I love this lesson synthesis. I hope you’re able to give it some time!
We hope this synthesis makes lots of room for lots of different kinds of thinking from lots of different kinds of students. No student is likely to capture the entirety of the relationship between diameter, radius, and circumference. But your class as a whole is likely to capture all of it.
Check out these student responses!
The diameter is 2 times as much as the radius. And the circumference is pi.
Radius is half of a diameter and circumference is the perimeter of a circle.
The relationship between them is pi.
The radius, diameter, and the circumferences relationship is that there is always a constant and a proportional relationship between each.
Keep an eye out for students who capture small and different glimpses of that relationship. Consider snapshotting and sharing them. You could ask here, “Pick one of your classmates’ responses and get ready to share what’s right about it.”
Other curricula might present your students with a definition of the relationship between the parts of a circle. What we’re inviting you to do here is to construct that definition using language from your students. That certainly asks more of you, but we hope your students will understand their value as mathematicians and learn more as a result.
Have a great lesson!
Dan & the Desmos Classroom Team
PS. Please give us feedback on the last lesson.
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