# Sorting Equations of Circles 2

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

- Translate between the equations of circles and their geometric features.
- Sketch a circle from its equation.

## Introduction

- 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.
- During the lesson, students work in small groups on a collaborative task, 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 review their initial solutions to the assessment task and then use what they have learned to either revise the same task or complete a different task.

## Materials required

- Each student will need copies of the assessment tasks
*Going Round in Circles 2*and*Going Round in Circles 2 (revisited)*, a mini-whiteboard, pen, and eraser*.* - Each small group of students will need the cut up
*Table**Headings: Categorizing Equations*,*Card Set:*Equations 1 and Card Set: Equations 2, a large sheet of paper for making a poster, and a glue stick. You may want to copy the card sets onto transparencies to be used on an overhead projector to support whole-class discussions. - There is also a projector resource to support whole-class discussions.

## Time needed

20 minutes before the lesson, a 90-minute lesson (or two shorter lessons), and 20 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of the class.

## Lesson Type

## Mathematical Practices

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
- MP4: Model with mathematics
- 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.F-IF: Interpret functions that arise in applications in terms of the context
- H.G-GPE: Translate between the geometric description and the equation for a conic section
- H.G-GPE: Use coordinates to prove simple geometric theorems algebraically