As I am organizing for next year, I am going to post some of the resources that I created for the year. The first one that I am sharing is my videos and notes for constructions. I find that my students had a difficult time getting started with any constructions. I attribute the difficulty with a couple of things:
1. The compasses that they were using were the standard cheapy compasses that come too many to a pack. The compasses broke quickly or could not maintain form. The next compasses that I used were the flat ones and I really did not like the muscle motion and the notched numbers. I settled later in the year on Circle Perfect Compasses.
2. I typically teach using inquiry methods. I have yet to determine a way to teach students how to use a compass using inquiry. While I can teach using traditional methods, I feel like I did something wrong to the students after doing them.
My videos were created on Robocompass using their pseudo language to make constructions. They have created quite a nifty tool for making constructions. I used the tool and did a screen recording with Quicktime. I took all of the videos and looped them in a Keynote file. I find that the videos were effective in teaching the students the basics, but they did not remember if they did not keep doing it throughout the year.
The notes were created in Notability and saved as a pdf file. I have created two versions of the notes. One is without the construction completed and the other is with the construction.
Notes with Constructions
Notes without Constructions
If you have the time, let me know how you would use these resources to teach the topic. I would love to hear it.
As I enter the world of Common Core for Geometry according to the MDC framework, finding supporting lesson materials has been a challenge. This is in particular because the curriculum uses transformations as an anchor for many topics. I have been fortunate to be part of a2i where I have gained a lot of knowledge and curriculum materials. The unit sample lesson sequences have been a particular help. That leaves the day to day lessons. Recently, Lisa Bejarano shared her unit plans and lesson sources for the year so far with a neat unit outline as well. I decided to try Lisa’s lesson sources out for the Similarity unit. Here is what I found for my self so far.
Photography Faux Pas and the Statue of Liberty lessons had great engagement and discussions around both of the lessons. I then looked forward and realized that the EngageNY and Khan Academy would both not be an easy fit for my students or technology in the classroom. I started down a new fork in the road and had a couple of great lessons on dilations. The first lesson was David Wee’s Everyone Dilates a Triangle. At this point, my students had a rough understanding of dilations and I wanted to sharpen their skills and had arguably one of my best lessons of the year:
Create a Dilation Poster
I assigned each group to make a poster based on their knowledge of dilations and a series of videos. I created 4 videos that I embedded to loop in an Keynote presentation. Each video had a few questions designed to deepen understanding of a part of dilation understanding. At the end of the videos, each group put together a poster collating all of their ideas on one dilation poster. While this was a great lesson, I spent 3 days on it and could have organized it better. Regardless of the organization, I will definitely stick with the idea for summarizing concepts. Students were really engaged and had great conversations.
I have completed the dilation portion of the unit and realized that the Statue of Liberty lesson would fit better as a bridge between dilations and similarity proofs.
This has been my best unit of the year so far and far better than last year. The resources from Lisa are amazing and a2i as well. I am lucky to have access to both.
So I have been debating whether or not to return to the blogging world. Last year, I found building a 180 blog the first time that I did Geometry to be draining for a number of reasons. The daily slog of a teacher is tough enough without recording it. And… when you are recording with your own critical eye, it becomes numbing after a while. I found that while I was recording a bunch of things, not much of it was ready for prime time nor up to my standards. I read all of these blogs of amazing things happening in classrooms across the country and realize that it requires an amazing amount of effort and time. I am all for the effort, but my time is parsed between family and work. I am trying my hardest to keep that balance on the right side of the scale. I do not know where the journey is going to take me this year, but I have made a couple of decisions.
1. I want to get back to blogging, but not at a daily pace.
2. I will keep a diary to record my successes and failures, but want to start by sharing things that work or ideas that seem cool to me that I want to try.
3. I want to be a more active member in the community of MBToS for the sharing, knowledge and to give back where I can.
4. I want to be a better teacher. If any of the first three prevent that from happening, I will cut back on them. However, I believe that they are necessary for it to happen.
I also want to spend more time editing blogs before sending them out. Most of my posts from last year were undercooked and needed more time in the oven.
I am excited to be back and will be sharing some of my ideas on how I am going to start my year shortly.
Protractors are no fun for the students. The lesson SAS – Drawing triangles was great for the students to discover and learn the material. I do believe that learning protractors will pay dividends in the long run. Important to note that students take a long time measuring and labeling triangles. It is a complete investment in time.
So we finished the proof today and I learned that my mechanics in doing proofs from 1985 was a bit rusty and I have to rebuild them up again. I expect my skills to be able to find the solution for each and every math problem on the fly. This is not the case; and today proved it. I did quickly transition to another activity “Angles, Angles, Angles” from the upcoming edition of Meaningful Math – Geometry. This was a great transition from the proof to other applications of angles. Students did struggle at first, but then were successful in doing the activity. The only challenge was creating an entry point for students who were not building the bridge between Algebra and Geometry. As I plan going forward, I look forward to mixing proofs, Algebra applications and hands on discovery to give the variety that students need to be successful.
Today, I spent time allowing all of the students use the protractor and try to discover the parallel proof for the angle sum property. None of the students arrived at the proof, and all of them tried. I am not sure if I took the best approach on this. I believe there is some scaffolding to get the students to arrive at line of logic for a proof. I will be continuing the proof on Tuesday with a scaffold of all students trying to find the congruent angles and review the definitions to get to a place where they can possibly see a path to a solution. I am reluctant to hand the proof to them, but will probably scaffold to the position. I do like the productive struggle.
Going into Geometry, I knew there were a bunch of manipulatives necessary, but did not realize the extent. Since I feel like I have to supply most of them, this has been a challenge. I do remember the challenges of using a protractor during the old Math A days. However, students did not have to be proficient in using it. Now, they need to know it to get through all of the different types of proofs and postulates of triangles. I think they will realize it is a necessity to gain the skill to prevent being annoyed with themselves. At least, I hope that is the case. If I remember, I will comment on this later.
Once the students tooled around bit with the protractor measuring angles of a triangle, we set out to prove the angle sum property. This is the first proof that we are doing as a class and all of them are struggling. I had all of them be quiet for 10 minutes studying the materials and then had a bunch of discussions at the table and as a class to get them further. Tomorrow will be a continuation of the journey into the proof.
So I had the chance to roll out the different versions of the proof in the honors class. It went seamlessly. Students finished the class trying to construct their own proof with moderate success. In my other class, they were trying to relearn how to use a protractor. One period was not enough, I will continue with the lesson and finish in the next day with a proof about the interior angles of a triangle. I have to remember to build in time for a pair share in some of the discussions. Many of the protocols are falling apart because I am not reinforcing them. It is time to get back to basics.
So I decided to talk with the students about proof. Students are definitely challenged by the concept and this is going to be a long road. To ease the road, I decided to introduce the two column version and flowchart version of the vertical angles proof. I think that this is the beginning of paving of a long road. The lesson ran a bit long and I decided to spend time on making sure the explanation was sound and did not spend time on a solid formative assessment. I look forward to building on the concept.
I walked into school and learned that I will have to leave early and my last period class was cancelled. In my regular geometry class, I spent the better part of the period trying to teach the nuances of proof. It is now abundantly clear to me that this topic will take a lot of time to learn. I also think my model of the vertical angles theorem will have to be revisited. (I do not think that supplementary angles can be stated as a given. This causes some confusion in the class.)