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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.
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