# Functions for Circles?

## Objective

SWBAT create the two functions needed to graph a circle and to explain why two functions are necessary.

#### Big Idea

Why do these circle equations not look like the other functions we have studied? In attempting to answer this question, students develop the function rules needed to graph a circle.

## Warm-Up

30 minutes

As usual, today's Warm-Up provides the opportunity for students to practice their algebraic skills and to begin to explore some new content. The Facilitating Today's Warm-Up document provides some specific teacher moves and goals related to each of the problems. As students work I will circulate around the room, carefully observing how students are working and diagnosing some of the obstacles that I will need to help students overcome. We are getting deep into the unit now, so my students are ready for some challenging content. Some are also in need of my attention.

20 minutes

## Apply New Learning

20 minutes

Once students have discussed the questions, they should be prepared to apply the same ideas and knowledge to the Circle Data Tables and Functions problem set, which can be part of their portfolio. For this problem set, I ask students to show their answers both graphically and algebraically if possible.

Students likely will not finish these questions today in class, so they can continue working on these questions throughout the next week which will hopefully allow them to develop deeper understanding of these ideas.

## Closing

10 minutes

Today's closing is straight-forward, but I always like to ask students what the key idea of the lesson was and I do so in this Exit Ticket. The students' answers often don’t match mine, but hearing their thoughts helps me understand what they understand. Hopefully they can connect this lesson back to radical functions and the idea that we have to restrict the range of a radical function so that it becomes a function. The restriction of domain is really the big idea of the lesson—so I have students share their ideas and then if it doesn’t come up, I will share it and ask students to make the connection.

This is another good time to define a “function” more formally, so that students exposed to the formal definition.