I have loved these rich tasks from YouCubed.org. I found myself puzzling over this particular puzzle about flipping coins this afternoon. It ties nicely to modular arithmetic. I believe in the end that for any number of coins n, its minimum number of flips is a function of (n mod 3) and floor(n/3), but I'll let you try it and see for yourself! As usual, I find that starting with smaller problems really helped me to generalize and see a pattern.
I also enjoyed the much simpler but accessible paper-folding task from Mark Driscoll. What I find to be really enjoyable to read is also Jo Boaler's commentary on each task, what questions she asks, and when she allows the kids to work independently versus talking to each other.
If you haven't already signed up to be on the YouCubed.org mailing list, I highly recommend it! I find myself jumping with excitement to open their emails. Even though some of the site's content targets middle-school teachers, it is so enjoyable to hear and read of the way Jo talks about mathematics.
On the upper end of open-middle problems, I had a lot of fun today thinking about the size of the tiny sphere that can fit snugly inside the space of a tetrahedron built from 4 larger spheres. As in, if you packed 4 equally sized spheres together like shown here (this is the top-down view) and then in the middle space fit in another tiny sphere, then how big is that tiny sphere's volume relative to the other bigger spheres? PCMI had problems like this in their Geometry sets from this year, and I enjoyed playing around with this particular problem. It's probably too challenging for most of our students to do, but a good one to keep in my arsenal nonetheless.
I hope you have enjoyed the tasks from today. Ciao!