Working with triangles

For the past two classes, the focus has been on working with triangles. Students are starting to improve on names and definitions but still have a long way to go. Although there were only two students who could name vertical angles before, after working through problems in which vertical angles are used, more students can identify the angles.

I have noticed a tendency for students to work through identifying congruent parts and then not to take a step back and look at what they had shown to be congruent parts. As a result, they finish finding congruent pieces and then just start guessing which congruence theorem applies. I keep telling students to take a step back and look at what they have now identified as congruent. This helps a little, but I am not confident in the transference. Unless students can do this on their own, they will be lost.

The problems the class has been working on cover a wide variety of topics in order to get them prepared for our upcoming test. I have been trying to push them to be able to write proofs on their own without any extra help. There seems to be slight progress on this front. Their issues are tied to what I just previously discussed; they get lost in the details and never take a step back to look at the whole picture.

Perhaps it will help if they are stopped periodically in their work and asked what they have demonstrated so far and what they still need to demonstrate? I need to check research to see if there is anything that will help on this front.

We are going to finish up working through these problems and then we'll take the test. Since the test doesn't cover mid-segments and related topics, I am skipping the topic in order to catch up with the rest of the geometry team.  I was planning on using the fire hydrant and warehouse placement investigations as outlined in the NCTM teacher's blog. It's unfortunate I don't have the time right now to fit these in; I think they would be productive investigations.

Up next, quadrilaterals and coordinate geometry proofs. I'm starting to look around at what's available from an inquiry-based approach. I sure hope there are some good pieces I can use.