## Sunday, February 5, 2012

Here is a Virtual Filing Cabinet for resources concerning Quadrilaterals.. This is part of an ongoing experiment in how to better share online teaching resources. If you like this post, then make your own post for a particular topic.

[Last Updated: 2/5/2012]

The Hard Parts

A lot of the traditional proofs of the properties of quadrilaterals depend very heavily on congruent triangles. One of the real challenges in teaching this topic is to change your students' perspectives. When they see a rhombus they should see four congruent triangles; when they see a parallelogram they should see two pairs of congruent triangles; when they see a kite they should see two pairs of congruent triangles arranged differently.

There are lots of challenges for novices that go along with this change in perspective. Students need to see triangles in quadrilaterals, even if the diagonals are absent. Students need to see parallel lines with a transversal even when the sides of the quadrilateral are not extended.

Another major theme of this unit is the hierarchy of shapes. A square is a rectangle, but it's also a rhombus. They are all parallelograms, though, and so what's true of parallelograms is true of them as well. This, plus a whole slew of new vocabulary.

For vocabulary, I like the approach of the Discovering Geometry series. Show kids a bunch of examples of things that are "trapezoids", show them a bunch of things that aren't, and then challenge them to formulate a definition that works. This is a pretty common approach, from what I can tell. Here's a post from misscalcul8 on her version of it.

Once you have the vocab down, you might want to make it more concrete and emphasize the relationships between these shapes. I've posted about an activity that I like where students create "family trees" for quadrilaterals.

One of the big challenges of this unit is (to my mind) getting students to see quadrilaterals as composed of triangles, as this generates all of the non-obvious properties of the quadrilaterals. I like this activity, which uses a series of tangram challenges of increasing difficult. It literally forces students to compose various quadrilaterals out of smaller shapes, including triangles. This can also serve as a concrete model that can be returned to over the course of the unit.

I'm still looking for resources for the actual nitty gritty of this unit which is the properties of the various quadrilaterals. I'll post resources as I find them, and please let me know if you have resources to add to this page.

#### 1 comment:

1. Most of the time student these two points one is that "a square is a rectangle, but it's also a rhombus. They are all parallelograms, though, and so what's true of parallelograms is true of them as well" and another is that "students need to see parallel lines with a transversal even when the sides of the quadrilateral are not extended".
Is the square root of 2 a Rational Number