Today was a continuation on proving triangles congruent and parts of triangles congruent. We did a ton of just practicing proofs. One way we reviewed for our test was to have pairs at the board. I forgot who I saw this idea from so I’m sorry I can’t give credit, but I definitely didn’t think of it myself. I wish I would have known about this strategy last year. Anyway, I gave each pair two out of 4 possible proofs and made it so that the group at the board next to them wasn’t doing the same two. The partners had to be using a different colored marker. Then they just had to redraw the figure and givens and then do their best to complete the proof. It was great group work and I loved that the students were happy with their successes. Groups kept erasing their work but I did get a picture of one group. While most groups switched off on who was writing on the board, this group chose to have one person always write out the statements and reasons and the other person mark everything in the figure. I liked how they talked about the different parts of their proof, especially when one started writing ASA and the other one showed why it was really AAS. Great discussions, happy students, happy teacher.
Our main activity today consisted of discovering the triangle congruence theorems and postulates. I used an activity (download below) where students had to construct 6 different triangles. Four of them can only form one triangle, two of them (AAA and SSA) don’t. I have students construct these in groups and then at the end I let them tape up their triangles on the board with all Triangle A’s together, Triangle B’s together, and so on. Students then do a gallery walk where they are asked to give what they notice about certain triangles. In the end, they see that SSS, SAS, ASA, and AAS gives us congruent triangles. One thing to note is that this take a long time. Even with groups of three and only six triangles, it took my class an hour to get them all done. Groups that finished early were asked to try to make different triangles with the same given information. But I think the time pays off in the end because the students can really see that AAA and SSA really don’t work and are pretty surprised that the others do.
We then practiced a lot of proofs and got into CPCTC before they took a quiz on it. The quizzes were ok…not great…but this quiz usually is. I leave a lot of feedback on what could help them in their proofs and usually this helps them a lot. Hopefully they actually look at my feedback. I usually get some comment like, “Well I knew we had to use CPCTC in the proof during class because we just talked about CPCTC but then in the quiz all I could think of was No Choice Theorem.” No Choice Theorem?! You mean the thing we literally did one example with and then never touched on again? Ok…I’m still searching for the best way to help students with proofs in such a small time frame. I feel like during the regular year when this unit spans weeks, it would be easier for students to build up to their reasonings.
Les étudiants pensent que les preuves sont trop difficiles, mais il n’est que le début!
Today started by continuing to look at basic composite area/perimeter problems. All that was used was circles, rectangles, and triangles. I gave students one of those Geo Joke worksheets with the corny jokes. The students loved it! I remember loving them too, even though the jokes are so bad. I feel like it has something to do with the answers being there so they can immediately check if their answer was correct or not.
We then started looking at special angle pairs – vertical, supplementary, complementary. We did our first proof to prove that angles supp to the same angles are congruent and I didn’t force a 2-column proof on them. I actually like the 2-column proof because it is very clear that every statement needs a reason, but I also went through four years of being a math major and if you did a two-column proof in a 400-level math class you would just get laughed at. So I accept paragraphs or bullets as long as each statement has a clear reason.
I also handed back their first quiz and didn’t have a score or any points on it a la Ashli Black. I saw this video last summer and was absolutely amazed at this concept of not putting down a grade for the student, but was way too scared to try it in my school. In summer school I have a little less stress from administration and parents. In this district they want it to be clear to students how many points each question is worth, so the students could figure out probably what their grade approximately was, but I just wrote a lot of feedback. Even with the quiz only being 2 pages, 6 questions and me only having 17 quizzes to grade, it still took me a solid hour to finish them all. I wish I had a stamp for the commonly used feedback items. I will admit, I was a little bummed by the lack of shock and response from my students. I know it’s summer school but they were still just silent getting them back. A kid asked if their grade was in the gradebook and I had to say that it would be. Maybe it won’t make such a positive shift away from grades. Maybe it was just because it was the first assessment. Maybe it was because it was 9am on a summer day. We will see how they react when they get their test back tomorrow with no grade. This time, I will not go over the answers to the test – that also could have been why there was little reaction.
We did our first review game – Math Bingo. I would share but it was pretty bad. I mean the kids were all over it – once again, it’s like an answer bank given to them. But I totally messed up their answer bank. I had made copies of an old bingo sheet I had from last year without remembering that I had changed it so only about half the answers were the same. I still had a few bingos but it stressed kids out that their answers weren’t showing up and ultimately might have hurt more than helped some of them. Oh well…I can’t beat myself up over it.
Quelquefois, ca ne va pas comme tu t’attends, mais tu apprends de ces moments.