Geogebra+experiments

This is my second go at creating a page because I managed to put my first one in the wrong place. Doh. In fact, I *still* think it's in the wrong place, but I think I'm getting closer...

For the triangle in a circle geogebra exercise, I explained to my son that we were supposed to be trying to find the triangle with the greatest area possible that would fit inside a circle. My son said "I guess that's going to be an equilateral triangle then." I told him to wait and see then set up the exercise and 'Jinged' it as he experimented. He immediately set about making a roughly equilateral triangle which touched the edge of the circle. Then he fiddled about with the controls a bit to figure out which of the readings on the left gave the area. Then he spent a while tweaking the triangle to make sure he had the greatest possible area. He concluded that 5.2 was the maximum reading he could get for the area, which coincided with the most equilateral triangle he could draw, which wasn't perfect but was pretty close.

He appeared to take very little notice of the information on the left until he actually needed any of it. After he'd roughly found the maximum area and was tweaking it, he kept an eye on the info on the lengths of the lines, I think to try to get them all exactly the same and see if it co-related to the maximum area, but I don't think he bothered to get his head around any more of the info than he needed to to solve the problem. He's very much the sort of person who will just jump straight in and fiddle without worrying about all the details, assuming he'll be able to fill in any gaps in his knowledge as he progresses.

media type="file" key="to_upload.swf" width="592" height="559"

For the paper folding exercise, we did a 'thought experiment' and he concluded that what he would do is to imagine the triangle drawn on the circle and then fold along the imaginary lines.

Interestingly, my husband, who is in his seventies, has had very little formal education and claims to have no imagination whatsoever, was listening to the 'lesson' and announced that to fold the paper into an equilateral triangle you'd have to start by folding the bottom up to the centre. I queried how he knew that and said that he could 'see' it when he was listening to the two of us talking about it. For someone 'with no imagination' I was pretty impressed - he hadn't even *seen* what was happening on screen and was relying on what he could overhear. I asked him more about this later and he said that he could see the circle in his mind and 'just split it into thirds', which makes sense but I can't see how that relates to folding the bottom of the circle to the centre, which seems more like quarters/fourths than thirds to me. I guess he's imagining it as a clock face, with 12 at the top, and 4 and 8 at the 'third' markers. Presumably, when you fold 6 to the centre, then the fold lines touch 8 and 4. I guess I'm going to have to go and fiddle now to double check...