Transcript Best Practices in Mathematics Teaching

Mental Arithmetic
Teaching Facts
Meaning
Relationships
Drill
A Few Questions
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What is the highest mountain in North America?
Answer: Mt. McKinley
What is the Capital of Argentina?
Answer: Buenos Aires.
What is the largest body of water in Africa?
Answer: Lake Victoria
Who won the Superbowl in 2000?
Answer: St. Louis Rams
Name one of the two vice presidents under Abraham Lincoln.
Answer: Hannibal Hamlin, Andrew Johnson
Who was assassinated in Sarajevo in 1914 which precipitated WWI?
Answer: Archduke Francis of Austria
How many facts must we
memorize?
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1
2 3
4
5
6
7
8
9 10
0
0
1
2
3
4
5
6
7
8
9 10
1
1
2
3
4
5
7
8
2
2 3
4
5
6
3
3
4
5
6
7
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4
5
6
7
8
5
5
6
7
8
9
6
6
7
8
9 10
7
9 10 11
`
8 9 10 11 12 13 14 15 16 17 18
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9 10 11 12 13 14 15 16 17 18 19
8
9
7
8
9 10 11
`
7 8 9 10 11 12
` 13
8 9 10 11 12
` 13 14
9 10 11 12
` 13 14
10 11 12
15
` 13 14
11 12
15 16
` 13
14 15 16 17
12
6
10 10 11 12 13 14 15 16 17 18 19 20
Now it is your turn
Basic Facts of base 5.
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0
1
2
3
4
10
0
1
2
3
4
10
Doubles and one more than doubles.
+
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0
1
2
3
4
5
6
7
8
9 10
1
2
3
4
5
6
7
8
9 10
7
8
3
4
5
5
6
9 10 11
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7 8 9 10 11 12
` 13
8 9 10 11 12
` 13 14
9 10 11 12
` 13 14
11 12
15
11 ` 13 14 15 16
` 13
12
15 16 17
6
1
1
2
2
3
3
3
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5
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5
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7
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8
9 10
7
9 10 11
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17 18
8 9 10 11 12 13 14 15
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19
9 10 11 12 13 14 15 16 17
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7
9
10 10 11 12 13 14 15 16 17 18 19
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0
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9 10
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9 10
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5
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8
6
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7
8
9 10
7
9 10 11 12
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8 9 10 11 12 13 14
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9 10 11 12 13 14 15 16
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9
7
6
9 10 11
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7 8 9 10 11 12
` 13
8 9 10 11 12
` 13 14
10 11 12
6
`
12 13 14 15
14 15 16
8
10 10 11 12 13 14 15 16 17 18
16 17
18
4+4
15+15
2+3
4+3
15+14
2+1
4+5
15+16
2+2
Encouraging the associate property a +(a+1) =(a+a)+1
2 3
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9 10
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9 10
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9 10 11
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6 7 8 9 10 11 12
` 13
8 9 10 11 12
Slide 7
` 13 14
10 11 12
5
`
12 13 14 15
6
14 15 16
7
16 17
8
18
2
3
9
10
5+4
7+6
10 + 7
56 + 43
4+5
6+7
7 + 10
43 + 56
Commutative Property for addition
A+B=B+A
2 3
4
5
6
7
8
9 10
0
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4
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6
7
8
9
1
4
5
6
7
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9 10
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7
8
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2
0
1
5
9 10 11
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8 9 10 11 12
` 13
10 11 12
` 13 14
12
6
14 15
7
16
3
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8
9
10
Place Value Relationship
10 + 1
10 + 2
10 + 3
-1
+10
10 + 5
+9
-1
+10
2 3
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8
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9 10
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9 10 11
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10 11 12
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` 13
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9 10
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9 10
Other Patterns
3+4
4+3
7-4
7-3
7 +3
7+4
7+2
10 + 3
11 + 3
15 + 3
Important Ideas in development
of Addition Subtraction
• Counting - Forward/Back
• Skip Counting 2,3 5’s
• Skip Counting from a number.
How many facts must we
memorize?
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1x3
1x9
34 x 1
1x 1,000,000
0x0
0 x 153,000
34 x 97 x 1543 x 0
Is There a Connection?
2+2+2
2x3
3+3+3+3
3x4
5+5+5+5
5x4
Is there a Pattern?
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3x2
6x2
3x7
6x7
3x9
6x9
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2x3
4x3
8x3
2x7
4x7
8x7
Ready for the Answer?
Meaning
Number Sense
Drill
Why only ten’s
• 5 x 10 = 50
• 5 x 3 = 15
• 5 x 13 =
• 4 x 10 =
• 4x4=
• 4 x 14 =
• 7 x 10 = 70
• 7 x 3 = 21
• 7 x 13 =
• 9 x 100 =
• 9x1=
• 9 x 99 =
What is this Child Doing?
QuickTime™ and a
Cinepak decompressor
are needed to see this picture.
Meanings of Multiplication
• Repeated Addition
• Array
• Matching
Repeated Addition
What is this?
QuickTime™ and a
Cinepak decompressor
are needed to see this picture.
Array
Matching
3 Shirts 4 Pants. How many outfits?
S3
S2
S1
P1
P2
P3
P4
Alternative Algorithms
Addition
Long form- Emphasizes Place
Value.
235
+ 89
14
110
200
324
2*100 +3*10 +5*1
+ 8*10 + 9*1
What is this?
QuickTime™ and a
Cinepak decompressor
are needed to see this picture.
Subtraction
235
-197
-2
-60
100
38
Equal Addends
5321
-68 9
Multiplication Long Form
34
x5
20 = 5 x 4
150 = 5 x 30
???? Why
5 x 34
Lattice 235 x 95
2
3
5
x
9
5
Meanings of Division
• Repeated Subtraction
• Distribute into Groups
• Inverse of Multiplication
Which One is this?
QuickTime™ and a
Cinepak decompressor
are needed to see this picture.
Inverse of Multiplication
x7
What’s the blue?
Distributive
Distributive
Distributive
Distributive
Distributive
12
3
=4
17 7
7
1245
-7
54
-49
55
-49
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177 R6
7
177
7
70
100
1245
-700
545
-490
55
-49
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