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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]

- Students will work cooperatively in a group.
- Students will practice a variety of problem-solving strategies including
pattern seeking

relating patterns

relating numbers

- 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:

- Students work in groups of four.

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

- Two students work together to place number tiles.

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

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

## Preparation:

- Determine the number of groups needed for the class.

- 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:

- Each group of students is given the puzzle and the placement of the first 3 numbers:

- Game rules are explained. Questions can be used as part of the game or as a way to process the game.
- Variations can include changing the placement of the original 3 starting numbers (but make certain that a magic square will be achievable).

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

Read about the math involved in constructing a 3x3 magic square, or

look through a whole Web unit about magic squares.

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