## winter_solstice_pivato.jpg - Section 1: Opening Circle & Admire this Photograph!

# Problem Solving and Review

Lesson 5 of 6

## Objective: SWBAT review the two student learning targets for Unit 4.

*75 minutes*

When students arrive in class, I have this photograph projected on the board. Here is the write up about the photo. Note that this image is made up of "43 *well-planned* (italics mine) exposures." I ask students what planning has to do with taking this picture. I want students to see how the photographer was able to so consistently space each image of the sun in this photograph. That took planning. What did the photographer have to know in order to make this happen? (Note to teachers: the modeling task on the Unit 4 exam is about the length of days in New York City. Take a look - this may inform some of the preview hints you drop during this conversation.)

With that in mind, I ask everyone to circle up, and I put the two SLTs for this unit posted on the board.

- Trig Functions 1: I can graph trigonometric functions with and without a calculator.
- Trig Functions 2: I can use trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Today is a review day, and I point to the board and the two learning targets that will be on tomorrow's exam.

There are two assignments that students can use to review for the exam: Problem Set #15, which was distributed at the end of the previous class, and the Delta Math assignment "Graphs of Trig Functions". I tell students that they should work on whichever assignment they prefer, but that the exam will look more like Problem Set #15. Computers are available to anyone who wants to use one, whether for Delta Math or for looking up information that will help them with the Problem Set.

After I give my opening notes, I ask students to whip around and say a sentence or two about what they're going to do in class today. Then we get to work.

#### Resources

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#### Work Time

*65 min*

Note to teachers: take a look at the Unit 4 exam to see what you should emphasize during today's lesson. My goals are to get students comfortable with a features of a periodic graph, and to spend some time focusing on the model. We haven't done much modeling since the fall semester, but most of my students are pretty quick to recall the steps for plotting points on the TI-83.

As students take their seats, I remind them to prepare **Cheat Sheets** for tomorrow's exam. I unlock the laptop cart and give computers to anyone who wants one, and I have extra copies of Problem Set #15 available.

**Problem Set #15 and Grading Habits by Observation**

This problem set consists of four questions that will get students to think about the features of the graph of periodic function, followed by two periodic modeling scenarios. I expect students to ask clarifying questions as they work, and they are equally likely to talk to each other or to me for help. If there are a lot of computers out, I might direct them to search the web for specific issues that arise.

I am not collecting this problem set, but I do walk around with a clipboard jotting notes about the perseverance & sense-making that each student is engaged in. I don't want to be overbearing, and I try to make light of it, but I also have the conversation a few times over the course of the class about how perseverance is usually an obvious trait. We discuss what it looks like, and I encourage students to demonstrate whatever they come up with. At the end of class, the exit slip will be a self assessment on the **first mathematical practice (MP1)**.

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With 5 minutes left in class, I direct students to look at **Habit 1: I can make sense of problems and persevere in solving them (MP1)**, which is the first learning target listed at the top of Problem Set #15. Throughout the semester, this SLT has been assessed on every problem set.

I'm not actually collecting the problem set. For today's Exit Slip I simply ask students to write me a brief note in which they describe how they persevered and made sense of problems during today's class and assign themselves a grade for this SLT.

**What I'm looking for is this**: I want to see that my students understand what the Habit means in the first place, and I want to see if their self-descriptions of perseverance match up with what I've got on my clipboard.

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- UNIT 1: Statistics: Data in One Variable
- UNIT 2: Statistics: Bivariate Data
- UNIT 3: Statistics: Modeling With Exponential Functions
- UNIT 4: Statistics: Using Probability to Make Decisions
- UNIT 5: Trigonometry: Triangles
- UNIT 6: Trigonometry: Circles
- UNIT 7: Trigonometry: The Unit Circle
- UNIT 8: Trigonometry: Periodic Functions