classroom structure discourse integers linear functions numeracy

Counting Circles Brainstorm

Let it be known that Sadie Estrella is a Hawaiian treasure.

She made her way north for SUM2015 in Saskatoon and I got the opportunity to learn from her about counting circles (as well as share an eventful dinner). 

It is probably good to understand her work on counting circles before reading a couple of ideas I had during her session. 

I went to her blog and searched for #countingcircle, and the results can be read here

She is so honestly passionate. You can tell that she cares when she talks. I immediately felt comfortable as the “student”. *****
Use this time to read Sadie’s work

A couple things struck me while she was talking:

  1. She had such a precision of language. At one point, she noticed herself saying “anything else?” and purposefully corrected it to “other ideas?” Such a little detail that makes the idea generation flow. 

As she was talking, I started to think where this routine would fit in my room. I teach high school, so most of my students are past counting 10s, but still struggle with numerical flexibility. I had two ideas that I would love to try in my room. One is a structure, and the other is a conversation.


Sadie had us counting by 11s and dissecting our thinking. She modelled similar counting circles with decimals, fractions, qualitative sections of time (i.e. quarter of), etc. One thing that I thought would be interesting is attaching a function to the circle. So as the students were counting inputs (0, 1, 2, 3…) they were audibly giving the output of the function. 

If we started with linear, my hope is that students would see the pattern of outputs quickly. Then we could have them skip input numbers (possibly for functions like y = 1/2x +3). Why is it easier to skip? As the group gained fluency, it would lead into a profitable conversation…


Certain counting gaps are simpler than others, and that may result in an increase in speed around the circle. This analysis of speed is a fantastic conversation. Once students see the pattern, the counting will speed up. Stopping the flow and asking, “Why can we do this so fast?” might be an effective stem to get kids talking about the patterns they’ve noticed. 

Keeping track of the circle speed would be a great assessment tool for pattern recognition. The danger here is equating speed with standardization and getting away from the good conversations that occur around the circle. The goal shouldn’t be to go fast, but going fast is a symptom of some great mathematics. 

If you cheated and didn’t read Sadie’s work, this makes no sense to you. I did that on purpose. Go read it now. 

Now don’t you wish you had done that to begin with?

The routine is simple; it can embed into your room as a daily or weekly activity. It makes thinking visible and connects learners. Win-Win. 


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