MCTM Strategies & Games

© Joan A. Cotter, Ph.D., 2012

Teaching the Arithmetic Facts Using Strategies and Games

MCTMMay 4, 2012

Duluth, Minnesota

by Joan A. Cotter, [email protected]

7 3 8 16 24 32 40

PowerPoint Presentation & HandoutRightStartMath.com >Resources


Learning the Facts


Learning the Facts

• Based on counting.

Limited success when:

Whether dots, fingers, number lines, or counting words.


Learning the Facts



• Based on rote memory.


Whether by flash cards or timed tests.


Learning the Facts


• Based on skip counting for multiplication facts.


• Based on rote memory.


Whether by flash cards or timed tests.


Counting ModelFrom a child's perspective


Counting ModelFrom a child's perspective

Because we’re so familiar with 1, 2, 3, we’ll use letters.

A = 1B = 2C = 3D = 4E = 5, and so forth


Counting Model From a child's perspective

F + E



A

F + E



A B

F + E



A CB

F + E



A FC D EB

F + E



AA FC D EB

F + E



A BA FC D EB

F + E



A C D EBA FC D EB

F + E



A C D EBA FC D EB

F + E

What is the sum?(It must be a letter.)



K

G I J KHA FC D EB

F + E



E + G

Add with your fingers.



H+ D

Add without your fingers.



Now memorize the facts!!

G + D




G + D

H + F




G + D

H + F

D + C




G + D

H + F

C + G

D + C



E

+ I


G + D

H + F

C + G

D + C



H – E

Subtract with your fingers.



J – F

Subtract without using your fingers.



Try skip counting by B’s to T: B, D, . . . T.



Try skip counting by B’s to T: B, D, . . . T.

What is D x E?


Memorizing Math


Memorizing Math

Percentage Recall

Immediately After 1 day After 4 wks

Rote 32 23 8

Concept 69 69 58

Some research:


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 about thinking.







• Often produce stress – children under stress stop learning.







• Often produce stress – children under stress stop learning.

• Are not concrete – they use abstract symbols.

Memorizing MathFlash cards:

9 + 7


AN ALTERNATIVE:

SUBITIZINGand

GAMES


Subitizing QuantitiesIdentifying without counting



• Five-month-old infants can subitize to 3.



• Three-year-olds can subitize to 5.




• Three-year-olds can subitize to 5.

• Five-year-olds can subitize 6 to 10 by using five as a subbase.



AddingName the quantity (practice subitizing).


Adding

4 + 3 =


Adding

4 + 3 = 7


Adding

4 + 3 =


Characteristics of a Good Game



• Produces learning through playing.




• Incorporates manipulatives.





• Teaches strategies.






• Encourages mental work.







• Detects errors; provides continuous assessment.







• Detects errors; provides continuous assessment.

• Is enjoyable.


Go to the Dump GameObjective: To learn the facts that total 10:

1 + 92 + 83 + 74 + 65 + 5


Go to the Dump GameObjective: To learn the facts that total 10:

1 + 92 + 83 + 74 + 65 + 5

Object of the game: To collect the most pairs that equal ten.


Go to the Dump Game

6 + = 10


Go to the Dump Game

6 + 4 = 10


Go to the Dump Game

Starting


7 2 7 9 5

7 42 61 3 8 3 4 9

Go to the Dump Game

Starting


Go to the Dump Game

Finding pairs

7 2 7 9 5

7 42 61 3 8 3 4 9


Go to the Dump Game

Finding pairs

7 2 7 9 5

7 2 1 3 8 3 4 9

4 6


Go to the Dump Game

Finding pairs

7 2 7 9 5

2 1 8 3 4 9

4 67 3


Go to the Dump Game

Finding pairs

7 2 7 9 5

1 3 4 9

4 62 82 8


Go to the Dump Game

Playing

7 2 7 9 5

1 3 4 9

4 62 82 8


Go to the Dump GameBlueCap, do you

have a 3?BlueCap, do you

have an 3?

Playing

7 2 7 9 5

1 3 4 9

4 62 82 8




have an 3?

Playing

7 2 7 9 5

1

3

4 9

4 62 82 8




have an 3?

Playing

2 7 9 5

1 4 9

4 62 82 8

7 3




have an 8?

Playing

2 7 9 5

1 4 9

4 62 82 8

7 3




have an 8?

Go to the dump.Playing

2 7 9 5

1 4 9

4 62 82 8

7 3


2



have an 8?

Go to the dump.Playing

2 7 9 5

1 4 9

4 62 82 8

7 3


Go to the Dump Game

Playing

2 2 7 9 5

1 4 9

4 62 82 8

7 3


Go to the Dump Game

PinkCap, do youhave a 6?Playing

2 2 7 9 5

1 4 9

4 62 82 8

7 3


Go to the Dump Game

PinkCap, do youhave a 6?PlayingGo to the dump.

2 2 7 9 5

1 4 9

4 62 82 8

7 3


5

Go to the Dump Game

Playing

2 2 7 9 5

1 4 9

4 62 82 8

7 3


Go to the Dump Game

Playing

5

2 2 7 9 5

1 4 9

4 62 82 8

7 3


Go to the Dump Game

YellowCap, doyou have a 9? Playing

5

2 2 7 9 5

1 4 9

4 62 82 8

7 3


Go to the Dump Game


5

2 2 7 5

1 4 9

4 62 82 8

7 3


Go to the Dump Game


5

2 2 7 5

1 4 9

4 62 82 8

7 3

9


Go to the Dump Game

Playing

5

2 2 7 5

4 9

4 62 81 9

7 3


2 9 1 7 7

Go to the Dump Game

Playing

5

2 2 7 5

4 9

4 62 81 9

7 3


Go to the Dump Game

Winner?

5 54 6

9 1


Go to the Dump Game

Winner?

5546

91


Go to the Dump Game

Play it again.


Fact Strategies


Fact Strategies

• A strategy is a way to learn a new fact or recall a forgotten fact.


Fact Strategies

• A strategy is a way to learn a new fact or recall a forgotten fact.

• A visualizable representation is part of a powerful strategy.


Fact StrategiesComplete the Ten

9 + 5 =



9 + 5 =

Take 1 from the 5 and give it to the 9.



9 + 5 = 14

Take 1 from the 5 and give it to the 9.


Fact StrategiesTwo Fives

8 + 6 =



8 + 6 =

10 + 4 = 14



7 + 5 =



7 + 5 = 12


Fact StrategiesGoing Down

15 – 9 =



15 – 9 =

Subtract 5;then 4.



15 – 9 = 6

Subtract 5;then 4.


Fact StrategiesSubtract from 10

15 – 9 =



15 – 9 =

Subtract 9 from 10.



15 – 9 = 6

Subtract 9 from 10.


Fact StrategiesGoing Up

15 – 9 =



15 – 9 =

Start with 9; go up to 15.



15 – 9 =

1 + 5 = 6

Start with 9; go up to 15.


Rows and Columns Game

Objective: To find a total of 15 by adding 2, 3, or 4 cards in row or column.



Objective: To find a total of 15 by adding 2, 3, or 4 cards in row or column.

Object of the game: To collect the most cards.


Rows and Columns Game8 7 1 9

6 4 3 3

2 2 5 6

6 3 8 8


Rows and Columns Game1 9

6 4 3 3

6 3 8 8


Rows and Columns Game1 9

6 4 3 3

6 3 8 8

7 6

2 1 5 1


Rows and Columns Game1

6 4 3 3

3 8 8

1 5 1


Multiplication StrategiesBasic facts



6 4 =(6 taken 4 times)



9 3 =



9 3 =

30



9 3 =

30 – 3 = 27



4 8 =



4 8 =

20 + 12 = 32



7 7 =



7 7 =

25



7 7 =

25 + 10 + 10



7 7 =

25 + 10 + 10 + 4 = 49


Multiples PatternsTwos

2 4 6 8 10

12 14 16 18 20


Multiples PatternsTwos

2 4 6 8 10

12 14 16 18 20

The ones repeat in the second row.


Multiples PatternsFours

4 8 12 16 20

24 28 32 36 40

The ones repeat in the second row.


Multiples PatternsSixes and Eights

6 12 18 24 30

36 42 48 54 60

8 16 24 32 40

48 56 64 72 80



6 12 18 24 30

36 42 48 54 60

8 16 24 32 40

48 56 64 72 80

The ones in the 8s show the multiples of 2.



6 12 18 24 30

36 42 48 54 60

8 16 24 32 40

48 56 64 72 80

6 4

6 4 is the fourth number (multiple).



6 12 18 24 30

36 42 48 54 60

8 16 24 32 40

48 56 64 72 80 8 7

8 7 is the seventh number (multiple).


Multiples PatternsNines

9 18 27 36 45

90 81 72 63 54

The second row is written in reverse order.Also the digits in each number add to 9.


Multiples PatternsThrees

3 6 9

12 15 18

21 24 27

30

The 3s have several patterns: Observe the ones.



3 6 9

12 15 18

21 24 27

30

The 3s have several patterns: The tens are the same in each row.



3 6 9

12 15 18

21 24 27

30

The 3s have several patterns: Add the digits in the columns.



3 6 9

12 15 18

21 24 27

30

The 3s have several patterns: Add the “opposites.”


Multiples PatternsSevens

7 14 21

28 35 42

49 56 63

70

The 7s have the 1, 2, 3… pattern.


Multiples PatternsSevens

7 14 21

28 35 42

49 56 63

70

Look at the tens.


Multiples Memory


Multiples Memory

Objective: To help the players learn the multiples patterns.


Multiples Memory

Object of the game: To be the first player to collect all ten cards of a multiple in order.

Objective: To help the players learn the multiples patterns.


Multiples Memory

The 7s envelope contains 10 cards, each with one of the numbers listed.

7 14 2128 35 4249 56 63

70


Multiples Memory

The 8s envelope contains 10 cards, each with one of the numbers listed.

8 16 24 32 4048 56 64 72 80


Multiples Memory

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80

8 16 24 32 4048 56 64 72 80


Multiples Memory

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


Multiples Memory

14

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


Multiples Memory

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


Multiples Memory

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


Multiples Memory

40

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


Multiples Memory

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


Multiples Memory

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


Multiples Memory

8

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


Multiples Memory

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


Multiples Memory

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


Multiples Memory

8

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


Multiples Memory

8 16 24 32 4048 56 64 72 80

88

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


Multiples Memory

8 16 24 32 4048 56 64 72 80

8856

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


Multiples Memory

8 16 24 32 4048 56 64 72 80

88

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


Multiples Memory

8 16 24 32 4048 56 64 72 80

88

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


Multiples Memory

8 16 24 32 4048 56 64 72 80

88

7

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


Multiples Memory

8 16 24 32 4048 56 64 72 80

88

7

14

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


Multiples Memory

8 16 24 32 4048 56 64 72 80

88

7 14

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


Multiples Memory

8 16 24 32 4048 56 64 72 80

88

7 14

24

7 14 2128 35 4249 56 6370

7 14 2128 35 4249 56 6370


7 14 2128 35 4249 56 6370

Multiples Memory

8 16 24 32 4048 56 64 72 80

88

7 14

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80


7 14 2128 35 4249 56 6370

Multiples Memory

8 16 24 32 4048 56 64 72 80

8 16 24 32 4048 56 64 72 80

7 14 2128 35 4249 56 6370


Multiplication Memory

Objective: To help the players master themultiplication facts.



Objective: To help the players master themultiplication facts.

Object of the game: To collect the most cards by matching the multiplier with the product.



Materials Needed:



Materials Needed:• Ten basic cards, numbered 1 to 10

3 4 5

8 9 10

2

7

1

6


3


Materials Needed:• Ten basic cards, numbered 1 to 10• A set of product cards (3s used here)

3 4 5

8 9 10

2

7

1

6

6 61827

91221

3

30

1524


3


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

3 4 5

8 9 10

2

7

1

6

3 x 6 61827

91221

3

30

1524


3


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

3 4 5

8 9 10

2

7

1

6

3 x 6 61827

91221

3

30

1524


3


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

3 4 5

8 9 10

2

7

1

6

3 x 6 61827

91221

3

30

1524


3 x


6 61827

91221

3

30

1524


3 x


6 61827

91221

3

30

1524

5


3 x


6 61827

91221

3

30

1524

5

3 taken 5 timesequals 15.


3 x


21

6 61827

91221

3

30

1524

5




6 61827

91221

3

30

1524

3 x



6 61827

91221

3

30

1524

3 x7



6 61827

91221

3

30

1524

7


3 x



21

6 61827

91221

3

30

1524

73 x




6 61827

91221

3

30

1524

3 x

7 21



2


6 61827

91221

3

30

1524

3 x

7 21


2


6 61827

91221

3

30

1524

33 x

7 21


2


12

6 61827

91221

3

30

1524

33 x

7 21




6 61827

91221

3

30

1524

3 x

7 21



6 61827

91221

3

30

1524

5

3 x

7 21



6 61827

91221

3

30

1524

5

153 x

7 21



7


6 61827

91221

3

30

1524

3 x

215 15



1


6 61827

91221

3

30

1524

3 x

38 24


Framing the Future of Mathematics in Minnesota

Math 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.


Teaching the Arithmetic Facts Using Strategies and Games

MCTMMay 4, 2012

Duluth, Minnesota

by Joan A. Cotter, [email protected]

7 3 8 16 24 32 40

PowerPoint Presentation & HandoutRightStartMath.com >Resources

MCTM Strategies & Games

Education

Transcript of MCTM Strategies & Games