The following is the narrative, in draft form, of an entire lesson given to my Period 1 Math 9 class last week. The notes were taken by my admin supervisor as part of my observation process as a new teacher. The class is (supposed to be) on CPCTC: that Congruent Parts of Congruent Triangles are Congruent. Much of the lesson, however, serves to reinforce the procedure of triangle proofs through examining the previous lesson’s homework. I offer the draft script unfiltered: me in my classroom with no comment. I am T (teacher), students are S.
T at door greeting S as they arrive. S arrive, sit, and talk. PTT showing on screen. T encourages early S to get started on PTT. T You have about 1 minute to the bell so pull your books out and get started on the PTT. Page 119.
10:35 Bell. T All right. S at door asking for S to see Ms. Manzur. T Are you trying to avoid Ms. Manzur to S summoned by her. T Ok, guys being on time is appreciated. S reenters and calls out to T I am not in trouble Mr. S in back talking to another. T S, you see everyone around you working on the PTT, you should be too. S calls out question about what to copy for PTT. (10:37 S walks in late) S calls out to have T to ask for help on PTT. Same S (girl) in back still talking to others around her. T Ok guys, I see some work, good. But I don’t see you copying anything down to one S. S calls out something to T.
10:38 T Ok, you know what I am going to add another minute here. Even if you don’t know how or understand you should at least copy down the blanks so you can fill them in. T walks around to check on S progress.
10:40 T So, I see most of you now have most of the proof filled out. You should keep filling it out as we discuss it. You have seen enough so you can get the structure of the proof there. You know what I did wrong is we should be numbering these. I chose to label these angles 1 and 2, why? I am looking for hands here. T calls on S and S replies. S calls out question. T answers. T continues explaining PTT. T Remember when I put my hand up I am looking for your hands, not a shout out. Next up. C is the midpoint. Now I have left both blanks. T Hands, who has an answer? T calls on S and S replies. S asks question about why T wrote something. T explains for class. S (girl) at back of room still talking with girl next to her. S suggests the final statement is the same as what is given. T clarifies why it is not, but rather is the concluding statement. T All right, any more questions on this. No questions from S.
10:46 T Let me remind you of some things in the unit. Today is something cryptically called CPCTC. Remember that I can help you in a review session during lunch or after school on Thursday. S question about when and how to use the ASA, SAS, etc. So here is the HWL on page 120 and while you do that I will walk around and check your HWK. T walks around with binder marking S who have completed and not completed HWK. Some S talking and some looking at the board comparing their answers to what is on screen.
10:48 T Ok, I am noticing a trend here. You guys know if you have problems you can come in at lunch or before and after school. Saying I don’t understand is not an excuse for not doing your HWK. T scrolls screen to see remaining HWK.
10:49 T So there’s a question I would like to highlight. Can I have you attention please? Remember, you guys are supposed to be checking your own HWK. I want to point out a few things. I have invented some numbers for these angles. You can do the sane. S Why in the second one is it SSS instead of SAS? T checks and says yes you can do that too. T So what S is suggesting is this and T shows work for S solution. This is going to go up online and you can check it, but I want to do #4 right now. S calls out a question. T I am going to do it right now.
10:53 T Explains problem #4 of HWK on page 121. So, I want the middle table here. What am I going to put here for parallel lines. Several S call out. T reminds others that middle table was answering. (10:54 S returns from bathroom) T Its clear I have to explain a little more. Once I knew these two lines were parallel given. I think we have AAS. S calls out I have a question. T explains answer. S calls out question. T explains. S How do you know where to start? T explains its not about where you start, it’s what is given. Is the side in-between those two angles? T I have some questions from the girls back here. T S, Yes. S asks question. T explains. I am going to keep going on to the next one. S interrupts, no. T Wait, I may answer your question with what I am going to show you next. S interrupts no. S (girl) with question gets up to ask S in front of her the question while T moves on with rest of class. T continues explain #4 while S copy down answers. S raises hand for question and T calls on S who explains another way to look at current step. T Finally, we know our side here, an angle, and an angle. Now we can say therefore triangle WHY is congruent to triangle FLY.
11:02 T Ok, so here is question 4 from the HWK to introduce the lesson. I want to introduce CPCTC- corresponding parts of congruent triangle are congruent. So, what this means is when you know the two triangles are congruent, then you know all this stuff is congruent. So, imagine you are given this instead: Prove HW is congruent with LF. How would you do that? T calls on S and replies with answer of using CPCTC. T Correct. It’s like your shortcut for parts. Once the triangles are congruent then you know the parts are congruent. S question. T answers. Several S talking. T brings S back. (11:07 S asks for permission to leave class).
11:08 T So, we are going through these examples and most are proofs that you are going to add one line to at the end. T shows example from 10-5 on page 122 and instructs S to try it. T Gives reminder that this sign means perpendicular and draws on board. T So, put the information you know on the diagram and do the draft.
11:10 Another S asks to go to the bathroom, T says no. Previous S returns from bathroom. S who asked to go to the bathroom calls out Mr. I don’t understand any of this. T Can I have your attention. Not as many of you are understanding this as I had hoped. T starts to explain the problem. S calls out a question. T Is that given, no. S asks question about labeling angles 1 and 2. T explains. T continues explaining the problem. T First of all, I think there is too much chatter. T What I am asking is I just put in these two right angles, what does it tell me about those angles? T calls on S and S replies. T Angle M and R are congruent. So now I have two pieces of information. S calls out something else. T I don’t think it gives us that information and looks at book. Which is not in-between the two angles? This one is going to be AAS. T Guys, I feel like I need to figure out a way to explain this. The list of possible choices (SSS, SAS, ASA, and AAS).
11:17 Another S asks to go to the bathroom. T Yes. S leaves to go to bathroom. T continues explaining problem 4 by putting intro statement and reason. S calls out question, T answers. T So, this is now the proof table. Next statement. Now I have to use the information that I am given. Why is NM congruent to PR? Back table with the girls. No S from back table answers. T clarifies and S answers. T writes in statements/reasons for 2-3. S calls out Mr. but in the test you are going to give us all that information, right. T replies.
11:21 S who went to bathroom returns. S question about the order of the statements/reasons. T explains the order. Same S previously denied bathroom asks to go again. T denies again. T continues explaining problem to class. T shows statements/reasons 4-7. T Ok, this is a triangle proof as we did yesterday. S calls out You didn’t put that thing (therefore symbol). T Yes, that is because we need a step 8, therefore. T explains how to make last statement/reason of proof.
11:24 T So what I would like you guys to try right now is example 2. Now, it doesn’t look like we have two triangles here, but we can draw this line here. S calls out question about total number of steps. T explains you can have as many as you need. T walks around to check S progress on example 2. S calls out question and T goes to help S.
11:26 T Ok, so let’s talk before we leave. Let’s at least figure out the top part. What’s it give us for information. S calls out one piece of given information. T what else? Another S calls out another piece of given information. T does it really tell us that? No, we can’t invent things. Another S calls out the next piece. Another S offers answer. T confirms those that apply and denies those that are not explicitly stated. T You are problem solving here. I can’t give you a recipe. T At this point, raise your hand if we know what the short cut is going to be. Several S raise their hand. T calls on S and S answers correctly.
11:30 T Your HWK for tonight is #1-3 on page 123. Before you leave I would like you to do the Socrative exit survey. T shows link and question #4 on screen. S begin talking with some doing Socrative exit survey using computers or phones. Several S start walking around looking for a device to complete the exit survey
11:33 Bell. S pack and leave.