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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 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.