Magic Square Assessment Instrument

[To be used as both Pre-test and Post-test]

1. Describe a powerful strategy for solving challenging non-routine problems.

2. Is it possible to place the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, in a box with three rows and three columns, so that the sum of each row, column, and diagonal is the same?

YES NO

If so, what would be that sum?

It not, why not?

3. What number can go in the middle of the Magic Square?

Can any other number go in the middle?

4. Could the Magic Square be solved with the numbers 2, 4, 6, 8, 10, 12, 14, 16, 18?

YES NO

If so, what would be that sum?

It not, why not?

5. How would you show students an easy way to solve similar problems?


Magic Square Answer Key

1. Describe a powerful strategy for solving challenging non-routine problems.

One of the most powerful problem-solving strategies is to find a simpler problem. In this case, instead of setting all rows, columns, and diagonals equal to the same number, we focused only on the rows. Once solved, we had an important piece of information that allowed us to solve more of the problem.

2. Is it possible to place the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, in a box with three rows and three columns, so that the sum of each row, column, and diagonal is the same?

YES

If so, what would be that sum?

Since the sum of all 9 numbers is 45, the sum of each row must be 15.

This is also consistent with the simple method we used. The only way we could get all three rows to have the same sum was to have that sum equal 15.

3. What number can go in the middle of the magic square?

Five is the only number that can go in the middle of the magic square.

Can any other number go in the middle?

4. Could the magic square be solved with the numbers 2, 4, 6, 8, 10, 12, 14, 16, 18?

YES

If so, what would be that magic number?

The magic number would be 30. Note that this is 2 x 15 (the magic number for the standard magic square.

5. How would you show students an easy way to solve similar problems?

In the previous case, we found that magic number is 2 x 15 (the magic number for the standard magic square. In general, if we multiply every number in a magic square by n, the new magic number is 15n.