A Math Forum Web Unit
Allan Adler's

Multiplying Magic Squares

Suzanne's Magic Squares || Multiplying Magic Squares: Contents || Exploring the Math

Objectives: [NCTM Standards: Number and Operations, Communication, and Connections]

  1. Students will work with arrays of numbers.
  2. Students will calculate and compare sums of numbers in the context of magic squares.
  3. Students will learn a method for multiplying two magic squares.


  1. Overhead transparencies or handouts:

      Multiplying Two Magic Squares
      The Product: 12x12 Magic Square
      12x12 Magic Square in 3x3 Blocks
      Empty 4x4 Grid
      Step One
      Step Two
      Step Three

  2. Blank paper
  3. Blank overhead transparency and pens
  4. Rulers
  5. Calculators

Selecting Two Magic Squares

    Consider two magic squares at random, A and B.

    Note: If the students have had limited experience with magic squares, refer to How to Find Magic Squares.

    Check for Understanding:

    1. What sum do you get when you add each row? column? diagonal? of the first magic square.
    2. Verify the second magic square. Explain why it is a magic square.

    If necessary, refer to Magic Squares.

Considering the Product of the Two Magic Squares

    The first magic square, A, is 3x3, and the second one, B, is 4x4. The 'product' of A and B, A*B, will be a 12x12 magic square.

    You may wish to refer to a mathematical explanation of why this is a product.

    Here is the 12x12 magic square product:

    Check for Understanding:

    1. Verify that this is magic square.
    2. Explain why it is a magic square.

    Suggestion: Students can work in groups to find the various sums and report back to the class to process.
Let's find out why this works.  
Continued next page.

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