A Math Forum Web Unit

Review Unit

Squaring Magic Squares, page 2



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Suzanne's Magic Squares || Multiplying Magic Squares: Contents || Exploring the Math
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Generating the third through ninth squares:

Using the second magic square, add 9 to each entry to get the third square. Using the third square, add 9 to each entry to get the fourth square. Continue this process until you have all nine magic squares.

[Suggestion: Have the students work in groups with calculators to generate the nine magic squares.]



    Check for understanding:

    1. Find the numbers in the upper righthand corners of successive magic squares. Subtract the smaller number from the larger. What is the difference?

    2. Do you see any other repeating number patterns? Hint:

      What is the sum of the first row of the first magic square?
      What is the sum of the first row of the ninth magic square?

      What is the sum of all nine entries of the first magic square?
      What is the sum of all nine entries of the ninth magic square?


    [Suggestion: Have the students work in groups using calculators to find the answers to these and/or class-generated questions.]


The Arrangement:

Now let's arrange the nine squares following the order of the numbers in Square A:



    Check for Understanding:

    1. Notice that the first magic square will be placed in the middle position in the top row of the large 3x3 grid.
    2. Notice that the second magic square will be placed in the righthand position in the bottom row of the large 3x3 grid.
    3. Where will the third magic square be placed?
    4. Where will the fourth, fifth, sixth, seventh, eighth, and ninth magic squares be placed?

Square A squared:

This 9x9 magic square is the square of Square A:



    Check for understanding:

    1. Verify that this is a magic square.
    2. Do you see any repeating number patterns? Hint:

      Find the sums of the rows or columns of Square A and the sums of the rows or columns of the square of Square A.
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