Magic Squares  

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Objectives:

[NCTM Grade K-4 Standards #1, #2, #3, and #8]
[NCTM Grade 5-8 Standards #1, #2,#3, and #7]
[NCTM Grade 9-12 Standards #1, #2, and #3]

1. Students will work cooperatively in a group.
2. Students will practice a variety of problem-solving strategies including
   pattern seeking
   relating patterns
   relating numbers
   
3. Students will be able to justify their results and explain their solutions.

Materials:

3x3 grid
number tiles "1" through "9"

Object of the game:

To make a 3x3 magic square.

Rules:

1. Students work in groups of four.

2. All students discuss strategies to use to complete the puzzle.

3. Two students work together to place number tiles.

4. Two students check the sums as number tiles are placed in the 3x3 grid.

5. The puzzle is complete when the sum of each row, column and diagonal is the same.
   

Preparation:

1. Determine the number of groups needed for the class.

2. Prepare one puzzle for each group. If number tiles of some sort are not available, use the handout to create enough number tiles for each group.

Procedure:

1. Each group of students is given the puzzle and the placement of the first 3 numbers:
   
   
2. Game rules are explained. Questions can be used as part of the game or as a way to process the game.
3. Variations can include changing the placement of the original 3 starting numbers (but make certain that a magic square will be achievable).

Questions considered by the whole group:

1. Are there strategies that will help the group quickly place the number tiles to make a magic square?
2. What number did the group place in the center cell? Can a reason be given why this number is unique?
3. What is the sum of each row, column, diagonal of the magic square? Is this a unique sum? Why/why not?
4. If the 1, 2, and 3 are placed as given, is there a unique solution to the puzzle? Why/why not?

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