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]
 Students will work with arrays of numbers.
 Students will calculate and compare sums of numbers in the
context of magic squares.
 Students will learn a method for multiplying two magic squares.
Materials:
 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
 Blank paper
 Blank overhead transparency and pens
 Rulers
 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:
 What sum do you get when you add each row? column? diagonal? of the first magic square.
 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:
 Verify that this is magic square.
 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.
