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
Analysing
Moving
Images
Extreme
Sports &
Maths
Classroom
Tested
BMX Lesson
Analysing
Still
Images
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
Steve McCann
(USA)
(Australia)
Haro Bikes
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
scoring system
extreme
events
and
 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)
Examples of Questions
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)
Vidshell Demonstration
Calculate Rider’s Maximum
Height
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)
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
What Didn’t Work & Recommendations
 Use an easier opening question
 Some found it difficult to overcome problems
with VidShell
 Consequences of positioning axes in different
places should be discussed
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 Paths
Create a bike path by;
 graphing several functions at once
 restricting the domain of each function
Exploring Rates of Change
Questions such as;
 Where is the path steepest?
know?
How do you
 When is the rider likely to be travelling fastest or
slowest? How can you tell?
Engage Students at Different Stages
Practising 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 Stages
In 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
Engage Students at Different Stages
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
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 YOU
Bernie McCann
and
Robyn 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.