sorting to algebra developing mathematical thinkers

Sorting to AlgebraDeveloping Mathematical

Thinkers

Algebraic Ideas Breaking it up

4 40 45591940

121 11

What does the “thick line” do?

4

What does the “thick line” do?

4 21

What does the “thick line” do?

4 21 25

What about this way?

100

What about this way?

100

27

What about this way?

100

73

27

Kindergarten Sorters

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

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.

6

4

7 3 10

Back to the very beginnings

Children can also summarize.

“Data” from the buttons.

blue gray

large

small

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

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

5

21

8

13

912

7 6

3

1st grade

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

63

38

25

1350

20 5

830

2nd grade

Relating addition and subtraction6

4

7 3 10

4 2

3 16

4

7 3 10

4 2

3 1

2nd grade

The subtraction algorithm

63

38

25

1350

20 5

830

25

38

63

-530

60 3

830

25 + 38 = 63 63 – 38 = 25

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

Place Value Bonus235 + 597

Place Value Bonus235 + 597

Place Value Bonus235 + 597

Place Value Bonus235 + 597

Place Value Bonus235 + 597

Place Value Bonus235 + 597

Place Value Bonus235 + 597

Place Value Bonus235 + 597

Place Value Bonus235 + 597 = 832

Cross Number Puzzles and Multiplication

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

Developing a familiar multiplication algorithm

The algebra connection: adding

4 2

3 1

10

4

6

37

4 + 2 = 6

3 + 1 = 4

10+ =7 3

The algebra connection: subtracting

7 3

3 1

6

4

10

24

7 + 3 = 10

3 + 1 = 4

6+ =4 2

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!

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

For more information about Cross Number Puzzles

and Think Math! visit thinkmath.edc.org