1. Singapore
Mathematics

2. Singapore Mathematics
This program teaches kids to
UNDERSTAND mathematical processes
through 3 stages:
Concrete Pictorial Abstract
Gemma Meharg PA MAthematics

3. Concrete Stage of Singapore
Mathematics This presentation
Students on place mats with disks. is available on the
Windsor web site.
25 + 17 =
Tens Ones
10 10 1 1 1 1 1
1 1 1 1 1
10
1 1
Gemma Meharg PA MAthematics

4. Singapore Mathematics
Concrete Pictorial Abstract
Gemma Meharg PA MAthematics

5. Pictorial Stage of Singapore
Mathematics
The student begins the transition to “paper and pencil ” with a
technique called branching.
1. 34 + 5
Separate each number
into 10s and 1s.
Place 10s outside and
1s to the inside.
Gemma Meharg PA MAthematics

6. Branching
1. 34 + 5 “Ring” the 10s.
4 5
30 +
Gemma Meharg PA MAthematics

7. Branching
Add the tens.
1. 34 + 5
4 5
30 +
30 + 0 = 30
Gemma Meharg PA MAthematics

8. Branching
Add the ones.
1. 34 + 5
4 5
30 +
30 + 0 = 30
5+4=9
Gemma Meharg PA MAthematics

9. Branching
Add the sums.
1. 34 + 5
4 5
30 +
30 + 0 = 30
5+4=9
30 + 9 = 39 Gemma Meharg PA MAthematics

10. Branching on your own.
Separate the tens
2. 24 + 32 = and ones.
Branch
tens on the outside
and
ones on the inside.
Gemma Meharg PA MAthematics

11. Branching on your own.
2. 24 + 32 =
20 4 + 2 30
Gemma Meharg PA MAthematics

12. Branching on your own.
2. 24 + 32 = Ring the tens.
20 4 + 2 30
Gemma Meharg PA MAthematics

13. Branching on your own.
2. 24 + 32 =
20 4 + 2 30
Gemma Meharg PA MAthematics

14. Branching on your own.
Now, add the tens.
2. 24 + 32 =
20 4 + 2 30
Gemma Meharg PA MAthematics

15. Branching on your own.
2. 24 + 32 =
20 4 + 2 30
20 + 30 = 50
Gemma Meharg PA MAthematics

16. Branching on your own.
2. 24 + 32 =
Add the ones.
20 4 + 2 30
20 + 30 = 50
Gemma Meharg PA MAthematics

17. Branching on your own.
2. 24 + 32 =
20 4 + 2 30
20 + 30 = 50
4+2=6
Gemma Meharg PA MAthematics

18. Branching on your own.
2. 24 + 32 =
Next add the sums.
20 4 + 2 30
20 + 30 = 50
4+2=6
Gemma Meharg PA MAthematics

19. Branching on your own.
2. 24 + 32 =
20 4 + 2 30
20 + 30 = 50
4+2=6
50 + 6 = 56
Gemma Meharg PA MAthematics

20. Branching on your own.
3. 73 + 16 =
Gemma Meharg PA MAthematics

21. Branching on your own.
3. 73 + 16 =
70 3 + 6 10
70 + 10 = 80
3+6=9
80 + 9 = 89
Gemma Meharg PA MAthematics

22. Branching with subtraction.
4. 48 - 32 =
Branch out the 10s and 1s.
Remember 10s are on the outside.
Ring the 10s.
Gemma Meharg PA MAthematics

23. Branching with subtraction.
4. 48 - 32 =
40 8 - 2 30
Be sure to place
the subtraction sign.
Gemma Meharg PA MAthematics

24. Branching with subtraction.
Subtract the 10s.
4. 48 - 32 =
40 8 - 2 30
Gemma Meharg PA MAthematics

25. Branching with subtraction.
4. 48 - 32 =
40 8 - 2 30
40 - 30 = 10
Gemma Meharg PA MAthematics

26. Branching with subtraction.
Subtract the 1s.
4. 48 - 32 =
40 8 - 2 30
40 - 30 = 10
Gemma Meharg PA MAthematics

27. Branching with subtraction.
4. 48 - 32 =
40 8 - 2 30
40 - 30 = 10
8–2=6
Gemma Meharg PA MAthematics

28. Branching with subtraction.
ADD
4. 48 - 32 = the differences.
40 8 - 2 30
40 - 30 = 10
8–2=6
Gemma Meharg PA MAthematics

29. Branching with subtraction.
We add because
we are putting the
4. 48 - 32 = 10s and 1s
together.
40 8 - 2 30
40 - 30 = 10
8–2=6
10 + 6 = 16
Gemma Meharg PA MAthematics

30. Branching on your own.
Branch the 10s and
1s.
5. 78 - 20 = 10 on the outside.
Gemma Meharg PA MAthematics

31. Branching on your own.
5. 78 - 20 =
70 8 - 0 20
Gemma Meharg PA MAthematics

32. Branching on your own.
Ring the 10s.
5. 78 - 20 =
70 8 - 0 20
Gemma Meharg PA MAthematics

33. Branching on your own.
5. 78 - 20 =
70 8 - 0 20
Gemma Meharg PA MAthematics

34. Branching on your own.
Subtract the 10s.
5. 78 - 20 =
70 8 - 0 20
Gemma Meharg PA MAthematics

35. Branching on your own.
5. 78 - 20 =
70 8 - 0 20
70 - 20 = 50
Gemma Meharg PA MAthematics

36. Branching on your own.
Subtract the 1s.
5. 78 - 20 =
70 8 - 0 20
70 - 20 = 50
Gemma Meharg PA MAthematics

37. Branching on your own.
5. 78 - 20 =
70 8 - 0 20
70 - 20 = 50
8–0=8
Gemma Meharg PA MAthematics

38. Branching on your own.
Add the
differences.
5. 78 - 20 =
70 8 - 0 20
70 - 20 = 50
8–0=8
Gemma Meharg PA MAthematics

39. Branching on your own.
We add because
we are putting the
5. 78 - 20 = 10s and 1s
together.
70 8 - 0 20
70 - 20 = 50
8–0=8
50 + 8 = 58
Gemma Meharg PA MAthematics

40. Branching on your own.
6. 95 - 41 =
Gemma Meharg PA MAthematics

41. Branching on your own.
6. 95 - 41 =
90 5 - 1 40
90 - 40 = 50
5–1=4
50 + 4 = 54
Gemma Meharg PA MAthematics

42. Branching WITH regrouping.
7. 7 + 9 =
Branching can be used to
help students learn sums
greater than 10.
Gemma Meharg PA MAthematics

43. Branching WITH regrouping.
7. 7 + 9 =
Think: What could be added
to 7 to make 10?
Gemma Meharg PA MAthematics

44. Branching WITH regrouping.
7. 7 + 9 =
3
7 + 3 = 10
Branch 3 from 9.
Ring the 10.
Gemma Meharg PA MAthematics

45. Branching WITH regrouping.
7. 7 + 9 =
3
Branch the other addend
from the 2nd addend.
3+_=9
Gemma Meharg PA MAthematics

46. Branching WITH regrouping.
7. 7 + 9 =
3 6
Now add.
Gemma Meharg PA MAthematics

47. Branching WITH regrouping.
7. 7 + 9 =
3 6
10 + 6 = 16
Gemma Meharg PA MAthematics

48. Branching on your own.
8. 4 + 8 =
What can I add to
4 to make 10?
Gemma Meharg PA MAthematics

49. Branching on your own.
8. 4 + 8 =
6
Ring the 10.
Gemma Meharg PA MAthematics

50. Branching on your own.
8. 4 + 8 =
6
Gemma Meharg PA MAthematics

51. Branching on your own.
8. 4 + 8 =
6
Complete branching of 8.
6 + __ = 8
Gemma Meharg PA MAthematics

52. Branching on your own.
8. 4 + 8 =
6 2
Gemma Meharg PA MAthematics

53. Branching on your own.
8. 4 + 8 =
6 2
Now add.
Gemma Meharg PA MAthematics

54. Branching on your own.
8. 4 + 8 =
6 2
10 + 2 = 12
Gemma Meharg PA MAthematics

55. Branching on your own.
9. 3 + 9 =
Gemma Meharg PA MAthematics

56. Branching on your own.
9. 3 + 9 =
Remember to make 10.
Then ring the 10.
Gemma Meharg PA MAthematics

57. Branching on your own.
Now add.
9. 3 + 9 =
7 2
Gemma Meharg PA MAthematics

58. Branching on your own.
9. 3 + 9 =
7 2
10 + 2 = 12
Gemma Meharg PA MAthematics

59. Branching WITH regrouping.
10. 15 + 28 =
Branch the addends
into 10s and 1s.
Branch 10s
to the OUTSIDE.
Gemma Meharg PA MAthematics

60. Branching WITH regrouping.
10. 15 + 28 =
10 5 + 8 20
Gemma Meharg PA MAthematics

61. Branching WITH regrouping.
10. 15 + 28 = Ring the 10s.
10 5 + 8 20
Gemma Meharg PA MAthematics

62. Branching WITH regrouping.
10. 15 + 28 =
10 5 + 8 20
Gemma Meharg PA MAthematics

63. Branching WITH regrouping.
10. 15 + 28 = Add the 10s.
10 5 + 8 20
10 + 20 = 30
Gemma Meharg PA MAthematics

64. Branching WITH regrouping.
Look at the 1s.
10. 15 + 28 = 5 + 8 is more
than 10.
10 5 + 8 20
This strategy
10 + 20 = 30
is used when the
child does not know
sums over 10.
Gemma Meharg PA MAthematics

65. Branching WITH regrouping.
We want to make
10. 15 + 28 = a sum 10.
10 5 + 8 20
10 + 20 = 30
5 + _ = 10
Gemma Meharg PA MAthematics

66. Branching WITH regrouping.
10. 15 + 28 =
10 5 + 8 20
5
10 + 20 = 30
Gemma Meharg PA MAthematics

67. Branching WITH regrouping.
Branch the 8
10. 15 + 28 = into 5 and _?
10 5 + 8 20
5
10 + 20 = 30
Gemma Meharg PA MAthematics

68. Branching WITH regrouping.
10. 15 + 28 =
10 5 + 8 20
5 3
10 + 20 = 30
Gemma Meharg PA MAthematics

69. Branching WITH regrouping.
Ring the sum
10. 15 + 28 = of 10.
10 5 + 8 20
5 3
10 + 20 = 30
Gemma Meharg PA MAthematics

70. Branching WITH regrouping.
Now add 1s.
10. 15 + 28 =
10 5 + 8 20
5 3
10 + 20 = 30
Gemma Meharg PA MAthematics

71. Branching WITH regrouping.
10. 15 + 28 =
10 5 + 8 20
5 3 10 + 20 = 30
10 + 3 = 13
Gemma Meharg PA MAthematics

72. Branching WITH regrouping.
Now add the sums.
10. 15 + 28 =
10 5 + 8 20
5 3
10 + 20 = 30
10 + 3 = 13
Gemma Meharg PA MAthematics

73. Branching WITH regrouping.
10. 15 + 28 =
10 5 + 8 20
5 3
10 + 20 = 30
10 + 3 = 13
30 + 13 = 43
Gemma Meharg PA MAthematics

74. Branching on your own.
Branch the
10s and 1s.
11. 49 + 43 =
Gemma Meharg PA MAthematics

75. Branching on your own.
11. 49 + 43 =
40 9 + 3 40
Gemma Meharg PA MAthematics

76. Branching on your own.
Now ring the
10s.
11. 49 + 43 =
40 9 + 3 40
Gemma Meharg PA MAthematics

77. Branching on your own.
11. 49 + 43 =
40 9 + 3 40
Gemma Meharg PA MAthematics

78. Branching on your own.
Now add the tens.
11. 49 + 43 =
40 9 + 3 40
Gemma Meharg PA MAthematics

79. Branching on your own.
11. 49 + 43 =
40 9 + 3 40
40 + 40 = 80
Gemma Meharg PA MAthematics

80. Branching on your own.
Now add the ones.
11. 49 + 43 =
40 9 + 3 40
40 + 40 = 80
Gemma Meharg PA MAthematics

81. Branching on your own.
11. 49 + 43 =
40 9 + 3 40
40 + 40 = 80
9 + 3 = 12
Gemma Meharg PA MAthematics

82. Branching on your own.
Now add the sums.
11. 49 + 43 =
40 9 + 3 40
40 + 40 = 80
9 + 3 = 12
Gemma Meharg PA MAthematics

83. Branching on your own.
11. 49 + 43 =
40 9 + 3 40
40 + 40 = 80
9 + 3 = 12
80 + 12 = 92
Gemma Meharg PA MAthematics

84. Branching on your own.
12. 96 + 17 =
Gemma Meharg PA MAthematics

85. Branching on your own.
12. 96 + 17 =
90 6 + 7 10
90 + 10 = 100
OR 6 + 7 = 13
100 + 13 = 113
Gemma Meharg PA MAthematics

86. Branching on your own.
12. 96 + 17 =
90 6 + 7 10
4 3 90 + 10 = 100
10 + 3 = 13
100 + 13 = 113
Gemma Meharg PA MAthematics

87. Branching WITH regrouping.
Branch into
10s and 1s. Ring
13. 85 - 28 = the 10s.
Gemma Meharg PA MAthematics

88. Branching WITH regrouping.
Remember the
subtraction sign.
13. 85 - 28 =
80 5 - 8 20
Gemma Meharg PA MAthematics

89. Branching WITH regrouping.
Look at the 1s.
13. 85 - 28 = We can rename.
80 5 - 8 20
Gemma Meharg PA MAthematics

90. Branching WITH regrouping.
13. 85 - 28 =
80 5 - 8 20
Students can use disks
to help with renaming.
Gemma Meharg PA MAthematics

91. Branching WITH regrouping.
85 is renamed as 70 + 15
10 10 10 1 1 1 1 1
80 5 - 8 20
10 10 10 1 1 1 1 1
10 1015
70
1 1
1 1 1
Gemma Meharg PA MAthematics

92. Branching WITH regrouping.
Subtract the 10s.
13. 85 - 28 =
80 5 - 8 20
70 15
70 – 20 = 50
Gemma Meharg PA MAthematics

93. Branching WITH regrouping.
Subtract the 1s.
13. 85 - 28 =
80 5 - 8 20
70 15 70 – 20 = 50
15 – 8 = 7
50 + 7 = 57
Gemma Meharg PA MAthematics

94. Branching WITH regrouping.
Add the differences.
13. 85 - 28 =
80 5 - 8 20
70 15 70 – 20 = 50
15 – 8 = 7
50 + 7 = 57
Gemma Meharg PA MAthematics

95. Branching on your own
Branch. Ring the 10s.
14. 70 - 43 =
Gemma Meharg PA MAthematics

96. Branching on your own
14. 70 - 43 =
70 0 - 3 40
Gemma Meharg PA MAthematics

97. Branching on your own
Check the 1s to see if
we need to rename.
14. 70 - 43 =
70 0 - 3 40
Gemma Meharg PA MAthematics

98. Branching on your own
Rename 70 + 0
as 60 + 10.
14. 70 - 43 =
70 0 - 3 40
Gemma Meharg PA MAthematics

99. Branching on your own
14. 70 - 43 =
70 0 - 3 40
60 10
Gemma Meharg PA MAthematics

100. Branching on your own
Subtract the 10s.
14. 70 - 43 =
70 0 - 3 40
60 10
Gemma Meharg PA MAthematics

101. Branching on your own
14. 70 - 43 =
70 0 - 3 40
60 10 60 – 40 = 20
Gemma Meharg PA MAthematics

102. Branching on your own
Subtract the 1s.
14. 70 - 43 =
70 0 - 3 40
60 10 60 – 40 = 20
Gemma Meharg PA MAthematics

103. Branching on your own
14. 70 - 43 =
70 0 - 3 40
60 10 60 – 40 = 20
10 – 3 = 7
20 + 7 = 27
Gemma Meharg PA MAthematics

104. Branching on your own
Add the differences.
14. 70 - 43 =
70 0 - 3 40
60 10 60 – 40 = 20
10 – 3 = 7
20 + 7 = 27
Gemma Meharg PA MAthematics

105. Branching on your own
14. 70 - 43 =
70 0 - 3 40
60 10 60 – 40 = 20
10 – 3 = 7
20 + 7 = 27
Gemma Meharg PA MAthematics

106. Branching on your own
15. 96 - 17 =
Gemma Meharg PA MAthematics

107. Branching on your own
15. 96 - 17 =
90 6 - 7 10
80 16 80 – 10 = 70
16 – 7 = 9
70 + 9 = 79
Gemma Meharg PA MAthematics

108. Singapore Mathematics
Concrete Pictorial Abstract
Gemma Meharg PA MAthematics

109. Left to Right Addition
Begins: Working from left to right, just like we read from left to
right.
16. 35
+ 22
50
First, add the 10s:
30 + 20 = 50
Gemma Meharg PA MAthematics

110. Left to Right Addition
35
16.
+ 22
50
+ 7
Next, add the 1s:
5+2=7
Gemma Meharg PA MAthematics

111. Left to Right Addition
35
+ 22
50
+ 16.
7
57
Last, add the sums:
50 + 7 = 57
Gemma Meharg PA MAthematics

112. Left to Right on your own.
17. 221
+ 345
Add the 100s
Gemma Meharg PA MAthematics

113. Left to Right on your own.
17. 221
+ 345
500
200 + 300 = 500
Gemma Meharg PA MAthematics

114. Left to Right on your own.
17.
221
+ 345
500
Add the 10s.
Gemma Meharg PA MAthematics

115. Left to Right on your own.
17.
221
+ 345
500
60
20 + 40 = 60
Gemma Meharg PA MAthematics

116. Left to Right on your own.
17.
221
+ 345
500
60
Add the 1s.
Gemma Meharg PA MAthematics

117. Left to Right on your own.
17.
221
+ 345
500
60
6
1+5=6
Gemma Meharg PA MAthematics

118. Left to Right on your own.
17.
221
+ 345
500
60
6
+
Last, add the sums.
Gemma Meharg PA MAthematics

119. Left to Right on your own.
17.
221
+ 345
500
60
6
566
+
500 + 60 + 6 = 566
Gemma Meharg PA MAthematics

120. Left to Right on your own.
18. 430
+ 559
Gemma Meharg PA MAthematics

121. Left to Right on your own.
18.
430
+ 559
900
80
9
989
+
Gemma Meharg PA MAthematics

122. Left to Right Subtraction
19. 48
– 21
Subtract the 10s.
Gemma Meharg PA MAthematics

123. Left to Right Subtraction
19. 48
– 21
20
40 – 20 = 20
Gemma Meharg PA MAthematics

124. Left to Right Subtraction
19. 48
– 21
20
Subtract the 1s.
Gemma Meharg PA MAthematics

125. Left to Right Subtraction
19. 48
– 21
20
7
8–1=7
Gemma Meharg PA MAthematics

126. Left to Right Subtraction
19. 48
– 21
20
7
+
Add the differences.
Gemma Meharg PA MAthematics

127. Left to Right Subtraction
19. 48
– 21
20
7
27
+
20 + 7 = 27
Gemma Meharg PA MAthematics

128. Left to Right on your own.
20. 878
– 213
Subtract the 100s.
Gemma Meharg PA MAthematics

129. Left to Right on your own.
20. 878
– 213
600
800 – 200 = 600
Gemma Meharg PA MAthematics

130. Left to Right on your own.
20. 878
– 213
600
Subtract the 10s.
Gemma Meharg PA MAthematics

131. Left to Right on your own.
20. 878
– 213
600
60
70 – 10 = 60
Gemma Meharg PA MAthematics

132. Left to Right on your own.
20. 878
– 213
600
60
Subtract the 1s.
Gemma Meharg PA MAthematics

133. Left to Right on your own.
20. 878
– 213
600
60
5
8–3=5
Gemma Meharg PA MAthematics

134. Left to Right on your own.
20.
– 213
878
600
60
5
+
Add the differences.
Gemma Meharg PA MAthematics

135. Left to Right on your own.
20.
– 213
878
600
60
5
665
+
600 + 60 + 5 = 665
Gemma Meharg PA MAthematics

136. Left to Right on your own.
21. 978
– 256
Gemma Meharg PA MAthematics

137. Left to Right on your own.
21. 978
– 256
700
20
2
722
+
Gemma Meharg PA MAthematics

138. Left to Right WITH
Regrouping
22.
+ 25
35
Add the tens.
Gemma Meharg PA MAthematics

139. Left to Right WITH
Regrouping
22.
+ 25
35
20 + 30 = 50
50
Gemma Meharg PA MAthematics

140. Left to Right WITH
Regrouping
22.
+ 25
35
50
Add the 1s.
Gemma Meharg PA MAthematics

141. Left to Right WITH
Regrouping
22.
+ 25
35
50
10
5 + 5 = 10
Gemma Meharg PA MAthematics

142. Left to Right WITH
Regrouping
22.
+ 25
35
50
10
60
+
Add the sums.
Gemma Meharg PA MAthematics

143. Left to Right on
your own.
23. 149
+ 522
Add the hundreds.
Gemma Meharg PA MAthematics

144. Left to Right on
your own.
23. 149
+ 522
600
100 + 500 = 600
Gemma Meharg PA MAthematics

145. Left to Right on
your own.
23. 149
+ 522
600
Add the 10s.
Gemma Meharg PA MAthematics

146. Left to Right on
your own.
23. 149
+ 522
600
60
40 + 20 = 60
Gemma Meharg PA MAthematics

147. Left to Right on
your own.
23. 149
+ 522
600
60
Add the 1s.
Gemma Meharg PA MAthematics

148. Left to Right on
your own.
23. 149
+ 522
600
60
11
+ 9 + 2 = 11
Gemma Meharg PA MAthematics

149. Left to Right on
your own.
23.
+ 522
149
600
60
11
+
Add the sums.
Gemma Meharg PA MAthematics

150. Left to Right on
your own.
23.
+ 522
149
600
60
11
671
+
600 + 60 + 11 = 671
Gemma Meharg PA MAthematics

151. Left to Right on
your own.
24. 645
+ 397
Gemma Meharg PA MAthematics

152. Left to Right on
your own.
24.397
+
645
900
130
12
1,042
+
Gemma Meharg PA MAthematics

153. 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 2 nd
grade teacher in the Windsor District.
Gemma Meharg PA MAthematics

154. Left to Right
Method 1 WITH Regrouping
25. 145
- 117
Subtract the 100s.
Gemma Meharg PA MAthematics

155. Left to Right
Method 1 WITH Regrouping
25. 145
- 117
000
100 – 100 = 0
Gemma Meharg PA MAthematics

156. Left to Right
Method 1 WITH Regrouping
25. 145
- 117
000
Subtract the 10s.
Gemma Meharg PA MAthematics

157. Left to Right
Method 1 WITH Regrouping
25. 145
- 117
000
30
40 – 10 = 30
Gemma Meharg PA MAthematics

158. Left to Right
Method 1 WITH Regrouping
145
25.117
-
000
30
Subtract the 1s.
Gemma Meharg PA MAthematics

159. Left to Right
Method 1 WITH Regrouping
145
25.117
-
000
30
2
5–7=
- I.O.U. 2 or -2
Gemma Meharg PA MAthematics

160. Use the number line to count
7 back from 5 to –2.
Gemma Meharg PA MAthematics

161. Left to Right
Method 1 WITH Regrouping
145
25.117
-
000
30
2
-
Count back 2
from 30.
Gemma Meharg PA MAthematics

162. Left to Right
Method 1 WITH Regrouping
145
25.117
-
000
30
2
- Count back because
of the subtraction
sign or -2.
Gemma Meharg PA MAthematics

163. Left to Right
Method 1 WITH Regrouping
145
25.117
-
000
30
2
28
-
Count back 2
from 30 = 29, 28
Gemma Meharg PA MAthematics

164. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
Subtract the 100s.
Gemma Meharg PA MAthematics

165. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100 200 – 100 = 100
Gemma Meharg PA MAthematics

166. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100
Subtract the 10s.
Gemma Meharg PA MAthematics

167. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100 70 – 90 = ?
Use the number line.
Gemma Meharg PA MAthematics

168. Use number line to count backwards.
Star t at 7 tens, count back 9 tens to
–2 tens.
-2 tens = I.O.U 20 or –20.
Gemma Meharg PA MAthematics

169. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100 70 – 90 = I.O.U. 20
- 20 or –20.
Gemma Meharg PA MAthematics

170. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100
- 20
Subtract before
moving to 1s.
Gemma Meharg PA MAthematics

171. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100
- 20 Count backward
80 2-tens from 100:
90, 80.
Gemma Meharg PA MAthematics

172. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100
- 20
80
Subtract the 1s.
Gemma Meharg PA MAthematics

173. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100
- 20
80
1 5–4=1
Gemma Meharg PA MAthematics

174. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100
- 20
80 Put the 10s and 1s
+ 1 together.
Gemma Meharg PA MAthematics

175. Left to Right
Method 1 WITH Regrouping
26. 275
- 194
100
- 20
80
+ 1
81 80 +1 = 81
Gemma Meharg PA MAthematics

176. Left to Right
Method 1 WITH Regrouping
27.
523
- 278
Subtract the 100s.
Gemma Meharg PA MAthematics

177. Left to Right
Method 1 WITH Regrouping
27.
523
- 278
300
500 – 200 = 300
Gemma Meharg PA MAthematics

178. Left to Right
Method 1 WITH Regrouping
27.
523
- 278
300
Subtract the 10s.
Gemma Meharg PA MAthematics

179. Left to Right
Method 1 WITH Regrouping
27.
523
- 278
300
Count backwards on
the number line.
Gemma Meharg PA MAthematics

180. Use number line to count backwards.
Star t at 2 tens, count back 7 tens to
–5 tens.
-5 tens = I.O.U 50 or –50.
Gemma Meharg PA MAthematics

181. Left to Right
Method 1 WITH Regrouping
27. 523
- 278
300
- 50
20 – 70 =
I.O.U. 50 or –50.
Gemma Meharg PA MAthematics

182. Left to Right
Method 1 WITH Regrouping
27. 523
- 278
300
- 50
Count back 5 tens
from 300.
Gemma Meharg PA MAthematics

183. Left to Right
Method 1 WITH Regrouping
27. 523
- 278
300
- 50
250
290, 280, 270,
260, 250
Gemma Meharg PA MAthematics

184. Left to Right
Method 1 WITH Regrouping
27. 523
- 278
300
- 50
250
Subtract the 1s.
Gemma Meharg PA MAthematics

185. Left to Right
Method 1 WITH Regrouping
27. 523
- 278
300
- 50
250
- 5
3 – 8 = I.O.U. 5
or -5.
Gemma Meharg PA MAthematics

186. Left to Right
Method 1 WITH Regrouping
27. 523
- 278
300
50
250
5 -
- Count 5 backward
from 250.
Gemma Meharg PA MAthematics

187. Left to Right
Method 1 WITH Regrouping
27.
523
- 278
300
50
250
-
5
245
- 249, 248, 247,
246, 245
Gemma Meharg PA MAthematics

188. Left to Right
Method 2 WITH Regrouping
25. 1 4 5
- 1 1 7 Look for I.O.U.s.
An I.O.U. means you
cannot do the subtraction
in the place value.
Gemma Meharg PA MAthematics

189. Left to Right
Method 2 WITH Regrouping
25. 1 4 5
- 1 1 7 1s column: 5 - 7
Gemma Meharg PA MAthematics

190. Left to Right
Method 2 WITH Regrouping
25. 1 4 5
- 1 1 7
Draw a circle above
the column to show
the I.O.U.
Gemma Meharg PA MAthematics

191. Left to Right
Method 2 WITH Regrouping
25. 1 4 5
- 1 1 7
Now we rename
or regroup.
Gemma Meharg PA MAthematics

192. Left to Right
Method 2 WITH Regrouping
3
25. 1 4 5
- 1 1 7
Take 1-ten from
the 4-tens
= 3-tens.
Gemma Meharg PA MAthematics

193. Left to Right
Method 2 WITH Regrouping
3 15
25. 1 4 5
- 1 1 7
1-ten = 10-ones.
Add the 10-ones
to the 5 in the 1s
column:
10 + 5 = 15
Gemma Meharg PA MAthematics

194. Left to Right
Method 2 WITH Regrouping
3 15
25. 1 4 5
- 1 1 7
Once the I.O.U.s
are completed.
Subtract from
left to right.
Gemma Meharg PA MAthematics

195. Left to Right
Method 2 WITH Regrouping
3 15
25. 1 4 5
- 1 1 7
Subtract the 100s.
Gemma Meharg PA MAthematics

196. Left to Right
Method 2 WITH Regrouping
3 15
25. 1 4 5
- 1 1 7
0 0 0
100 – 100 = 0
Gemma Meharg PA MAthematics

197. Left to Right
Method 2 WITH Regrouping
3 15
25.1
- 1 7
1 4 5
0 0 0
Subtract the 10s.
Gemma Meharg PA MAthematics

198. Left to Right
Method 2 WITH Regrouping
3 15
25.1
- 1 7
1 4 5
0 0 0
2 0
30 – 10 = 20
Gemma Meharg PA MAthematics

199. Left to Right
Method 2 WITH Regrouping
3 15
25.1
- 1 7
1 4 5
0 0 0
2 0
8
Subtract the 1s.
Gemma Meharg PA MAthematics

200. Left to Right
Method 2 WITH Regrouping
3 15
25.1
- 1 7
1 4 5
0 0 0
2 0
8
15 – 7 = 8
Gemma Meharg PA MAthematics

201. Left to Right
Method 2 WITH Regrouping
3 15
25.1
- 1 7
1 4 5
0 0 0
2 0
8
+
Add the
differences.
Gemma Meharg PA MAthematics

202. Left to Right
Method 2 WITH Regrouping
3 15
25.1
- 1 7
1 4 5
0 0 0
2 0
8
2 8
+
0 + 20 + 8 = 28
Gemma Meharg PA MAthematics

203. Left to Right
Method 2 WITH Regrouping
26.1
- 9 4
2 7 5
Look for I.O.U.s.
Gemma Meharg PA MAthematics

204. Left to Right
Method 2 WITH Regrouping
26.1
- 9 4
2 7 5
10 column:
7-tens – 9-tens
Gemma Meharg PA MAthematics

205. Left to Right
Method 2 WITH Regrouping
Draw a circle
26.1 2 7 5
- 9 4 above the column
to show the I.O.U.
Gemma Meharg PA MAthematics

206. Left to Right
Method 2 WITH Regrouping
26.1
- 9 4
2 7 5
Now we rename
or regroup.
Gemma Meharg PA MAthematics

207. Left to Right
Method 2 WITH Regrouping
1
Take 1-hundred
26.1
- 9 4
2 7 5
from 2-hundreds
= 1-hundreds.
Gemma Meharg PA MAthematics

208. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
1-hundred = 10-tens
Add 10-tens to the 7
in the 10s column:
7-tens + 10-tens =
17-tens
Gemma Meharg PA MAthematics

209. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
Once the I.O.U.s
are completed.
Subtract from
left to right.
Gemma Meharg PA MAthematics

210. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
Subtract the
100s.
Gemma Meharg PA MAthematics

211. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
0 0 0
100 – 100 = 0
Gemma Meharg PA MAthematics

212. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
0 0 0
Subtract the
tens.
Gemma Meharg PA MAthematics

213. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
0 0 0
8 0
17-tens – 9 tens
= 8-tens
Gemma Meharg PA MAthematics

214. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
0 0 0
8 0
Subtract the
ones.
Gemma Meharg PA MAthematics

215. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
0 0 0
8 0
1
5–4=1
Gemma Meharg PA MAthematics

216. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
0 0 0
8 0
1
+
Add the
differences.
Gemma Meharg PA MAthematics

217. Left to Right
Method 2 WITH Regrouping
1 17
26.1
- 9 4
2 7 5
0 0 0
8 0
1
8 1
+
0 + 80 + 1 = 81
Gemma Meharg PA MAthematics

218. Left to Right
Method 2 WITH Regrouping
27. 5 2 3
- 2 7 8 Look for I.O.U.s.
An I.O.U. means you
cannot do the subtraction
in the place value.
Gemma Meharg PA MAthematics

219. Left to Right
Method 2 WITH Regrouping
Place a circle above
27. 5 2 3
- 2 7 8 the column(s) that
requires an I.O.U.
Gemma Meharg PA MAthematics

220. Left to Right
Method 2 WITH Regrouping
27. 5 2 3
- 2 7 8 Both the 10s and 1s
require an I.O.U.
Gemma Meharg PA MAthematics

221. Left to Right
Method 2 WITH Regrouping
27. 5 2 3
- 2 7 8
Rename the columns.
Gemma Meharg PA MAthematics

222. Left to Right
Method 2 WITH Regrouping
1 13
27. 5 2 3
- 2 7 8
Rename the columns
Gemma Meharg PA MAthematics

223. Left to Right
WITH Regrouping
11
Method 2
4 1 13
27. 5 2 3
- 2 7 8
Rename the columns
Gemma Meharg PA MAthematics

224. Left to Right WITH
Regrouping
11
Method 2
4 1 13
27. 5 2 3
- 2 7 8
Subtract the 100s.
Gemma Meharg PA MAthematics

225. Left to Right WITH
Regrouping
11
Method 2
4 1 13
27. 5 2 3
- 2 7 8
2 0 0
400 – 200 = 200
Gemma Meharg PA MAthematics

226. Left to Right WITH
Regrouping
11
Method 2
4 1 13
27. 5 2 3
- 2 7 8
2 0 0
Subtract the 10s.
Gemma Meharg PA MAthematics

227. Left to Right WITH
Regrouping
11
Method 2
4 1 13
27.2
- 7 8
5 2 3
2 0 0
4 0
11-tens – 7-tens
= 4-tens
Gemma Meharg PA MAthematics

228. Left to Right WITH
Regrouping
11
Method 2
4 1 13
27.2
- 7 8
5 2 3
2 0 0
4 0
Subtract the 1s.
Gemma Meharg PA MAthematics

229. Left to Right WITH
Regrouping
11
Method 2
4 1 13
27.2
- 7 8
5 2 3
2 0 0
4 0
5
13 – 8 = 5
Gemma Meharg PA MAthematics

230. Left to Right WITH
Regrouping
11
Method 2
4 1 13
27.2
- 7 8
5 2 3
2 0 0
4 0
5
+
Add the
differences.
Gemma Meharg PA MAthematics

231. Left to Right WITH
Regrouping
11
Method 2
4 1 13
27.2
- 7 8
5 2 3
2 0 0
4 0
5
2 4 5
+
200 + 40 + 5 =
245.
Gemma Meharg PA MAthematics

232. Abstract Stage of Singapore
Mathematics
Ends with traditional “short-cut” method:
1
25
+ 17
42
Gemma Meharg PA MAthematics

233. 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

234. Linda King
Singapore Math Coach
Lking@windsor.k12.mo.us
(636) 464 – 4400, extension 4399
Gemma Meharg PA MAthematics