Tuesday, March 3, 2015

The Common Core standards have brought us many changes to our Geometry curriculum, including less of an emphasis on special quadrilaterals and their properties.  We used to spend an entire chapter talking about parallelograms, rectangles, rhombuses, kites, and trapezoids.  Some of the newer curriculums such as Engage NY give this topic a couple of lessons worth of attention, with the focus being on proving properties of parallelograms.  The Common Core Standard here is G-CO-11, which states:

Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

With the emphasis being on proving the properties/theorems, I am rethinking the way that I approach this material.  Below is an Edpuzzle video that students can watch before we begin talking about parallelograms.

My hope here is to get students to review vocabulary related to quadrilaterals such as sides, angles, and diagonals, and to make some observations about what is happening with the parallelogram in the video as it is being transformed.

The video above gives concrete measures for both angles and segment lengths, so to transition to abstract thinking I've made a few more videos for students to take a look at.  Below is a Google Form that students can go through to both watch introductory videos and to answer some questions before we launch into a class conversation.  There are additional videos on pages 2-3 of this form, and I will post the videos below so that you don't have to input answers into the form in order to proceed to the next page. If you want to fill out the form just for fun go right ahead, as this is a copy of my original form.

Video 2:

After this video the Google Form asks students to identify the pair of congruent angles that justifies why the marked pair of sides are parallel.

Video 3:

This video asks students to recall what a diagonal is, and also asks students to make an observation about congruences formed by intersecting diagonals.

These videos may need a bit more context, but basically I am hoping to show students how to see that all parallelograms are formed by rotating a triangle 180 degrees about the midpoint of one of its sides.  From here, corresponding parts are congruent, and we begin to see why many of the parallelogram properties are true.  Between the Edpuzzle video and the google form, I am asking students to make some of the observations about congruent parts of parallelograms that we will later prove.  I'll note that this is still in draft form and my first attempt at flipping, so any feedback is welcomed.