## See ya Later, Skater Boi

By Diana Godines, February 27, 2017

### Grade Level

- High School

### Category

- Summer Design Institute

### Subject Area

- Mathematics

### Lesson Time

450 minutes - Five 90-minute classes

### Introduction

Through the course of the lesson, students will investigate the differences between linear and exponential functions, graphically and algebraically. In order to investigate these two important parent functions, student will review previously taught parent functions at home before the in class lesson, through a flipped classroom.
Students will participate in a design challenge in which the end result will be a low-resolution prototype of a skate park that includes skate ramps made of linear and exponential functions. The teacher will first introduce the design process in this lesson by becoming familiar with a specific user, a skater. Based on the insight acquired from the user(s), students will create a park to suit a specific skaters needs.
Students will then present their prototypes to a panel of community judges and display their work at an in class design fair.

### National Standards

CCSS.Math.Content.HSF-LE.A.1a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
CCSS.Math.Content.HSF-LE.A.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
CCSS.Math.Content.HSF-LE.A.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
CCSS.Math.Content.HSF-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

### Objectives

Student will be able to analyze and graph linear functions.
Student will be able to analyze and graph exponential functions.
Student will be able to identify linear and exponential growth and decay in the real world.
Student will be able to calculate complex linear and exponential functions.
Students will design a skate park with 3 linear functions and 3 exponential functions built into the model.
Students will observe real world examples of increasing and decreasing graphs.
Students will be able to create graphs of linear and exponential functions by understanding input and output, slope and basic calculations of functions.
Students will be introduced to the design process in this lesson by becoming familiar with a specific user, a skater. Based on the insight acquired from the user(s), students will create a park to suit a specific skaters needs.
Students will create a prototype of a skate park. They will make a low-resolution model of a skate park with linear and exponential functions describing each ramp.
Students will present the prototype to classmates and professionals from the community.

### Resources

Projector

**IN-CLASS VIDEO***In-Class Video #1: “Sk8ter Boi” by Avril Lavigne*https://www.youtube.com/watch?v=TIy3n2b7V9k*In-Class Video #2: Skate Park Examples*Best Concrete Skateparks of 2011*http://youtu.be/y8-jb2E2BPs***HOMEWORK VIDEOS***Homework Day 1:Graphing and Analyzing Linear Functions:*http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie and Analyzing Linear Functions Homework Day 2:*Graphing and Analyzing Exponential Functions***:**http://youtu.be/Rim9-qiRxps**IN CLASS HANDOUTS**In-Class Handout #1: Sk8ter Boi Lyrics In-Class Handout #2: Sk8ter Boi Observations**OTHER:****Vocabulary: Miriam Webster Dictionary Online http://www.merriam-webster.com/ Flipped Classroom Information http://www.knewton.com/flipped-classroom/**### Materials

Composition Book for Notes
Rulers
Paint
Markers
Graph Paper
Graphing Calculator
Recyclable Items for Skatepark Low-Resolution Prototype: Straws, Foil, Tape, Cardboard, Pipe Cleaners, rubber bands, etc
Computers to Research (if needed)

### Vocabulary

**Exponential Function:**a function whose value is a constant raised to the power of the argument, esp. the function where the constant is e.

**Linear Function:**a mathematical function in which the variables appear only in the first degree, are multiplied by constants, and are combined only by addition and subtraction

**Low Resolution Prototype::**\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"Prototyping is the iterative development of artifacts – digital, physical, or experiential – intended to elicit qualitative or quantitative feedback.\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\" (Geehr, 2008)

**Open Ended Questions:**Questions in which there is not a right or wrong answer, allowing people to answer in a way that is not planned or controlled

**Slope**: a surface of which one end or side is at a higher level than another; a rising or falling surface.

**User:**a person or thing that uses something; in design a user is often the client of the prototype created

### Procedures

**Day 1:**

**GOAL**: Create a skate park with linear and exponential functions built in to the park. (Students will not know this leading into the lesson.) Warm Up: (20 minutes) Students will write in their journal to describe the difference between linear and exponential functions. Students are encouraged to draw pictures, write stories and accurately answer the question using mathematical vocabulary. Students can plug in and into the calculator to look at graphical differences. Students will share out to classmates to recall similarities and differences between Linear and Exponential Functions. Video and Discussion (25 minutes) Students will watch Avril Levigne’s “Sk8ter Boi” video (In Class Video #1). After the video, teacher will give students the lyrics to the song. (In-Class Handout #1 - Attached) Teacher will lead discussion to go through lyrics of the song and make observations about a specific “User” (Class will not define the user until later on.) Teacher will lead discussion to define who users are in a design challenge. Teacher will talk generally about getting to know a specific person. Teacher and students will discuss the difference between open ended and closed ended questions. Teacher will inform students that it is important to interview and not just make assumptions of users based solely on observations. Teacher will inform students that they will work through the design process in order to answer the question “How might we create a skate park that meets a specific users needs?” Teacher will inform students that a prototype of a skate park will be built after the duration of the lesson. Observations (15 minutes): We will make general observations about the video and “skaters” in general. Students will get into pairs and answer the following three questions (See PowerPoint): (15 minutes) 1.) What is a “skater boi” according to the video? 2.) Have you ever been to a skate park? 3.) What did you notice about the clothing of skaters in the video? Design Challenge Introduction (20 minutes):

**To help focus the design challenge, we will look at what a “user” means. The teacher will explain that the skaters are our users. The video at the beginning of the lesson was analyzing public perception of skaters. The students, by conducting interviews for homework, real-life skaters will inform the “real” life of a skater, their needs, and their wants. To close the lesson for the day, the teacher will lead a discussion on who users are in a design challenge and why it’s important to actually interview the users during the design process rather than working on assumptions of who the users are. Closing Lesson: (10 minutes) Recall Linear vs Exponential Functions vocabulary, similarities, differences, function notation, etc. Homework: Watch “Graphing and Analyzing Linear Functions” Khan Academy Video and complete Homework #1 before next class period.**

**Day 2:**Warm Up (10 minutes) Students and teacher will discuss open ended vs closed ended questions. Students will create one open ended question about the school to practice open ended questions Independent Practice (15 minutes): Students will get graph paper and a graphing calculator and input the following into the calculator:and . They will graph the functions side by side by looking at the table and plotting points. Student graphs will look similar to the attachment “Linear vs Exponential Graphs” doc. Interview (In Pairs) (20 minutes) Teacher will discuss the difference between open ended and closed ended questions. Students will identify friends/family members who are “skaters”. In pairs they will have 5 minutes to come up with 5 open-ended questions for students regarding skating in skate parks i.e. likes, dislikes, ramps, tricks, different skateboards. Students will re-conduct interviews with more clarity for next class period. Investigate: (30 minutes) Introduce In-Class Video #2 Best Concrete Skateparks of 2011 Students will then focus on the Design Challenge by starting on the Investigate stage of the design steps. Students will get into groups of 3 and look online to research different types of skate parks and take notes and watch videos on current skateparks and how to alter/improve them. Guided Practice: Teacher Led Lesson (15 minutes) Students will graph the following functions y=-3x+1 and y=(-2)^x in their calculators on the same screen and discuss the differences with the person sitting next to them. Students will answer “What do you notice is different about these graphs?“ Teacher will discuss differences between types of functions with the class and discuss previous night homew

**After discussion, studentsotice that these graphs are negative and “facing” a different way than the 2 previous graphs. Homework (5): Students will interview 2 skater friends with the questions that were created in class and bring back next class period to “unpack” the information presented through interviews and research**

**Day 3**: Warm Up (15 minutes) Teacher and students will spend time “unpacking” the information from the face to face and video interviews from last night’s homework. Teacher will re-enforce the use of open-ended questions during the interview stage. Design Challenge (60 minutes) Students will brainstorm “What do Skaters Want?”. Teacher will encourage answer to be created from the needs and wants of a skate park as well as in other interests. Students will create and draw a sketch of a composite character from the information gathered during research of skate park and interviews. Homework Expectations and Handout: (15 minutes) Students will watch a video on YouTube: Linear Vs Exponential Functions. Video discusses and plots a linear function based on Wal-Mart data. The next video discusses investing money in a graph and the graph increasing by a constant factor of 5% and creates an exponential function.

**Day 4**Class Field Trip: (Measure Stairs) (30 minutes) Students will measure linear functions in real life by investigating the high school stairwells. Students will investigate slope by measuring the length across the stair steps and the height of the stair steps. They will then put the information in a table and graph on a coordinate grid.

**Prototype: (45 minutes)**Students will prototype for one hour during class period, while organizing a PowerPoint presentation that will be presented the following class period. Prepare Presentation: (15 minutes) Teacher will clarify the expectation of the presentation with students and filter questions regarding the equations of the slopes and curves.

**Day 5**: Students will present a 90 minute presentation with the finished prototype to the class and a panel of judges. The panel will be comprised of : 2 school administrators and 2 community members. Students will give a 5 minute presentation During the presentation, students will be required to answer the following: i.What is a Linear Function? ii.What is an Exponential Function? iii.Who is your User? iv. What are the unique items about your prototype? Students will present the prototype and present 3 linear functions and 3 exponential functions and the equations associated to with different parts of the skate park represented as functions. Function data must have the equation, a table and the graph drawn on graph paper. Functions will be presented in a Poster Presentation. Students will have to filter questions from the panel of judges after the 5-minute presentation. Time will allow for 15 minutes total for 5 teams.

### Assessment

Students will present to a panel of judges and graded according to a rubric. (See attached – Rubric #1)

### Enrichment Extension Activities

If there is a skate park close by, teachers can start the lesson by going to a skate park and making general observation before initiating the lesson.
Other types of functions can be included in the making of the skate park: quadratic, cubic, absolute value, etc.
Teachers could highlight how many of each type of function needs to be built into the skate park.
Students can extend the lesson to investigate Engineering careers in the future. Teacher and students can discuss the progress of a low-resolution prototype to accuracy in Engineering fields.

### Teacher Reflection

In an initial reflection (without having implemented in the classroom), the skate park and focus on “skaters” only could be reviewed more closely to include bikes, as well.
Students should have a solid understanding of exponential and linear functions.
Students could also include numerous types of parent functions, squaring functions, square root functions, absolute value functions, etc.