##
* *Reflection:
Ahoy team! What can you see? Finding functions. - Section 3: Closure - Spyglass Problem

I always over plan! And this lesson was no exception. Time is always my biggest battle. My students were engaged and working hard from bell to bell and a majority of the class was just barely graphing by the end of the hour. So I decided to cut problems #5-6. The honors teacher on campus reported that all of her students completed it and the timing was great.

*My number one enemy... time!*

*My number one enemy... time!*

# Ahoy team! What can you see? Finding functions.

Lesson 2 of 16

## Objective: Students will be able to collect and analyze data using a "spyglass" and then review linear concepts to model this data.

#### Introduction

*5 min*

Today is the first day that students will be working together in their teams and probably the first day in a while that students have done some math. I am going to start class by introducing the mathematical practices to my students using a poster of the practices that I have posted in my classroom. I hope that by being really explicit with my students about the mathematical practices it will help them to self-assess their ability to be a good math student and will help them improve in this area (and it will help me to always be reviewing the math practices!) Today, I will help my students to focus on **Mathematical Practice 1: Make sense of problems and persevere in solving them**. To me, this practice is not something we can 'teach' our students. Instead, it is more about motivating our students to even care to try and also giving them the pieces they need to be successful problem solvers. I am guessing that although the math in this activity is not difficult, the activity overall will be challenging for students as they haven’t had to read directions and work together all summer long! So I will be sure to define perseverance for my students and set the expectation that students should be working on something at all times. Whether it be working on solving the problem or working on figuring out what they don’t know. I would also like for students to focus on how to work well as a team today. So I am going post the Basic TEAM rules and review these with my students before they start on today’s activity. I will continue to reference these rules throughout the school year when we have a team based activity.

#### Resources

*expand content*

**Teacher Preparation: **Students will need some supplies for today’s lesson: butcher paper (to mark viewing area on), ruler, yard stick, and ‘viewing tubes.’ The viewing tubes can just be old paper towel rolls or you can have students make their own viewing tube. If students will be making their tubes you will also need plain paper and tape. Students should make tubes about 11 inches long with a diamter of 1 inch.** **

**Environment: **In this activity students work together in their teams on a problem that isn’t too

complex. The purpose of this is so that we can see how teams work together and so that students can start to get comfortable in their teams. I think it is important for students to be working with their tablemates that they will sit with for some time. (I like to regroup students every quarter.)This is a great time to sit back and analyze these teams and make any changes you see fit.

**Narrative:** Give every student a copy of the Tubular Vision and Spyglass Problem handout. Students will need to work in teams to complete this activity. The Tubular Vision handout gives students directions on how to complete the data collection and the Spyglass Problem handout is where students will record their findings and answer extension questions. The data collection definitely needs to be completed in class, but the Spyglass Problem handout could be completed as homework if students are not able to get the work done in class. In this 30 minutes, I would want my students to get through collecting the data and graphing the data. They should also start working on finding the equation to model the data.

Students will first be analyzing the *width* of the viewing window. They should be collecting data from positions about 1-3 meters from the board. Be sure that students are collecting at least 8 data points. I will also be checking that students have correctly identified the independent variable(distance from the end of tube to wall) and dependent variable (width of the region they can view) and that they are correctly labeling their graph.

Since every skill and concept in this lesson should be review for students, I am not planning on giving much assistance. I predict that students should have no problems (as long as they read the directions!) through question 3 on the worksheet. However, I do predict that writing the equation of the line will be difficult for some of my students. (see next section of lesson for what I plan to do about that)

Throughout this activity students will be working on **Mathematical Practice 2: reasoning abstractly and quantitatively **although it will not be explicit to them. They will be required to collect numerical data and then make conclusions based on this data. There is also a strong focus on **Mathematical Practice 4: modeling** in this activity as students use linear functions to model the data they collect. We will also get a glimpse at student’s current habits for **Mathematical Practice 6: attending to precision. **

*expand content*

I agree with you about having students present right off the bat! :) Students need to know that this is the expectation from the get-go and that your class is a safe environment in which to do that. I use a peer evaluation tool that asks for all the students in the 'audience' to author one positive comment about the presenter (in their journal), and this also gets students familiar with who is in their class. You can ask the audience to share some of those comments and address each presenter aloud. When I review their journals, I add a few of the comments to the presenter's journal to let them know what others thought about their ideas. Later in the year, I have students author a team's response in the presenter's journal. It makes everyone feel welcome and that presenting is something that you do to share your ideas in a forum that is accepting of you AND your differences! :)

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Getting to Know You, Getting to Know All About You...
- LESSON 2: Ahoy team! What can you see? Finding functions.
- LESSON 3: Function Zoo - Basic Function Families
- LESSON 4: Parent Functions
- LESSON 5: Shifting Functions: How do they move?
- LESSON 6: Shifting Functions: How can we describe them?
- LESSON 7: Dicey Functions Day 1: Piecewise functions are basic functions... just cut up!
- LESSON 8: Dicey Functions Day 2: Piecewise functions are basic functions... just cut up!
- LESSON 9: Fun with Functions: Basic Inverse and Function Operations
- LESSON 10: Compositions in Context
- LESSON 11: Inundated with Inverses: Restricting the Range of an Inverse (Day 1 of 2)
- LESSON 12: Inundated with Inverses: Algebraic Inverse and Composition to Verify (Day 2 of 2)
- LESSON 13: Jeopardy: Basic Functions
- LESSON 14: Review Day
- LESSON 15: Test Review
- LESSON 16: Basic Functions Test