The concept circle I use most often has 8 sections with the smaller circle in the middle. Students do not have to use all of the sections, but having 8 provides flexibility. What is placed in the outside sections relates in some way to what is placed in the middle section.

I always remind people that the concept circle task provides the opportunity for rich mathematical learning, However, it’s our questioning that focuses the thinking and helps all students make key connections in their learning. As you consider the concept circle tasks below, it’s important to consider the kinds of questions you can ask to foster deep mathematical thinking.

Here are some possible questions you may wish to pose:

What patterns do you see?

How is this outer section different from the middle section?

How can two people have different answers and still be correct?

How did you arrive at your models for each section?

What strategy helped you to arrive at your solutions?

What would happen if we changed the middle section from ….. to ……?

Here are some possible questions you may wish to pose:

What patterns do you see?

How is this outer section different from the middle section?

How can two people have different answers and still be correct?

How did you arrive at your models for each section?

What strategy helped you to arrive at your solutions?

What would happen if we changed the middle section from ….. to ……?

Diverse Learners

You can modify the concept circle task by modifying:

  • the number of outer sections students complete
  • what students place in the middle circle
  • the kinds of changes/examples required in the outside sections

I have found that concept circles work really well for my ELL students, as the activities use only key written vocabulary and sometimes no written words at all! The teachers I have worked with noted high engagement level from all of their diverse learners.

Resources

I’m sharing concept circles from my own practice and several wonderful samples teachers have shared with me on twitter and/or through my professional learning sessions. There are many, many ways to use concept circles. More ideas can be found in my books Math Expressions (2012) and Teaching Math with Meaning (2018), and also on my twitter account @CathyMarksKrpan. I’ll update this site periodically with additional concept circle activities. Looking forward to hearing about your experiences and seeing some of your examples!

Please find a link to the concept circle PDF below. For my activities, I have had them enlarged approximately 24in x48in

Examples of Concept Circle Activities

Proportional Reasoning

Number Quantities (more/less)

Decimals

Proportional Reasoning

Number Quantities (more/less)

Decimals

Patterning

Translations & Transformations of Functions

Out of Doors Explorations

Patterning

Translations & Transformations of Functions

Out of Doors Explorations

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