I've been itching to do some neat Geoboard exploration with my Geometry classes, ever since our shipment of math goodies arrived. So, today during my prep period, I randomly pulled together a Geoboard activity for my honors kids to start on during our overflow time. We started it near the end of class, as a change of pace after doing some practice for an upcoming quiz. The kids got through only the first three problems, but it was a really fun / productive time for them! Check it out. I liked it a lot, so I am now thinking about using this activity for my regular kids next week, as warm up before their next big project. The honors kids will probably have some extra time this week to finish off the whole assignment, so I can preview how it would go for my regular classes. :)
(It was fun to observe that kids couldn't immediately build a 5x6 rectangle, because their instinct is to count points/lines instead of # of spaces. Fixing their misconception via adjusting the rubberbands is surely a lot more fun than making them re-draw a shape on a grid!!)
I did a sequence with Geoboards and my froshlings a few years back: we figured out Pick's formula from data. Kids collected arbitrary polygons with the relevant data: area, number of vertices, number of enclosed points, number of points on edges (but not on vertices), and we plotted these in various ways to figure out the formula. Then STARTED down the path of figuring out how you might prove such a thing. Worked great.
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