9 9+1
9+2
9+3
9+4
9+5
9+6
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Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10
Skip count by 2
Number in Middle
Commutativity
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1 1+1
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1+9
2 2+1
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3 3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4 4+1
4+2
4+3
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4+5
4+6
4+7
4+8
4+9
5 5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6 6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7 7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8 8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9 9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10
Skip count by 2
Number in Middle
Commutativity
Your thoughts….
Multiplication
• Talk about ‘groups of ‘• Talk about ‘families’• Give strategies for when we don’t know what
to do • There is NOT an endless supply of basic facts
What do we already know?
Start in grade 3Learn up to 5 x 5
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0
1 0
2 0
3 0
4 0
5 0
6
7
8
9
10
• Zero groups of
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0
1 0 1 2 3 4 5
2 0 2
3 0 3
4 0 4
5 0 5
6
7
8
9
10
• Zero groups of• 1 group of
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0
1 0 1 2 3 4 5
2 0 2 10
3 0 3 15
4 0 4 20
50 5
10
15 20 25
6
7
8
9
10
• Zero groups of• 1 group of• Counting by 5’s
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0
1 0 1 2 3 4 5
2 0 2 4 6 8 10
3 0 3 6 15
4 0 4 8 20
50 5
10
15 20 25
6
7
8
9
10
• Zero groups of• 1 group of• Counting by
5’s• Counting by
2’s
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0
1 0 1 2 3 4 5
2 0 2 4 6 8 10
3 0 3 6 9 15
4 0 4 8 16 20
50 5
10
15 20 25
6
7
8
9
10
• Zero groups of
• 1 group of• Counting by
5’s• Counting by
2’s• Doubles
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0
1 0 1 2 3 4 5
2 0 2 4 6 8 10
3 0 3 6 9 12 15
40 4 8
12 16 20
50 5
10
15 20 25
6
7
8
9
10
• Zero groups of• 1 group of• Counting by
5’s• Counting by
2’s• Doubles• Families
Important to remember
Teach through families2 x 3 = 6 3 x 2 = 66 ÷ 3 = 2 6 ÷ 2 = 3
Work the teaching of division right into the teaching of the multiplication….
Other strategies up to this point?
So that is it for Grade 3
Let’s move on to grade 4……
Expand what they already know
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5
2 0 2 4 6 8 10
3 0 3 6 9 12 15
40 4 8
12 16 20
50 5
10
15 20 25
6 0
7 0
8 0
9 0
10 0
• Zero groups of
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
10 1 2 3 4 5 6 7 8 9
10
2 0 2 4 6 8 10
3 0 3 6 9 12 15
40 4 8
12 16 20
50 5
10
15 20 25
6 0 6
7 0 7
8 0 8
9 0 9
10 0
10
• Zero groups of• 1 group of
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10
3 0 3 6 9 12 15
40 4 8
12 16 20
50 5
10
15 20 25 30 35 40 45 50
6 0 6 30
7 0 7 35
8 0 8 40
9 0 9 45
10 0
10 50
• Zero groups of• 1 group of• Counting by
5’s
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15
40 4 8
12 16 20
50 5
10
15 20 25 30 35 40 45 50
60 6
12 30
70 7
14 35
80 8
16 40
90 9
18 45
10 0
10
20 50
• Zero groups of• 1 group of• Counting by
5’s• Counting by
2’s
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 30
4 0 4 8 12 16 20 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 30 60
7 0 7 14 35 70
8 0 8 16 40 80
9 0 9 18 45 90
10 0
10 20 30 40 50 60 70 80 90
100
• Zero groups of
• 1 group of• Counting by
5’s• Counting by
2’s• 10’s
A side note about tens
• 10 X 6• 100 X 7• 1000 X 8
• 10 x 5• 30 x 5• 40 x 7
Working with 9’s
What do you know?
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 27 30
4 0 4 8 12 16 20 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 30 54 60
7 0 7 14 35 63 70
8 0 8 16 40 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0
10 20 30 40 50 60 70 80 90
100
• Zero groups of
• 1 group of• Counting by
5’s• Counting by
2’s• 10’s• 9’s
09182736455463728190
The fours…• Relate the 4’s to the 2’s…
• 2x1• 2x2 4x1• 2x3• 2x4 4x2 – families here• 2x5• 2x6 4x3• 2x7• 2x8 4x4• 2x9• 2x10 4x5
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 24 30 54 60
7 0 7 14 28 35 63 70
8 0 8 16 32 40 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0
10 20 30 40 50 60 70 80 90
100
• Zero groups of
• 1 group of• Counting by
5’s• Counting by
2’s• 10’s• 9’s• 4’s
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 24 30 54 60
7 0 7 14 28 35 63 70
8 0 8 16 32 40 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0
10 20 30 40 50 60 70 80 90
100
• Zero groups of• 1 group of• Counting by
5’s• Counting by
2’s• 10’s• 9’s• 4’s
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 24 30 36 54 60
7 0 7 14 28 35 49 63 70
8 0 8 16 32 40 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0
10 20 30 40 50 60 70 80 90
100
• Zero groups of
• 1 group of• Counting by
5’s• Counting by
2’s• 10’s• 9’s• 4’s• Doubles
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0
10 20 30 40 50 60 70 80 90
100
• Zero groups of
• 1 group of• Counting by
5’s• Counting by
2’s• 10’s • 9’s• 4’s• Doubles• Families
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0
10 20 30 40 50 60 70 80 90
100
• Zero groups of
• 1 group of• Counting by
5’s• Counting by
2’s• 10’s • 9’s• 4’s• Doubles• Families
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