Mathematics reveals hidden patterns that help us understand the world around us.   And, although the language of mathematics is based on rules that must be learned, it is important  that children be encouraged to move beyond memorizing basic algorithms.  In order to support opportunities for critical thinking about mathematics, our problem solving focus has made a dynamic shift in three critical ways:

• Seeking solutions, not just memorizing procedures
• Exploring patterns, not just memorizing formulas
• Formulating possible solutions, not just doing exercises

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TANDEMS

RULES
>Each player has 5 men in a line on his side of the board.

>The winner is the first player to get all his men across the board on to the line of squares on the far side.

Players take turns to move. When it is his turn, each player must move two of his men one square each in the SAME direction. The move may be in any direction including diagonally.

Only one man is allowed in any square, there is no jumping and the black squares cannot be used.

Tandems Gameboard

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The Deca Tree

And on each branch, there are 10 twigs.

And on each twig, there are 10 leaves.

AND THEN ONE DAY…………..

A woodcutter came along and cut down one trunk from the tree.
Then he cut off one branch from another trunk of the tree.
Then he cut off one twig from another branch.
Finally, he pulled one leaf from another twig.

How many leaves were left on the tree then?

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Why do this problem?
This problem provides children an opportunity to experience place value.  It shows in a pictorial way what zeros do to a number when multiplying by 10 and 100.

IF your children found this problem interesting, you might pose similiar problems with a five-branched “Penta Tree” or an eight branched “Octa” tree.