#TMC18 Discovering Geometry through Drawing and Discussion {Jennifer Fairbanks, Kathy Campbell}

Discovering Geometry through Drawing and Discussion from Verbal Cues at Whiteboards
Jennifer Fairbanks
Kathy Campbell
Morning Session 9:30-11:30

Use flippity.net to split students into groups of three; one marker per group. Rotate markers for new problems. Alternatively, have the groups rotate and add to the previous work or check for errors.

Use a script to have students discover instead of a lecture.

Attending to precision in geometry is like learning a new language.

Explain how three points define a plane by throwing out three ping pong balls and having students hold them up and visualize the plan.

Correcting units, labels, and capitalization on a daily basis in a "fishbowl" effect reinforces why precision is important.

You need mistakes to have good discussions.

{I'm thinking I would whiteboard for instruction and then use a graphic organizer answer key and have students sort and glue as a way to process. Also take a picture of  the board work and post in Google Classroom.}


If you are short on time, try starting with the hardest problem first.

Give verbal directions so that the words on a worksheet aren't a barrier.

The student writing is not the one doing the problem- the partner is telling them what to write. All people use the calculators when needed.

Have students write in black first, then shift groups and look for errors and comment in colored markers.

When writing scripts, things to think about:

  • when to switch markers
  • do only some parts need to be erased
  • what is the point of the lesson
  • how can you start with what they know
  • scaffold up
If one group is really strong and finishes early send each to a different group to assist.

Variation 1: each group has a different problem. After starting their problem, have groups switch and pick up where the original group left off. (trig identities, proofs, etc)

Variation 2: Write an equation in vertex form. Next group graphs it. Third group writes it in standard form, etc

Variation 3: Same diagram but three different proofs. Rotate groups so students have to really think about the givens.

VRG Variation: hand out a deck of cards but don't tell students how you are sorting; have them hold up the cards. Scan the cards and if you see people who shouldn't be together, pick suits or pairs or whatever you need. Students won't switch cards because they don't know if that will be beneficial.


When you are trying something new, start with the lesson you hate.

For large classes, it may be hard for everyone to look at others' work. Instead of a Stand and Talk, for students who approached the problem in different ways, maybe a Sit and Talk would work better.


  • when to switch markers 
  • to make sure everyone look at every group's work
  • when calculators are needed
  • to make an answer key
  • the misconceptions students will have
  • possible mistakes
  • using as much vocabulary as possible

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