The Magic Square Art Project started as activity I used to do with my middle school students as a culminating project to a series of lessons about magic squares. With any mathematics lesson, I like to add in a fun component that allows students to merge mathematics and some other area of study. In this case it was art.

Students studied the definition of magic squares prior to this activity and then related magic squares to algebra. Our final project was to create a large magic square and look for patterns in the numbers after they were placed on the paper. There are multiple patterns that can be discovered and this is where the project can turn into something more unique for each student.

Supplies

For this project, use as many sheets of graph paper as you want based on your time and the size of art you want to create. I would start with one sheet of 1cm graph paper or dot paper for the first time.

A ruler or any straightedge,
A pair of scissors or paper cutter,
A few sharp pencils,
A pencil sharpener,
A roll of clear tape (optional)
A few colored pencils, crayons, or markers

Step 1: Gather Your Materials

You will need the following items

A set of colored pencils
A straightedge or ruler
A few sharpened pencils
A pencil sharpener
A pair of scissors or paper cutter
A roll of clear tape
1 cm square graph paper or dot paper (any size will do, the larger size is easier the first time you do this)
A trash can for recyclables

Step 2: Cut the Edges

To begin this activity, trim the edges from your paper if you choose to use more than one sheet as shown above. This is especially important if each column does not match up perfectly. See pictures above.

Step 3: Line Up Each Row and Tape the Pages Together

Once each sheet of paper is trimmed, line each row up and tape the pages together using clear tape. This only needs to be done if you want to make the project bigger than 8.5 x 11in. Be careful to line up the sheets so that each section is still equally spaced. I usually tape the back of the paper together if I want to use more than one sheet of paper. Use the longest piece of tape possible. This is one error I have found that can affect the ease with which you complete your project. You do not want bumps from the tape in the paper if you use multiple small pieces of tape.

Step 4: Choose the Size and Start "Dotting"

You must have an odd number of rows and columns for this art project to work so here is where it is ok to trim your paper once more to make sure you have an odd numbered square. I am using a 27 x 27 square. Notice in my picture that I left the remaining rows.

Once you choose your size (remember you must choose an odd number), Start your magic square by drawing in dots at each corner. This is not mandatory, but does help as you move through the project to keep things lined up and your eyes from getting too tired from staring at the paper. Find the top center of the paper and label this first point “1.” Remember that you are labeling the corners, not the spaces of the graph paper.

If you are using dot paper, you will simply number the dots, not corner.

Step 5: Review the Guideliness for Making Magic Squares

A square is considered to be a magic square because all of its diagonals, rows and columns add up to the same number, called the magic number. Follow the steps for creating a large magic square until you label all of the corners of the graph paper. This will take some concentration and time. Be careful if you decide to use more than one or two sheets of graph paper. This can be a challenging “eye” problem.

You can use this site to help you remember how to make a magic square if needed.

(Making Magic Squares – Math Fun Facts (hmc.edu))

-Start with the number one that we entered from the last step. It should be in the center of the top row. You already should have placed a "1" in this spot. Now since we are at the top of the page, we will move diagonally squares and place the numbers 2, 3, 4, etc. It’s easy: after placing a number, just remember to always move diagonally. The only thing you must remember is to imagine the matrix has “wrap-around”, i.e., if you move off one edge of the magic square, you re-enter on the other side. From the 1 you move up/right (with wraparound) to the bottom right corner to place a 2. Then you move again diagonally until you are at the edge of the paper (with wraparound) to the left to place the next number. Continue moving diagonally placing numbers again until you hit the end of the paper or another number. If a number is in the spot you end up at, then place the next number directly below the previous number. and start a new diagnoal line. See the pictures above.

Step 6: Connect Points

Once you add all of the numbers to your magic square, use your straightedge or ruler to start connecting each number in order. Be careful to draw straight lines so the pattern can be clearly seen as you connect all points.

Step 7: Use Your Colored Pencils to Highlight a Pattern

Now that you have completed the magic square pattern and connected all of the points, use your colored pencils to shade in any pattern that you can find.

Introduction: Magic Square Art