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1. 1. SingaporeMathematics
2. 2. Singapore MathematicsThis program teaches kids to UNDERSTAND mathematical processes through 3 stages:Concrete Pictorial Abstract Gemma Meharg PA MAthematics
3. 3. Concrete Stage of SingaporeMathematics 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. 4. Singapore MathematicsConcrete Pictorial Abstract Gemma Meharg PA MAthematics
5. 5. Pictorial Stage of SingaporeMathematicsThe 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. 6. Branching 1. 34 + 5 “Ring” the 10s. 4 5 30 + Gemma Meharg PA MAthematics
7. 7. Branching Add the tens. 1. 34 + 5 4 5 30 + 30 + 0 = 30 Gemma Meharg PA MAthematics
8. 8. Branching Add the ones. 1. 34 + 5 4 5 30 + 30 + 0 = 30 5+4=9 Gemma Meharg PA MAthematics
9. 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. 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. 11. Branching on your own. 2. 24 + 32 = 20 4 + 2 30 Gemma Meharg PA MAthematics
12. 12. Branching on your own. 2. 24 + 32 = Ring the tens. 20 4 + 2 30 Gemma Meharg PA MAthematics
13. 13. Branching on your own. 2. 24 + 32 = 20 4 + 2 30 Gemma Meharg PA MAthematics
14. 14. Branching on your own. Now, add the tens. 2. 24 + 32 = 20 4 + 2 30 Gemma Meharg PA MAthematics
15. 15. Branching on your own. 2. 24 + 32 = 20 4 + 2 30 20 + 30 = 50 Gemma Meharg PA MAthematics
16. 16. Branching on your own. 2. 24 + 32 = Add the ones. 20 4 + 2 30 20 + 30 = 50 Gemma Meharg PA MAthematics
17. 17. Branching on your own. 2. 24 + 32 = 20 4 + 2 30 20 + 30 = 50 4+2=6 Gemma Meharg PA MAthematics
18. 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. 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. 20. Branching on your own. 3. 73 + 16 = Gemma Meharg PA MAthematics
21. 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. 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. 23. Branching with subtraction. 4. 48 - 32 = 40 8 - 2 30 Be sure to place the subtraction sign. Gemma Meharg PA MAthematics
24. 24. Branching with subtraction. Subtract the 10s. 4. 48 - 32 = 40 8 - 2 30 Gemma Meharg PA MAthematics
25. 25. Branching with subtraction. 4. 48 - 32 = 40 8 - 2 30 40 - 30 = 10 Gemma Meharg PA MAthematics
26. 26. Branching with subtraction. Subtract the 1s. 4. 48 - 32 = 40 8 - 2 30 40 - 30 = 10 Gemma Meharg PA MAthematics
27. 27. Branching with subtraction. 4. 48 - 32 = 40 8 - 2 30 40 - 30 = 10 8–2=6 Gemma Meharg PA MAthematics
28. 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. 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. 30. Branching on your own. Branch the 10s and 1s. 5. 78 - 20 = 10 on the outside. Gemma Meharg PA MAthematics
31. 31. Branching on your own. 5. 78 - 20 = 70 8 - 0 20 Gemma Meharg PA MAthematics
32. 32. Branching on your own. Ring the 10s. 5. 78 - 20 = 70 8 - 0 20 Gemma Meharg PA MAthematics
33. 33. Branching on your own. 5. 78 - 20 = 70 8 - 0 20 Gemma Meharg PA MAthematics
34. 34. Branching on your own. Subtract the 10s. 5. 78 - 20 = 70 8 - 0 20 Gemma Meharg PA MAthematics
35. 35. Branching on your own. 5. 78 - 20 = 70 8 - 0 20 70 - 20 = 50 Gemma Meharg PA MAthematics
36. 36. Branching on your own. Subtract the 1s. 5. 78 - 20 = 70 8 - 0 20 70 - 20 = 50 Gemma Meharg PA MAthematics
37. 37. Branching on your own. 5. 78 - 20 = 70 8 - 0 20 70 - 20 = 50 8–0=8 Gemma Meharg PA MAthematics
38. 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. 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. 40. Branching on your own. 6. 95 - 41 = Gemma Meharg PA MAthematics
41. 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. 42. Branching WITH regrouping. 7. 7 + 9 = Branching can be used to help students learn sums greater than 10. Gemma Meharg PA MAthematics
43. 43. Branching WITH regrouping. 7. 7 + 9 = Think: What could be added to 7 to make 10? Gemma Meharg PA MAthematics
44. 44. Branching WITH regrouping. 7. 7 + 9 = 3 7 + 3 = 10 Branch 3 from 9. Ring the 10. Gemma Meharg PA MAthematics
45. 45. Branching WITH regrouping. 7. 7 + 9 = 3 Branch the other addend from the 2nd addend. 3+_=9 Gemma Meharg PA MAthematics
46. 46. Branching WITH regrouping. 7. 7 + 9 = 3 6 Now add. Gemma Meharg PA MAthematics
47. 47. Branching WITH regrouping. 7. 7 + 9 = 3 6 10 + 6 = 16 Gemma Meharg PA MAthematics
48. 48. Branching on your own. 8. 4 + 8 = What can I add to 4 to make 10? Gemma Meharg PA MAthematics
49. 49. Branching on your own. 8. 4 + 8 = 6 Ring the 10. Gemma Meharg PA MAthematics
50. 50. Branching on your own. 8. 4 + 8 = 6 Gemma Meharg PA MAthematics
51. 51. Branching on your own. 8. 4 + 8 = 6 Complete branching of 8. 6 + __ = 8 Gemma Meharg PA MAthematics
52. 52. Branching on your own. 8. 4 + 8 = 6 2 Gemma Meharg PA MAthematics
53. 53. Branching on your own. 8. 4 + 8 = 6 2 Now add. Gemma Meharg PA MAthematics
54. 54. Branching on your own. 8. 4 + 8 = 6 2 10 + 2 = 12 Gemma Meharg PA MAthematics
55. 55. Branching on your own. 9. 3 + 9 = Gemma Meharg PA MAthematics
56. 56. Branching on your own. 9. 3 + 9 = Remember to make 10. Then ring the 10. Gemma Meharg PA MAthematics
57. 57. Branching on your own. Now add. 9. 3 + 9 = 7 2 Gemma Meharg PA MAthematics
58. 58. Branching on your own. 9. 3 + 9 = 7 2 10 + 2 = 12 Gemma Meharg PA MAthematics
59. 59. Branching WITH regrouping. 10. 15 + 28 = Branch the addends into 10s and 1s. Branch 10s to the OUTSIDE. Gemma Meharg PA MAthematics
60. 60. Branching WITH regrouping. 10. 15 + 28 = 10 5 + 8 20 Gemma Meharg PA MAthematics
61. 61. Branching WITH regrouping. 10. 15 + 28 = Ring the 10s. 10 5 + 8 20 Gemma Meharg PA MAthematics
62. 62. Branching WITH regrouping. 10. 15 + 28 = 10 5 + 8 20 Gemma Meharg PA MAthematics
63. 63. Branching WITH regrouping. 10. 15 + 28 = Add the 10s. 10 5 + 8 20 10 + 20 = 30 Gemma Meharg PA MAthematics
64. 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. 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. 66. Branching WITH regrouping. 10. 15 + 28 = 10 5 + 8 20 5 10 + 20 = 30 Gemma Meharg PA MAthematics
67. 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. 68. Branching WITH regrouping. 10. 15 + 28 = 10 5 + 8 20 5 3 10 + 20 = 30 Gemma Meharg PA MAthematics
69. 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. 70. Branching WITH regrouping. Now add 1s. 10. 15 + 28 = 10 5 + 8 20 5 3 10 + 20 = 30 Gemma Meharg PA MAthematics
71. 71. Branching WITH regrouping. 10. 15 + 28 = 10 5 + 8 20 5 3 10 + 20 = 30 10 + 3 = 13 Gemma Meharg PA MAthematics
72. 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. 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. 74. Branching on your own. Branch the 10s and 1s. 11. 49 + 43 = Gemma Meharg PA MAthematics
75. 75. Branching on your own. 11. 49 + 43 = 40 9 + 3 40 Gemma Meharg PA MAthematics
76. 76. Branching on your own. Now ring the 10s. 11. 49 + 43 = 40 9 + 3 40 Gemma Meharg PA MAthematics
77. 77. Branching on your own. 11. 49 + 43 = 40 9 + 3 40 Gemma Meharg PA MAthematics
78. 78. Branching on your own. Now add the tens. 11. 49 + 43 = 40 9 + 3 40 Gemma Meharg PA MAthematics
79. 79. Branching on your own. 11. 49 + 43 = 40 9 + 3 40 40 + 40 = 80 Gemma Meharg PA MAthematics
80. 80. Branching on your own. Now add the ones. 11. 49 + 43 = 40 9 + 3 40 40 + 40 = 80 Gemma Meharg PA MAthematics
81. 81. Branching on your own. 11. 49 + 43 = 40 9 + 3 40 40 + 40 = 80 9 + 3 = 12 Gemma Meharg PA MAthematics
82. 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. 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. 84. Branching on your own. 12. 96 + 17 = Gemma Meharg PA MAthematics
85. 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. 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. 87. Branching WITH regrouping. Branch into 10s and 1s. Ring 13. 85 - 28 = the 10s. Gemma Meharg PA MAthematics
88. 88. Branching WITH regrouping. Remember the subtraction sign. 13. 85 - 28 = 80 5 - 8 20 Gemma Meharg PA MAthematics
89. 89. Branching WITH regrouping. Look at the 1s. 13. 85 - 28 = We can rename. 80 5 - 8 20 Gemma Meharg PA MAthematics
90. 90. Branching WITH regrouping. 13. 85 - 28 = 80 5 - 8 20 Students can use disks to help with renaming. Gemma Meharg PA MAthematics
91. 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. 92. Branching WITH regrouping. Subtract the 10s. 13. 85 - 28 = 80 5 - 8 20 70 15 70 – 20 = 50 Gemma Meharg PA MAthematics
93. 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. 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. 95. Branching on your own Branch. Ring the 10s. 14. 70 - 43 = Gemma Meharg PA MAthematics
96. 96. Branching on your own 14. 70 - 43 = 70 0 - 3 40 Gemma Meharg PA MAthematics
97. 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. 98. Branching on your own Rename 70 + 0 as 60 + 10. 14. 70 - 43 = 70 0 - 3 40 Gemma Meharg PA MAthematics
99. 99. Branching on your own 14. 70 - 43 = 70 0 - 3 40 60 10 Gemma Meharg PA MAthematics
100. 100. Branching on your own Subtract the 10s. 14. 70 - 43 = 70 0 - 3 40 60 10 Gemma Meharg PA MAthematics
101. 101. Branching on your own 14. 70 - 43 = 70 0 - 3 40 60 10 60 – 40 = 20 Gemma Meharg PA MAthematics
102. 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. 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. 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. 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. 106. Branching on your own 15. 96 - 17 = Gemma Meharg PA MAthematics
107. 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. 108. Singapore MathematicsConcrete Pictorial Abstract Gemma Meharg PA MAthematics
109. 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. 110. Left to Right Addition 35 16. + 22 50 + 7 Next, add the 1s: 5+2=7 Gemma Meharg PA MAthematics
111. 111. Left to Right Addition 35 + 22 50 + 16. 7 57 Last, add the sums: 50 + 7 = 57 Gemma Meharg PA MAthematics
112. 112. Left to Right on your own. 17. 221 + 345 Add the 100s Gemma Meharg PA MAthematics
113. 113. Left to Right on your own. 17. 221 + 345 500 200 + 300 = 500 Gemma Meharg PA MAthematics
114. 114. Left to Right on your own. 17. 221 + 345 500 Add the 10s. Gemma Meharg PA MAthematics
115. 115. Left to Right on your own. 17. 221 + 345 500 60 20 + 40 = 60 Gemma Meharg PA MAthematics
116. 116. Left to Right on your own. 17. 221 + 345 500 60 Add the 1s. Gemma Meharg PA MAthematics
117. 117. Left to Right on your own. 17. 221 + 345 500 60 6 1+5=6 Gemma Meharg PA MAthematics
118. 118. Left to Right on your own. 17. 221 + 345 500 60 6 + Last, add the sums. Gemma Meharg PA MAthematics
119. 119. Left to Right on your own. 17. 221 + 345 500 60 6 566 + 500 + 60 + 6 = 566 Gemma Meharg PA MAthematics
120. 120. Left to Right on your own. 18. 430 + 559 Gemma Meharg PA MAthematics
121. 121. Left to Right on your own. 18. 430 + 559 900 80 9 989 + Gemma Meharg PA MAthematics
122. 122. Left to Right Subtraction 19. 48 – 21 Subtract the 10s. Gemma Meharg PA MAthematics
123. 123. Left to Right Subtraction 19. 48 – 21 20 40 – 20 = 20 Gemma Meharg PA MAthematics
124. 124. Left to Right Subtraction 19. 48 – 21 20 Subtract the 1s. Gemma Meharg PA MAthematics
125. 125. Left to Right Subtraction 19. 48 – 21 20 7 8–1=7 Gemma Meharg PA MAthematics
126. 126. Left to Right Subtraction 19. 48 – 21 20 7 + Add the differences. Gemma Meharg PA MAthematics
127. 127. Left to Right Subtraction 19. 48 – 21 20 7 27 + 20 + 7 = 27 Gemma Meharg PA MAthematics
128. 128. Left to Right on your own. 20. 878 – 213 Subtract the 100s. Gemma Meharg PA MAthematics
129. 129. Left to Right on your own. 20. 878 – 213 600 800 – 200 = 600 Gemma Meharg PA MAthematics
130. 130. Left to Right on your own. 20. 878 – 213 600 Subtract the 10s. Gemma Meharg PA MAthematics
131. 131. Left to Right on your own. 20. 878 – 213 600 60 70 – 10 = 60 Gemma Meharg PA MAthematics
132. 132. Left to Right on your own. 20. 878 – 213 600 60 Subtract the 1s. Gemma Meharg PA MAthematics
133. 133. Left to Right on your own. 20. 878 – 213 600 60 5 8–3=5 Gemma Meharg PA MAthematics
134. 134. Left to Right on your own. 20. – 213 878 600 60 5 + Add the differences. Gemma Meharg PA MAthematics
135. 135. Left to Right on your own. 20. – 213 878 600 60 5 665 + 600 + 60 + 5 = 665 Gemma Meharg PA MAthematics
136. 136. Left to Right on your own. 21. 978 – 256 Gemma Meharg PA MAthematics
137. 137. Left to Right on your own. 21. 978 – 256 700 20 2 722 + Gemma Meharg PA MAthematics
138. 138. Left to Right WITHRegrouping22. + 25 35 Add the tens. Gemma Meharg PA MAthematics
139. 139. Left to Right WITHRegrouping22. + 25 35 20 + 30 = 50 50 Gemma Meharg PA MAthematics
140. 140. Left to Right WITHRegrouping22. + 25 35 50 Add the 1s. Gemma Meharg PA MAthematics
141. 141. Left to Right WITHRegrouping22. + 25 35 50 10 5 + 5 = 10 Gemma Meharg PA MAthematics
142. 142. Left to Right WITHRegrouping22. + 25 35 50 10 60 + Add the sums. Gemma Meharg PA MAthematics
143. 143. Left to Right on your own.23. 149 + 522 Add the hundreds. Gemma Meharg PA MAthematics
144. 144. Left to Right on your own. 23. 149 + 522 600 100 + 500 = 600 Gemma Meharg PA MAthematics
145. 145. Left to Right on your own. 23. 149 + 522 600 Add the 10s. Gemma Meharg PA MAthematics
146. 146. Left to Right on your own. 23. 149 + 522 600 60 40 + 20 = 60 Gemma Meharg PA MAthematics
147. 147. Left to Right on your own. 23. 149 + 522 600 60 Add the 1s. Gemma Meharg PA MAthematics
148. 148. Left to Right on your own. 23. 149 + 522 600 60 11 + 9 + 2 = 11 Gemma Meharg PA MAthematics
149. 149. Left to Right on your own. 23. + 522 149 600 60 11 + Add the sums. Gemma Meharg PA MAthematics
150. 150. Left to Right on your own. 23. + 522 149 600 60 11 671 + 600 + 60 + 11 = 671 Gemma Meharg PA MAthematics
151. 151. Left to Right on your own.24. 645 + 397 Gemma Meharg PA MAthematics
152. 152. Left to Right on your own.24.397 + 645 900 130 12 1,042 + Gemma Meharg PA MAthematics
153. 153. Left to Right SubtractionwithRenaming/RegroupingThe 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. 154. Left to RightMethod 1 WITH Regrouping 25. 145 - 117 Subtract the 100s. Gemma Meharg PA MAthematics
155. 155. Left to RightMethod 1 WITH Regrouping 25. 145 - 117 000 100 – 100 = 0 Gemma Meharg PA MAthematics
156. 156. Left to RightMethod 1 WITH Regrouping 25. 145 - 117 000 Subtract the 10s. Gemma Meharg PA MAthematics
157. 157. Left to RightMethod 1 WITH Regrouping 25. 145 - 117 000 30 40 – 10 = 30 Gemma Meharg PA MAthematics
158. 158. Left to RightMethod 1 WITH Regrouping 145 25.117 - 000 30 Subtract the 1s. Gemma Meharg PA MAthematics
159. 159. Left to RightMethod 1 WITH Regrouping 145 25.117 - 000 30 2 5–7= - I.O.U. 2 or -2 Gemma Meharg PA MAthematics
160. 160. Use the number line to count7 back from 5 to –2. Gemma Meharg PA MAthematics
161. 161. Left to RightMethod 1 WITH Regrouping 145 25.117 - 000 30 2 - Count back 2 from 30. Gemma Meharg PA MAthematics
162. 162. Left to RightMethod 1 WITH Regrouping 145 25.117 - 000 30 2 - Count back because of the subtraction sign or -2. Gemma Meharg PA MAthematics
163. 163. Left to RightMethod 1 WITH Regrouping 145 25.117 - 000 30 2 28 - Count back 2 from 30 = 29, 28 Gemma Meharg PA MAthematics
164. 164. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 Subtract the 100s. Gemma Meharg PA MAthematics
165. 165. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 200 – 100 = 100 Gemma Meharg PA MAthematics
166. 166. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 Subtract the 10s. Gemma Meharg PA MAthematics
167. 167. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 70 – 90 = ? Use the number line. Gemma Meharg PA MAthematics
168. 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. 169. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 70 – 90 = I.O.U. 20 - 20 or –20. Gemma Meharg PA MAthematics
170. 170. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 - 20 Subtract before moving to 1s. Gemma Meharg PA MAthematics
171. 171. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 - 20 Count backward 80 2-tens from 100: 90, 80. Gemma Meharg PA MAthematics
172. 172. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 - 20 80 Subtract the 1s. Gemma Meharg PA MAthematics
173. 173. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 - 20 80 1 5–4=1 Gemma Meharg PA MAthematics
174. 174. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 - 20 80 Put the 10s and 1s + 1 together. Gemma Meharg PA MAthematics
175. 175. Left to RightMethod 1 WITH Regrouping 26. 275 - 194 100 - 20 80 + 1 81 80 +1 = 81 Gemma Meharg PA MAthematics
176. 176. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 Subtract the 100s. Gemma Meharg PA MAthematics
177. 177. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 500 – 200 = 300 Gemma Meharg PA MAthematics
178. 178. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 Subtract the 10s. Gemma Meharg PA MAthematics
179. 179. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 Count backwards on the number line. Gemma Meharg PA MAthematics
180. 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. 181. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 - 50 20 – 70 = I.O.U. 50 or –50. Gemma Meharg PA MAthematics
182. 182. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 - 50 Count back 5 tens from 300. Gemma Meharg PA MAthematics
183. 183. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 - 50 250 290, 280, 270, 260, 250 Gemma Meharg PA MAthematics
184. 184. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 - 50 250 Subtract the 1s. Gemma Meharg PA MAthematics
185. 185. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 - 50 250 - 5 3 – 8 = I.O.U. 5 or -5. Gemma Meharg PA MAthematics
186. 186. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 50 250 5 - - Count 5 backward from 250. Gemma Meharg PA MAthematics
187. 187. Left to RightMethod 1 WITH Regrouping 27. 523 - 278 300 50 250 - 5 245 - 249, 248, 247, 246, 245 Gemma Meharg PA MAthematics
188. 188. Left to RightMethod 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. 189. Left to RightMethod 2 WITH Regrouping 25. 1 4 5 - 1 1 7 1s column: 5 - 7 Gemma Meharg PA MAthematics
190. 190. Left to RightMethod 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. 191. Left to RightMethod 2 WITH Regrouping 25. 1 4 5 - 1 1 7 Now we rename or regroup. Gemma Meharg PA MAthematics
192. 192. Left to RightMethod 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. 193. Left to RightMethod 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. 194. Left to RightMethod 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. 195. Left to RightMethod 2 WITH Regrouping 3 15 25. 1 4 5 - 1 1 7 Subtract the 100s. Gemma Meharg PA MAthematics
196. 196. Left to RightMethod 2 WITH Regrouping 3 15 25. 1 4 5 - 1 1 7 0 0 0 100 – 100 = 0 Gemma Meharg PA MAthematics
197. 197. Left to RightMethod 2 WITH Regrouping 3 15 25.1 - 1 7 1 4 5 0 0 0 Subtract the 10s. Gemma Meharg PA MAthematics
198. 198. Left to RightMethod 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. 199. Left to RightMethod 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. 200. Left to RightMethod 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. 201. Left to RightMethod 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. 202. Left to RightMethod 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. 203. Left to RightMethod 2 WITH Regrouping 26.1 - 9 4 2 7 5 Look for I.O.U.s. Gemma Meharg PA MAthematics
204. 204. Left to RightMethod 2 WITH Regrouping 26.1 - 9 4 2 7 5 10 column: 7-tens – 9-tens Gemma Meharg PA MAthematics
205. 205. Left to RightMethod 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. 206. Left to RightMethod 2 WITH Regrouping 26.1 - 9 4 2 7 5 Now we rename or regroup. Gemma Meharg PA MAthematics
207. 207. Left to RightMethod 2 WITH Regrouping 1 Take 1-hundred 26.1 - 9 4 2 7 5 from 2-hundreds = 1-hundreds. Gemma Meharg PA MAthematics
208. 208. Left to RightMethod 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. 209. Left to RightMethod 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. 210. Left to RightMethod 2 WITH Regrouping 1 17 26.1 - 9 4 2 7 5 Subtract the 100s. Gemma Meharg PA MAthematics
211. 211. Left to RightMethod 2 WITH Regrouping 1 17 26.1 - 9 4 2 7 5 0 0 0 100 – 100 = 0 Gemma Meharg PA MAthematics
212. 212. Left to RightMethod 2 WITH Regrouping 1 17 26.1 - 9 4 2 7 5 0 0 0 Subtract the tens. Gemma Meharg PA MAthematics
213. 213. Left to RightMethod 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. 214. Left to RightMethod 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. 215. Left to RightMethod 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. 216. Left to RightMethod 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. 217. Left to RightMethod 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. 218. Left to RightMethod 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. 219. Left to RightMethod 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. 220. Left to RightMethod 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. 221. Left to RightMethod 2 WITH Regrouping 27. 5 2 3 - 2 7 8 Rename the columns. Gemma Meharg PA MAthematics
222. 222. Left to RightMethod 2 WITH Regrouping 1 13 27. 5 2 3 - 2 7 8 Rename the columns Gemma Meharg PA MAthematics
223. 223. Left to Right WITH Regrouping 11Method 2 4 1 13 27. 5 2 3 - 2 7 8 Rename the columns Gemma Meharg PA MAthematics
224. 224. Left to Right WITHRegrouping 11Method 2 4 1 13 27. 5 2 3 - 2 7 8 Subtract the 100s. Gemma Meharg PA MAthematics
225. 225. Left to Right WITHRegrouping 11Method 2 4 1 13 27. 5 2 3 - 2 7 8 2 0 0 400 – 200 = 200 Gemma Meharg PA MAthematics
226. 226. Left to Right WITHRegrouping 11Method 2 4 1 13 27. 5 2 3 - 2 7 8 2 0 0 Subtract the 10s. Gemma Meharg PA MAthematics
227. 227. Left to Right WITHRegrouping 11Method 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. 228. Left to Right WITHRegrouping 11Method 2 4 1 13 27.2 - 7 8 5 2 3 2 0 0 4 0 Subtract the 1s. Gemma Meharg PA MAthematics
229. 229. Left to Right WITHRegrouping 11Method 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. 230. Left to Right WITHRegrouping 11Method 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. 231. Left to Right WITHRegrouping 11Method 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. 232. Abstract Stage of SingaporeMathematics Ends with traditional “short-cut” method: 1 25 + 17 42 Gemma Meharg PA MAthematics
233. 233. WHY are we doing all these extrasteps in Singapore Math? Branching and Left-to-Right Methods build understanding as students learn computation. Gemma Meharg PA MAthematics
234. 234. Linda King Singapore Math Coach Lking@windsor.k12.mo.us(636) 464 – 4400, extension 4399 Gemma Meharg PA MAthematics