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Concept Circles
Concept Circles are a wonderful way to reinforce concepts and vocabulary and can be used across all grade levels and content areas. Simply put, a concept circle is a circle that is divided up into 4 parts, and each part or sector of the circle contains a word or concept. There are different versions of concept circles described below. Students need to determine which part or sector of the circle does NOT belong and they need to justify their reasoning with a WHY statement. Pushing for the why pushes students to think critically about how the other parts of the circle relate to one another. The beauty of the concept circle is that answers can vary depending on how students support their thinking.
VERSION # 1
In answer to the question, WHICH SECTOR DOES NOT BELONG AND WHY?” students again came up with different answers, both of which are correct. Most students said the 1 does not belong…WHY? because it is neither prime nor composite. Students need to have an understanding of prime and composite numbers which are critical concepts in number theory.
 Another response was that the number 64 did not belong…WHY?... because it’s the only even number and the other numbers are odd. Yet another justification as to why the number 64 did not belong? It’s the only number that is NOT a power of 3. This generated a discussion of what power of 3 the other numbers were? Nine is 3 to the power of 2 and 81 is 3 to the power of 4, but what about the number 1? How is that a power of 3? This brought the group back to a previously learned concept that any number to the zero power is 1, therefore 3 to the power of zero is 1.
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Here is another example
Which Equation Does Not Belong?
Variations of Concept Circles
VERSION # 2 requires students to name the concept circle when all 4 sectors are filled in. Again, asking students to explain their thinking requires students to provide a justification for their answer.
In the math example shown, students found 2 different names for the same concept circle, either of which are accurate. Both of these names reinforce important vocabulary i.e. “Positive integers” and “Perfect squares”. Another name that would also be appropriate would be “Square numbers”. Discussion could follow as to how they know these names are appropriate. “What is a perfect square? Can you think of another number that would be a perfect square?” OR “What is an integer? Would the name Positive Numbers also work? Does that give us as much information as the name Positive Integers?”
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VERSION # 3 three sectors of the concept circle are filled in and students need to fill in the 4th sector with a word, concept or number that would complete the circle. A justification statement would need to support the student’s answer.
Once students have had experiences working with concept circles, VERSION # 4 has students create their own concept circles to share with the class or with one another to solve.
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