sorting to algebra developing mathematical thinkers

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Sorting to Algebra Developing Mathematical Thinkers

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Page 1: Sorting to Algebra Developing Mathematical Thinkers

Sorting to AlgebraDeveloping Mathematical

Thinkers

Page 2: Sorting to Algebra Developing Mathematical Thinkers
Page 3: Sorting to Algebra Developing Mathematical Thinkers
Page 4: Sorting to Algebra Developing Mathematical Thinkers

Algebraic Ideas Breaking it up

4 40 45591940

121 11

Page 5: Sorting to Algebra Developing Mathematical Thinkers

What does the “thick line” do?

4

Page 6: Sorting to Algebra Developing Mathematical Thinkers

What does the “thick line” do?

4 21

Page 7: Sorting to Algebra Developing Mathematical Thinkers

What does the “thick line” do?

4 21 25

Page 8: Sorting to Algebra Developing Mathematical Thinkers

What about this way?

100

Page 9: Sorting to Algebra Developing Mathematical Thinkers

What about this way?

100

27

Page 10: Sorting to Algebra Developing Mathematical Thinkers

What about this way?

100

73

27

Page 11: Sorting to Algebra Developing Mathematical Thinkers

Kindergarten Sorters

Page 12: Sorting to Algebra Developing Mathematical Thinkers

4 + 5 = 9

3 + 1 = 4

7

Addition and SubtractionFrom sorting to algebra

Challenge: can you find some

that don’t work?

5x + 3y = 23

2x + 3y = 11

Is there anything interesting about Is there anything interesting about addition and subtraction addition and subtraction sentences?sentences?

13+ =6 51 4

Page 13: Sorting to Algebra Developing Mathematical Thinkers

Back to the very beginningsPicture a young child with a small pile of buttons.

Natural to sort.

We help children refine and extend what is already natural.

Page 14: Sorting to Algebra Developing Mathematical Thinkers

6

4

7 3 10

Back to the very beginnings

Children can also summarize.

“Data” from the buttons.

blue gray

large

small

Page 15: Sorting to Algebra Developing Mathematical Thinkers

large

small

blue gray

AbstractionIf we substitute numbers for the original objects…

6

4

7 3 10

6

4

7 3 10

4 2

3 1

Page 16: Sorting to Algebra Developing Mathematical Thinkers

A Cross Number PuzzleDon’t always start with the question!

5

21

8

13

912

7 6

3

1st grade

Page 17: Sorting to Algebra Developing Mathematical Thinkers

Building the addition algorithmOnly multiples of 10 in yellow. Only less than 10 in blue.

63

38

25

1350

20 5

830

2nd grade

Page 18: Sorting to Algebra Developing Mathematical Thinkers

Relating addition and subtraction6

4

7 3 10

4 2

3 16

4

7 3 10

4 2

3 1

2nd grade

Page 19: Sorting to Algebra Developing Mathematical Thinkers

The subtraction algorithm

63

38

25

1350

20 5

830

25

38

63

-530

60 3

830

25 + 38 = 63 63 – 38 = 25

Page 20: Sorting to Algebra Developing Mathematical Thinkers

The subtraction algorithm

63

38

25

1350

20 5

830

25

38

63

520

60 3

830

25 + 38 = 63 63 – 38 = 25

50 13

Page 21: Sorting to Algebra Developing Mathematical Thinkers

Place Value Bonus235 + 597

Page 22: Sorting to Algebra Developing Mathematical Thinkers

Place Value Bonus235 + 597

Page 23: Sorting to Algebra Developing Mathematical Thinkers

Place Value Bonus235 + 597

Page 24: Sorting to Algebra Developing Mathematical Thinkers

Place Value Bonus235 + 597

Page 25: Sorting to Algebra Developing Mathematical Thinkers

Place Value Bonus235 + 597

Page 26: Sorting to Algebra Developing Mathematical Thinkers

Place Value Bonus235 + 597

Page 27: Sorting to Algebra Developing Mathematical Thinkers

Place Value Bonus235 + 597

Page 28: Sorting to Algebra Developing Mathematical Thinkers

Place Value Bonus235 + 597

Page 29: Sorting to Algebra Developing Mathematical Thinkers

Place Value Bonus235 + 597 = 832

Page 30: Sorting to Algebra Developing Mathematical Thinkers

Cross Number Puzzles and Multiplication

Page 31: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 32: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 33: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 34: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 35: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 36: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 37: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 38: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 39: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 40: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 41: Sorting to Algebra Developing Mathematical Thinkers

Developing a familiar multiplication algorithm

Page 42: Sorting to Algebra Developing Mathematical Thinkers

The algebra connection: adding

4 2

3 1

10

4

6

37

4 + 2 = 6

3 + 1 = 4

10+ =7 3

Page 43: Sorting to Algebra Developing Mathematical Thinkers

The algebra connection: subtracting

7 3

3 1

6

4

10

24

7 + 3 = 10

3 + 1 = 4

6+ =4 2

Page 44: Sorting to Algebra Developing Mathematical Thinkers

The eighth-grade look

5x 3y

2x 3y 11

23 5x + 3y = 23

2x + 3y = 11

12+ =3x 0x = 4

3x 0 12

All from sorting buttons!

Page 45: Sorting to Algebra Developing Mathematical Thinkers

Algebra At the Core Kindergarten – Grade 5

Focus on underlying principles allows“two for the price of one”

subtraction is un-additiondivision is un-multiplication

Mastery of traditional algorithms Easier and more exciting to learn and explore

More competently used

Page 46: Sorting to Algebra Developing Mathematical Thinkers

For more information about Cross Number Puzzles

and Think Math! visit thinkmath.edc.org