It has been busy-ville in gealgerobophysicsulus-town, so I have barely had time to catch my breath over the last few days of music performances, school events, and preparations for the end of the semester.
My efforts over the past couple days in Geometry have focused on getting in a bit of understanding of congruent triangles. We have used some Geogebra sketches I designed to have them build a triangle with specific requirements. With some feedback from some Twitter folks (thanks a_mcsquared!) and students after doing the activities, I’ve got these the way I want them.
Constructing a 7-8-9 triangle: Download here. (For discovering SSS)
Constructing a 3-4-45 degree triangle: Download here. (For discovering SAS)
Looking for an ASA postulate. Download here. (Clearly for ASA explorations.) – This one I made a quick change before class to making it so that the initial coordinates of the base of the triangle are randomized when loading the sketch. This almost guarantees that every student will have a differently oriented triangle. This makes for GREAT conversations in class. Here are three of the ones students created this afternoon:
I’m doing a lot of thinking about making these sorts of activities clearly driven by simple, short instructions. This is particularly in light of a few of the students in my class with limited English proficiency. Creating these simple activities is also a lot more fun than just asking students to draw them by hand, guess, or just listen to me tell them the postulates and theorems. Having a room full of different examples of clearly congruent triangles calls upon the social aspect of the classroom. Today they completed the activity and showed each other their triangles and had good interactions about why they knew they had to be congruent.
Last year I had them construct the triangles themselves, but the power of the end message was weakened by the written steps I included in the activity. Giving them clear instructions made the final product, a slew of congruent (or at least approximately in the case of 7-8-9) triangles a nice “coincidence” to lead to generalizing the idea.