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Singapore MathDeveloping conceptual understanding of mathematics
Bill JacksonScarsdale Public Schools
Not to be copied or used without the express consent of the author.
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Addition with regrouping (grade 1)
9 + 3 = 10 + 2
Composing a higher value unit is the basis for regrouping in addition.
Take 1 from the 3 and add it to 9 to make 10.
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Addend decomposition method (grade 1)
Add 9 + 4 by making 10 first.
9 + 4 7 + 81 3
9 + 1 = 10
10 + 3 = 13
Students learn to manipulate numbers to their advantage, internalize mathematical properties, and go beyond counting.
5 2
2 + 8 = 10
10 + 5 = 15
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Subtraction with regrouping (grade 1)
12 - 4 = 6 + 2
Decomposing a higher value unit is the basis for subtraction with regrouping.
Decompose the 12 into 10 and 2, subtract 4 from the 10 and then add the 2.
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Minuend decomposition method (grade 1)
12 - 410 2
10 - 4 = 6
6 + 2 = 8
When subtracting with regrouping, think of the complement of the subtrahend (to make 10) and then add the ones from the minuend.
15 - 6 4 + 5 = 9
13 - 8 2 + 3 = 5
11 - 3 7 + 1 = 8
minuend subtrahend
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Addition with renaming36 + 28
Add the ones.
6 ones + 8 ones = 14 ones
14 ones = 1 ten and 4 ones
Add the tens.
1 tens + 3 tens + 2 tens = 6 tens
1
36
+ 28
4
10 10
1 1 1 1
1 1 1 1
110 10
1
11 1
1
10 10
1
36
+ 28
64
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Subtraction with renaming62 - 43
Subtract the ones.
12 ones - 3 ones = 9 ones
Subtract the tens.
5 tens - 4 tens = 1 ten
110 10 110
10 10
10
1 1 1 1 1
1 1 1 1 1
62
- 43
9
5 12
62
- 43
19
5 12
6 tens 2 ones = 5 tens 12 ones
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Multiplication facts
Important mathematical properties and algebraic manipulation are taught informally.
6 x 5
6 x 16 x 2
6 x 6 = 30 + 6
5 1
6 x 7 = 30 + 12
5 2
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Multiplication algorithm
10 10 10 10 1 1
42 x 3
402 x 3 Multiply the
ones by 3.
4 2
x 3
61 1
1 1
Multiply the tens by 3.
4 2
x 3
1 2 6
10 10 10 10
10 10 10 10
100
= 40 x 3 + 2 x 3
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Division algorithmPartitive (equal share) division
73 ÷ 2Divide the tens by 2.
1 1110 10 10
101010
10
3 6 R 1
2) 7 3
6
1 3
1 2
1
1 1 1 1 1
1 1 1 1 1
10 10 10 10 10 10
1 1 1
1 1 1
1 1 1
1 1 1
Divide the ones by 2.
= 70 ÷ 2 + 3 ÷ 2
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Methods for mental addition Make a 10.
176 + 8 = 180 + 4
4 4
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Methods for mental addition Use addition facts and rename.
176 + 8 = 170 + 14
170 6
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Methods for mental addition Add the tens then the ones.
53 + 34 = 53 + 30 + 4
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Methods for mental addition Make 100 (numbers close to 100)
457 + 98 = 455 + 100
455 2
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Methods for mental addition Add 100 and subtract the difference.
457 + 98 = 457 + 100 - 2
100 - 2
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Methods for mental subtraction Subtract the same place values (no
renaming)
155 - 40 = 110 + 5
5 150
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Methods for mental subtraction Subtract from a 10 (renaming)
176 - 8 = 162 + 6
6 170
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Methods for mental subtraction Rename a 10 as ones and recall the fact (renaming).
176 - 8 = 160 + 8
160 16
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Multiplication table of 33 X 1 = 3
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Multiplication table of 33 X 1 = 33 X 2 = 6
+ 3
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Multiplication table of 33 X 1 = 33 X 2 = 63 X 3 = 9
+ 3
+ 3
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Multiplication table of 33 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 12
X 2
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Multiplication table of 33 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 15
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Multiplication table of 33 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 153 X 6 = 183 X 7 = ?3 X 8 = ?3 X 9 = ?3 X 10 = ?
X 2
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Multiplication table of 33 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 153 X 6 = ?3 X 7 = ?3 X 8 = ?3 X 9 = ?3 X 10 = ?
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Multiplication table of 3 is easy!3 X 1 = 3
3 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 153 X 6 = ?3 X 7 = 213 X 8 = ?3 X 9 = ?3 X 10 = ?
3 X 2 + 3 X 5
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Multiplication table of 6 is easy!3 X 1 = 3
3 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 153 X 6 = 183 X 7 = 213 X 8 = 243 X 9 = 273 X 10 = 30
6 X 4 = 12 + 12
6 X 7 = 21+ 21
6 X 8 = 24+ 24