# LATIN SQUARES Reindeer Squares Critical Thinking GATE Differentiated

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PROBLEM SOLVING: Reindeer Squares (Latin Squares)

Use Reindeer Squares to teach your students deductive reasoning while disguising it as lots of fun. Reindeer Squares are square arrays of n x n rows and columns in which n items fill the cells so that no item is used more than once in each row and column. Known as Latin Squares in mathematics, they are used for statistical analysis. If they seem familiar, they should; Sudoku is a 9 x 9 Latin Square.

Begin by demonstrating how a 3 x 3 array works. Cut apart the 6 x 6 colored array of tiles found at the end of this unit. Using 3 each of 3 colors, place them on the 3 x 3 array in standardized form; i.e. both the 1st row and 1st column display the colors in the same order.

Distribute a Reindeer Squares 4 x 4 board to each student with 4 tiles each of 4 colors. Ask them to place their tiles on the board without repeating a color in any row or column. Be prepared! One of your students is bound to discover that making diagonal stripes will allow him/her to solve the Reindeer Squares with ease. Do not let them stop with that realization. For a 3 x 3 array, there are 12 possible solutions. Dare them to find all 12. For a 4 x 4 array, there are 576 permutations!! Now that's a challenge any bright, gifted, and/or talented students should love. Moreover, this is a wonderful, calming activity for this exciting time of year.

As a teacher who is dedicated to differentiated instruction, I have used Reindeer Squares successfully with 1st through 3rd graders. You could also set Reindeer Squares up as a math center or sponge activity.

If your students love them as much as mine do, the next logical step is to introduce Sudoku. It's certainly appropriate for 3rd graders. Need help? Look for my power point product, How to Play Sudoku.

Your students may enjoy these editions of Latin Squares as well:
Patriotic Squares
Monkey Squares
Pumpkin Squares
Turkey Squares

Barb Evans
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