Area of Quadrilaterals

Last year I wanted students to discover the area formulas of quadrilaterals by breaking them down into rectangles and triangles. Except, I didn't explicitly tell them that. Instead I assigned groups different quadrilaterals, told them to find the area of a few specific examples and then come up with a formula. It didn't go so well, although a couple groups did get where I'd hoped with little to no support. The rest of them balked at my vague instructions. I constantly struggle between providing so much support that no one has to think, and so little support that everyone gets so frustrated they can't think. Ashli posted a great quote about that recently: "The clearer you are about what you want, the more likely you are to get it, but the less likely it is to mean anything" -Dylan Wiliam

This year I took an online course in Geometry, Measurement and Technology where we had to write a lesson that used technology. I chose this topic for my lesson, but I struggled to make the tech useful and to decide how much support to give. I made my own applet on GeoGebra since I couldn't find one I liked (a learning experience on its own). I'm actually rather pleased with how the applet works and think that it has added value over paper since students can see so many examples and I can give them a much more subtle nudge to be sure they see the patterns. [overall instructions] [applet instructions] Now that the constraints of the online course are over I definitely plan to re-work the handouts I give to students so that they go in order (it was surprisingly difficult to manage two handouts that jumped back and forth plus a laptop). I will also restructure it so that students experiment in class and write a lab report for homework.

Side note: I'm aiming for one lab report per quarter, full write up, following the science department's format. I like doing them, but only enough to be willing to grade them four times a year. First quarter was parallel lines and a transversal via GeoGebra, second quarter was congruent triangle rules via NCTM, third quarter will be area formulas (this year it counted as a lab, no report, in my mind) and fourth quarter is still up for grabs. Maybe something trig?

The students who carefully read the instructions and completed each step were quite successful in working independently. This was an activity where I refused to answer most questions, instead directing them back to the typed instructions, their chart or the computer for further exploration. The tricky part about this activity is that most students have seen some of these area formulas before so they know what they're "supposed to get." It was a great experience for the students who chose a trapezoid and managed to start with rectangles/triangles, factor/simplify and end up with the familiar trapezoid formula. For those who didn't reach that point it seemed more contrived than our usual discoveries since they are used to discovering ideas they'd never seen before, as opposed to proving something they knew but didn't understand.