This is what I wrote last year about today's lesson:
Well, Lesson 8-6 of the U of Chicago text is on areas of trapezoids. Once again, this is pretty straightforward, but here are some of the key issues:
-- The text derives the trapezoid area by dividing it into triangles. The text refers to dividing a polygon into triangles as triangulating the polygon.
-- The text uses inclusive definitions, so a parallelogram is a trapezoid. If you're wondering why there's a section for areas of trapezoids but not of parallelograms, this is why. Recall that the most useful fact about a trapezoid that isn't isosceles is its area formula.
Actually, here's another issue about inclusive definitions. Sometimes, it appears that students more easily recognize that squares and rhombuses are both kites (as I mentioned in yesterday's lesson) than that parallelograms are trapezoids. A student I once had saw a picture of a baseball diamond on my 14-1 worksheet and kept referring to it as "kite" and "rhombus." This isn't the first time that I've heard a student call a rhombus a "kite," despite the students using texts with exclusive definitions.