"Mars!" exclaimed someone. Immediately their curiosity was piqued.
They can't see you, obviously, but they can sense your presence. They can sense your presence and location if you are standing on the same color ground as them. If they can reach you with their arms, they'll grab you and eat you. (Why do you think that's the unit of measure?) Their arms don't bend. So if you're standing on the same color of ground as one of these creatures, you're safe if you're <1 or >1 arm-length away. And, of course, you're safe if you're standing on different colored ground.
Your mission is to landscape this ground so that you can plant crops outdoors and have food. How can you do it?
That last student question really lassoed us into the realm of mathematics. It took a really long time to get there. Was that time investment worth it? Can attention be sustained at this level once we move deeper into the math? I guess we'll see over the next 5 weeks.
We began class today playing function machines. This activity allowed people to arrive at different times without missing a big math concept. The kids had great fun. We spent about 10 minutes on function machines, then about 40 minutes on the Botso problem. Just when we were starting to discuss strategies for the coloring of the plane (in math-speak), Z asked if we could go back to function machines.
"I thought that this was going to be a math class," he said, a bit disappointedly.
"I want to keep talking about the aliens," said a few other kids.
"Talking about the aliens is math," I replied.
"It is?" said a few.
"I didn't know that geometry is a type of math," said R.
What's the smallest number of colors you need so no 2 points of same color are 1 unit apart in the plane?
Earlier today, we did some pretty simple functions that everyone "got" quickly – add 2, subtract 1, etc. Now we made the machine a lot more complex in order to do a higher-order task. The kids called out numbers to go "in." When they put in 1,645, out came 822 1/2. Etc. After we had a bunch of input/output pairs on the board, conjectures began. Almost everyone thought that the machine was either doing subtraction or division because the out numbers were smaller than the in numbers. A few students saw the sense in trying smaller numbers to discern the pattern (many were having fun putting in very large "numbers" like a hundred billion thousand six million). This helped a bit, but then we were out of time without a conclusion. To be continued next week.