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## See ya Later, Skater Boi

By Diana Godines, February 27, 2017

• High School

• 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 https://youtu.be/y8-jb2E2BPs HOMEWORK VIDEOS Homework Day 1:Graphing and Analyzing Linear Functions: https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie and Analyzing Linear Functions Homework Day 2:Graphing and Analyzing Exponential Functions: https://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 https://www.merriam-webster.com/ Flipped Classroom Information https://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

### 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.