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A magic square is an arrangement of the numbers from 1 to n^2 (n-squared) in an n x n matrix, with each number occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same.

Since Magic Squares are a little too advanced for most kindergarteners, I developed a lesson using game theory. The rules for Race to 15 are as follows:

What is game theory? It is the science of strategic thinking:

The key to number sense is the ability to see how numbers pair together. I call these anti-numbers. One pair of anti-nines is 4 and 5 because their sum is 9.

For example, it is critical that our young Mathletes can identify anti-tens of 10 and 0, 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5. The best part of this lesson was when several of the children began asking about the anti-tens for numbers like 11 and 12. I challenged them to come up with their own solutions; they came up with 11 and -1, 12 and -2 and so on. 

After studying coordinate point dilations using multiplication of whole numbers greater than one for enlargements and fractions between 0 and 1 for reductions, I wanted the children to explore the wonders of grid drawing dilations.