MCTM Strategies & Games

Teaching the Arithmetic Facts Using Strategies and Games

MCTMMay 4, 2012

Duluth, Minnesota

by Joan A. Cotter, Ph.D.JoanCotter@RightStartMath.com

7 3 8 16 24 32 40

PowerPoint Presentation & HandoutRightStartMath.com >Resources

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

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

A FC D EB

AA FC D EB

A BA FC D EB

A C D EBA FC D EB

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

G I J KHA FC D EB

Add with your fingers.

Add without your fingers.

Now memorize the facts!!

H – E

Subtract with your fingers.

J – F

Subtract without using your fingers.

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

What is D x E?

Memorizing Math

Percentage Recall

Immediately After 1 day After 4 wks

Rote 32 23 8

Concept 69 69 58

Some research:

Memorizing Math

Percentage Recall

Rote 32 23 8

Concept 69 69 58

Some research:

Memorizing Math

Percentage Recall

Rote 32 23 8

Concept 69 69 58

Some research:

Memorizing Math

Percentage Recall

Rote 32 23 8

Concept 69 69 58

Some research:

Memorizing Math

Percentage Recall

Rote 32 23 8

Concept 69 69 58

Some research:

Memorizing Math

Percentage Recall

Rote 32 23 8

Concept 69 69 58

Some research:

Memorizing Math

Percentage Recall

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.

• Are not concrete – they use abstract symbols.

Memorizing MathFlash cards:

AN ALTERNATIVE:

SUBITIZINGand

Subitizing QuantitiesIdentifying 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 by using five as a subbase.

AddingName the quantity (practice subitizing).

Adding

4 + 3 =

Adding

4 + 3 =

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.

• 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 + = 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 42 61 3 8 3 4 9

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

Go to the Dump Game

Finding pairs

7 2 7 9 5

7 2 1 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

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

4 62 82 8

have an 3?

Playing

2 7 9 5

4 62 82 8

have an 8?

Playing

2 7 9 5

4 62 82 8

have an 8?

Go to the dump.Playing

2 7 9 5

4 62 82 8

have an 8?

Go to the dump.Playing

2 7 9 5

4 62 82 8

Go to the Dump Game

Playing

2 2 7 9 5

4 62 82 8

Go to the Dump Game

PinkCap, do youhave a 6?Playing

2 2 7 9 5

4 62 82 8

Go to the Dump Game

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

2 2 7 9 5

4 62 82 8

Go to the Dump Game

Playing

2 2 7 9 5

4 62 82 8

Go to the Dump Game

Playing

2 2 7 9 5

4 62 82 8

Go to the Dump Game

YellowCap, doyou have a 9? Playing

2 2 7 9 5

4 62 82 8

Go to the Dump Game

2 2 7 5

4 62 82 8

Go to the Dump Game

2 2 7 5

4 62 82 8

Go to the Dump Game

Playing

2 2 7 5

4 62 81 9

2 9 1 7 7

Go to the Dump Game

Playing

2 2 7 5

4 62 81 9

Go to the Dump Game

Winner?

5 54 6

Go to the Dump Game

Winner?

Go to the Dump Game

Winner?

Go to the Dump Game

Play it again.

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 =

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

9 + 5 =

9 + 5 = 14

Fact StrategiesTwo Fives

8 + 6 =

10 + 4 = 14

7 + 5 =

7 + 5 = 12

Fact StrategiesGoing Down

15 – 9 =

Subtract 5;then 4.

15 – 9 =

Subtract 5;then 4.

15 – 9 =

Subtract 5;then 4.

15 – 9 = 6

Subtract 5;then 4.

Fact StrategiesSubtract from 10

15 – 9 =

Subtract 9 from 10.

15 – 9 =

Subtract 9 from 10.

15 – 9 =

Subtract 9 from 10.

15 – 9 = 6

Subtract 9 from 10.

Fact StrategiesGoing Up

15 – 9 =

Start with 9; go up to 15.

15 – 9 =

1 + 5 = 6

Rows and Columns Game

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

6 4 3 3

2 2 5 6

6 3 8 8

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

6 4 3 3

6 3 8 8

2 1 5 1

6 4 3 3

6 3 8 8

2 1 5 1

6 4 3 3

6 3 8 8

2 1 5 1

Rows and Columns Game1

6 4 3 3

Multiplication StrategiesBasic facts

6 4 =(6 taken 4 times)

30 – 3 = 27

20 + 12 = 32

25 + 10 + 10

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

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 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

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

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

12 15 18

21 24 27

The 3s have several patterns: Observe the ones.

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

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

12 15 18

21 24 27

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

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

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

12 15 18

21 24 27

12 15 18

21 24 27

12 15 18

21 24 27

Multiples PatternsSevens

7 14 21

28 35 42

49 56 63

The 7s have the 1, 2, 3… pattern.

7 14 21

28 35 42

49 56 63

7 14 21

28 35 42

49 56 63

7 14 21

28 35 42

49 56 63

7 14 21

28 35 42

49 56 63

Look at the tens.

7 14 21

28 35 42

49 56 63

Look at the tens.

7 14 21

28 35 42

49 56 63

Look at the tens.

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

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

8 16 24 32 4048 56 64 72 80

Multiples Memory

7 14 2128 35 4249 56 6370

8 16 24 32 4048 56 64 72 80

Multiples Memory

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

Multiples Memory

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

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

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

Multiples Memory

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

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 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

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

Multiples Memory

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

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

Multiples Memory

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

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

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

Multiplication Memory

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

8 9 10

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

8 9 10

6 61827

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

8 9 10

3 x 6 61827

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

8 9 10

3 x 6 61827

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

8 9 10

3 x 6 61827

6 61827

3 taken 5 timesequals 15.

6 61827

215 15

6 61827

215 15

6 61827

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, Ph.D.JoanCotter@RightStartMath.com

7 3 8 16 24 32 40

PowerPoint Presentation & HandoutRightStartMath.com >Resources

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