Pentomino possibilities:

1) Define them and get students to find them (see §16.3 LE 12)

2) Go from pentominoes to nets and work with different nets made of squares

3) Tesselate with them

4) A game: Get (or design and print out) a regular checkerboard. Make a set of pentominoes out of squares the size of the squares on the board. Two players take turns placing one pentomino at a time on the board until no play is possible, either because there are no more pentominoes or because there is no space in which any remaining pentomino can be placed. The winner is the one who plays the last tile. For this to be a lesson, there needs to be serious consideration of strategy.

If your “class” is a bunch of your contemporaries, you may start with #1 above and proceed to this game and work on strategy with them. If you do that, you must record the progress of your thinking as a group (and make sure to maintain some balance in who is doing the thinking!)