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Space Diagonal

After 8 years teaching Geometry from this textbook, I finally made the lesson on Space Diagonals more interesting than saying: Do Pythag twice. Sure  I always do the Space Diagonal Dance, to much laughter, but the PrBL model wins. No, I don't have a video of the dance (that I know of).

I happened to have brought donuts for a meeting so I had this box.

I made up a story told them the legend of the Prince who made his butler leave the castle on a quest to find a delicious bread stick, the crunchy kind. The Prince told his butler that he was not to return until he found the longest bread stick that would fit in the box.
I gave them the box dimensions, put them into groups and handed out the white boards. It wasn't as easy as I thought it would be. They discussed and argued for about 7 minutes before coming up with the solution. I walked around and monitored, giving feedback and hints. A group presented their approach before starting independent practice, er a worksheet, for homework.

At first they thought the longest would be the bottom's diagonal.