Upcoming SlideShare
×

# MCTM Strategies & Games

3,824 views
3,790 views

Published on

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
3,824
On SlideShare
0
From Embeds
0
Number of Embeds
4
Actions
Shares
0
17
0
Likes
0
Embeds 0
No embeds

No notes for slide

### MCTM Strategies & Games

1. 1. Teaching the Arithmetic Facts Using Strategies and Games by Joan A. Cotter, Ph.D. JoanCotter@RightStartMath.com MCTM May 4, 2012 Duluth, Minnesota 7 3 8 16 24 32 40PowerPoint Presentation & Handout RightStartMath.com >Resources © Joan A. Cotter, Ph.D., 2012
2. 2. Learning the Facts © Joan A. Cotter, Ph.D., 2012
3. 3. Learning the FactsLimited success when:• Based on counting. Whether dots, fingers, number lines, or counting words. © Joan A. Cotter, Ph.D., 2012
4. 4. Learning the FactsLimited success when:• Based on counting. Whether dots, fingers, number lines, or counting words.• Based on rote memory. Whether by flash cards or timed tests. © Joan A. Cotter, Ph.D., 2012
5. 5. Learning the FactsLimited success when:• Based on counting. Whether dots, fingers, number lines, or counting words.• Based on rote memory. Whether by flash cards or timed tests.• Based on skip counting for multiplication facts. © Joan A. Cotter, Ph.D., 2012
6. 6. Counting ModelFrom a childs perspective © Joan A. Cotter, Ph.D., 2012
7. 7. Counting Model From a childs perspectiveBecause we’re so familiar with 1, 2, 3, we’ll use letters. A=1 B=2 C=3 D=4 E = 5, and so forth © Joan A. Cotter, Ph.D., 2012
8. 8. Counting ModelFrom a childs perspective F +E © Joan A. Cotter, Ph.D., 2012
9. 9. Counting Model From a childs perspective F +EA © Joan A. Cotter, Ph.D., 2012
10. 10. Counting Model From a childs perspective F +EA B © Joan A. Cotter, Ph.D., 2012
11. 11. Counting Model From a childs perspective F +EA B C © Joan A. Cotter, Ph.D., 2012
12. 12. Counting Model From a childs perspective F +EA B C D E F © Joan A. Cotter, Ph.D., 2012
13. 13. Counting Model From a childs perspective F +EA B C D E F A © Joan A. Cotter, Ph.D., 2012
14. 14. Counting Model From a childs perspective F +EA B C D E F A B © Joan A. Cotter, Ph.D., 2012
15. 15. Counting Model From a childs perspective F +EA B C D E F A B C D E © Joan A. Cotter, Ph.D., 2012
16. 16. Counting Model From a childs perspective F +EA B C D E F A B C D E What is the sum? (It must be a letter.) © Joan A. Cotter, Ph.D., 2012
17. 17. Counting Model From a childs perspective F +E KA B C D E F G H I J K © Joan A. Cotter, Ph.D., 2012
18. 18. Counting ModelFrom a childs perspective E +G Add with your fingers. © Joan A. Cotter, Ph.D., 2012
19. 19. Counting ModelFrom a childs perspective H +DAdd without your fingers. © Joan A. Cotter, Ph.D., 2012
20. 20. Counting Model From a childs perspectiveNow memorize the facts!! G +D © Joan A. Cotter, Ph.D., 2012
21. 21. Counting Model From a childs perspectiveNow memorize the facts!! H + G F +D © Joan A. Cotter, Ph.D., 2012
22. 22. Counting Model From a childs perspectiveNow memorize the facts!! H + G F +D D+C © Joan A. Cotter, Ph.D., 2012
23. 23. Counting Model From a childs perspectiveNow memorize the facts!! H + G F +D D C+C +G © Joan A. Cotter, Ph.D., 2012
24. 24. Counting Model From a childs perspective Now memorize the facts!! HE + G I F+ +D D C +C +G © Joan A. Cotter, Ph.D., 2012
25. 25. Counting Model From a childs perspective H –ESubtract with your fingers. © Joan A. Cotter, Ph.D., 2012
26. 26. Counting Model From a childs perspective J –FSubtract without using your fingers. © Joan A. Cotter, Ph.D., 2012
27. 27. Counting Model From a childs perspectiveTry skip counting by B’s to T: B, D, . . . T. © Joan A. Cotter, Ph.D., 2012
28. 28. Counting Model From a childs perspectiveTry skip counting by B’s to T: B, D, . . . T.What is D x E? © Joan A. Cotter, Ph.D., 2012
29. 29. Memorizing Math © Joan A. Cotter, Ph.D., 2012
30. 30. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
31. 31. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
32. 32. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
33. 33. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
34. 34. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
35. 35. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
36. 36. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
37. 37. Memorizing Math 9 +7Flash cards: © Joan A. Cotter, Ph.D., 2012
38. 38. Memorizing Math 9 +7Flash cards:• Are often used to teach rote. © Joan A. Cotter, Ph.D., 2012
39. 39. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them. © Joan A. Cotter, Ph.D., 2012
40. 40. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them.• Don’t work for those with learning disabilities. © Joan A. Cotter, Ph.D., 2012
41. 41. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them.• Don’t work for those with learning disabilities.• Give the false impression that math isn’t aboutthinking. © Joan A. Cotter, Ph.D., 2012
42. 42. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them.• Don’t work for those with learning disabilities.• Give the false impression that math isn’t aboutthinking.• Often produce stress – children under stress stoplearning. © Joan A. Cotter, Ph.D., 2012
43. 43. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them.• Don’t work for those with learning disabilities.• Give the false impression that math isn’t aboutthinking.• Often produce stress – children under stress stoplearning.• Are not concrete – they use abstract symbols. © Joan A. Cotter, Ph.D., 2012
44. 44. AN ALTERNATIVE: SUBITIZING and GAMES © Joan A. Cotter, Ph.D., 2012
45. 45. Subitizing QuantitiesIdentifying without counting © Joan A. Cotter, Ph.D., 2012
46. 46. Subitizing Quantities Identifying without counting• Five-month-old infants can subitize to 3. © Joan A. Cotter, Ph.D., 2012
47. 47. Subitizing Quantities Identifying without counting• Five-month-old infants can subitize to 3.• Three-year-olds can subitize to 5. © Joan A. Cotter, Ph.D., 2012
48. 48. Subitizing Quantities Identifying without counting• Five-month-old infants can subitize to 3.• Three-year-olds can subitize to 5.• Five-year-olds can subitize 6 to 10 byusing five as a subbase. © Joan A. Cotter, Ph.D., 2012
49. 49. AddingName the quantity (practice subitizing). © Joan A. Cotter, Ph.D., 2012
50. 50. AddingName the quantity (practice subitizing). © Joan A. Cotter, Ph.D., 2012
51. 51. AddingName the quantity (practice subitizing). © Joan A. Cotter, Ph.D., 2012
57. 57. Characteristics of a Good Game © Joan A. Cotter, Ph.D., 2012
58. 58. Characteristics of a Good Game • Produces learning through playing. © Joan A. Cotter, Ph.D., 2012
59. 59. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. © Joan A. Cotter, Ph.D., 2012
60. 60. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. © Joan A. Cotter, Ph.D., 2012
61. 61. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. • Encourages mental work. © Joan A. Cotter, Ph.D., 2012
62. 62. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. • Encourages mental work. • Detects errors; provides continuous assessment. © Joan A. Cotter, Ph.D., 2012
63. 63. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. • Encourages mental work. • Detects errors; provides continuous assessment. • Is enjoyable. © Joan A. Cotter, Ph.D., 2012
64. 64. Go to the Dump GameObjective: To learn the facts that total 10: 1+9 2+8 3+7 4+6 5+5 © Joan A. Cotter, Ph.D., 2012
65. 65. Go to the Dump GameObjective: To learn the facts that total 10: 1+9 2+8 3+7 4+6 5+5Object of the game: To collect the most pairs that equal ten. © Joan A. Cotter, Ph.D., 2012
66. 66. Go to the Dump Game 6+ = 10 © Joan A. Cotter, Ph.D., 2012
67. 67. Go to the Dump Game 6+ = 10 © Joan A. Cotter, Ph.D., 2012
68. 68. Go to the Dump Game 6 + 4 = 10 © Joan A. Cotter, Ph.D., 2012
69. 69. Go to the Dump Game Starting © Joan A. Cotter, Ph.D., 2012
70. 70. Go to the Dump Game 72 7 9 5 72 1 3 8 4 6 34 9 Starting © Joan A. Cotter, Ph.D., 2012
71. 71. Go to the Dump Game 72 7 9 5 72 1 3 8 4 6 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
72. 72. Go to the Dump Game 72 7 9 5 72 1 3 8 4 6 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
73. 73. Go to the Dump Game 72 7 9 5 72 1 3 8 4 6 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
74. 74. Go to the Dump Game 72 7 9 5 4 6 72 1 3 8 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
75. 75. Go to the Dump Game 72 7 9 5 4 6 72 1 3 8 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
76. 76. Go to the Dump Game 72 7 9 5 4 6 72 1 3 8 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
77. 77. Go to the Dump Game 72 7 9 5 7 3 4 6 2 1 8 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
78. 78. Go to the Dump Game 72 7 9 5 2 8 4 6 1 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
79. 79. Go to the Dump Game 72 7 9 5 2 8 4 6 1 34 9 Playing © Joan A. Cotter, Ph.D., 2012
80. 80. Go to the Dump Game BlueCap, do you have an3? have a 3? 72 7 9 5 2 8 4 6 1 34 9 Playing © Joan A. Cotter, Ph.D., 2012
81. 81. Go to the Dump Game BlueCap, do you have an3? have a 3? 72 7 9 5 3 2 8 4 6 1 4 9 Playing © Joan A. Cotter, Ph.D., 2012
82. 82. Go to the Dump Game 7 3 BlueCap, do you have an3? have a 3? 2 7 9 5 2 8 4 6 1 4 9 Playing © Joan A. Cotter, Ph.D., 2012
83. 83. Go to the Dump Game 7 3 BlueCap, do you have an3? have a 8? 2 7 9 5 2 8 4 6 1 4 9 Playing © Joan A. Cotter, Ph.D., 2012
84. 84. Go to the Dump Game 7 3 BlueCap, do you have an3? have a 8? 2 7 9 5 2 8 4 6 1 4 9 Go to the dump. Playing © Joan A. Cotter, Ph.D., 2012
85. 85. Go to the Dump Game 7 3 BlueCap, do you have an3? have a 8? 2 2 7 9 5 2 8 4 6 1 4 9 Go to the dump. Playing © Joan A. Cotter, Ph.D., 2012
86. 86. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 4 9 Playing © Joan A. Cotter, Ph.D., 2012
87. 87. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 4 9 PinkCap, do you Playing have a 6? © Joan A. Cotter, Ph.D., 2012
88. 88. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 4 9 PinkCap, do youGo to the dump. Playing have a 6? © Joan A. Cotter, Ph.D., 2012
89. 89. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 5 4 9 Playing © Joan A. Cotter, Ph.D., 2012
90. 90. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 5 4 9 Playing © Joan A. Cotter, Ph.D., 2012
91. 91. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 5 4 9YellowCap, doyou have a 9? Playing © Joan A. Cotter, Ph.D., 2012
92. 92. Go to the Dump Game 7 3 2 2 7 5 2 8 4 6 1 5 4 9YellowCap, doyou have a 9? Playing © Joan A. Cotter, Ph.D., 2012
93. 93. Go to the Dump Game 7 3 2 2 7 5 2 8 4 6 19 5 4 9YellowCap, doyou have a 9? Playing © Joan A. Cotter, Ph.D., 2012
94. 94. Go to the Dump Game 7 3 2 2 7 5 2 1 8 9 4 6 5 4 9 Playing © Joan A. Cotter, Ph.D., 2012
95. 95. Go to the Dump Game 7 3 2 2 7 5 2 1 8 9 4 62 9 1 7 7 5 4 9 Playing © Joan A. Cotter, Ph.D., 2012
96. 96. Go to the Dump Game 9 1 4 6 5 5 Winner? © Joan A. Cotter, Ph.D., 2012
97. 97. Go to the Dump Game 9 1 4 6 5 Winner? © Joan A. Cotter, Ph.D., 2012
98. 98. Go to the Dump Game 9 1 4 6 5 Winner? © Joan A. Cotter, Ph.D., 2012
99. 99. Go to the Dump Game Play it again. © Joan A. Cotter, Ph.D., 2012
100. 100. Fact Strategies © Joan A. Cotter, Ph.D., 2012
101. 101. Fact Strategies• A strategy is a way to learn a new fact orrecall a forgotten fact. © Joan A. Cotter, Ph.D., 2012
102. 102. Fact Strategies• A strategy is a way to learn a new fact orrecall a forgotten fact.• A visualizable representation is part of apowerful strategy. © Joan A. Cotter, Ph.D., 2012
103. 103. Fact Strategies Complete the Ten9+5= © Joan A. Cotter, Ph.D., 2012
104. 104. Fact Strategies Complete the Ten9+5= © Joan A. Cotter, Ph.D., 2012
105. 105. Fact Strategies Complete the Ten9+5= © Joan A. Cotter, Ph.D., 2012
106. 106. Fact Strategies Complete the Ten 9+5=Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
107. 107. Fact Strategies Complete the Ten 9+5=Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
108. 108. Fact Strategies Complete the Ten 9+5=Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
109. 109. Fact Strategies Complete the Ten 9 + 5 = 14Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
110. 110. Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
111. 111. Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
112. 112. Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
113. 113. Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
114. 114. Fact Strategies Two Fives8+6=10 + 4 = 14 © Joan A. Cotter, Ph.D., 2012
115. 115. Fact Strategies Two Fives7+5= © Joan A. Cotter, Ph.D., 2012
116. 116. Fact Strategies Two Fives7+5= © Joan A. Cotter, Ph.D., 2012
117. 117. Fact Strategies Two Fives7 + 5 = 12 © Joan A. Cotter, Ph.D., 2012
118. 118. Fact Strategies Going Down15 – 9 = © Joan A. Cotter, Ph.D., 2012
119. 119. Fact Strategies Going Down15 – 9 = © Joan A. Cotter, Ph.D., 2012
120. 120. Fact Strategies Going Down 15 – 9 =Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
121. 121. Fact Strategies Going Down 15 – 9 =Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
122. 122. Fact Strategies Going Down 15 – 9 =Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
123. 123. Fact Strategies Going Down 15 – 9 = 6Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
124. 124. Fact Strategies Subtract from 1015 – 9 = © Joan A. Cotter, Ph.D., 2012
125. 125. Fact Strategies Subtract from 10 15 – 9 =Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
126. 126. Fact Strategies Subtract from 10 15 – 9 =Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
127. 127. Fact Strategies Subtract from 10 15 – 9 =Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
128. 128. Fact Strategies Subtract from 10 15 – 9 = 6Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
129. 129. Fact Strategies Going Up15 – 9 = © Joan A. Cotter, Ph.D., 2012
130. 130. Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
131. 131. Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
132. 132. Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
133. 133. Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
134. 134. Fact Strategies Going Up 15 – 9 = 1+5=6Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
135. 135. Rows and Columns GameObjective: To find a total of 15 by adding 2, 3, or 4cards in row or column. © Joan A. Cotter, Ph.D., 2012
136. 136. Rows and Columns GameObjective: To find a total of 15 by adding 2, 3, or 4cards in row or column.Object of the game: To collect the most cards. © Joan A. Cotter, Ph.D., 2012
137. 137. Rows and Columns Game 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
138. 138. Rows and Columns Game 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
139. 139. Rows and Columns Game 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
140. 140. Rows and Columns Game 1 9 6 4 3 3 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
141. 141. Rows and Columns Game 7 6 1 9 6 4 3 3 2 1 5 1 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
142. 142. Rows and Columns Game 7 6 1 9 6 4 3 3 2 1 5 1 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
143. 143. Rows and Columns Game 7 6 1 9 6 4 3 3 2 1 5 1 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
144. 144. Rows and Columns Game 1 6 4 3 3 1 5 1 3 8 8 © Joan A. Cotter, Ph.D., 2012
145. 145. Rows and Columns Game © Joan A. Cotter, Ph.D., 2012
146. 146. Multiplication Strategies Basic facts © Joan A. Cotter, Ph.D., 2012
147. 147. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
148. 148. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
149. 149. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
150. 150. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
151. 151. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
152. 152. Multiplication Strategies Basic facts9× 3= © Joan A. Cotter, Ph.D., 2012
153. 153. Multiplication Strategies Basic facts9× 3= © Joan A. Cotter, Ph.D., 2012
154. 154. Multiplication Strategies Basic facts9× 3=30 © Joan A. Cotter, Ph.D., 2012
155. 155. Multiplication Strategies Basic facts9× 3=30 – 3 = 27 © Joan A. Cotter, Ph.D., 2012
156. 156. Multiplication Strategies Basic facts4× 8= © Joan A. Cotter, Ph.D., 2012
157. 157. Multiplication Strategies Basic facts4× 8= © Joan A. Cotter, Ph.D., 2012
158. 158. Multiplication Strategies Basic facts4× 8= © Joan A. Cotter, Ph.D., 2012
159. 159. Multiplication Strategies Basic facts4× 8=20 + 12 = 32 © Joan A. Cotter, Ph.D., 2012
160. 160. Multiplication Strategies Basic facts7× 7= © Joan A. Cotter, Ph.D., 2012
161. 161. Multiplication Strategies Basic facts7× 7= © Joan A. Cotter, Ph.D., 2012
162. 162. Multiplication Strategies Basic facts7× 7=25 © Joan A. Cotter, Ph.D., 2012
163. 163. Multiplication Strategies Basic facts7× 7=25 + 10 + 10 © Joan A. Cotter, Ph.D., 2012
164. 164. Multiplication Strategies Basic facts7× 7=25 + 10 + 10+ 4 = 49 © Joan A. Cotter, Ph.D., 2012
165. 165. Multiples Patterns Twos2 4 6 8 1012 14 16 18 20 © Joan A. Cotter, Ph.D., 2012
166. 166. Multiples Patterns Twos 2 4 6 8 1012 14 16 18 20The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
167. 167. Multiples Patterns Fours 4 8 12 16 2024 28 32 36 40The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
168. 168. Multiples Patterns Sixes and Eights6 12 18 24 3036 42 48 54 608 16 24 32 4048 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
169. 169. Multiples Patterns Sixes and Eights6 12 18 24 3036 42 48 54 608 16 24 32 4048 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
170. 170. Multiples Patterns Sixes and Eights6 12 18 24 3036 42 48 54 608 16 24 32 4048 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
171. 171. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
172. 172. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
173. 173. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
174. 174. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
175. 175. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
176. 176. Multiples Patterns Sixes and Eights 6 12 18 24 30 6× 4 36 42 48 54 60 8 16 24 32 40 48 56 64 72 806 × 4 is the fourth number (multiple). © Joan A. Cotter, Ph.D., 2012
177. 177. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 8× 78 × 7 is the seventh number (multiple). © Joan A. Cotter, Ph.D., 2012
178. 178. Multiples Patterns Nines 9 18 27 36 45 90 81 72 63 54The second row is written in reverse order.Also the digits in each number add to 9. © Joan A. Cotter, Ph.D., 2012
179. 179. Multiples Patterns Threes 3 6 9 2 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
180. 180. Multiples Patterns Threes 3 6 9 2 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
181. 181. Multiples Patterns Threes 3 6 9 2 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
182. 182. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
183. 183. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
184. 184. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
185. 185. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
186. 186. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
187. 187. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
188. 188. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
189. 189. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
190. 190. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns:The tens are the same in each row. © Joan A. Cotter, Ph.D., 2012
191. 191. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns:Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
192. 192. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns:Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
193. 193. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns:Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
194. 194. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
195. 195. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
196. 196. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
197. 197. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
198. 198. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
199. 199. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
200. 200. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
201. 201. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
202. 202. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
203. 203. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
204. 204. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
205. 205. Multiples Memory © Joan A. Cotter, Ph.D., 2012
206. 206. Multiples MemoryObjective: To help the players learn themultiples patterns. © Joan A. Cotter, Ph.D., 2012
207. 207. Multiples MemoryObjective: To help the players learn the multiples patterns.Object of the game: To be the first player to collect all tencards of a multiple in order. © Joan A. Cotter, Ph.D., 2012
208. 208. Multiples Memory 7 14 21 28 35 42 49 56 63 70The 7s envelope contains 10 cards,each with one of the numbers listed. © Joan A. Cotter, Ph.D., 2012
209. 209. Multiples Memory 8 16 24 32 40 48 56 64 72 80The 8s envelope contains 10 cards,each with one of the numbers listed. © Joan A. Cotter, Ph.D., 2012
210. 210. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
211. 211. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
212. 212. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
213. 213. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 63 1470 © Joan A. Cotter, Ph.D., 2012
214. 214. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
215. 215. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
216. 216. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 40 © Joan A. Cotter, Ph.D., 2012
217. 217. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
218. 218. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
219. 219. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
220. 220. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
221. 221. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
222. 222. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
223. 223. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
224. 224. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 63 5670 8 © Joan A. Cotter, Ph.D., 2012
225. 225. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
226. 226. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
227. 227. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
228. 228. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 87 © Joan A. Cotter, Ph.D., 2012
229. 229. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 14 70 87 © Joan A. Cotter, Ph.D., 2012
230. 230. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 87 14 © Joan A. Cotter, Ph.D., 2012
231. 231. Multiples Memory 7 14 21 28 35 42 49 56 63 70 24 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 87 14 © Joan A. Cotter, Ph.D., 2012
232. 232. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 87 14 © Joan A. Cotter, Ph.D., 2012
233. 233. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
234. 234. Multiplication MemoryObjective: To help the players master themultiplication facts. © Joan A. Cotter, Ph.D., 2012
235. 235. Multiplication MemoryObjective: To help the players master themultiplication facts.Object of the game: To collect the most cards by matchingthe multiplier with the product. © Joan A. Cotter, Ph.D., 2012
236. 236. Multiplication MemoryMaterials Needed: © Joan A. Cotter, Ph.D., 2012
237. 237. Multiplication Memory1 2 3 4 5 6 7 8 9 10 Materials Needed: • Ten basic cards, numbered 1 to 10 © Joan A. Cotter, Ph.D., 2012
238. 238. Multiplication Memory 31 2 3 4 5 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) © Joan A. Cotter, Ph.D., 2012
239. 239. Multiplication Memory 31 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie note with “3 x” written on it © Joan A. Cotter, Ph.D., 2012
240. 240. Multiplication Memory 31 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 = Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie with “3 x” written on it • A stickie with “=” written on it © Joan A. Cotter, Ph.D., 2012
241. 241. Multiplication Memory 31 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 = Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie with “3 x” written on it • A stickie with “=” written on it • A manipulative with groups of five © Joan A. Cotter, Ph.D., 2012
242. 242. Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
243. 243. Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
244. 244. Multiplication Memory 53x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
245. 245. Multiplication Memory 53x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
246. 246. Multiplication Memory 53x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
247. 247. Multiplication Memory 53x =3 taken 5 times equals 15. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
248. 248. Multiplication Memory 5 213x =3 taken 5 times equals 15. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
249. 249. Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
250. 250. Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
251. 251. Multiplication Memory3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
252. 252. Multiplication Memory3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
253. 253. Multiplication Memory3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
254. 254. Multiplication Memory3x = 7 3 taken 7 times equals 21. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
255. 255. Multiplication Memory 213x = 7 3 taken 7 times equals 21. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
256. 256. Multiplication Memory3x = 3 taken 7 times equals 21. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
257. 257. Multiplication Memory3x = 2 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
258. 258. Multiplication Memory3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
259. 259. Multiplication Memory3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
260. 260. Multiplication Memory3x = 2 3 3 taken 3 times equals 9. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
261. 261. Multiplication Memory3x = 2 3 12 3 taken 3 times equals 9. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
262. 262. Multiplication Memory3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
263. 263. Multiplication Memory3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
264. 264. Multiplication Memory 53x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
265. 265. Multiplication Memory 53x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
266. 266. Multiplication Memory 53x =3 taken 5 times equals 15. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
267. 267. Multiplication Memory 53x = 153 taken 5 times equals 15. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
268. 268. Multiplication Memory3x =3 taken 5 times equals 15. 5 15 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
269. 269. Multiplication Memory3x = 5 15 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
270. 270. Multiplication Memory3x = 8 24 3 6 9 12 15 18 1 3 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
271. 271. Framing the Future of Mathematics in MinnesotaMath in Minnesota starts with the youngest.Let’s build on their natural ability to subitize.Keep joy in math; use games, not flash cards.Help them to use their minds to visualize. © Joan A. Cotter, Ph.D., 2012
272. 272. Teaching the Arithmetic Facts Using Strategies and Games by Joan A. Cotter, Ph.D. JoanCotter@RightStartMath.com MCTM May 4, 2012 Duluth, Minnesota 7 3 8 16 24 32 40PowerPoint Presentation & Handout RightStartMath.com >Resources © Joan A. Cotter, Ph.D., 2012