addition and subtraction_strategies_11-1.09.09
TRANSCRIPT
Singapore Mathematics
Singapore Mathematics
This program teaches kids to UNDERSTAND mathematical processes through 3 stages:
Concrete Pictorial Abstract
Gemma Meharg PA MAthematics
Concrete Stage of Singapore Mathematics
Students on place mats with disks.
25 + 17 =
Gemma Meharg PA MAthematics
Tens Ones
1 11 1 1
11 11
1
1
1
10 10
10
This presentationis available on theWindsor web site.
Singapore Mathematics
Concrete Pictorial Abstract
Gemma Meharg PA MAthematics
Pictorial Stage of Singapore MathematicsThe student begins the transition to “paper and pencil” with a
technique called branching.
1. 34 + 5
Gemma Meharg PA MAthematics
Separate each numberinto 10s and 1s.
Place 10s outside and1s to the inside.
Branching
1. 34 + 5
4 5
Gemma Meharg PA MAthematics
30 +
“Ring” the 10s.
Branching
1. 34 + 5
4 5
Gemma Meharg PA MAthematics
30
Add the tens.
30 + 0 = 30
+
Branching
1. 34 + 5
4 5
Gemma Meharg PA MAthematics
30
Add the ones.
30 + 0 = 305 + 4 = 9
+
Branching
1. 34 + 5
4 5
Gemma Meharg PA MAthematics
30
Add the sums.
30 + 0 = 305 + 4 = 9
30 + 9 = 39
+
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 = Separate the tens and ones.
Branchtens on the outside
and ones on the inside.
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 =
4 2 3020 +
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 = Ring the tens.
4 2 3020 +
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 =
4 220 30+
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 =Now, add the tens.
4 220 30+
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 =
20 + 30 = 50
4 220 30+
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 =
20 + 30 = 50
4 220 30
Add the ones.
+
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 =
20 + 30 = 504 + 2 = 6
4 220 30+
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 =
20 + 30 = 504 + 2 = 6
4 220 30
Next add the sums.
+
Branching on your own.
Gemma Meharg PA MAthematics
2. 24 + 32 =
20 + 30 = 504 + 2 = 6
50 + 6 = 56
4 220 30+
Branching on your own.
Gemma Meharg PA MAthematics
3. 73 + 16 =
Branching on your own.
Gemma Meharg PA MAthematics
3. 73 + 16 =
70 + 10 = 803 + 6 = 9
80 + 9 = 89
3 670 10+
Branching with subtraction.
Gemma Meharg PA MAthematics
4. 48 - 32 =
Branch out the 10s and 1s.Remember 10s are on the outside.
Ring the 10s.
Branching with subtraction.
Gemma Meharg PA MAthematics
4. 48 - 32 =
8 240 30-
Be sure to place the subtraction sign.
Branching with subtraction.
Gemma Meharg PA MAthematics
4. 48 - 32 =
8 240 30-
Subtract the 10s.
Branching with subtraction.
Gemma Meharg PA MAthematics
4. 48 - 32 =
40 - 30 = 10
8 240 30-
Branching with subtraction.
Gemma Meharg PA MAthematics
4. 48 - 32 =
40 - 30 = 10
8 240 30-
Subtract the 1s.
Branching with subtraction.
Gemma Meharg PA MAthematics
4. 48 - 32 =
40 - 30 = 108 – 2 = 6
8 240 30-
Branching with subtraction.
Gemma Meharg PA MAthematics
4. 48 - 32 =
40 - 30 = 108 – 2 = 6
8 240 30-
ADD the differences.
Branching with subtraction.
Gemma Meharg PA MAthematics
4. 48 - 32 =
40 - 30 = 108 – 2 = 6
10 + 6 = 16
8 240 30-
We add becausewe are putting the
10s and 1s together.
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
Branch the 10s and1s.
10 on the outside.
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
8 070 20-
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
8 070 20-
Ring the 10s.
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
8 070 20-
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
8 070 20-
Subtract the 10s.
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
70 - 20 = 50
8 070 20-
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
70 - 20 = 50
8 070 20-
Subtract the 1s.
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
70 - 20 = 508 – 0 = 8
8 070 20-
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
70 - 20 = 508 – 0 = 8
8 070 20-
Add the differences.
Branching on your own.
Gemma Meharg PA MAthematics
5. 78 - 20 =
70 - 20 = 508 – 0 = 8
50 + 8 = 58
8 070 20-
We add becausewe are putting the
10s and 1s together.
Branching on your own.
Gemma Meharg PA MAthematics
6. 95 - 41 =
Branching on your own.
Gemma Meharg PA MAthematics
6. 95 - 41 =
90 - 40 = 505 – 1 = 4
50 + 4 = 54
5 190 40-
Branching WITH regrouping.
Gemma Meharg PA MAthematics
7. 7 + 9 =
Branching can be used tohelp students learn sums
greater than 10.
Branching WITH regrouping.
Gemma Meharg PA MAthematics
7. 7 + 9 =
Think: What could be addedto 7 to make 10?
Branching WITH regrouping.
Gemma Meharg PA MAthematics
7. 7 + 9 =
3
7 + 3 = 10Branch 3 from 9.
Ring the 10.
Branching WITH regrouping.
Gemma Meharg PA MAthematics
7. 7 + 9 =
3
Branch the other addend from the 2nd addend.
3 + _ = 9
Branching WITH regrouping.
Gemma Meharg PA MAthematics
7. 7 + 9 =
3
Now add.
6
Branching WITH regrouping.
Gemma Meharg PA MAthematics
7. 7 + 9 =
3
10 + 6 = 16
6
Branching on your own.
Gemma Meharg PA MAthematics
8. 4 + 8 =
What can I add to 4 to make 10?
Branching on your own.
Gemma Meharg PA MAthematics
8. 4 + 8 =
Ring the 10.
6
Branching on your own.
Gemma Meharg PA MAthematics
8. 4 + 8 =
6
Branching on your own.
Gemma Meharg PA MAthematics
8. 4 + 8 =
Complete branching of 8.6 + __ = 8
6
Branching on your own.
Gemma Meharg PA MAthematics
8. 4 + 8 =
26
Branching on your own.
Gemma Meharg PA MAthematics
8. 4 + 8 =
Now add.
6 2
Branching on your own.
Gemma Meharg PA MAthematics
8. 4 + 8 =
10 + 2 = 12
6 2
Branching on your own.
Gemma Meharg PA MAthematics
9. 3 + 9 =
Branching on your own.
Gemma Meharg PA MAthematics
9. 3 + 9 =
Remember to make 10. Then ring the 10.
Branching on your own.
Gemma Meharg PA MAthematics
9. 3 + 9 =
7
Now add.
2
Branching on your own.
Gemma Meharg PA MAthematics
9. 3 + 9 =
7 2
10 + 2 = 12
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
Branch 10s to the OUTSIDE.
Branch the addends into 10s and 1s.
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
810 205 +
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
8
Ring the 10s.
10 205 +
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
810 205 +
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
8
Add the 10s.
10 + 20 = 30
10 205 +
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
8
Look at the 1s.5 + 8 is more
than 10.
10 205 +
10 + 20 = 30This strategy
is used when the child does not know
sums over 10.
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
8
We want to make a sum 10.
10 205 +
5 + _ = 1010 + 20 = 30
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
810 205
5
+
10 + 20 = 30
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
8
Branch the 8 into 5 and _?
10 205
5
+
10 + 20 = 30
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
810 205
5
+
310 + 20 = 30
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
8
Ring the sum of 10.
10 205
5
+
3 10 + 20 = 30
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
8
Now add 1s.
10 205
35
+
10 + 20 = 30
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
810 205
35
+
10 + 20 = 30
10 + 3 = 13
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
8
Now add the sums.
10 205
35
+
10 + 20 = 3010 + 3 = 13
Branching WITH regrouping.
Gemma Meharg PA MAthematics
10. 15 + 28 =
810 205
35
+
10 + 20 = 3010 + 3 = 1330 + 13 = 43
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
Branch the10s and 1s.
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
340 409 +
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
340 409 +
Now ring the10s.
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
340 409 +
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
340 409 +
Now add the tens.
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
340 409 +
40 + 40 = 80
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
340 409 +
40 + 40 = 80
Now add the ones.
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
340 409 +
40 + 40 = 809 + 3 = 12
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
340 409 +
40 + 40 = 809 + 3 = 12
Now add the sums.
Branching on your own.
Gemma Meharg PA MAthematics
11. 49 + 43 =
340 409 +
40 + 40 = 809 + 3 = 12
80 + 12 = 92
Branching on your own.
Gemma Meharg PA MAthematics
12. 96 + 17 =
Branching on your own.
Gemma Meharg PA MAthematics
12. 96 + 17 =
790 106 +
90 + 10 = 1006 + 7 = 13
100 + 13 = 113OR
Branching on your own.
Gemma Meharg PA MAthematics
12. 96 + 17 =
790 106 +
90 + 10 = 10010 + 3 = 13
100 + 13 = 113
4 3
Branching WITH regrouping.
Gemma Meharg PA MAthematics
13. 85 - 28 =
Branch into 10s and 1s. Ring
the 10s.
Branching WITH regrouping.
Gemma Meharg PA MAthematics
13. 85 - 28 =
5 880 20-
Remember the subtraction sign.
Branching WITH regrouping.
Gemma Meharg PA MAthematics
13. 85 - 28 =
5 880 20-
Look at the 1s.We can rename.
Branching WITH regrouping.
Gemma Meharg PA MAthematics
13. 85 - 28 =
5 880 20-
Students can use disks to help with renaming.
Branching WITH regrouping.
Gemma Meharg PA MAthematics
85 is renamed as 70 + 15
5 880 20-
70 15
10 110
1010
10
101010
1 11
1
1
1111
11111
Branching WITH regrouping.
Gemma Meharg PA MAthematics
13. 85 - 28 =
5 880 20-
70 15
Subtract the 10s.
70 – 20 = 50
Branching WITH regrouping.
Gemma Meharg PA MAthematics
13. 85 - 28 =
70 – 20 = 5015 – 8 = 7
50 + 7 = 57
5 880 20-
70 15
Subtract the 1s.
Branching WITH regrouping.
Gemma Meharg PA MAthematics
13. 85 - 28 =
70 – 20 = 5015 – 8 = 7
50 + 7 = 57
5 880 20-
70 15
Add the differences.
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
Branch. Ring the 10s.
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
0 370 40-
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
0 370 40-
Check the 1s to see if we need to rename.
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
0 370 40-
Rename 70 + 0 as 60 + 10.
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
0 370 40-
60 10
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
0 370 40-
60 10
Subtract the 10s.
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
60 – 40 = 20
0 370 40-
60 10
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
60 – 40 = 20
0 370 40-
60 10
Subtract the 1s.
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
60 – 40 = 2010 – 3 = 7
20 + 7 = 27
0 370 40-
60 10
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
60 – 40 = 2010 – 3 = 7
20 + 7 = 27
0 370 40-
60 10
Add the differences.
Branching on your own
Gemma Meharg PA MAthematics
14. 70 - 43 =
60 – 40 = 2010 – 3 = 7
20 + 7 = 27
0 370 40-
60 10
Branching on your own
Gemma Meharg PA MAthematics
15. 96 - 17 =
Branching on your own
Gemma Meharg PA MAthematics
15. 96 - 17 =
80 – 10 = 7016 – 7 = 9
70 + 9 = 79
6 790 10-
80 16
Singapore Mathematics
Concrete Pictorial Abstract
Gemma Meharg PA MAthematics
Left to Right AdditionBegins: Working from left to right, just like we read from left to right.
16. 35
+ 22
50
Gemma Meharg PA MAthematics
First, add the 10s: 30 + 20 = 50
Left to Right Addition
35
+ 22
50
+ 7
Gemma Meharg PA MAthematics
Next, add the 1s: 5 + 2 = 7
16.
Left to Right Addition
35
+ 22
50
+ 7 57
Gemma Meharg PA MAthematics
Last, add the sums: 50 + 7 = 57
16.
Left to Right on your own.
221
+ 345
Gemma Meharg PA MAthematics
Add the 100s
17.
Left to Right on your own.
221
+ 345
500
Gemma Meharg PA MAthematics
17.
200 + 300 = 500
Left to Right on your own.
221
+ 345
500
Gemma Meharg PA MAthematics
Add the 10s.
17.
Left to Right on your own.
221
+ 345
500
60
Gemma Meharg PA MAthematics
20 + 40 = 60
17.
Left to Right on your own.
221
+ 345
500
60
Gemma Meharg PA MAthematics
Add the 1s.
17.
Left to Right on your own.
221
+ 345
500
60
6
Gemma Meharg PA MAthematics
1 + 5 = 6
17.
Left to Right on your own.
221
+ 345
500
60
6
Gemma Meharg PA MAthematics
Last, add the sums.
17.
+
Left to Right on your own.
221
+ 345
500
60
6
566
Gemma Meharg PA MAthematics
500 + 60 + 6 = 566
17.
+
Left to Right on your own.
430
+ 559
Gemma Meharg PA MAthematics
18.
Left to Right on your own.
430
+ 559
900
80
9
989
Gemma Meharg PA MAthematics
18.
+
Left to Right Subtraction
48
– 21
Gemma Meharg PA MAthematics
Subtract the 10s.
19.
Left to Right Subtraction
48
– 21
20
Gemma Meharg PA MAthematics
40 – 20 = 20
19.
Left to Right Subtraction
48
– 21
20
Gemma Meharg PA MAthematics
Subtract the 1s.
19.
Left to Right Subtraction
48
– 21
20
7
Gemma Meharg PA MAthematics
8 – 1 = 7
19.
Left to Right Subtraction
48
– 21
20
7
Gemma Meharg PA MAthematics
Add the differences.
19.
+
Left to Right Subtraction
48
– 21
20
7
27
Gemma Meharg PA MAthematics
20 + 7 = 27
19.
+
Left to Right on your own.
878
– 213
Gemma Meharg PA MAthematics
Subtract the 100s.
20.
Left to Right on your own.
878
– 213
600
Gemma Meharg PA MAthematics
800 – 200 = 600
20.
Left to Right on your own.
878
– 213
600
Gemma Meharg PA MAthematics
Subtract the 10s.
20.
Left to Right on your own.
878
– 213
600
60
Gemma Meharg PA MAthematics
70 – 10 = 60
20.
Left to Right on your own.
878
– 213
600
60
Gemma Meharg PA MAthematics
Subtract the 1s.
20.
Left to Right on your own.
878
– 213
600
60
5
Gemma Meharg PA MAthematics
8 – 3 = 5
20.
Left to Right on your own.
878
– 213
600
60
5
Gemma Meharg PA MAthematics
Add the differences.
20.
+
Left to Right on your own.
878
– 213
600
60
5
665
Gemma Meharg PA MAthematics
600 + 60 + 5 = 665
20.
+
Left to Right on your own.
978
– 256
Gemma Meharg PA MAthematics
21.
Left to Right on your own.
978
– 256
700
20
2
722
Gemma Meharg PA MAthematics
21.
+
Left to Right WITH Regrouping
35
+ 25
Gemma Meharg PA MAthematics
Add the tens.
22.
Left to Right WITH Regrouping
35
+ 25
50
Gemma Meharg PA MAthematics
20 + 30 = 50
22.
Left to Right WITH Regrouping
35
+ 25
50
Gemma Meharg PA MAthematics
Add the 1s.
22.
Left to Right WITH Regrouping
35
+ 25
50
10
Gemma Meharg PA MAthematics
5 + 5 = 10
22.
Left to Right WITH Regrouping
35
+ 25
50
10
60
Gemma Meharg PA MAthematics
Add the sums.
22.
+
Left to Right on your own.
149
+ 522
Gemma Meharg PA MAthematics
Add the hundreds.
23.
Left to Right on your own.
149
+ 522
600
Gemma Meharg PA MAthematics
100 + 500 = 600
23.
Left to Right on your own.
149
+ 522
600
Gemma Meharg PA MAthematics
Add the 10s.
23.
Left to Right on your own.
149
+ 522
600
60
Gemma Meharg PA MAthematics
40 + 20 = 60
23.
Left to Right on your own.
149
+ 522
600
60
Gemma Meharg PA MAthematics
Add the 1s.
23.
Left to Right on your own.
149
+ 522
600
60
11
Gemma Meharg PA MAthematics
9 + 2 = 11
23.
+
Left to Right on your own.
149
+ 522
600
60
11
Gemma Meharg PA MAthematics
Add the sums.
23.
+
Left to Right on your own.
149
+ 522
600
60
11
671
Gemma Meharg PA MAthematics
600 + 60 + 11 = 671
23.
+
Left to Right on your own.
645
+ 397
Gemma Meharg PA MAthematics
24.
Left to Right on your own.
645
+ 397
900
130
12
1,042
Gemma Meharg PA MAthematics
24.
+
Left to Right Subtraction with Renaming/Regrouping
The following three problems are demonstrated using 2 different methods of renaming or regrouping for subtraction.
Method 1 is the official Singapore math method of renaming/regrouping in left-to-right subtraction.
Method 2 originated with Stefanie Limpert, a 2nd grade teacher in the Windsor District.
Gemma Meharg PA MAthematics
Left to Right WITH Regrouping
145
- 117
Gemma Meharg PA MAthematics
Subtract the 100s.
25.
Method 1
Left to Right WITH Regrouping
145
- 117
000
Gemma Meharg PA MAthematics
100 – 100 = 0
25.
Method 1
Left to Right WITH Regrouping
145
- 117
000
Gemma Meharg PA MAthematics
Subtract the 10s.
25.
Method 1
Left to Right WITH Regrouping
145
- 117
000
30
Gemma Meharg PA MAthematics
40 – 10 = 30
25.
Method 1
Left to Right WITH Regrouping
145
- 117
000
30
Gemma Meharg PA MAthematics
Subtract the 1s.
25.
Method 1
Left to Right WITH Regrouping
145
- 117
000
30
2
Gemma Meharg PA MAthematics
5 – 7 =I.O.U. 2 or -2
25.
-
Method 1
Use the number line to count 7 back from 5 to –2.
Gemma Meharg PA MAthematics
Left to Right WITH Regrouping
145
- 117
000
30
2
Gemma Meharg PA MAthematics
Count back 2 from 30.
25.
-
Method 1
Left to Right WITH Regrouping
145
- 117
000
30
2
Gemma Meharg PA MAthematics
Count back because of the subtraction sign or -2.
25.
-
Method 1
Left to Right WITH Regrouping
145
- 117
000
30
2
28
Gemma Meharg PA MAthematics
Count back 2 from 30 = 29, 28
25.
-
Method 1
Left to Right WITH Regrouping
275 - 194
Gemma Meharg PA MAthematics
Subtract the 100s.
26.
Method 1
Left to Right WITH Regrouping
275 - 194 100
Gemma Meharg PA MAthematics
200 – 100 = 100
26.
Method 1
Left to Right WITH Regrouping
275 - 194 100
Gemma Meharg PA MAthematics
Subtract the 10s.
26.
Method 1
Left to Right WITH Regrouping
275 - 194 100
Gemma Meharg PA MAthematics
70 – 90 = ?Use the number line.
26.
Method 1
Use number line to count backwards. Start at 7 tens, count back 9 tens to –2 tens. -2 tens = I.O.U 20 or –20.
Gemma Meharg PA MAthematics
Left to Right WITH Regrouping
275 - 194 100
- 20
Gemma Meharg PA MAthematics
70 – 90 = I.O.U. 20or –20.
26.
Method 1
Left to Right WITH Regrouping
275 - 194 100
- 20
Gemma Meharg PA MAthematics
Subtract before moving to 1s.
26.
Method 1
Left to Right WITH Regrouping
275 - 194 100
- 20 80
Gemma Meharg PA MAthematics
Count backward 2-tens from 100:90, 80.
26.
Method 1
Left to Right WITH Regrouping
275 - 194 100
- 20 80
Gemma Meharg PA MAthematics
Subtract the 1s.
26.
Method 1
Left to Right WITH Regrouping
275 - 194 100
- 20 80 1
Gemma Meharg PA MAthematics
5 – 4 = 1
26.
Method 1
Left to Right WITH Regrouping
275 - 194 100
- 20 80 1
Gemma Meharg PA MAthematics
Put the 10s and 1s together.
26.
+
Method 1
Left to Right WITH Regrouping
275 - 194 100
- 20 80 1 81
Gemma Meharg PA MAthematics
80 +1 = 81
26.
+
Method 1
Left to Right WITH Regrouping
523
- 278
Gemma Meharg PA MAthematics
Subtract the 100s.
27.
Method 1
Left to Right WITH Regrouping
523
- 278
300
Gemma Meharg PA MAthematics
500 – 200 = 300
27.
Method 1
Left to Right WITH Regrouping
523
- 278
300
Gemma Meharg PA MAthematics
Subtract the 10s.
27.
Method 1
Left to Right WITH Regrouping
523
- 278
300
Gemma Meharg PA MAthematics
Count backwards on the number line.
27.
Method 1
Use number line to count backwards. Start at 2 tens, count back 7 tens to –5 tens. -5 tens = I.O.U 50 or –50.
Gemma Meharg PA MAthematics
Left to Right WITH Regrouping
523
- 278
300
- 50
Gemma Meharg PA MAthematics
20 – 70 =I.O.U. 50 or –50.
27.
Method 1
Left to Right WITH Regrouping
523
- 278
300
- 50
Gemma Meharg PA MAthematics
Count back 5 tens from 300.
27.
Method 1
Left to Right WITH Regrouping
523
- 278
300
- 50
250
Gemma Meharg PA MAthematics
290, 280, 270, 260, 250
27.
Method 1
Left to Right WITH Regrouping
523
- 278
300
- 50
250
Gemma Meharg PA MAthematics
Subtract the 1s.
27.
Method 1
Left to Right WITH Regrouping
523
- 278
300
- 50
250
- 5
Gemma Meharg PA MAthematics
3 – 8 = I.O.U. 5 or -5.
27.
Method 1
Left to Right WITH Regrouping
523
- 278
300
50
250
5
Gemma Meharg PA MAthematics
Count 5 backwardfrom 250.
27.
-
-
Method 1
Left to Right WITH Regrouping
523
- 278
300
50
250
5
245
Gemma Meharg PA MAthematics
249, 248, 247, 246, 245
27.
-
-
Method 1
Left to Right WITH Regrouping
1 4 5
- 1 1 7
Gemma Meharg PA MAthematics
Look for I.O.U.s.
25.
An I.O.U. means you cannot do the subtraction
in the place value.
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
Gemma Meharg PA MAthematics
1s column: 5 - 7
25.
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
Gemma Meharg PA MAthematics
Draw a circle abovethe column to showthe I.O.U.
25.
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
Gemma Meharg PA MAthematics
Now we renameor regroup.
25.
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
Gemma Meharg PA MAthematics
Take 1-ten from the 4-tens= 3-tens.
25.3
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
Gemma Meharg PA MAthematics
1-ten = 10-ones.Add the 10-onesto the 5 in the 1scolumn:10 + 5 = 15
25.153
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
Gemma Meharg PA MAthematics
Once the I.O.U.sare completed. Subtract fromleft to right.
25.153
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
Gemma Meharg PA MAthematics
Subtract the 100s.
25.153
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
0 0 0
Gemma Meharg PA MAthematics
100 – 100 = 0
25.153
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
0 0 0
Gemma Meharg PA MAthematics
Subtract the 10s.
25.
153
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
0 0 0
2 0
Gemma Meharg PA MAthematics
30 – 10 = 20
25.
153
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
0 0 0
2 0
8
Gemma Meharg PA MAthematics
Subtract the 1s.
25.
153
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
0 0 0
2 0
8
Gemma Meharg PA MAthematics
15 – 7 = 8
25.
153
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
0 0 0
2 0
8
Gemma Meharg PA MAthematics
Add thedifferences.
25.
153
+
Method 2
Left to Right WITH Regrouping
1 4 5
- 1 1 7
0 0 0
2 0
8
2 8
Gemma Meharg PA MAthematics
0 + 20 + 8 = 28
25.
153
+
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
Gemma Meharg PA MAthematics
26.Look for I.O.U.s.
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
Gemma Meharg PA MAthematics
26. 10 column:7-tens – 9-tens
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
Gemma Meharg PA MAthematics
26. Draw a circleabove the columnto show the I.O.U.
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
Gemma Meharg PA MAthematics
26. Now we renameor regroup.
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
Gemma Meharg PA MAthematics
26. Take 1-hundredfrom 2-hundreds= 1-hundreds.
1
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
Gemma Meharg PA MAthematics
26. 1-hundred = 10-tens Add 10-tens to the 7in the 10s column:7-tens + 10-tens =17-tens
171
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
Gemma Meharg PA MAthematics
26.
171
Once the I.O.U.sare completed. Subtract fromleft to right.
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
Gemma Meharg PA MAthematics
26.
171
Subtract the 100s.
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
0 0 0
Gemma Meharg PA MAthematics
26.
171
100 – 100 = 0
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
0 0 0
Gemma Meharg PA MAthematics
26.
171
Subtract thetens.
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
0 0 0
8 0
Gemma Meharg PA MAthematics
26.
171
17-tens – 9 tens= 8-tens
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
0 0 0
8 0
Gemma Meharg PA MAthematics
26.
171
Subtract the ones.
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
0 0 0
8 0
1
Gemma Meharg PA MAthematics
26.
171
5 – 4 = 1
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
0 0 0
8 0
1
Gemma Meharg PA MAthematics
26.
171
Add the differences.
+
Method 2
Left to Right WITH Regrouping
2 7 5
- 1 9 4
0 0 0
8 0
1
8 1
Gemma Meharg PA MAthematics
26.
171
0 + 80 + 1 = 81
+
Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
Gemma Meharg PA MAthematics
Look for I.O.U.s.
27.
An I.O.U. means you cannot do the subtraction
in the place value.
Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
Gemma Meharg PA MAthematics
Place a circle abovethe column(s) thatrequires an I.O.U.
27.
Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
Gemma Meharg PA MAthematics
Both the 10s and 1srequire an I.O.U.
27.
Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
Gemma Meharg PA MAthematics
Rename the columns.27.
Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
Gemma Meharg PA MAthematics
Rename the columns27.
1 13
Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
Gemma Meharg PA MAthematics
Rename the columns27.
1 13
11
4Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
Gemma Meharg PA MAthematics
Subtract the 100s.
27.
1 13
11
4Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
2 0 0
Gemma Meharg PA MAthematics
400 – 200 = 200
27.
1 13
11
4Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
2 0 0
Gemma Meharg PA MAthematics
Subtract the 10s.
27.
1 13
11
4Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
2 0 0
4 0
Gemma Meharg PA MAthematics
11-tens – 7-tens= 4-tens
27.
1 13
11
4Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
2 0 0
4 0
Gemma Meharg PA MAthematics
Subtract the 1s.
27.
1 13
11
4Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
2 0 0
4 0
5
Gemma Meharg PA MAthematics
13 – 8 = 5
27.
1 13
11
4Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
2 0 0
4 0
5
Gemma Meharg PA MAthematics
Add thedifferences.
27.
1 13
11
4
+
Method 2
Left to Right WITH Regrouping
5 2 3
- 2 7 8
2 0 0
4 0
5
2 4 5
Gemma Meharg PA MAthematics
200 + 40 + 5 =245.
27.
1 13
11
4
+
Method 2
Abstract Stage of Singapore Mathematics
Ends with traditional “short-cut” method:
1
25
+ 17
42
Gemma Meharg PA MAthematics
WHY are we doing all these extra steps in Singapore Math?
Branching and Left-to-Right Methods build understanding as students learn computation.
Gemma Meharg PA MAthematics
Linda King
Singapore Math Coach
(636) 464 – 4400, extension 4399
Gemma Meharg PA MAthematics