If you want to make games or puzzles for use in your classroom, you may find you need to make your own game or puzzle pieces (or “tiles”).
You want them to be stiff and durable, and with enough heft that they feel comfortable in the hand and are easy to handle and to manipulate. You also want them to be easy and inexpensive to make.
Here’s how you can get all of that using commonly available paper materials. (Of course this process won’t be suitable for all puzzles—it depends on the nature of the puzzle. But this should do the trick for most conventional style puzzles. And this same process can be used for a lot of game pieces as well.)

— a computer and printer
— ‘free cut’ label paper (sticky-back paper that is not pre-scored) 
— a paper cutter (A razor tool or box cutter will do in a pinch.)
— stiff backing  (In Japan, I use 板目用紙 — “Itame Youshi.”)

Design the puzzle on your computer.

Print it out on the free-cut label paper.

STEP THREE (optional):
Laminate the sheet of label paper. Trim off the edges of the paper. (This will also remove the edges where the two layers of lamination sheet are fused together. Don’t worry. That’s what you want!)

Peel the sticky backing off the label paper and adhere the sheet to the stiff backing.

Carefully cut out your puzzle pieces.

Looks nice. Feels good in the hand. Holds up well through multiple uses.

NOTE: I also recommend color-coding your puzzles if there are multiple sets. They will be easier to organize, and if you have more than one set being used at the same time, it will make it MUCH easier to sort everything out if pieces from different puzzles get mixed up!

Here is a YouTube video showing how I make mine: