Circles - Geometry

I try to meld together as many different topics as I can in my Geometry class. Trigonometry? All based in the unit circle. All the fancy chord theorems for cirlces? Similar triangles. Equations for circles and completing the square? Check. I find it helps to take what seem like divergent topics and give them a common thread.

Equations of
Circles 1
​- Card Sort

This gem of a lesson comes from the wonderful people at the Mathematics Assessment Project. Students come up with equations for circles on the origin and the transformations off the origin. I've created a presentation and broken the pdf of the lesson out into student worksheets (S1, S2, S3). Eventually, I would like to put these cards into a Desmos Activity Builder so I don't have to have the students cut the cards every year. Next year. :)

Equations of
Circles 2
- Card Sort

This is a companion lesson to the Equations of Circles 1 by the M.A.P.. Here, students explore the particulars of a circle by analyzing the equation. This also includes completing the square to turn the equation for a circle into standard form. I've created a presentation and separated the original pdf into student worksheets for printing (S1, S2, S3).

Practice with segment relationships inside of circles.

I picked up these problems from various places. They are sourced in the document. Sometimes you need some decent application problems to put into practice all the theorems we've developed as a class.

Review of tangent, chord and secant theorems for circles

I give students a big circle with a couple of details filled in. Then, they need to figure out the rest of the information in the circle. It's like a big puzzle.

Desmos Art!

I give students a simple assignment--using the equations we know, create something cool. Kids love it. I love it.

I've got some more fun tasks once you include volume and surface area.