Here's a little more of our process as we follow up our interests. This research and sharing goes during the day, between playing, practicing, laundry, etc... (notice how it's morphed)
Hey! This MIT tenured professor, an origami mathematician, was home schooled. How cool is that?
Following some links we found TreeMaker on Robert Lang's website. If you want to try it yourself, scroll down the Treemaker site to find the free downloads. He gives you access to the source code, if you are interested in playing with/modifying the program itself.
My 11 yo spends a few minutes playing with the newly downloaded TreeMaker while his younger brothers look on. He's intrigued, but the LEGOs call, and he also wants to use GameMaker to program.
Later, my husband and 11yo play with TreeMaker some more. It's neat that my son was learning about "lines of symmetry" in his Life of Fred book and then it comes up again in origami. They print out something to fold. It takes them a while to figure out the meaning of the fold lines, but they end up with something with 5 flaps that could be turned into an animal or person. Cool!
Grr.... The PBS show I wanted isn't showing on the one station we get here. (We don't have cable or satellite TV) The library doesn't have it. .... Ha! I found "Independent Lens, Between the Folds" at Netflix. Yea me!
Random: A fellow homeschooler posted to my local group this link to Box Car and One Eyed Jack games to teach math. Nothing to to with origami, but I bet the kids would enjoy some of these.
I discover Math Mansion and find a couple of videos on line. I let the kids watch them on my lap top while I brush my teeth this morning. 8 and 5 year old love it, 11 yo isn't impressed.
Anyway, you get the idea. One idea leads into another. I share what I find with the kids. Eventually something sparks their interest and they follow that until they're done. The amazing thing to me, after having been the student who promptly forgotten content as soon as the test was done, is that the kids remember this stuff ages later. What they learn having fun, exploring, and investigating for themselves, they remember. They OWN that stuff.