Sorting to Algebra Developing Mathematical Thinkers.

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Presentation transcript:

Sorting to Algebra Developing Mathematical Thinkers

Cross Number Puzzles P uzzles are not "dessert" for after the "real" work is done. Selected properly and introduced thoughtfully, they can be the real work. EDC

What am I supposed to do? What CAN I do?

Algebraic Ideas Breaking it up

What does the “thick line” do? 4

421

What does the “thick line” do? 42125

What about this way? 100

What about this way?

What about this way?

Kindergarten Sorters

4 + 5 = = 4 7 Addition and Subtraction From sorting to algebra Challenge: can you find some that don’t work? 5x + 3y = 23 2x + 3y = 11 Is there anything interesting about addition and subtraction sentences? 13 +=

Back to the very beginnings Picture a young child with a small pile of buttons. Natural to sort. We help children refine and extend what is already natural.

Back to the very beginnings Children can also summarize. “Data” from the buttons. bluegray large small

large small bluegray Abstraction If we substitute numbers for the original objects…

A Cross Number Puzzle Don’t always start with the question! st grade

Building the addition algorithm Only multiples of 10 in yellow. Only less than 10 in blue nd grade

Relating addition and subtraction nd grade

The subtraction algorithm = 6363 – 38 = 25

The subtraction algorithm = 6363 – 38 =

Place Value Bonus

Place Value Bonus

Place Value Bonus

Place Value Bonus

Place Value Bonus

Place Value Bonus

Place Value Bonus

Place Value Bonus

Place Value Bonus = 832

Cross Number Puzzles and Multiplication

Developing a familiar multiplication algorithm

The algebra connection: adding = = = 7 3

The algebra connection: subtracting = = 4 6 += 4 2

The eighth-grade look 5x5x3y3y 2x2x3y3y x + 3y = 23 2x + 3y = = 3x3x0 x = 4 3x3x0 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-addition division 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