Sorting Equations of Circles 1
This lesson unit is intended to help you assess how well students are able to:
- Use the Pythagorean theorem to derive the equation of a circle.
- Translate between the geometric features of circles and their equations.
- Before the lesson, students work individually on an assessment task that is designed to reveal their current understanding and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
- After a whole-class introduction students work collaboratively, categorizing equations and geometric descriptions of circles.
- At the end of the lesson there is a whole-class discussion.
- In a follow-up lesson, students again work alone on a similar task to the pre-lesson task.
- Each student will need a copy of the assessment tasks, Going Round in Circles and Going Round in Circles (revisited), a mini-whiteboard, pen, and eraser.
- Each small group of students will need Card Set: Equations (cut up before the lesson), an enlarged copy of the Categorizing Equations table, a compass, and a glue stick.
- You may want to copy the Card Set: Equations and the Categorizing Equations table onto transparencies to be used on an overhead projector to support whole-class discussions.
- There is a projector resource to support whole-class discussions.
15 minutes before the lesson, a 70-minute lesson (or two shorter lessons), and 15 minutes in a follow-up lesson. Timings are only approximate.
This lesson involves a range of mathematical practices from the standards, with emphasis on:
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning
Mathematical Content Standards
This lesson asks students to select and apply mathematical content from across the grades, including the content standards:
- H.A-CED: Create equations that describe numbers or relationships
- H.G-GPE: Translate between the geometric description and the equation for a conic section