GPS Technology and Computerised analysis of the collected data has found its way into many sports, especially Australian Rules Football.
GPS units are sewn into players Football jumpers, and the players tracked during a game. All of their movements around the ground are mathematically captured onto computer storage.
This data is mathematically processed by computers and then used as a standard part of post match discussions with Players.
Here is a short video which shows a post match GPS report for Hawks player Stephen Gilham.
Knowing some mathematics and computing could be useful, especially if you are considering a career path into professional football.
In today’s computerised world, an understanding of mathematical principles has become more important than ever in everyone’s daily life.
“Learn Maths Through Footy”
Image Source: Herald Sun Newspapers
The Melbourne newspaper the “Herald Sun” produces a very reasonably priced “Learn Maths Through Footy” PDF booklet each year during the Football season.This is an excellent publication and we highly recommend it.
Unfortunately, this year’s booklet finished selling around mid August. So if you missed out, then keep an eye out for the booklet next year.
The Herald Sun “LMTF” workbook includes a wide variety of activities, which vary from graphing to problem solving and geometry.
Each worksheet provides links to current football statistics to increase interest and engagement among students.
Here is a list of the “LMTF” 2011 booklet’s Worksheets.
1 A new angle 2 Accurate kicking 3 Club membership 4 Compare height & weight 5 Complex areas 6 Cost of lunch 7 Energy to burn 8 Evacuating the MCG – circles 9 Fitness 10 Football grounds & area 11 Football ladder spreadsheet 12 Goal-kicking percentages 13 Ladder logic 14 MCG facts & figures 15 Number lines 16 Player injuries 17 Player salaries 18 Predicting results 19 Problem solving 20 Problem solving with equations 21 Stem and leaf comparisons 22 Using calculators to compare 23 Using graphs to compare 24 What’s in a name – probability? 25 Who is the best player?
Worksheet 5 is on Player GPS, and covers Perimeter, Area, and Speed.
If you do not have the 2011 “LMTF” Workbook, then there are some Free Worksheets on topics other than GPS available on this site:
Note that in this diagram, the player starts in the middle cross shaped part of the diagram and does the top left hand path. He then runs back through the start to do the bottom right hand path, and ends up back at the middle start point.
If you are using this type of problem with students who do not know Pythagoras Theorem, then it will be necessary to calculate the two missing sides and supply these values to students.
Maths Questions which can follow on from the above diagram are as follows:
1. What was the total distance the player ran ?
2. What was the longest continuous straight line distance he ran during this passage of play ?
3. If the player’s average speed was 1.6 meters per second, How long did it take him to run through this passage of play diagram? (Give answer in both seconds and minutes).
4. Find the area of the ground enclosed by the path that he followed ?
5. What activities might the player have been doing along this path, eg. chasing an opponent, taking possession of the ball, kicking the ball, returning to his set position, and so on.
AFL GPS Detailed Report
“FitSense Australia” undertook a detailed study of Player GPS data for the AFL using data gathered during several recent football seasons.
This study was conducted by FitSense Australia as a funded project by the AFL Research Board.
Full details of the Fitsense report can be found at the Link below.
What follows is a summary of some key parts of the report.
The main mathematics involved is related to Poynomials, and so it needs to be mentioned here that Junior School students will not have studied these yet, as they are a Senior School maths topic.
All game files were analysed using a number of steady state and movement pattern variables:
Total distance (km) Average speed (km/hr) Exertion index Exertion index per minute Time spent in speed zones (min:sec) Number of surges over specified speeds Longest continuous time above specified speeds (seconds) Acceleration / deceleration profile
Exertion Index
The word “exertion” refers to the active use of strength, power, etc. in relation to exercise, energetic activity, and effort.
“Exertion Index” is a quantifiable level of physical load developed by FitSense Australia. This measure allows a relationship to be drawn between game load, fatigue, and the total load between players.
The exertion index used to assess GPS data in the Fitsense study is based on the sum of a weighted instantaneous speed, a weighted accumulated speed over 10 seconds, and a weighted accumulated speed over 60 seconds.
This ensures both short sharp efforts, and long sustained efforts are analysed equally.
The weighting is based on a Polynomial Relationship in which high speeds achieve a higher exertion value than lower speeds.
Exertion index is measured in arbitrary units.
The formula to determine exertion index is:
Exertion Index = (Sum of EI1 + Sum of EI10 + Sum of EI60) / 300
Where:
EI1 = (v4 x 0.000009) – (v3 x 0.001) + (v2 x 0.0356) – (v x 0.0596) – 0.0172
EI10 = (V104 x -0.00003) – (V103 x 0.0004) + (V102 x 0.0477) – (V10 x 0.0476) + 0.1056
EI60 = (V604 x -0.00003) – (V603 x 0.0004) + (V602 x 0.0477) – (V60 x 0.0476) + 0.1056
v = speed in kilometres per hour captured at 1 Hz.
V10 = average speed in kilometres per hour of the last ten 1 Hz speed samples.
V60 = average speed in kilometres per hour of the last sixty 1 Hz speed samples.
“Exertion Index Per Minute” is a measure of game intensity and is determined by dividing exertion index by playing time.
“Efficiency” is a measure of the work requirements for game involvement and game impact. Measured by dividing exertion index by total number of possessions.
Results of the Fitsense GPS Report
Some key findings of the Fitsense GPS Report were as follows.
The game intensity estimated from GPS monitoring has increased by 17% in the period from 2005-2010.
The most successful teams completed less overall work. This pattern was evident when comparing top 4 to bottom 4 placed teams as well as all teams’ finishing position on the ladder.
This finding has important implications for recovery and injury rates as it indicates that performance level (and the underpinning factors of skill, tactics and coaching of both teams) can influence physical demands of the players.
Workloads were substantially lower in rounds 18-22 compared with other stages of the season (home and away games, and the final series). This contradicts the 2009 finding, however it is likely this varies year to year depending on the competition for finals positions towards the end of the season.
There was a 15% reduction in workload from quarter 1 to quarter 4.
Here at Passy World we have always thought that the bottom teams started “slacking off” during the final few games of the season, and we were correct!
It has been mathematically proven by Fitsense that average AFL player exertion drops during Rounds 18 to 22.
The average workload for these rounds was over 5% less than the season average.
This is shown quite clearly in the following “Box and Whisker Plot” from the “Fitsense” Report.
Image Source: http://sport.fitsense.com.au
The Fitsense report also found that the teams that are going well have less player exertion than the low performing teams.
This difference is attributed to the best teams having superior coaching, tactics, and skills; which forces the weaker teams to “give chase” far more.
GPS is an amazing technology that has a variety of data collection and tracking capabilities.
Many company vehicles are fitted with GPS, and head office can see where a vehicle is at any time.
Companies also get alerts automatically sent from malfunctioning machinery that are offsite at customer’s premises, with GPS location of the machine provided on a map.
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AFL Football is a great competitive game played in Australia during the winter months.
Statistics is the branch of mathematics involved with the practice and science of collecting and analyzing numerical data in large quantities.
When applied to Sports, Statistics is used to examine, “How Many”, “What Type”, “How Long”, “How Effective”, and so on.
Statistics have become a key part of AFL Football over the last few years, and it is hard to find any commentary of a game that is not filled with Statistics.
Here is a great two minute video about how Statistics are compiled in real time by “Champion Data” during an AFL football match.
Here is another excellent video about the mathematics involved with being a sports statistician.
If you enjoyed those videos, you might like to do some Sports Statistics of your own, for someone you know playing a sport, or even for yourself. Later in this post we will look at a very low cost computer devices that record and track Player Stats for a variety of different sports.
Learn Maths Through Footy
Image Source: Herald Sun Newspapers
The Melbourne newspaper the “Herald Sun” produces a very reasonably priced “Learn Maths Through Footy” PDF booklet each year during the Football season.It is an excellent publication, and we highly recommend it.
Unfortunately, this year’s booklet finished selling around mid August. So if you missed out, then keep an eye out for the booklet next year.
The Herald Sun “LMTF” workbook includes a wide variety of activities, which vary from graphing to problem solving and geometry.
Each worksheet provides links to current football statistics to increase interest and engagement among students.
Here is a list of the worksheets in the “LMTF” 2011 booklet.
1 A new angle 2 Accurate kicking 3 Club membership 4 Compare height & weight 5 Complex areas 6 Cost of lunch 7 Energy to burn 8 Evacuating the MCG – circles 9 Fitness 10 Football grounds & area 11 Football ladder spreadsheet 12 Goal-kicking percentages 13 Ladder logic 14 MCG facts & figures 15 Number lines 16 Player injuries 17 Player salaries 18 Predicting results 19 Problem solving 20 Problem solving with equations 21 Stem and leaf comparisons 22 Using calculators to compare 23 Using graphs to compare 24 What’s in a name – probability? 25 Who is the best player?
A typical Statistics type exercise provided in the Herald Sun 2011 Workbook asks a series of question about AFL Club Memberships, such as:
Is it true that Juniors and Concession ticket holders make up the majority of club memberships ?
If you do not have a Workbook, then there are some Free Worksheets available at the link below:
One excellent activity covered in the LMTF booklet involves mathematically examining recent AFL Club membership numbers. There is a table of Membership Numbers, broken down by Adults, Concessions, and Juniors, at the following link.
Which Clubs have had increases in Memberships between 2009 and 2010 ?
Which Club had the biggest increase in membership numbers ?
Which Club had the biggest Percentage increase in membership ?
Which Club had the largest decrease in membership numbers ?
Which Club had the largest percentage decrease in membership numbers ?
If the Club with largest number values, is different to the club with the largest Percentage value, then this could lead to some discussion.
Questions could also be setup about Adult versus Junior members and so on.
This is just one of many Statistics exercises that could be done using Football Statistics.
Other AFL Statistics activities could be working out Who is the best player, Which team is best at offence, and which one at defence, Which team wins most at which Ground, From what range are most goals kicked from, and so on.
AFL Statistics Websites
If you want plenty of AFL Statistics, including the ability to compare current players side by side, then this site is a must:
“SportZstats” is a simple to use system that can be used to compile results for any team sport including soccer, basketball, netball, cricket, rugby union, rugby league, American football, hockey and AFL Football.
You can get access to online stats diaries at sportzstats.com, where you can record all your stats, and graph your progress.
Here is a quick thirty second video by Peter Daicos about Sportzstats.
That’s it for Footy Statistics. We will also be doing some other posts on AFL Football in the next few days, since it is Footy Finals month here in Melbourne Australia.
Great AFL Finals Moments Video
If you don’t think AFL is one of the most exciting fast paced games in the world, then watch this video.
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There are a lot of Mathematics instructional videos on the Internet. Many of these are simply of a teacher at a whiteboard that has been captured on video.
However, others use narration with PowerPoint slides, or are music filmclips and are very well done indeed.
Many math videos can be found simply by searching YouTube, but it often takes a very long time to sort through the results and find the best ones.
In this lesson we take a look at the best sets of videos that we have found available online for free.
In our comprehensive list of video sites below, we have tried to find groups of videos that are all of very good quality.
Here at Passy World we strongly believe in accommodating modern students’ technological learning styles by showing them math videos in class.
Using our Passy World list of Video resources will save you lots of time. It will also ensure that only quality materials are obtained.
Most of these videos can be embedded by teachers on Learning Management Systems, as well as on other websites and blogs that students can then use.
They can also be displayed full screen for presenting during math lessons.
Brightstorm
This is an awesome site that has over 2000 math videos. These videos cover Algebra, Geometry, Algebra 2, Trigonometry, Pre-calculus and Calculus.
The videos are mostly of a real teacher giving a stand up lesson at a white board. They are professionally made and have full screen and embed code. They are not downloadable.
Following the intro lesson video, there are usually several more videos showing example problems that run for about two minutes each. These flow on automatically while on the Brightstorm site.
Brightstorm no longer appears to supply embed code, and so the videos need to be watched on their site. However, they do have quite a few of their videos up on YouTube.
Here is a sample video from Brightstorm:
This is an excellent math videos site and can be accessed at the link below.
This site has a full range of videos ranging from Year 7 to University level. All the usual topics are covered: Algebra, Geometry, Trigonometry, Statistics, and Calculus.
In addition, they also have several TI calculator video tutorials.
Each video is preceded by a 30 second advertisement, which is a little annoying, but this obvioulsy helps fund the site. The videos can be watched fullscreen, and are downloadable as FLV Flash Files. So on a computer we would need to download the free “VLC Media Player” to view our downloads.
The videos do not have any embed code, so we cannot easily put them onto our own web page.
From the videos we watched, they are narrated computer whiteboard or slideshow lessons, or actual movies, and are very professionally made.
Click the link below to see a sample video from the site:
It is a very interesting site, in that the videos are made by Teachers and then uploaded to the site, and get rated by other teachers and students.
This is a diagram from their site on how it works.
We really like this site at Passy World, especially since we have the option of downloading the videos, and having them on our Laptop ready to show to a class.
Khan Academy has hundreds of free videos. The videos average about 10 minutes in length.
All videos are “chalk and talk” lessons on a computer screen, using multiple colored pens on a black background, with voice narration the whole way through.
Topics covered include Arithmetic, Pre-Algebra, Algebra, Geometry, Precalculus, Probability, Calculus, Linear Algebra, and Differential Equations.
There are also worksheets of problems for most of the videos.
These are great videos for students to watch individually, but due to their average length I am not sure that they would work as well for classroom presentation.
The videos are especially good for senior high school and first year University math.
This is an awesome site of free videos made by Mr McKeague and his community college students in the USA.
The videos are short 2 to 5 minute videos that cover specific topics in Number, Geometry, Algebra, Exponents, Trigonometry, and Calculus.
The videos can be viewed full screen, but there is not any embed code supplied to put them onto your own site. They are also not downloadable and thus cannot be stored on your own computer.
This is an excellent non-profit site ran by Robert Ahdoot in the USA.
He likes to dress up and add comedy to his videos, and is doing a great job at this resulting in millions of online views.
As of September 2011, his site contains around 60 lesson videos. These videos cover the American Alegebra 1 and 2 as well as Geometry. In Australia they would be suitable for Middle School to Year 11 level.
There are five minute preview videos on his YouTube channel, but on his “Yay Math” site there are complete lessons also hosted on YouTube, which does supply embed code.
Here is a typical “Yay Math” video.
The link to the full set of Yay Math Videos is as follows:
Richard is a great presenter who uses brilliant interactive graphics in his videos.
His presentations are passionate, well thought out, and well delivered.
His YouTube channel has nearly 300 videos on topics from all areas of mathematics that range in level from Junior High School right through to Senior levels.
Here is a typical video from Richard’s channel.
Richard’s channel can be accessed at the following link:
Derek Owens has a YouTube channel with great Calculus and Physics videos. He has hundreds of videos on his channel, and it is well worth checking out for Senior Maths videos.
Derek has embedding disabled on his videos, but if you want to see a really good Calculus video, then click the link below.
This is an amazing site, and has small snippets from famous films where Mathematics is mentioned. The videos can be made full screen size, and perhaps there might be some there that would be suitable for an ice-breaker to a lesson. The other nice thing as that we can click on the MP4 link and save the video to our own computer.
If watching the Flash SWF version live, it needs pausing to let it load in and then play it. So it would probably be best to save the .MP4 version and show it to a class.
The only thing is that many of the popular movie clips do have some bad language in them, and so may be only suitable for senior students.
For example the “Hangover” clip would be great for Probability, and the Die Hard 3 clip on “7 wives to St Ives” would be a great reminder to students to read exam questions very thoroughly. But both of these have coarse language in them that may offend some viewers.
The link to all of the Math in Movies clips is as follows:
This is a great site for “Maths in the Real World” videos.
Unfortunately the site does not have a Search facility, and it is a matter of using the left hand sidebar links, to manually go through videos and find ones that are good enrichment material for various maths topics.
For example the following video on precious stone cutting is great to use with classes while studying Geometry.
The following video links playing drums to mathematics. This is a great video to show students when doing Fractions.
Eg. This particular video is great to use when discussing fractions – equivalent fractions, reducing, multiplying, dividing, finding common denominators, etc.
This site has lots of free Math videos. Sometimes it appears as if the Videos are only for sale on DVD, but if we list the “individual Program Descriptions” we can watch a very small version of the video for free. HOWEVER, we can only do this if we are located in the USA or Canada.
There is also no full screen or embed code available. So outside of North America, it would appear that the DVD of videos has to be purchased. However there could be problems if the videos are only NTSC and not available in PAL format.
There are some very interesting videos to watch as part of the “Mathematics Illuminated” series.
But they can only be watched small size without any full screen option available.
This means that we would probably put a link to them on a website, for students to watch them individually, rather than present them to a whole classroom.
They also have a great little set of problem solving animated Problem Solving videos. In these videos, word problems are given, key information highlighted and extracted, and then working out to reach the answer shown.
The guy who presents these is a little bit quirky at times, but they are well filmed with him working on the board, and also have embed code available. They are hosted from YouTube and have full screen available, as well as a download button, which is actually a really cool link into KeepVid.
This site covers Fractions, Decimals, as well as Algebra, Trigonometry and Calculus to senior math level. However, the site does not seem to have any Geometry videos.
This site does have a “Math” channel, but the quality of the videos is extremely variable. The videos can be made full size, and there is embed code, but it doesn’t seem to work in WordPress. The videos can however be downloaded to your own device, and this could be quite a useful feature.
This is a YouTube channel with a lot of videos going up to Calculus level.
Presentation is fairly plain, with a filmed lesson at the whiteboard. However he does have several hundred videos on his channel and covers a lot of math areas.
This site has lots of links to videos about all types of K to 12 School subjects.
A lot of the math videos simply link to Khan Academy, or various YouTube videos. However, their website is a fantastic index of videos, and there are science videos that can be found and used for showing maths in the real world.
Here is a sample video we found using the Neo K12 website.
The BBC has an awesome collection of Maths in the Real World type video clips as part of its “Learning Zone” broadband facility.
Simply search for Mathematics and the clips will come up.
Unfortunately due to UK TV licensing, these clips are not available to anyone located outside the UK.
However, if you pay for a VPN connection to watch the BBC from overseas through a third party provider, it is possible to watch the clips. However it is fairly expensive to run one of these services, and we found here in Australia that the speed was not always totally reliable.
Although not all of the videos we have listed are engaging enough to use for classroom presentation, they are great to embed onto websites and learning management systems.
Students can then be directed to watch the videos at home, especially if they have missed lessons, or fallen behind, and need to catch up on work.
Maths 4 Real
Just before we finish up, we will mention the brilliant “Maths 4 Real” DVD videos.
THESE ARE NOT FREE, but we have regularly used them in our Year 7 to 10 classes and they are superb.
As well as covering Math topics, they also give excellent real world applications as well.
If you are in the UK, they can be purchased online here:
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Image Source: http://bridge.tm.mbs.ac.uk
In this post we have used Adobe Fireworks to make mini posters of a number of Measurement Formulas for length, area, and volume. We have not included all shapes, and we have not covered Surface Area. We plan to do these in a future post. The information presented here is invaluable to students revising Measurement. PerimeterPerimeter is the total length around the OUTSIDE of any shape. It is given the special name of “Circumference” when dealing with circular shapes. Image Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsArea The following formulas give the Areas of common shapes such as Squares, Rectangles, Parallelograms, Triangles, Trapeziums, and Circles.Image Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsArea of a Rhombus A Rhombus is a Parallelogram that has all four sides equal. We can work out its area using Base x Height, but we can also work out the same area by multiplying the two internal diagonals together, and dividing by 2. Image Source: http://www.thefreemathtutor.comAnswers to Rhombus Questions: Q1. 418 sq cm, 41600 sq mm, 0.0006 sq m. Q2. 91 sq cm Q3. (1000×2) / 10 = 200mm. Q4. (120×2) / 30 = 8m. Area of a KiteA Kite is a similar shape to a Rhombus, and its area is obtained by multiplying together its diagonals. Image Source: http://www.coolmath.comSummary of Area FormulasHere is a set of formulas that are used in mathematics for finding areas. Image Source: http://www.math-videos-online.comImage Source: http://www.grc.nasa.govThe following SlideShare Powerpoint contains all of the above formulas as well as Measurement Conversions and Volumes of Prisms. Click the bottom right hand corner full screen button to view as a presentation.
[slideshare id=9114306&doc=measurementformulasppt-110902171100-phpapp01]
Related ItemsPerimeterCircumferenceArea of Simple ShapesArea of a CircleInteresting CirclesComposite AreasTall Buildings and Huge Water DamMy Virtual HomeIf you enjoyed this post, why not get a free subscription to our website.You can then receive notifications of new pages directly to your email address. Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button. To find out exactly how free subscription works, click the following link: How Free Subscription WorksIf you are a subscriber to Passy’s World of Mathematics, and would like to receive a free PowerPoint of the Measurement Formulas in this lesson, valued at $4.99, but 100% free to you as a Subscriber, then email us at the following address:Please state in your email that you wish to obtain the free subscriber copy of the “Measurement Formulas” PowerPoint.This PowerPoint is the same as the one shown in the Slideshare Presentation in this post, but has sharper quality images on it. It can be printed out as slides in color on A4 paper, and then enlarged on a color photocopier to A3 and laminated to create mini wall posters for a Math Classroom.Enjoy, Passy]]>
Image Source: http://bridge.tm.mbs.ac.uk
In this post we have used Adobe Fireworks to make mini posters of a number of Measurement Formulas for length, area, and volume. We have not included all shapes, and we have not covered Surface Area. We plan to do these in a future post. The information presented here is invaluable to students revising Measurement. PerimeterPerimeter is the total length around the OUTSIDE of any shape. It is given the special name of “Circumference” when dealing with circular shapes. Image Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsArea The following formulas give the Areas of common shapes such as Squares, Rectangles, Parallelograms, Triangles, Trapeziums, and Circles.Image Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsImage Source: Passy’s World of MathematicsArea of a Rhombus A Rhombus is a Parallelogram that has all four sides equal. We can work out its area using Base x Height, but we can also work out the same area by multiplying the two internal diagonals together, and dividing by 2. Image Source: http://www.thefreemathtutor.comAnswers to Rhombus Questions: Q1. 418 sq cm, 41600 sq mm, 0.0006 sq m. Q2. 91 sq cm Q3. (1000×2) / 10 = 200mm. Q4. (120×2) / 30 = 8m. Area of a KiteA Kite is a similar shape to a Rhombus, and its area is obtained by multiplying together its diagonals. Image Source: http://www.coolmath.comSummary of Area FormulasHere is a set of formulas that are used in mathematics for finding areas. Image Source: http://www.math-videos-online.comImage Source: http://www.grc.nasa.govThe following SlideShare Powerpoint contains all of the above formulas as well as Measurement Conversions and Volumes of Prisms. Click the bottom right hand corner full screen button to view as a presentation.
[slideshare id=9114306&doc=measurementformulasppt-110902171100-phpapp01]
Related ItemsPerimeterCircumferenceArea of Simple ShapesArea of a CircleInteresting CirclesComposite AreasTall Buildings and Huge Water DamMy Virtual HomeIf you enjoyed this post, why not get a free subscription to our website.You can then receive notifications of new pages directly to your email address. Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button. To find out exactly how free subscription works, click the following link: How Free Subscription WorksIf you are a subscriber to Passy’s World of Mathematics, and would like to receive a free PowerPoint of the Measurement Formulas in this lesson, valued at $4.99, but 100% free to you as a Subscriber, then email us at the following address:Please state in your email that you wish to obtain the free subscriber copy of the “Measurement Formulas” PowerPoint.This PowerPoint is the same as the one shown in the Slideshare Presentation in this post, but has sharper quality images on it. It can be printed out as slides in color on A4 paper, and then enlarged on a color photocopier to A3 and laminated to create mini wall posters for a Math Classroom.Enjoy, Passy]]>
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