BMX Bicycles, Dirt Jumps, Movies and Mathematics

BMX Bicycles, Dirt Jumps, Movies and Mathematics

Bernie McCann(Santa Maria College)

Robyn Pierce(University of Ballarat)

Session Content

Extreme

Sports

Extreme

Sports &

Maths

Analysing

Still

Images

Analysing

Moving

Images

Classroom

Tested

BMX Lesson

Further

Engaging

Possibilities

BMX Extreme Sports Events

Dirt Jumping

Vert

Street

Flatland

BMX Stunt Bike Riding

The BMX riders perform tricks as they ride on or over different surfaces and obstacles

Gravity Games 2004

Cleveland Ohio USA

BMX Park Course

In the Dirt, Street and Vert Events, for each run, riders are scored out of 100 for ;

height

degree of difficulty of tricks

smoothness and balance

number of tricks how well the course is used

BMX Video of Dirt, Vert and Street Events

BMX Stunt Bike Riding Provides a Strong Context For

engaging students

analysing quadratic functions

modelling paths

discussing rate of change

applying arithmetic

Analysing Still and Moving Images

GridPic fits curves to still images VidShell for simple analysis of video images RITEMATHS Project Website

http://extranet.edfac.unimelb.edu.au/ DSME/RITEMATHS

Quadratic Functions

Path of any projectile, under influence of gravity may be modelled using a quadratic

GridPic Demonstration

Ryan Nyquist

(USA)

Haro Bikes

Steve McCann

(Australia)

Mongoose

Moving Images

Paths of moving objects can be traced using

programs such as VidShell:

1. Use a short video clip

2. Move frame by frame

3. Mark object in each frame

4. Transfer co-ordinates to spreadsheet or graphing calculator to model the flight

Year 10 BMX Lesson - Aims

1. Develop a mathematical model for the flight path of a BMX stunt-bike rider

2. Use the mathematical model to estimate the rider’s:

i. height given horizontal distance from start of jump

ii. horizontal distance from take-off point given his height

iii. maximum height attained

Lesson Content

Introduction

Demonstrate Vidshell

Use quadratic function to find horizontal and vertical positions of BMX rider

Estimate rider’s maximum jump height

Introduction Describe BMX extreme events and

scoring system

Introduce video analysis tools for investigating BMX rider flight paths, ramp shapes and ramp positions

Show BMX movie

Raise questions to start students thinking about how mathematics can be used to examine the flight path and more

Examples of Questions 1. If you were a BMX rider,

what information about the dirt jumps and rider’s flight path would help you in your training.

2. What does the rider aim to do over each jump?

3. What determines the rider’s maximum height?

Planet X Games (Sydney 2001)

4. How can we find the maximum height reached by the rider?

5. At what angle should the up ramp be placed to allow the rider to reach the maximum height?

Planet X Games (Sydney 2001)

Examples of Questions

Vidshell Demonstration

Doing quadratic regression on coordinates from another video gives

y= -0.20x2 +0.73x+0.40

In turning point form y= -0.20(x-1.82)2 +1.07

So maximum height is 2.95 m

(ie.1.07 + 1.88)

Calculate Rider’s Maximum Height

Rider’s Maximum Jump Height Worksheet In groups, students design a procedure for estimating

the maximum jump height

Use VidShell to collect flight path co-ordinates

Find regression line with graphics calculator

Compare graphs of flight path co-ordinates and regression line

Estimate maximum height

and more

What Worked Well in BMX Lesson? Students handled VidShell satisfactorily

Maths was at the right level for Yr 10 classes

Students were engaged and teachers liked the modelling activity

Assignment looked complicated but was not

Students understood the VidShell demonstration

What Didn’t Work & Recommendations Time consuming to set up at start of lesson

Connections over a wireless network link can be slow for movies

Teacher introduction must cover both BMX context and relevant mathematics

Students should have a lead-in lesson on modelling and regression

Use an easier opening question

Some found it difficult to overcome problems with VidShell

Consequences of positioning axes in different places should be discussed

What Didn’t Work & Recommendations

Ideas For Other Lessons

Estimate the heights reached by two riders. What factors may have contributed to the heights reached by the riders?

Show two different dirt jumps and describe the differences between the two up ramp shapes and the differences between the up and down ramp shapes. Estimate the maximum height that may be reached by a rider in each case.

Ideas For Other Lessons

One BMX rider thinks that the maximum height reached by a rider partly depends on the length of the up ramp. Do you agree with this statement? Explain why?

Modelling PathsCreate a bike path by;

graphing several functions at once

restricting the domain of each function

Exploring Rates of ChangeQuestions such as;

Where is the path steepest? How do you know?

When is the rider likely to be travelling fastest or slowest? How can you tell?

Engage Students at Different StagesPractising applied arithmetic; Judge BMX skills

riders usually given three runs best two averaged to arrive at final score

Develop own scoring system Judge riders in a number of different videos

Engage Students at Different StagesIn an integrated curriculum; Plan series of BMX dirt jumps in a local park

minimise impact on the park minimise impact nearby residential area consider maintenance costs cater for novice and advanced riders

At higher level;

examine tangent lines to curve made by rider’s pathway at takeoff point

discuss position, velocity and acceleration

consider applications of differential calculus

Engage Students at Different Stages

Conclusion

Real world contexts may be used in various ways to increase students’ engagement with mathematics

BMX riding appeals to students and can be analyzed using still and moving images

THANK YOUBernie McCann

andRobyn Pierce

http://extranet.edfac.unimelb.edu.au/DSME/RITEMATHS

RITEMATHS is a project of the University of Melbourne and the University of Ballarat with seven industry partners and funded by Australian Research

Council's Linkage Grant Scheme for 2004-6.