Mental Arithmetic Teaching Facts Meaning Relationships Drill.

Mental ArithmeticTeaching Facts

Meaning

Relationships

Drill

A Few Questions

• What is the highest mountain in North America?

• Answer: Mt. McKinley

• What is the Capital of Argentina?

• Answer: Buenos Aires.

• What is the largest body of water in Africa?

• Answer: Lake Victoria

• Who won the Superbowl in 2000?

• Answer: St. Louis Rams

• Name one of the two vice presidents under Abraham Lincoln.

• Answer: Hannibal Hamlin, Andrew Johnson

• Who was assassinated in Sarajevo in 1914 which precipitated WWI?

• Answer: Archduke Francis of Austria

How many facts must we memorize?

+ 2 10987654310

2

10

9

8

7

6

5

4

3

1

0 2 10987654310

2 109876543 11`

1

2 109876 11`

12543

10

9

8

7

6

5

4

3

10

9

8

7

6

5

4

11

10

9

8

7

6

5 1310987 11`

12

14

17

16

15

19

18

11

2012

6

1310987 11`

12

14131098 11`

12

151413109 11`

12

1615141310 11`

12

171615141311`

12

18171615141312

19181716151413

Now it is your turn

Basic Facts of base 5.

+ 2 4310

2

4

3

1

0

10

10

Doubles and one more than doubles.

+ 2 10987654310

2

10

9

8

7

6

5

4

3

1

0 2 1098765431

109876543 11`

1

2 109876 11`

1253

10

9

8

7

6

5

4

3

10

9

8

7

6

5

4

11

10

9

8

7

6

5 1310987 11`

12

14

17

16

15

19

18

11

12

131097 11`

12

141398 11`

12

151413109 11`

16151310 11`

12

1715141311`

12

171615141312

19181716151413

`

+ 2 10987654310

2

10

9

8

7

6

5

4

3

1

0 2 109876543

10987654 11`2 109876 11

`12

10

9

8

7

6

5

4

3

10

9

8

7

6

5

4

11

10

9

8

7

6

131098 11`

12

14

17

16

15

18

11

12

1310 11`

12

14138 12

1514109

1610 11`

12

141311`

12

1615141312

181716151413

`

2+2

2+3

2+1

4+4

4+3

4+5

15+15

15+14

15+16

Encouraging the associate property a +(a+1) =(a+a)+1

Slide 7

+ 2 10987654310

2

10

9

8

7

6

5

4

3

1

0 109876543

10987654 11`109876 11

`12

131098 11`

12

14

17

16

15

18

1310 11`

12

141312

1514

16

5 + 4

4+5

7 + 6

6 + 7

10 + 7

7 + 10

56 + 43

43 + 56

Commutative Property for additionA + B = B + A

+ 2 10987654310

2

10

9

8

7

6

5

4

3

1

0 9876543

10987654

109876 11`1098 11

`12

1310 11`

12

141312

1514

16

Place Value Relationship

+10

+10

-1

-1

+9

10 + 1

10 + 2

10 + 3

10 + 5

+ 2 10987654310

2

10

9

8

7

6

5

4

3

1

0 876543

987654

109876

1098 11`10 11

`12

1312

14

+ 2 10987654310

2

10

9

8

7

6

5

4

3

1

0

Other Patterns

3 + 44 + 37 - 47 - 3

7 +37+47+2

10 + 311 + 315 + 3

Important Ideas in development of Addition Subtraction

• Counting - Forward/Back

• Skip Counting 2,3 5’s

• Skip Counting from a number.

How many facts must we memorize?

• 1x3• 1x9• 34 x 1• 1x 1,000,000• 0 x 0• 0 x 153,000• 34 x 97 x 1543 x 0

Is There a Connection?

2 + 2 + 2

2 x 3

3 + 3 + 3 + 3

3 x 4

5 + 5 + 5 + 5

5 x 4

Is there a Pattern?

• 3 x 2 • 6 x 2 • 3 x 7• 6 x 7 • 3 x 9• 6 x 9

• 2 x 3• 4 x 3• 8 x 3• 2 x 7• 4 x 7• 8 x 7

Ready for the Answer?

Meaning

Number Sense

Drill

Why only ten’s

• 5 x 10 = 50• 5 x 3 = 15• 5 x 13 =

• 7 x 10 = 70• 7 x 3 = 21• 7 x 13 =

• 4 x 10 =• 4 x 4 = • 4 x 14 =

• 9 x 100 = • 9 x 1 =• 9 x 99 =

What is this Child Doing?

QuickTime™ and aCinepak decompressor

are needed to see this picture.

Meanings of Multiplication

• Repeated Addition

• Array

• Matching

Repeated Addition

What is this?

QuickTime™ and aCinepak decompressor

are needed to see this picture.

Array

Matching

3 Shirts 4 Pants. How many outfits?

S2

S3

S1

P2 P3 P4P1

Alternative Algorithms

Addition

Long form- Emphasizes Place Value.

235+ 89 14110200324

2*100 +3*10 +5*1+ 8*10 + 9*1

What is this?

QuickTime™ and aCinepak decompressor

are needed to see this picture.

Subtraction

235-197 -2 -60 100 38

Equal Addends

5 3 2 1- 6 8 9

Multiplication Long Form

34x5

20 = 5 x 4150 = 5 x 30

5 x 34???? Why

Lattice 235 x 952 3 5

x

9

5

Meanings of Division

• Repeated Subtraction

• Distribute into Groups

• Inverse of Multiplication

Which One is this?

QuickTime™ and aCinepak decompressor

are needed to see this picture.

Inverse of Multiplication

x7

What’s the blue?

Distributive

Distributive

Distributive

Distributive

Distributive

12

€

÷3 = 4

7 1245

1

-754

7

-4955

-49

7

6

7 1245

100

-700545

-49055

-496

707

177

177 R6