Starting Geometry with Definitions

Every year, geometry starts with students defining many key terms so that we can use this vocabulary as we work through the content. For some reason, this school year, I couldn’t remember what I’d done in the past and I took this to mean that it wasn’t as awesome as it could be. As I planned the first few days I had these ideas in mind:

  • I wanted students to know 16 key geometry terms.
  • I wanted to use the frayer models that fit in students interactive notes as Sarah Hagan describes here.
  • I wanted students to develop their own definitions and not simple copy from a book so that they owned the vocabulary and processed each term.
  • I wanted to create and foster a culture of collaboration in my class as the school year began.
  • I wanted students to depend on their peers and teacher provided resources for support of content and not rely on the teacher as the purveyor of information.
  • I wanted to be able to easily verify student’s definitions for accuracy outside of class time.
  • I wanted to pre-assess students ability to write effective definitions and writing in general.

I love the Kagan Geometry book  (but really wish it was available in a digital format) I don’t always follow the prescribed structures, but the resources can be very useful. There are pages in this book for developing definitions that contain only images of examples and non examples – which fit well with the frayer model that I planned to use. In searching the MTBoS for ideas, I found this post by Pam Wilson.

This what I ended up doing. I am satisfied with the way this went and will do it again next year:

The setup:

I copied the terms, blown up large onto different colored card stock  &  laminated them. Each color represented a group, so I make 5 colors with 3 words per color & I kept one to use as an example with the whole class. I also made a ton of copies of Sarah’s Frayer model for students to use.

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The implementation:

1. I used the widget example from Discovering Geometry (chapter 1). It shows strange blobs and says “these are widgets”, then there is another group of strange blobs and it says “these are not widgets”. I have students define widgets in their groups. Then they read their definition and we try to draw a counterexample. Then we discussed what makes a good definition and we were ready to go!

2 I projected the “perpendicular lines” examples and non examples. We completed a frayer model for the term.

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3. Students worked in small groups with their 3 terms copying the examples & non-examples, then writing good definitions for each term. I set a timer for 10 minutes.

4. Groups rotate to another station. repeat. 10 minute timer.

5. This continued until the end of class. Students turned in their completed Frayer model sheets.

<At this point each student had about half of the 16 words defined.>

6. That evening I read their definitions (every single one!) and wrote feedback in the margins. No grade.

7. The next class period, I gave all of the students back their definitions with my feedback and gave them time to correct or improve their work.

8. Give one, get one – Speed dating style! Students each got a blank Frayer definition sheet and sat across from a student who was not in their original group. The would talk, find a term that they needed and share. Each students would give one definition to their partner and get one from their partner. Then a timer would go off and they would rotate & repeat.

9. While the students speed dated, I listened and taped pickers to the back of their interactive notebooks.

10. As a quick check for understanding, the students used their plickers and answered multiple choice questions on the terms for the last 10 minutes of class.

11. Homework was to cut them out and put them on specified pages of their interactive notes.

12. I made a Word Wall by simply taping the laminated cards to the wall after the lesson. Easy Pezy!

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Basic Geometry Constructions 4-tab Foldable

[update: 10/05/15: I no longer use this in my classes because I developed a better sequence of lessons for teaching geometry where students deduce each construction using reasoning instead of copying steps from a website or myself.]

Following an activity developing definitions in geometry, the first major unit of geometry will be constructions.

I plan to take 2 class periods to complete this foldable for their interactive note books with time for practice.  Each tab has space for both the steps and an example for segments and angles, except of course the last tab which contains constructing a line parallel to another line through a point and constructing a perpendicular line.

Instead of just talking at my students, I’m considering having students complete these notes in pairs using this website for directions:

Then I can circulate and provide support as needed. I’ll update this post after using this with students reflecting on its usefulness.

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