Exploring polygons with… sticky notes!

You can only match the full length of the sides: short to short, or long to long. 

In Math this week we’ve begun our exploration of geometry. Yesterday we took triangles made from square sticky notes cut on the diagonal, and we explored to see how many different polygons we could make by joining two of these triangles. There was a restriction, though; you could only join triangles by making sides touch fully, as shown in the picture to the right. The students discovered that you can only make three polygons this way: a square, a parallelogram, and a bigger triangle (not shown here).

That was just the warm-up, however. Today we explored to see what polygons could be made this way if you’re using four triangles. Most of the children predicted that they’d probably only find a few more ways; some suggested that since it was twice as many triangles, that there might be 6 polygons that could be made, since that would be twice three. It was delightful to hear their exclamations of surprise as they discovered that there were far more than that! In fact, there are fourteen possible polygons you can make, but while many students found close to that number, “finding them all” actually isn’t the point of this exploration. (Perhaps you’ll want to try it out at home with your child – see if you can find all 14, and then, see if you can find a way to convince someone that you’ve found all the possible ways!)

The actual point of this work was to get the children to begin noticing the attributes (characteristics) of different polygons, as well as to talk about congruence and what it means for two shapes to be congruent. Ms Marcy and I got the students thinking about that today as we circulated and conferred. Children noticed that “number of sides” was an attribute of their polygons, along with the number of angles, or vertices (the points where two sides meet). Some talked about the parallel sides that some of their polygons displayed. Some noticed right angles. Eric noted that one of his quadrilaterals had two sides that were the same length, along with one long side and one shorter side.

Tomorrow, to deepen this thinking, the children will be taking the polygons they’ve made and deciding how they want to sort them into groups, based on their attributes. This is an example of how our approach to Math allows for multiple entry-points. Partnerships might choose to group based on the number of sides (and that’s fine), but others may group based on parallel sides, or length of sides, or the size of the angles. Each partnership will work with this assignment in a way that makes sense to them. At the end, however, as we share our work with our classmates, the children will be exposed to other ways that these polygons could be grouped, based on different attributes.

And this gets to one of the “big ideas” of geometry in third grade: that certain shapes can be classified in more than one way, depending on which attributes you focus on. A square is a square, but it’s also a rectangle, a rhombus, a parallelogram, and a quadrilateral – and a polygon, too, of course!

Below are some photos of 301 from this morning. (My apologies for not having photos of 302 today; I didn’t have my phone with me.)