I recently got an email from someone who saw some of my many posts on geometry (you can see all my posts about geometry by clicking here). I realized I never shared them formally and everything is a bit scattered. So I’m going to try to include a few resources here. But the real joy is in all the blogposts, honestly.
I taught Advanced Geometry at my school for two years (2014-2016), and I wrote the curriculum with a good friend and dear colleague. We both hadn’t taught geometry before and decided we’d do a super deep dive and come up with a sequencing that made sense to us, and that prioritized conjecturing and noticing. In fact, we were so excited by this process that we shared our thinking both about how we built up the curriculum but also how we collaborated at a conference. Below are our slides, but you can also click here and go to the slideshow and read some of our presenter notes for each slide for more detail.
We were super intentional about everything. We carefully thought through how we wanted to motivate everything, and we didn’t want to give anything away throughout the course. In other words, we wanted kids to do all the heavy lifting and to be the mathematicians that we knew they could be.
Below is a word document with all our skills/topics (you can download the .docx file here: All Topic Lists Combined). The order might seem a little strange (we end, for example, the year with triangle congruence), but it worked for us! Everything was done on purpose (in this case, congruence is just a special case of similarity… so that came beforehand, along with trig which is all about exploiting similarity!). We eschewed two-column proofs for different forms (paragraph proofs, flowchart proofs, and anything else that showed logical reasoning).
Oh wait! For some reason our work on Area and Volume didn’t have a topic list. And I just looked and my core packet for Area and Volume derivations (where kids just figure things out on their own) has handdrawn images in it, but I didn’t scan a PDF of those. Well, at some point in the future if I remember, I’ll try to write a post to share that. (We did it after kids learned trigonometry, so they had a lot of flexibility. For example, I think kids came up with like 6 different methods to find the area of a trapezoid when they were asked to create a formula and justify it!)
I hope this is helpful for anyone trying to think through geometry. As I said before, the best thing might be to just read the blogposts, but this is a bit of an overview.
What the distinction between advanced and regular geometry?
Great Q. I think there might be a difference in course content (advanced might cover more but I don’t totally remember… this was a few years ago and I don’t have a great memory). But in advanced, we had a lot more depth/abstractness and the pace was significantly quicker (less review, and I think less scaffolding).
Thanks that leads me to a followup: how did students pick which version they took?
Hihi- at my school (an independent school) many students were in our middle school. So their 8th grade teachers made the determination. Students joining the high school from a different middle school took a placement exam. Over the years, the exam changed (from one we had for ages, to one we created ourselves which incorporated problem solving, to one that is electronic whose name I forgot but seems to give us reliable results). Students don’t really have a “choice.”
I’ve been stealing content, ideas, and inspiration from your blog for years. I am now curious about what you assign for homework – especially after the “counterattack” lesson driving home that they need to use precise language in their definitions, and that developing this precision in language is hard. I’m about to start the Similarity and Congruence portion of our integrated course and I like to start by showing them how much precision matters with shapes. I also try to drive home the point that the figures we look at will not always be drawn to scale – to have a healthy skepticism about what they think might be true just by looking at the picture.
In any case, I’m wondering about follow up tasks – homework, so to speak. Some stuff you include mentions Home Enjoyment problems clearly referencing a text book, but this also doesn’t seem your style, considering how much content you generate yourself. I’m thinking you might have other material now posted.
Are you comfortable making more of your handouts available in a single repository, including following assignments if you have any? I’ll share what I have taken from you, what I’ve stolen from other teachers, and what I have made myself as a gesture of fair trade :)
That’s from a collection of materials I use for the Similarity and Congruence Unit from our third integrated course (uses the McGraw Hill text, Core Plus). It doesn’t have the blog posts to go with each one that might explain a little more what I did with those. It’s from two Fall semesters ago – some of it I’m still more or less happy with, other stuff I’ll definitely change or jettison. unfortunately, I’m not great about keeping reflective notes, so I’m not sure which is which until I try using it again :)
Anyway, I’m especially curious about follow tasks to be done at home. I find so often that work out of the textbooks don’t match well enough the more innovative lesson materials you use (and I steal).
Northampton High School
I’m so glad you find what I’ve posted useful. I generally write a post when something strikes me or inspires me and I want to share it with others. The textbook we used (I only taught this twice) is by Jurgenson. Unfortunately, I am not organized enough to have the nightly work ready to hand over. What I usually did for nightly work is assign a little bit out of the packets and then based on what I’d see, I create a few additional questions on problem areas and ask them to work them. For more routine practice, I would definitely use Jurgenson. But that also means that I don’t have a list of things for nightly work. Sorry I can’t be of more help!