# Graphing Periodic Functions

## Objective

SWBAT recognize amplitude, period, and midline in an equation, and apply the definitions of these terms as they graph periodic functions.

#### Big Idea

Students continue to construct definitions for each parameter of a periodic function.

## Opener: Check In Quiz

10 minutes

As students arrive in class, I give them a copy of today's Check In Quiz.  I tell them they have 10 minutes to complete Side 1.

Both sides of this quiz are the same, except for the Mathematical Habit.  Side 1 is an assessment of Mathematical Habit #1, while the reverse includes Habit #6.  As class begins, I want to see that students are demonstrating the habit of perseverance in problem solving.  Even if they're not sure exactly how to graph this function, is there evidence that they're trying to make sense of it (MP1)?  On the second side, which will be completed at the end of class, Habit #1 is replaced with Habit #6.  Once students have a chance to practice what they need to know how precisely can the apply this knowledge?  How precisely can they use the words amplitude, midline and period?  How precisely can they graph this function (MP6)?

There is no prescribed question written in the reflection space because I will give students a few different options for that.

This really serves as a "before and after" sort of quiz.  Students are in the process of establishing their knowledge about graphing periodic functions.  Some will be able to do this correctly at the start of class, but most will need a little practice with amplitude, midline, and/or period.  This quiz gives them the chance to see where they're at before getting to work today.

## Mini-Lesson: How to Annotate & What We're Looking For

10 minutes

When I tell students that their 10 minutes are up, I simultaneously post Slide #2 of graphing periodic functions. On this slide I offer students three possible reflection questions.  I like giving students a choice of reflection prompts because I've found it leads to better thinking.

Then, I say, "I'm going to collect this quiz in a few minutes, but, everyone is going to have another crack at the quiz at the end of class." As I'm collecting quizzes, I post Slide_3, which includes today's learning target.  We'll have a brief whole-class discussion in which students share what they need to know in order to be able to complete the problem on the Check In Quiz.

How to Annotate a Graph - Linear Function Example

One thing that might trip students up on this quiz (at least so far) is that some are not sure what it means to "annotate a graph."  In order to continue to connect this new knowledge to old knowledge of functions and their graphs, I provide a quick example of how I might annotate the graph of a linear function (see Slide #4).

After showing this example, I move to Slide #5 which lists the features of a linear function next to the features of a periodic function.  I say, "Just like you (students) have grown comfortable with graphing linear functions, you can do the same with periodic functions.  The goal of today's lesson is try to be able to understand the words amplitude, midline, and period, and to understand how these parameters appear in equations and on graphs of periodic functions."

## Practice Time on Delta Math: Graphing Periodic Functions

40 minutes

There is a Delta Math assignment called Graphing Periodic Functions that students will work on right now. This activity was assigned during the previous class.

I tell students that as they work on the laptops, they should have their notebooks at the ready, so they can jot down any new understandings about these key vocabulary words.

As students get to work I check my Delta Math teacher dashboard to see if anyone is already done with this assignment.  I also take a quick skim through the work my students have done on the opening quiz.  If any students can already demonstrate mastery of SLT Trig Functions 1, I'll set them up with a few more challenging problems or Delta Math modules.  For the majority of my students, I expect that this is not the case, and this lesson is exactly where we need to be.

## Closing: Check In Quiz & Reflection

15 minutes

As students return their laptops to the cart, I return their Quizzes to them. I remind students that this is same problem from the start of class, and that everyone should try to sketch the most precisely annotated graph they can.

After students work for 10 minutes, I pose new reflection questions using Slide_7.  I will collect quizzes when students have completed their reflections or as they leave the classroom.