Slope And Function:  The Foundations of Extreme Sports



Students are at the point where they have worked with linear equations and are moving into further applications and understanding how lines are related, whether parallel, perpendicular, slope, etc... Students are also beginning to learn about the concepts of relations and functions and assessing pertinent information.

This project will tie all these areas together and enable the students to better understand the application of functions and relations, and how they apply to everyday life.

While there are many practical applications for the use of math, most 7th and 8th grade students still have problems relating what they are being taught to how this may apply to the world around them.  Keeping their attention and enabling students to bring math to life is what this unit is about.  Sparking at minimal the student to stop every once in a while to look at life around them and how math and other school subjects may come into play through the things they do each day.  Extreme Sports such as snowboarding, ski jumping, inline skating, skateboarding, bicycle motocross and the such are growing in pop culture each year; from the Olympics, to ESPN’s X-Games, music videos, and computer games.  Utilizing Extreme Sports will hopefully engage the students’ creativity.


For this project students will be assigned into groups of 4 - 5 students to research Extreme Sports via the Internet, TV, Video and magazines and determine how slope and function f(x) enables athletes to safely and efficiently accomplish the tricks and moves involved to excel in their respective sports. Students will use the Internet and various media sources for research, build mock arenas, ramps or applicable slope related equipment via Geometer’s Sketchpad, determine the costs of entering into their sports including lessons, equipment, medical costs and travel and represent these costs in Microsoft Excel, and create a class presentation via PowerPoint sharing all their data. Final results will be integrated into a Microsoft Word and Excel document to be turned in following their presentations.


This project is broken in to four individual weeks that each build upon one another.  Students will receive a unit plan overview at the beginning of the project to help them understand the full scope of the project and the timelines, followed by individual handouts each week to help guide them through each step of the process.  Students need to have access to the computer lab for at least one 50-minute period per week for research and project development. 


Some resources that will be used to help students better understand the scope of this project and relate to how slope and function f(x) are integral in various aspects of life include video excerpts from ESPN’s X-Games, “Making of the X-Games”, guest speakers including an athlete, video game designer, and a extreme sport course designer.  The videos will be used to help spark their interest at the beginning of each section and get them thinking.  The guest speakers will end each section in order to help the students look forward and also consider possible career opportunities that require their math skills.


Technology is fully integrated into this project since it is a key part of the learning process and better understanding math and the goals of this project.  The number of computers required during this project is 1 computer per every 2 students with Internet access.  Students will be using the following applications in order to complete their projects: Microsoft Excel, Geometer's Sketchpad, Internet Explorer, Microsoft PowerPoint or Hyperstudio Stack, and Microsoft Word.


Project Overview


The following is a weekly project overview with the weekly goals and objectives and the desired student outcomes.  Please consult the attached calendar for detailed objectives and procedures broken out by day.


Week 1 – Introduction to Slope and Extreme Sports.  Students will utilize the Internet to research Extreme Sports and to determine their sport of choice.  Students will utilize to bookmark any websites they may use for their team projects.  Students will submit their chosen sport and their websites at the end of the week. 

Video: Excerpts from ESPN’s X-Games. 

Guest Speaker: X-Games Athlete.


Week 2 – Students will investigate what all is involved in their chosen sport.  What training is required, what equipment does the athlete need, how are courses and ramps designed, how the sport originated, and what costs are involved for an athlete to become competitive?  Students should also look at what other industries or professions support their chosen sport.  Students will create an Excel spreadsheet to show all costs and summarizing overall cost of entry to their sport. 

Video: X-Box or Nintendo extreme sport video games. (Computer based games can also be used).

Guest Speaker: Video Game Designer. 

Quiz: mid-point, distance and slope formula.


Week 3 – Getting dirty.  Students working as teams will use this week to actually get their hands on building a mock course with ramps or half-pipes, or the apparatus required in their chosen sports.  Students will use Lego’s, building blocks, Hot Wheel track or similar resources to build their apparatuses.  Once their apparatuses are built teams will measure the slope and determine any relations that exist in their structures and record this data using Geometer’s Sketchpad.   The students will then spend a day in the area around the school trying to locate structures that are similar to the apparatuses they have just created.  Students will submit their Geometer’s Sketchpad version of their apparatus. 

Video:  Making of ESPN’s X-Games. 

Guest Speaker: Extreme sports course designer. 


Week 4 – Multimedia.  Students have already seen videos, played video games, used the Internet, TV, and other resources, and along the way heard a lot of music.  But what is this music?  What types of music have they heard?  What do they like, not like?  How does the music enhance what they are watching?  Now how can they use music to help them in math?  Students will write a quick song in music style of their choice that will help them to remember their formula of choice.  Student presentations will occur at the end of the week with each student team giving a ten-minute oral presentation to the class utilizing PowerPoint slides or a HyperStudio stack.  Final project portfolios are due by end of week. 

Video: Music videos. 

Presentations: Student teams, ten minutes each. 

Quiz: Slope and Functions.


Student Outcomes:


Activity Checklist

Quiz - Mid-point formula, distance formula, and slope.

Quiz - Relations and Functions

Final Class Project - Includes PowerPoint presentation, and a report in Microsoft Windows documenting their findings. Students may also integrate photos, Excel spreadsheet, or graphing data.

Class Presentation - Groups will present their findings via PowerPoint to class.


Some possible URL’s to help get the student started:


Extreme Sports
Includes information, videos, news, and articles on snow, skate, surf, motocross, bike, and wake sports


Extreme TV
Extreme Sports Channel, a rapidly expanding global 24 hour television channel broadcasting in over 50 countries dedicated to action sports

All Extreme Sports is home to extreme sports multimedia action. Extreme Sports Movies, Pictures, News, Games, Free Stuff, Music, Links, Shopping and More!

ESPN X Games
ESPN hosts the X games twice a year. Once for Winter sports and once for Summer sports.

Results, calendars and everything you need to find your favorite Extreme sports.


Search Engine


CA- California K-12 Academic Content Standards

Subject : Mathematics

Grade : Grades Eight Through Twelve
The standards for grades eight through twelve are organized differently from those for kindergarten through grade seven. In this section strands are not used for organizational purposes as they are in the elementary grades because the mathematics studied in grades eight through twelve falls naturally under discipline headings: algebra, geometry, and so forth. Many schools teach this material in traditional courses; others teach it in an integrated fashion. To allow local educational agencies and teachers flexibility in teaching the material, the standards for grades eight through twelve do not mandate that a particular discipline be initiated and completed in a single grade. The core content of these subjects must be covered; students are expected to achieve the standards however these subjects are sequenced.

Standards are provided for algebra I, geometry, algebra II, trigonometry, mathematical analysis, linear algebra, probability and statistics, Advanced Placement probability and statistics, and calculus. Many of the more advanced subjects are not taught in every middle school or high school. Moreover, schools and districts have different ways of combining the subject matter in these various disciplines. For example, many schools combine some trigonometry, mathematical analysis, and linear algebra to form a pre-calculus course. Some districts prefer offering trigonometry content with algebra II.

Area : Algebra I
Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations.

Standard 7.0: Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

Standard 8.0: Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

Standard 16.0: Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.

Standard 17.0: Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.

Standard 18.0: Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.



Weekly Lesson Plans Objective and Procedure Calendar









Week 1

Objective: Introduce the slope formula and one of it’s applications.

Procedure: Show a short film on ESPN’s X-Games.  Discuss where slope fits into extreme sports.  Lecture on what is the slope formula and do sample problems.  Assign the homework for the week, and do some in-class problems.

Materials: VCR/TV, Video, Overhead, Algebra books.

Objective: Introduce “Slope, Functions and Extreme Games” group projects, and assign groups.

Procedure: Review homework and turn in.  Introduce project – Students will break into groups of 4-5 students to create a project on how slope works in a particular sport.  Student groups can choose any sport, though extreme sports have the most obvious examples of slope.  Provide students with a project handout that includes the objective, procedure, requirements, and a sample project.  Review handout and answer all questions.  Project will require student to research their sport via the Internet, media, TV or any other available means.  Students will be required to create a PowerPoint or HyperStudio presentation, a Word document summarizing the project, and a model of the use of slope and function in their chosen sports.

Materials: Project Handout, Group Assignment

Objective: Orientate students to Internet search engines.

Procedure: Walk students through “How to Search the Internet” handout, and have them do sample searches on either Google or AltaVista.  Students in groups will then begin to research extreme sports websites and determine which sport they will use for their projects.  Students will create bookmarks in for their projects.

Materials: “How to Search the Internet” Handout, 8 Lab Computers, 1 Instructional Computer with Projection, Internet Access

Objective:  Build a better understanding of slope.  Review midpoint, distance and slope formulas.  Did what they researched yesterday help them better understand how these formulas are used?

Procedure: Full class lecture on the formulas working sample problems from their textbooks.  Handout on slope and ramps that includes discussion topics for the class.  Review homework with in class examples.

Materials: Algebra books, slope and ramps handout.

Objective: Meet an athlete. 

Procedure: Guest Speaker: Extreme sport athlete.  Include Q&A

Materials: Extreme sports athlete, projection device for speaker if requested.

Week 2

Objective:  Introduce extreme sport video games and their relation to math.

Procedure:  Demonstration of a couple different extreme games video games on either X-Box, GameCube, or Playstation, followed by lecture on their impact on pop culture and relation to math.

Materials:  Video games and player.  Computer based games can also be used.

Objective:  Supply and Demand.  What is it and why is slope so important?

Procedure:  Lecture on supply and demand and it’s relation to slope.  What causes a positive slope? Negative slope?  Students will then break into small group discussions about how supply and demand affects the making of video games.  What do game developers have to consider when creating their games?  Groups will then share their findings with the class as a whole.

Materials: Supply and Demand handout.

Objective:  Assess the cost of entry into extreme sport being researched.

Procedure: In the computer lab, students will use the Internet to research what it costs to get started and become competitive in their respective sports.  This needs to include training, equipment, facility rental costs, coaches, travel, medical and such.  Students will then compile their findings in an Excel spreadsheet, summarizing approximate costs per year, number of years to become competitive, and overall total costs.

Materials: 1 Computer/2 Students, Internet Access, Microsoft Excel, Sample Excel Spreadsheet

Objective:  It’s not just math…  Students will begin to look at other academic areas to determine what other subjects are used in extreme sports.  Science, economics, advertising?

Procedure:  Students will brainstorm other subject areas that apply to extreme sports.  Then in small groups each team will be assigned a subject area to discuss how that particular subject plays into extreme sports.  Each group will then review their findings to the class.

Materials: Chalkboard or easel for brainstorming session.

Objective: Evaluate understanding of formulas.  How video game designers integrate slope and function into their jobs.

Procedure: Quiz: midpoint, distance and slope formula.

Materials: Quiz, video game designer, projection device for speaker if requested.

Week 3

Objective: Building apparatuses with slopes.

Procedure: Students will work in their project teams and build an apparatus related to their sport.  Students can use any materials available in the classroom including Legos, building blocks, Hot Wheels track, etc…

Students will then measure the heights and lengths of their apparatus and determine the slopes and record this data.  Students will use this data on Wednesday to create their apparatuses in Geometer’s Sketchpad.

Materials: Building supplies such as tape, paper, Lego’s, building blocks, Hot Wheels track, etc…  Rulers and protractors.

Objective: Sloping the hood.  Students will identify structures in the community that tie into slope and function.

Procedure:  Students will work with their project teams and explore the area around the school.  Their goal is to identify structures similar to the models they built in class on Monday.  Students will then measure these structures and record their data for use in Wednesday’s lab.

Materials: Tape measures and digital cameras if available.

Objective:  Recreate model apparatus from Mondays class in Geometer’s Sketchpad.

Procedure:  In the lab students will take measurements from the models they built in class on Monday, or from structures they identified in the neighborhood on Tuesday, and create a graphic model of their sports apparatus.  This graphic model will then be incorporated into their class presentation and project portfolio.  Rough sketches are due on Friday.

Materials:  Computer lab, Geometer’s sketchpad.

Objective:  Further awareness of careers involving mathematics in extreme sports.

Procedure:  Show the video “Making of ESPN’s X-Games” showing how the stages are built for the games.  Students will then discuss as a class their ideas and opinions.  Via discussion class will wrap up with a class brainstorming session of other jobs that may be related to what they learned via today’s discussion.

Materials:  VCR/TV, “Making of ESPN’s X-Games” video.

Objective:  Students will meet a course designer and have the opportunity to ask questions.

Procedure:  Guest speaker: Extreme sport course designer.  The designer will start out with a lecture and then open the class up for Q&A.

Materials: Extreme sport course designer, projection device for speaker if requested.

Week 4

Objective: Students will identify ways to utilize music in math.

Procedure:  In extreme sports music is used to set the tone of the event, highlight video games, and the broadcasting of the sport.  Via lecture and class discussion students will try to better understand the impact music has on the sport.  They will then brainstorm ways they can use music to better understand or learn mathematical formulas.  Students will finally break into small groups and write songs in the format of choice to help them memorize slope, distance or mid-point formula.

Materials:  Music videos featuring extreme sports.  y=mx+b song set to the tune “YMCA” by Village People.

Objective:  Test knowledge of functions.

Procedure: Give students a test covering slope, mid-point, and distance formula as well as functions and relations.

Materials: Test.

Objective:  Finalize Reports and Presentations.

Procedure: Students will spend the day in the lab or in the classroom finalizing their written reports and PowerPoint or Hyperstudio presentations.   Students may also choose to rehearse their presentations.

Materials:  Computer lab.

Objective: Students presenting will learn presentation skills while other students learn more about how slope and functions relate to their world

Procedure: Student groups will have 10 minutes to present their projects via a PowerPoint or HyperStudio presentation.  Students will submit their reports upon completing presentation.

Materials: Computer, Projector, Screen

Objective: Students presenting will learn presentation skills while other students learn more about how slope and functions relate to their world

Procedure: Student groups will have 10 minutes to present their projects via a PowerPoint or HyperStudio presentation.  Students will submit their reports upon completing presentation.

Materials: Computer, Projector, Screen



Notes, Suggested Modifications, Concerns


The project “Slope and Function: The Foundations of Extreme Sports” is a very comprehensive approach to integrating popular culture and technology into the classroom.  While the unit plan and timelines are complete and cover a broad array of materials and teaching resources it is meant mainly to be a guide and create ideas and possibilities.  In it’s entirety it is up to each individual instructor to understand their students current knowledge of applications, and ability of their students ability to master new content and adjust the project accordingly.  Any one week can be made into two weeks, or any of the four weekly plans can be used independent of one another, though the final weeks plan is a compilation of previous projects.  The main idea and goal of this project is to begin to enable students to understand how math fits into their everyday lives, and how so much can be taken for granted.  It will also hopefully make them aware of some career opportunities, cross-subject relations with math, and encourage them to continue to pursue math in their studies.


It is understood that not all students will relate to extreme sports at the same level or even show any interest in sports at all.  But there is a broad range of sports that fall into this category as well as some other activities that may relate.  If there is a group of students that aren’t really motivated by this activity due to a disinterest in sports, either pair them with some one else in the class that is highly involved in these types of sports to help motivate the team, or ask the group to brainstorm other ideas that they could tie into the same theme.  You never know what you may learn.


As stated up front this is a fully integrated technology lesson plan.  It is understood that various schools and classrooms have a varying degree of resources available and may not be able to integrate technology so deeply.  Any of the technology areas can use a variety of substitutes to accomplish the same goals.  If Internet access isn’t available contact a publish of an extreme sports magazine and ask them to donate past issues.  Call ESPN and request any videos they may have available.  Use the school library for books on sports or use of encyclopedias.  There are a variety of ways to modify this unit plan within any given constraints.


In schools where the technology is available this lesson plan also makes the assumption that students are already proficient in use of the Internet for research projects, and the use of the following applications: Microsoft Excel, PowerPoint and Word, HyperStudio Stack, Geometer’s Sketchpad, and either Internet Explore or Netscape Navigator.  If the students are not familiar with any of these applications this project can be modified to be a great instructional tool to introduce students to the use of these applications.  Plan on dedicating one 50-minute period to the instruction of each required application.


While not highlighted via the unit plan it is highly recommended that an activity checklist be created for the students.  The checklist should include all required student output, quizzes, and learning objectives with due dates and scoring percentages for each area.  This will help the students stay aware of what is required of them and by when.  It can also serve as a weekly status report for you as the teacher to make sure students are progressing in a timely matter.  This checklist should tie directly into the plan’s rubric.


And lastly, assign the project teams.  Make sure that in each group you have a student with strengths in at least one of each area so that each student can contribute to the total project and so that no student feels left out or team feels overwhelmed.  These teams will be working together for four weeks and need to be able to work efficiently and affectively for the duration of projects.  As the teacher you know your students best so I leave this comment at that.  If you have inclusion students in your classroom, make sure the team they are assigned to utilizes those students’ strengths while helping to develop some of their IEP goals.  Small group projects can be some of the best ways to help inclusion students progress via the support of their peers.


Good luck, enjoy and have fun with this project.  And make sure your students have fun, which is what this project is all about.


For additional information or changes to this unit plan please go to: