Math Delights

by Yul Inn, founder of www.funmathclub.com, who leads interesting and fun math workshops
and Getting Smarter Every Day Book C, by Dale Seymour, page 71
and SEED (Slumberger Excellence in Education Development) website, www.planetseed.com/node/18315

Polyominoes are shapes made from squares that are connected edge-to-edge. You can form polyominoes with any number of squares. The following are a few sample polyominoes:

Monomino	Domino	Tromino
Tetromino	Pentomino	Hexomino

Polyomino A is considered distinct from Polyomino B if you can orient one, or a copy of one, by moving, turning, or flipping it and placing it on top of the other so that they don't match exactly. To the right are two tetrominoes that look different, but they are considered congruent because you can orient Tetromino A or a copy of Tetromino A on top of Tetromino B. What do you need to do to put Tetromino A on top of Tetromino B?

Tetrromino A

Tetrromino B

How many distinct (non-congruent) dominoes can you find?

How many distinct (non-congruent) trominoes can you find?

How many distinct (non-congruent) tetrominoes can you find?

Draw each tetromino on this graph paper. If you found less than 5, look for more. If you found more than 5, make sure each one of them is distinct. Color each of the distinct tetrominoes in a different color. Then cut them out.

Use each of your tetromino pieces at most once to create the shapes on the Tetromino Puzzle worksheet. Which shapes are impossible to construct? Why?