Review Unit
Squaring 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 apply a method for multiplying two magic squares.
Materials:
Overhead transparencies or handouts:
 Large empty 3x3 grid
The nine cells in numerical order
Ordering the cells to make a magic square
The completed 9-cell magic square
Blank paper
Blank overhead transparency and pens
Rulers
Calculators
Definition:
To square a number means to multiply it by itself.
[Just as we can talk about squaring a number, we can talk about squaring something with any notion of multiplication. We can square an nxn matrix by multiplying it by itself under matrix multiplication, and we can square a magic square by multiplying it by itself.]
Considering Square A:
Remember the method we followed to multiply Square A by Square B? (To review, return to Classroom Activities.) If this method can be used to 'multiply' two magic squares, let's use it to square a magic square.
To square Square A, we'll follow the same steps, but instead of using Squares A and B, we'll use Square A twice.
Square A Square A
We'll again need a large grid. It will have as many cells as
there are cells in Square A.
 Check for Understanding:
Verify that Square A is a magic square.
How many cells does Square A have?
How many cells will we need in the large grid?
Generating the second square:
Following the multiplication method, we will fill the nine cells in the empty 3x3 grid. We will begin by adding the same number to each entry in Square A to make a new magic square.
Square A is made up of nine entries. When we add 9 to each of them, we get
We will continue this process by adding 9 to each entry to make each successive cell.
Continued next page
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