Transcript Computation grades k-6 - Pembina Trails School Division

COMPUTATION
STRATEGIES
Presentation for Parents March 2013
Flexible Thinking
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There are many ways to solve problems.
The more ways we solve a problem, the deeper our
understanding of the mathematics.
When we ask "How would you do that?" or "Can you
show me another way?" we are helping children
understand math better.
Encourage children to use what they know to solve
problems.
Traditional algorithms involving lining up columns rely
heavily on memorizing procedures and can work
against developing number sense.
85% of all calculations we do involve mental math.
Addition and Subtraction Facts
Grades 1, 2 and 3
Students will learn mental mathematics strategies to
determine basic addition and related subtraction
facts to 18.
Doubles
3+3=6
One More
One Less
3+1=4
3-1=2
Making
10
8+5=
8+2+3=
10+3=
Friendly
Numbers
7+3=
6 +4=
5+5=
Commutative
Property
(Flip)
3+9=
9+3=
Think
Addition for
subtraction
15-6=
6+?=15
Counting
back
7-2=
Think 7
6, 5
Number
families
3+4=7
7+3=7
7-4=3
7-3=4
Counting
on
7+2=
Think 7
8, 9
Zero
Property
7-0=7
5+0=5
Doubles
1+1=2
2+2=4
3+3=6
4+4=8
5+5=10
6+6=12
7+7=14
8+8=16
9+9=18
DOUBLES +1
DOUBLES -1
THINK
SO….
5+6=
5+5 = 10
5+6 = 11
FOR
THINK
SO….
4+5=
5+5 = 10
4+5 = 9
FOR
Commutative Property
(Flip)
FOR
THINK
SO….
3+9=
9+3 = 12
3+9 = 12
Friendly Number 10
1+9
2+8
3+7
4+6
9+1
8+2
7+3
6+4
5+5
Make 10
When 1 of the numbers you are adding is
7,8 or 9
Go to 10
And add the rest
For
Think
So…
8+5
8+2+3
10 + 3 = 13
8+5 = 13
Counting on
For 6+2 =
Start at the largest number and count forwards:
6…7,8
So 6+2 = 8
______________________
6
7
8
Counting Back
For 6-2 =
Start at the largest number and count backwards:
6…5,4
So 6-2 = 4
___________
4
5
6
Think Addition for Subtraction
For 12- 5=
Think 5 + __ = 12
So 12 – 5 = 7
______________________
5
10
12
Zero Property
Any number + 0 or -0
Remains the same
5+0=5
9-0=9
Number Families
If I know that
3+4=7
I also know that
4+3=7
7-4=3
7-3=4
0,1,2/Doubles/ Near Doubles/Make 10
0
1
2
3
4
5
6
7
8
9
0
0
1
2
3
4
5
6
7
8
9
1
1
2
3
4
5
6
7
8
9
10
2
2
3
4
5
6
7
8
9
10
11
3
3
4
5
6
7
8
9
10
11
12
4
4
5
6
7
8
9
10
11
12
13
5
5
6
7
8
9
10
11
12
13
14
6
6
7
8
9
10
11
12
13
14
15
7
7
8
9
10
11
12
13
14
15
16
8
8
9
10
11
12
13
14
15
16
17
9
9
10
11
12
13
14
15
16
17
18
+
Computation Strategies for Addition
and Subtraction of Large Numbers
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Students will use personal strategies to add
and subtract numbers in problem solving situations.
Blank Number Lines
24+8=
+4
+4
__________________
24
28
32
Place Value
(decomposing numbers)
24+15=
20+10=30
4+5=9
30+9=39
Think Addition for Subtraction
52-23=
23+?=52
+20
+7
+2
_____________________
23
43
50
52
Place Value
(Left to Right)
425
+368
700
80
13
795
Place Value
Decomposing Numbers
334 + 419 =
(300 + 400) + (30 + 10) + (4 + 9)
700
+
40
+
13
753
Place Value
Place Value Left to Right
334
+ 419
Add the 100s
700
Add the 10s
40
Add the 1s
+ 13
753
Blank Number Line
Number Line
334 + 419 =
+300
419
+30
719
+1
+3
749 750
753
Think Addition for Subtraction
828 - 729 =
70+28+1=99
+1
+70
729 730 800
+28
828
Multiplication and Divison Facts
Grades 3-6
Students will demonstrate and apply different mental
mathematical strategies to develop recall of basic
multiplication facts to 9 x 9 and related division
facts.
Use a fact you
know:
I know 5x8=40
so…
5x9=45
Distributive
Property
7x6=
(5x6) + (2x6)
Think Multiplication for
Division:
20÷5=
Think how many groups of
5 are in 20?
Or
5x?=20
Doubling/
Halving
6x4=
Visualize
Arrays
3x2=
6÷3=2
think
12x2=
Fact
families
3x4=12
4x3=12
12÷4=3
12÷3=4
Commutative
Property
3x9=
9x3=
Doubling and Halving
Doubling and Halving
*halve one number and double
the other number
15 x 4 =
30 x 2=
So 30 x 2 = 60
Skip Counting from a Known Number
Skip Counting from a Known Number
6X7=
I know that 5 X 7 = 35
So…6 X 7 = 35 + 7 = 42
Distributive Property
6X7
(6 X 5 =)+(6 X 2 =)
30 + 12
42
Commutative Property
6 X 7=
7x6=
Arrays
3x2=
2x3=
6÷3=2
6÷2=3
Fact Families
6 X 7=42
7x6=42
42÷6=7
42÷7=6
Think Multiplication for Division
20÷5=
Think how many groups of
5 are in 20?
Or 5x?=20
Computation Strategies for
Multiplication
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Students will demonstrate an understanding of
multiplication by using different strategies to
determine answers.
Distributive Property:
4 x 86 =
(4 x 80) + (4 x 6)
320 + 24=344
Repeated Addition
25x4=
25+25+25+25=
Traditional Algorithm
(Left to Right)
26
X8
160
+ 12
172
62x21=1302
x
20
1
60
1200
60
2
40
2
Repeated Addition
15 x 6 =
Add 15 six times
15 + 15 + 15 + 15 + 15 + 15 =
30 +
30 +
90
30
Place Value
(Distributive Property)
15 x 6
(10 x 6) + (5 x 6)
60
+
30 =
x
10
5
6
60
30
90
Place Value
(Left to Right)
Place Value Left to Right
15
x
6
60
+30
90
Computation Strategies for Division
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Students will demonstrate an understanding of
division by using different strategies to determine
answers.
Fair Sharing
92 ÷4 =
92
20 20 20 20
3 3
3 3
Algorithm
Division
Place Value
4
136
-120
16
-16
0
30
+ 4
34
For More information
Pembina Trails School Division
http://www.pembinatrails.ca/program/earlyyears/Li
nk%205/Numeracy.html
Manitoba Education and Literacy
http://www.edu.gov.mb.ca/k12/parents/index.html
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