MCTM Strategies & Games
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MCTM Strategies & Games MCTM Strategies & Games Presentation Transcript

  • 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
  • Learning the Facts © Joan A. Cotter, Ph.D., 2012
  • Learning the FactsLimited success when:• Based on counting. Whether dots, fingers, number lines, or counting words. © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • Counting ModelFrom a childs perspective © Joan A. Cotter, Ph.D., 2012
  • 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
  • Counting ModelFrom a childs perspective F +E © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspective F +EA © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspective F +EA B © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspective F +EA B C © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspective F +EA B C D E F © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspective F +EA B C D E F A © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspective F +EA B C D E F A B © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspective F +EA B C D E F A B C D E © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • Counting ModelFrom a childs perspective E +G Add with your fingers. © Joan A. Cotter, Ph.D., 2012
  • Counting ModelFrom a childs perspective H +DAdd without your fingers. © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspectiveNow memorize the facts!! G +D © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspectiveNow memorize the facts!! H + G F +D © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspectiveNow memorize the facts!! H + G F +D D+C © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspectiveNow memorize the facts!! H + G F +D D C+C +G © Joan A. Cotter, Ph.D., 2012
  • 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
  • Counting Model From a childs perspective H –ESubtract with your fingers. © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspective J –FSubtract without using your fingers. © Joan A. Cotter, Ph.D., 2012
  • Counting Model From a childs perspectiveTry skip counting by B’s to T: B, D, . . . T. © Joan A. Cotter, Ph.D., 2012
  • 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
  • Memorizing Math © Joan A. Cotter, Ph.D., 2012
  • Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  • Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  • Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  • Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  • Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  • Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  • Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  • Memorizing Math 9 +7Flash cards: © Joan A. Cotter, Ph.D., 2012
  • Memorizing Math 9 +7Flash cards:• Are often used to teach rote. © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • 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
  • 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
  • AN ALTERNATIVE: SUBITIZING and GAMES © Joan A. Cotter, Ph.D., 2012
  • Subitizing QuantitiesIdentifying without counting © Joan A. Cotter, Ph.D., 2012
  • Subitizing Quantities Identifying without counting• Five-month-old infants can subitize to 3. © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • AddingName the quantity (practice subitizing). © Joan A. Cotter, Ph.D., 2012
  • AddingName the quantity (practice subitizing). © Joan A. Cotter, Ph.D., 2012
  • AddingName the quantity (practice subitizing). © Joan A. Cotter, Ph.D., 2012
  • Adding4+3= © Joan A. Cotter, Ph.D., 2012
  • Adding4+3= © Joan A. Cotter, Ph.D., 2012
  • Adding4+3= © Joan A. Cotter, Ph.D., 2012
  • Adding4+3=7 © Joan A. Cotter, Ph.D., 2012
  • Adding4+3= © Joan A. Cotter, Ph.D., 2012
  • Characteristics of a Good Game © Joan A. Cotter, Ph.D., 2012
  • Characteristics of a Good Game • Produces learning through playing. © Joan A. Cotter, Ph.D., 2012
  • Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. © Joan A. Cotter, Ph.D., 2012
  • Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. © Joan A. Cotter, Ph.D., 2012
  • Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. • Encourages mental work. © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • 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
  • Go to the Dump Game 6+ = 10 © Joan A. Cotter, Ph.D., 2012
  • Go to the Dump Game 6+ = 10 © Joan A. Cotter, Ph.D., 2012
  • Go to the Dump Game 6 + 4 = 10 © Joan A. Cotter, Ph.D., 2012
  • Go to the Dump Game Starting © Joan A. Cotter, Ph.D., 2012
  • Go to the Dump Game 72 7 9 5 72 1 3 8 4 6 34 9 Starting © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Go to the Dump Game 72 7 9 5 2 8 4 6 1 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
  • Go to the Dump Game 72 7 9 5 2 8 4 6 1 34 9 Playing © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Go to the Dump Game 9 1 4 6 5 5 Winner? © Joan A. Cotter, Ph.D., 2012
  • Go to the Dump Game 9 1 4 6 5 Winner? © Joan A. Cotter, Ph.D., 2012
  • Go to the Dump Game 9 1 4 6 5 Winner? © Joan A. Cotter, Ph.D., 2012
  • Go to the Dump Game Play it again. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies• A strategy is a way to learn a new fact orrecall a forgotten fact. © Joan A. Cotter, Ph.D., 2012
  • 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
  • Fact Strategies Complete the Ten9+5= © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Complete the Ten9+5= © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Complete the Ten9+5= © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Complete the Ten 9+5=Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Complete the Ten 9+5=Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Complete the Ten 9+5=Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Complete the Ten 9 + 5 = 14Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Two Fives8+6=10 + 4 = 14 © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Two Fives7+5= © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Two Fives7+5= © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Two Fives7 + 5 = 12 © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Down15 – 9 = © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Down15 – 9 = © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Down 15 – 9 =Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Down 15 – 9 =Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Down 15 – 9 =Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Down 15 – 9 = 6Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Subtract from 1015 – 9 = © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Subtract from 10 15 – 9 =Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Subtract from 10 15 – 9 =Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Subtract from 10 15 – 9 =Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Subtract from 10 15 – 9 = 6Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Up15 – 9 = © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  • Fact Strategies Going Up 15 – 9 = 1+5=6Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • 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
  • 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
  • Rows and Columns Game 1 9 6 4 3 3 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • Rows and Columns Game 1 6 4 3 3 1 5 1 3 8 8 © Joan A. Cotter, Ph.D., 2012
  • Rows and Columns Game © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts9× 3= © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts9× 3= © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts9× 3=30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts9× 3=30 – 3 = 27 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts4× 8= © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts4× 8= © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts4× 8= © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts4× 8=20 + 12 = 32 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts7× 7= © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts7× 7= © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts7× 7=25 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts7× 7=25 + 10 + 10 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Strategies Basic facts7× 7=25 + 10 + 10+ 4 = 49 © Joan A. Cotter, Ph.D., 2012
  • Multiples Patterns Twos2 4 6 8 1012 14 16 18 20 © Joan A. Cotter, Ph.D., 2012
  • Multiples Patterns Twos 2 4 6 8 1012 14 16 18 20The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
  • Multiples Patterns Fours 4 8 12 16 2024 28 32 36 40The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
  • Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
  • Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
  • Multiples Memory © Joan A. Cotter, Ph.D., 2012
  • Multiples MemoryObjective: To help the players learn themultiples patterns. © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Multiplication MemoryObjective: To help the players master themultiplication facts. © Joan A. Cotter, Ph.D., 2012
  • 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
  • Multiplication MemoryMaterials Needed: © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • 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
  • 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
  • Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory 53x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory 53x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory 53x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • Multiplication Memory3x = 2 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • Multiplication Memory3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory 53x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory 53x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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
  • 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
  • Multiplication Memory3x = 5 15 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • Multiplication Memory3x = 8 24 3 6 9 12 15 18 1 3 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 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
  • 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