First of all, it should be called the "Pythagorean Theorem," because Pythagoras had nothing to do with inventing or discovering it. The Chinese knew about it hundreds of years before, and the Mesopotamians? Like 1300 years before! Zip Zap....
Okay, this is a really REALLY cool activity that uses the "Pythagorean" Theorem to solve a very important question: how can you ship an 11 foot fishing pole, when the shipping box can't be any more than 10 feet in length?
Take some time to scratch your head, okay?
Okay, the answer is this: you get a box that's 10' x 10' and put it in diagonally!
But that won't be necessary, because you can use smaller boxes and still fit the damned pole in diagonally. What size? Well, that's what your students are going to investigate in this activity: how many boxes can you make that have a diagonal that is 11 feet long, if you can only build them in 1 foot increments? And which one would have the least surface area, because they are priced by the square foot?
Ah, but the fun does not end there: what would happen if you were able to make the box in half-foot increments instead? It turns out you can make more sizes of boxes. Maybe there's a better box that will fit just as well and cost less? Well, try it and see....
AND THERE'S MORE! A third investigation looks at what would happen if you could make the boxes in 1 inch increments. Turns out, yes, there are even more boxes you can make. In fact, there are many, many boxes, and there may be one that is even cheaper to make!
AND MUCH MUCH MORE! Because along came Bob - Bob Ablah, a shipping clerk at Just for the Halibut (the fishing rod company) who comes up with the idea of using a taller box so you can put the rod on a "double diagonal" that should use an even smaller box..... and can you fit the rod in the box that he suggests? And if it does work, will it be cheaper to use that box?
Comes complete with fuller than fuller explanation of how to teach this unit, and full answer key and explanations.