A Pattern With Circles

Facilitator(s): Sophie Grifith
Date of Meeting: November 13th
Problem: pdf

In CAMI Meetings and in class with students, we often want a prompt to get students generating their own mathematical questions to answer, rather than giving them a predetermined math problem that everyone needs to solve. In the November evening meeting, we started off by considering some prompts and sentence starters to get students asking questions that will lead to math explorations.

Here are a sentence-starters that we came up with:

  • How many…?
  • How many ways…?
  • Is this always true?
  • Could this pattern continue?
  • Would it be possible to…
  • What would happen if…?

And a few questions we can ask to get students thinking mathematically:

  • Why would I show you this? 
  • What’s the point?
  • What do you see that relates to math?
  • How do you see this?

What questions do you ask students to get them thinking? What kinds of questions do you want them to ask themselves?

After that, Sophie showed us a drawing of some circles. 

What do you notice? What do you wonder? 

When we looked at these circles, we had a *lot* of ideas and questions. In the exploration that followed, we found that one of the biggest challenges was drawing new images, especially with more than four circles. Some of us made pencil/paper drawings, and some of us tried to use online software. Sarah proposed making some pre-existing images on Geogebra or Desmos so that students could play with the images and explore math questions without needing to struggle with making the images themselves.

Check out some of the images we came up with!

Jamboard: (includes photos of pen-and-paper drawings) https://jamboard.google.com/d/1hWOdKlHIPZ-J42ENTMsIkSBaW-zJidgd2x1sJYHUYxI/viewer

Geogebra: (includes images that one group made during the meeting)


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