August 1, 2012

ReThinking Geometry

The Common Core Standards came out, and they said "teach everything in Geometry by transformations" which just about no book does...  I finished my second year of teaching 4 sections of geometry, 2 levels each year which used different books...  Matt posted that he was tired of starting with undefined terms, he wants to jump straight into triangles...  PCMI had a big focus on questioning this year...  My department head starts geometry with patterns and conjectures...

This morning I took all of those ideas that have been rattling around my head, and I made a curriculum map.  This is the first time that I've ever planned out an entire course.  In the past I've just followed the textbook, maybe switching around a couple chapters when someone suggested it.  Last year I invented the curriculum for a course, but I made it up as I went along because it was for severe special ed and I went into each topic having no idea what their prior knowledge would be.  Having taught Geometry for 2 years, and to over 200 students, I finally have the knowledge to decide how I want this course to work.  Obviously I don't expect this to go perfectly; I would love advice on the orders you've tried and had successes or challenges with.  But it was great to be able to sit down and really have a sense of how everything connects, where students thrive and what activities work well.  That will most definitely not be the case as I start teaching PreCalculus this year!

I will share the map below, but be warned that it's very much meant for me, so there are lots of obscure references.  Quite a few of the activities are ones that I've blogged about, so if you're interested in learning more about something try the search bar or just leave a comment and I'll add in the details.

Rethink Geo

I'm also starting Standards Based Grading this year.  The standards list is probably more accessible to the general public.  I don't plan to give this to students since there is no way to write a standards list for Geometry that doesn't give away the surprises I want them to discover.  I may even let them decide on some of the wording.  I'm really happy that I ended up with 25 standards since it's such an awesome number.  That said I may end up breaking some apart, adding things in (skills I assume they have from Algebra that are lacking?) or cutting some (trig for the fundamentals class).

Geo Standards List

 If you want to further engage in the conversation about geometry, head over to our wiki or tweet with the hashtag #rethinkgeo.  My next step is to come up with some sort of intro to each unit that gets students started asking questions (for the points and segments in triangles unit that question is: three cities are building an airport to share, what is the fairest location for the airport?).  Then I want to start writing/sorting problems that assess each standard so I have a pile to pick from for quizzes, tests and reassessments.  Geometry questions are particularly difficult to come up with off the top of your head since the diagrams can be seriously misleading if you don't think the whole thing through!


  1. >That will most definitely not be the case as I start teaching PreCalculus this year!

    If your pre-calc includes trig, the best thing I did was to hit it twice, triangle trig as my 2nd unit, and circle-based trig functions toward the end. I re-thought pre-calc last year, and the course felt much more sensible after I made it my own. Let me know if I can help you with that one.

  2. My school starts with Trig so we don't lose kids in the review, and then review after/throughout. It is definitely a huge part of the course. I'll certainly be looking for activities and advice throughout the year. If you have some sort of curriculum guide I'd love to look at it, just so I have an idea of different ways to sequence and connect topics.

    1. Tina, I shared a doc on dropbox. Email me at suevanhattum on hotmail if I can be of any help.

  3. Tina,

    We will be starting our Geometry curriculum with some very basic definitions/concepts, but then we are going right into transformations. I have taught Geometry for 4 years total and although this isn't the way we have been teaching it the more I think about this sequencing the more I like it. I also feel like connecting rigid transformations with congruency and dilations with similarity it will ultimately give students a better understanding of both.

  4. I came up with this with some help from other teachers in my department as we were trying to get ready for Common Core. I haven't revised it since we put it together, but it would be my starting point if I found out I had to teach geometry this year (which I don't).

    Let me know if you have questions; it's not fleshed out as much as your list appears to be. I thought you might appreciate something to compare ...

  5. I've been reading up on SBG a lot this summer, of course this encourages me but also overwhelms me, feel like I need another year to pull it off. Guess what? One of my co-presenters (professor at UCSB) did GREAT hands-on lessons on transformations with the participants. I took copious notes but wish I could clone him to come into my room to teach it.

    Thanks for all the share here, Tina. I'm really interested in your Geometry standards!

  6. Thanks for the feedback everyone.

    Fawn: Last year I started easing into SBG by doing regular quizzes and tried to quiz on each topic we covered. But I graded them 2 points per problem like I always have. It was easier to come up with a standards list when I had all those quizzes to look back on. Also, I'd love to see that lesson, blog about it please!

  7. My department is also working on redesigning our geometry course, and there were several teachers who were very nervous to do this without a text. We basically broke down every standard that we are going to be teaching, and then translated it all into a list of standards that we feel we can teach.

    If you're interested in what we we're going to attempt, I wrote a blog post ( with links to our department's work in Google Docs. I'll be blogging this fall about how teaching it goes!

    1. Awesome! I just subscribed to your blog so I can follow along. Now to dig into all those google docs.

  8. I am getting severely beat up by Geometry this year. I keep having great ideas like yours (ie: lets not kill them with proofs the first month of school and make them hate Geometry and tune out) but bow to pressure to follow the school/district pacing. I THOUGHT last year we had a group that would look to radically change things. But teachers are such creatures of habit and as long as we're encouraged (read - pressured to) work from a textbook (which is old) and until we fully adopt CCS everyone just wants to plod through the book.

    Last year I taught more than I had in several years due to pressure. Of course my students did worse than they've done in years. This year, I vowed not to. I still hate what I've done in these first 6 weeks of school.

    I will be re-thinking from here forward. Thanks for your great info. I'll be looking at it for sure.