In this post, I share thoughts about my Geometry Labs (free download), and complement some of Mimi Yang’s notes about it. (In fact, this post was suggested by the existence of Mimi’s notes. You may find those useful, as she lists which topics are supported by various labs.)
First, big-picture thoughts.
- The book includes obviously curricular content, but also material which is not standard classroom fare. I hope you can find a use for the labs about puzzles, symmetry, tiling, and so on. Some are not so far from things you have to teach, and some are just, well, interesting.
- Most of the labs require the use of manipulative materials. This is not because hands-on activities magically confer understanding! The idea is to use those labs to trigger reflection and discussion. If you don’t have the manipulatives, I encourage you to get them — you won’t regret it, and your students will be grateful.
- Most of the labs include a discussion section. Those questions often make it possible to get at important ideas, especially if you use them to structure whole-class and/or small group conversations, or as prompts for student writing.
- I know that most teachers do not read teacher notes, which is fine: most of the labs are self-explanatory. However I encourage you to check out the Connections, Corrections, Extensions, and Revisions on the book’s home page. Those include ideas I had after writing the book, and input from teachers who use it. I will not duplicate those here!
And now, more specific comments.
- I’ve used Lab 1.1 as a Day 1 activity for my Geometry class many, many times. It gets students to start doing math right away, it communicates that the course will be engaging and will involve some hands-on work, and it leads into logical discussions about visual content — geometry!
- Students come into a Geometry class with a wide range of understandings about what angles even are. The first few labs help to even the playing field.
- Labs 1.7-1.10 are built around the inscribed angle theorem. This work is interesting and has few prerequisites. There is no reason to wait until late in the course to tackle it.
- Lab 2.3 can be used to introduce some basic vocabulary. It’s a great activity, probably best suited for middle school.
- There are a number of “walking polygons” labs (3.3, 3.5, 3.6, and 6.2). Those work well with programming turtle graphics in Scratch or Snap.
- Some of the labs calling for compass and straightedge are actually more accessible and more fun by adding patty paper to the toolbox. (Labs 3.1, 3.2, 6.1, and perhaps others.)
- It is not obvious that Labs 7.3 and 7.4 (tiling with triangles, quadrilaterals, and regular polygons) are highly curricular. They can be done early in the year as another way to think about angles. See this blog post.
- Lab 8.1 is my go-to activity for Day 1 of Algebra 1. It is also an activity that seems to work with just about any group: grades 6-12, teachers, even parents. It has the right mix of access and challenge, and is a classic case of “low threshold, high ceiling.”
- Lab 9.4 is a great example of non-random drill. Students use the Pythagorean theorem repeatedly, which is good practice, but they can much reduce the tedium by noticing patterns. They are encouraged to use color, which is always fun.
Well, that’s all for now!
I’ll probably insert some of the above into the Geometry Labs home page. If you use these labs and would like to contribute connections, corrections, extensions, or revisions, get in touch!
— Henri