triangles

I was so excited working with triangles this week as I was trying to come up with a way to have kids discover the rule that the interior angles of polygons add up to the number of sides minus 2 times 180. With my math team we started with octagons and then tried other polygons. We made triangles from the center of the octagon out to each angle. The had done enough investigation to know that the interior angles of a triangle equal 180, so they used this knowledge. Of course they first just multiplied the number of triangles by 180 and then we talked about the angles around that center point. Brilliant! 

With my 4th graders, some of whom were having trouble distinguishing acute and obtuse angles, I went to the wedge. I provided them with 4 in x  4 in squares and we used them to measure angles. Smaller than the wedge was acute, larger than the wedge was obtuse. This was far more effective for most than the paper patty protractors we had made. They hadn't had enough experience for the protractors to make sense. Now they are working on investigating different triangles like we did on Thursday. I had several kids come up and ask me, "Is it possible to make a right equilateral triangle?" I am amazed at how successful all of my kids are using the 4 x 4 wedge and creating right, isosceles, scalene, acute, obtuse and combinations of these triangles. The excitement continues......