My First Two Days of Geometry

My first two days went well, so I thought I’d share. Plus, if you happen to be another geometry teacher, I need your help with something (I’ll get to that later).


I have the desks divided into partners. I’ve got a seating chart; the students have their names and faces on the projector so they can find their seat. (I don’t paste things to the desks themselves; I’ve seen students tear off cards / names / whatever and try to swap them.)

As students come in I gave them a bingo card, with the instruction to fill the integers 1-24 in random positions.


Then we play syllabus bingo.


I have to get out a lot of facts to start, and it’s kind of dull and students don’t totally pay attention, so I have the beeping and flashing of lights and some Jolly Ranchers for the students who say BINGO.

There is a disadvantage to the random order, but it turns out not too bad, and if something seems awry I can always go off sequence to fill in details.

One of the entries (“News of the Day”) needs a little explanation. Even with a closer I often seem to have a few spare minutes remaining at the end of a class, so rather than having students millling about randomly I like to share bits of math / science / engineering news they likely haven’t heard of. At the level I teach the students are on the phase where they are deciding what they really want to do with their lives, and I don’t mind giving a little nudge in the STEAM direction. This time around it was the Lexus Hoverboard (which yes, I know, is cheating, but still neat):

That takes up about half the period. Then it’s time for Counterexamples.


(Click the image for a DOC file, although you will need to customize it for your own classroom.)

This is terrific as simultaneously an icebreaker (“11. No Amphi students like to draw.”) and a minor check of prior knowledge (“17. All functions are linear.”)


As students came in I had them pick six pieces of paper of their favorite color (off a table in the back).

I started with a game of hot potato using a basketball, and when I called time the person holding the ball came up to the computer and saw this:


I asked them to describe the image using only words, no hand gestures, and had the rest of the class copy the picture to the best of their ability. (The trapezoid someone said “was like the Pizza Hut sign”.)

The generally poor performance on the task led me to nudge to the importance of vocabulary. I then had them take their five blank papers and fold them into a book (and staple the edge). This book will be their vocabulary book which they will slip into a back flap of their composition notebook and be able to use throughout the year. Then I gave eight words:

1. Point 2. Line 3. Line segment 4. Ray 5. Plane 6. Scalene triangle 7. Isosceles triangle 8. Equilateral triangle

and had them either use the glossary in their textbook or the data plan of their cell phones to look them up and define in their own words. (6-8 might seem strange to toss in, but our textbook assumes the students know the words already, so I thought I’d get them out of the way.)

This took a while for some students. It reached the phase where 3 or 4 students were working while the rest were done, so I had another volunteer student come up and play the describe-a-picture game with another picture:


This time I encouraged them to use their vocabulary to help things out (students referred to their newly-made glossary as the activity was happening). It went better than the first time.

I didn’t do any notational specifics (ray AB having a line with an arrow over it, etc.) but those details will hit on day 3.

By the time round 2 of the game was done everyone had finished their vocabulary books, so I did some more hot potato and had people share their definitions. Understanding was key. In one case a person didn’t know what the definition they wrote down meant (for “plane”) so we worked through an interpretation.


I told them we were going to play the game one more time, but we as a class were going to draw a picture then describe it by writing a paragraph down. A volunteer came and did the drawing and everyone did the writing, and I told them I was going to solicit help from the fine teachers that I happen to know in other states and even other countries and send their descriptions and try to have those teachers get their geometry classes to draw a copy based solely on those descriptions.

Yes, I mean you guys. Do you teach geometry? Could I use your class? Pretty please? Comment below or email me (see “About”) and I will hook you up. It will be fun!


The write-up was the closer, and classes did have a few spare minutes, so I showed the Hendo Hoverboard. Engineering!


6 Responses

  1. I teach geom (and other things). If you can give me a couple days I will have my class try.

  2. Quick question. Let’s see an enterprising tech company had a lesson where student #1 described a drawing and was randomly paired with a student _in_ the class who had to draw the description. Reverse and repeat. Any reason that’d be less preferable than another class in another state? Any reason aside from the global village thing?

    • It should work just fine.

      The global village aspect is more of a method of completely separating the student from their picture. If you just try it in class low-tech the students don’t quite get the point as well (they are after all just RIGHT THERE near the student drawing the picture). However, a high-tech variant could instant-anonymize in such a way you’d get a similar effect.

  3. The sports-scoring counterexample was on the brink of driving me crazy, by the way.

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