EndreWhiteMane: Speaking of puzzles, do you know of any inexpensive puzzle printing software? Something where I could use my own picture and it would overlay the puzzle pieces for me to cut out.
zeogold: Can't say I do, but I know of a website where you can use your own picture, pay some money, and they'll send you a physical puzzle.
http://www.createjigsawpuzzles.com/
If you go through the entire process of picking a puzzle and number of pieces, then go to "start your design" and upload an image, you'll see a preview of what it looks like. You could open this preview in a new tab and print it out and use that.
It would be a little difficult to precisely cut out most jigsaw puzzle pieces considering the shape of them. Are you looking for a less-traditional shape, such as triangles or squares?
What I was going to do is mount it to foam core board and cut it with a stencil cutter. That's like an x-acto knife but has a fine blade and swivels. The pieces would be quite large, about a dozen pieces per puzzle. Each piece would contain one element of an overall subject.
Think like each food group make up an overall balanced diet.
Edit: That website is awesome, low prices too. Thanks!