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!
I thought yesterday was a bit boring. Today was fun.
We started by practicing graphing and writing equations for parallel and perpendicular lines. Regular practice stuff. Nothing amazing. A student who missed class yesterday (which is a pretty big deal) was working with a volunteer tutor that just happened to be in the math wing that day so it was a good time for class practice while he could catch up.
We then reviewed the parallel lines and angle sum unit with a Place Your Bets game. I had a 10-question PowerPoint (download below) just with questions and answer choices. I was used to playing this game with a sheet where they would put their work and wager with numbers. I’ll put that below to download as well but it’s for sure not as fun as the way that Sarah Hagan does Place Your Bets. I of course forgot to take pictures but it looked similar to the ones Sarah has. Except I realized this morning that the room I am using for summer school is completely bare so I do not have chips or unit cubes or anything small and plentiful. So I improvised and used ripped up colored paper. That was a mistake but also smart…I first had the kids just rip the papers up into small pieces and didn’t specify how many they needed. I probably should have set a limit because the kids went kind of bonkers with this…I also remember seeing that Sarah set a limit for how much could be bet each round, and thought 25 was a good amount. That was a lot. I ended up getting different colors of paper and making green (what we started with) equal to 1, pink was 5, red was 10, and purple was 25. It was super fun but took also a lot longer than I expected. I actually only got through 6 questions in 45 minutes but then wanted to have the kids do some practice in their notes before our test. I know we didn’t get through a lot of review but the kids had great ideas and I learned something new about this game. Even though it was long, kids were all saying they wished they could do more, so I’m going to try to incorporate it without so much scrambling later.
We then had our second test. I gave back their quiz, which once again had no points marked. I think that since I gave them back when they were still doing group work, it brought out a little more discussion on their mistakes. I forgot to do the thing where they grade themselves like I said I would before, but I liked how they just were talking about how they did and maybe stopping that would have been bad.
I then went into our next unit and introduced congruent figures. I started them with this Illustrative Mathematics task that I found from Kate Nowak. We were able to have an awesome discussion about what it must mean for figures to be congruent, especially with Set C that has to be “flipped”. At first all groups were just eyeballing. I did a quick Plickers assessment for each set to see if the class thought that the shapes were congruent. All sets except A had a disagreement within the class. I said that we have to agree before we move on. The kids went back to discussing/arguing about the shapes in front of them, but then a student told me that it was hard for him to tell if some angles were really the same just from the looks. I asked him if there was anything that would help him make it easier to tell. He said a protractor, another student said she wanted scissors to see if they fit on top of each other. It’s funny how these ideas catch on like wildfire. Eventually all students had a tool – protractor, ruler, or scissors. Talk about Using Appropriate Tools Strategically (CCSS MP5)!!! We then did Plickers again and only had a disagreement on the flipping of C. So then I told them the definition of congruent figures and we had another discussion…at the end of the day everyone was agreeing on all sets! What a great way to end the day!
Nous sommes d’accord! Nous sommes d’accord! 🙂