Math Takes Shape in First Grade

A most exciting and brain stretching exploration of shapes took place in first grade this week as the students explained and defined a variety of shapes.  The triangle was the easiest with its three sides and three points, tips, corners or angles (as we will call them).  As the shapes had similar attributes it became more difficult to explain explicitly what made each unique.  For example, an oval was described as this: a mix of a rectangle and a circle but it's not either, it has no points, it's a stretched out circle but only on the top and bottom, it has no sides, it has curved lines.  A circle was described thus: it's like an oval but the stretched out part is smaller, it's a squeezed oval to be round, it has curved lines, it is round, very round!, it's a little curve with no edges (as opposed to lines), it is almost an oval but smaller and rounder, it has one curved edge, it is a non-stopping curve.  It was tricky to describe one without comparing it to the other.

This only got more sticky when we came to our four sided shapes: square, rectangle, rhombus and trapezoid! We had many comparisons with one shape being another only squished or stretched out, or being two triangles without a line, or a triangle with the top cut off.  But with careful observations we came to these conclusions: a square has four equal sides, four equal angles and it is symmetrical.  A rectangle has two long sides and two short sides and four equal angles. A rhombus has four diagonal lines, two narrow angles and two wider angles. A trapezoid has two straight lines, a short top, and a long bottom, two diagonal lines and four angles, the top two are equal and the bottom two are equal but the top and bottom angles are different.  Wow!  Lots of explaining of ideas and changing minds was happening with each different description! It was wonderful to listen to and watch as the students challenged and compared their ideas. We never imagined we would have such a long and fascinating discussion!

A few other thoughts that came up (but were not agreed upon by all) after one student pointed out that an oval was still an oval even if you turned it on its side included these: a rhombus is a square turned on its side,  a trapezoid is only symmetrical when it's right side up and not if its standing on a point, a trapezoid is not a trapezoid when it is standing on a point and a triangle and an oval do not change no matter how you turn them.  What do you think???

As our discussion wrapped up, some students started making shapes with their bodies, another shared shape animals she was drawing and later in the day students were creating all the shapes on geo boards.  We loved seeing these extensions! And, we discovered that there are shapes with more sides than four.  We learned the names of those with as many as ten sides! What a fantastic way to begin a study!!