I needed a legit looking die, so there needed to be dots. Not just dots, but symmetrical dots. In order to complete this, I couldn't just eyeball it, so I used my knowledge of midpoints and bisectors and hacked away at each surface until they were all symmetrically designed. This is certainly not saying that designing a die is a Mathalicious lesson, but it felt good creating something that had a ton of math that kids would seem to inherently ask fo or just reach for on their own.
To start off the lesson, I would have kids draw 6 squares and attempt to create the 6 faces of a die without a ruler or compass. As their frustration level grows, begin to give them more tools (or wait until they request it, depending on your level of evil desired) until they finally are begging to do a construction to complete the task. The year that I taught Geometry, I didn't have too many students begging to do a construction, so hopefully this would encourage kids to use their resources.
Once they have their paper-drawn draft (or whiteboard, for all you paperless folks), kids design their die in Sketchup and check them with their partner for accuracy.
*** Things to mention about the printing process ***
Because the dice are so small, a friend told me to space them out and slow down the extrusion speed. This gave the plastic more time to cool down going from one layer to the next and the slower extrusion helped lay a good layer of plastic. I also used a 12mm cude instead of the 7 for the simple reason of size and the printer's ability to be precise within those confines. Finally, use GLUE! My first print had curled edges because I went skinny on the glue - never again (I say that about once every other week).
NOW, from this point, I would have the class check for accuracy. Measure them, sure, but there's more. I would have the groups roll the dice > 100 times and log their sums, then compare them to the probabilities of rolling 2-12 with 2 dice. If there are any extreme differences, we can have a good discussion about what happened and analyze the dice for faults.
Either way, this seems like it would be a ton of fun with a math class and it's one more reason why I miss the classroom. Hopefully someone out there who has a class and access to a printer will try this out and give me some feedback on it.
For the full lesson plan, go to AirWolf3D's website. As always, I'm open for making it better
Happy "Snake Eyes" Fishing