mental arithmetic teaching facts meaning relationships drill
Post on 15-Jan-2016
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Mental ArithmeticTeaching Facts
Meaning
Relationships
Drill
A Few Questions
• 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?
+ 2 10987654310
2
10
9
8
7
6
5
4
3
1
0 2 10987654310
2 109876543 11`
1
2 109876 11`
12543
10
9
8
7
6
5
4
3
10
9
8
7
6
5
4
11
10
9
8
7
6
5 1310987 11`
12
14
17
16
15
19
18
11
2012
6
1310987 11`
12
14131098 11`
12
151413109 11`
12
1615141310 11`
12
171615141311`
12
18171615141312
19181716151413
Now it is your turn
Basic Facts of base 5.
+ 2 4310
2
4
3
1
0
10
10
Doubles and one more than doubles.
+ 2 10987654310
2
10
9
8
7
6
5
4
3
1
0 2 1098765431
109876543 11`
1
2 109876 11`
1253
10
9
8
7
6
5
4
3
10
9
8
7
6
5
4
11
10
9
8
7
6
5 1310987 11`
12
14
17
16
15
19
18
11
12
131097 11`
12
141398 11`
12
151413109 11`
16151310 11`
12
1715141311`
12
171615141312
19181716151413
`
+ 2 10987654310
2
10
9
8
7
6
5
4
3
1
0 2 109876543
10987654 11`2 109876 11
`12
10
9
8
7
6
5
4
3
10
9
8
7
6
5
4
11
10
9
8
7
6
131098 11`
12
14
17
16
15
18
11
12
1310 11`
12
14138 12
1514109
1610 11`
12
141311`
12
1615141312
181716151413
`
2+2
2+3
2+1
4+4
4+3
4+5
15+15
15+14
15+16
Encouraging the associate property a +(a+1) =(a+a)+1
Slide 7
+ 2 10987654310
2
10
9
8
7
6
5
4
3
1
0 109876543
10987654 11`109876 11
`12
131098 11`
12
14
17
16
15
18
1310 11`
12
141312
1514
16
5 + 4
4+5
7 + 6
6 + 7
10 + 7
7 + 10
56 + 43
43 + 56
Commutative Property for additionA + B = B + A
+ 2 10987654310
2
10
9
8
7
6
5
4
3
1
0 9876543
10987654
109876 11`1098 11
`12
1310 11`
12
141312
1514
16
Place Value Relationship
+10
+10
-1
-1
+9
10 + 1
10 + 2
10 + 3
10 + 5
+ 2 10987654310
2
10
9
8
7
6
5
4
3
1
0 876543
987654
109876
1098 11`10 11
`12
1312
14
+ 2 10987654310
2
10
9
8
7
6
5
4
3
1
0
Other Patterns
3 + 44 + 37 - 47 - 3
7 +37+47+2
10 + 311 + 315 + 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?
• 1x3• 1x9• 34 x 1• 1x 1,000,000• 0 x 0• 0 x 153,000• 34 x 97 x 1543 x 0
Is There a Connection?
2 + 2 + 2
2 x 3
3 + 3 + 3 + 3
3 x 4
5 + 5 + 5 + 5
5 x 4
Is there a Pattern?
• 3 x 2 • 6 x 2 • 3 x 7• 6 x 7 • 3 x 9• 6 x 9
• 2 x 3• 4 x 3• 8 x 3• 2 x 7• 4 x 7• 8 x 7
Ready for the Answer?
Meaning
Number Sense
Drill
Why only ten’s
• 5 x 10 = 50• 5 x 3 = 15• 5 x 13 =
• 7 x 10 = 70• 7 x 3 = 21• 7 x 13 =
• 4 x 10 =• 4 x 4 = • 4 x 14 =
• 9 x 100 = • 9 x 1 =• 9 x 99 =
What is this Child Doing?
QuickTime™ and aCinepak decompressor
are needed to see this picture.
Meanings of Multiplication
• Repeated Addition
• Array
• Matching
Repeated Addition
What is this?
QuickTime™ and aCinepak decompressor
are needed to see this picture.
Array
Matching
3 Shirts 4 Pants. How many outfits?
S2
S3
S1
P2 P3 P4P1
Alternative Algorithms
Addition
Long form- Emphasizes Place Value.
235+ 89 14110200324
2*100 +3*10 +5*1+ 8*10 + 9*1
What is this?
QuickTime™ and aCinepak decompressor
are needed to see this picture.
Subtraction
235-197 -2 -60 100 38
Equal Addends
5 3 2 1- 6 8 9
Multiplication Long Form
34x5
20 = 5 x 4150 = 5 x 30
5 x 34???? Why
Lattice 235 x 952 3 5
x
9
5
Meanings of Division
• Repeated Subtraction
• Distribute into Groups
• Inverse of Multiplication
Which One is this?
QuickTime™ and aCinepak decompressor
are needed to see this picture.
Inverse of Multiplication
x7
What’s the blue?
Distributive
Distributive
Distributive
Distributive
Distributive
12
€
÷3 = 4
7 1245
1
-754
7
-4955
-49
7
6
7 1245
100
-700545
-49055
-496
707
177
177 R6