<div class="gmail_quote">On Sat, Sep 5, 2009 at 2:23 AM, K. K. Subramaniam <<a href="mailto:subbukk@gmail.com">subbukk@gmail.com</a>> wrote: <blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> <div class="im">On Friday 04 Sep 2009 10:12:36 pm Maria Droujkova wrote: > Circle is one of the hardest in Scratch. Unless I am missing a command. </div>Maria, Could you be more specific please? hardest to understand through Scratch or hardest to create after having understood? Subbu </blockquote><div> The smooth circle is hard (trig?), the approximation of a circle by polygons is easy. Actually, it's one of the first thing, beyond going straight 10 steps, many kids I worked with try in Scratch: - When Space is pressed - Move 10 steps - Turn right 15 degrees This polygon looks "close enough" to kids that they call it "circle." This discussion was very helpful. A Math Club I lead for 5-6 years old is crazy about Scratch. The last unit we did, all August, was on maps and mazes, suggested by kids based on their roleplays (pirates mostly). That lead into some interesting shape work. I was eying these puzzles, but wanted some story tie-in. This conversation reminded me of Flatland. Luckily, last year a very nice short movie came out, quite accessible to 4-6 year olds: <a href="http://www.youtube.com/watch?v=C8oiwnNlyE4">http://www.youtube.com/watch?v=C8oiwnNlyE4</a> In that story, Triangle parents have Square kids, Square parents have Pentagon kids and so on. The more angles there are, the higher the society status, until polygons have so many angles that they look like Circles, at which point they become (evil) priests. So, I am thinking of inviting kids to work with this in Scratch. Hopefully, we will arrive at a general way of programming regular polygon angles, as a time-saving device (from doing every shape by hand). But this is not the main mathematical reason I want this. The last time polygon approximation came up for this kids, we were making gift boxes (general prisms) out of paper. First, kids drew pictures, say, a dinosaur or a light saber, then made the boundary into straight segments, then drew rectangular flaps next to each segment, cut out and lifted flaps to form the box. My hope is that Scratch polygons will be another entry into this calculus example space devoted to approximation. Ideas and advice appreciated. Cheers, Maria Droujkova Make math your own, to make your own math. <a href="http://www.naturalmath.com" target="_blank">http://www.naturalmath.com</a> social math site <a href="http://mathfuture.wikispaces.com/" target="_blank">http://mathfuture.wikispaces.com/</a> Math 2.0 interest group home </div></div>