The Olympic Games provide an excellent context for measuring and presentational work. Jon Swain offers some practical ideas. Athletics will always provide opportunities for using and applying maths in the real world, particularly in respect of number, measurement, and handling data. Pupils can become engaged in collecting, recording, analysing, and present information and data in various forms; some from their own investigations; and some from secondary material such as World and Olympic records, which are easily available from the Guinness Book of Records and various athletics magazines.
This summer's Olympic Games in Atlanta should help to capture children's imaginations and stimulate further interest. Teachers could devise a mini triple jump; much of the work will come from the gathering and analysing of the statistics arising from these events. The ideas here are particularly suitable for pupils working at key stage 2, and the beginning of key stage 3.
A great deal of maths can be devised from investigations into finding heart beats and pulse rates which can be found on many points of the body (wrist, inside upper arm,neck, back of knee, heart, temple). However, if too many of the class find it difficult to locate and count their heart or pulse, they can measure their rates of breathing per minute.
A table of heart beats opens the possibility of many questions: What is the mean average; how many times would your heart beat during your lifetime if you lived to 75? How many beats has your heart made, approximately, in your lifetime so far? Does the rate of your heart beat change after running, and by how much? Why does it increase? Does it increase more if you sprint 50 metres, rather than walk or jog 50 metres? How long does the heart beat take to return to its usual rate after sprinting for, say 100 metres?
Pupils should be encouraged to ask their own questions. These may be based on class tables and graphs. For instance: who has the highest rate, the lowest rate in the class, and by how much? Do girls differ from boys? Further research can be conducted to find out how class rates differ from adult rates or different age rates within the school. Moreover, is there a link between the rate of heart beat and the best runners, either in terms of speed, say over 50 m, or stamina, say of 4 laps of the athletics track.
This work could then lead on to finding out how fit you are. You need: a stop watch, and a box 50cm high.
A Step up on to a box, or stool, and down again. Step up and down at a speed of 5 times in 10 seconds.
B Make sure you straighten your legs and stand up each time you step on and off the box. Carry on doing this for 4 minutes.
C Rest for one minute, and then get your partner to count your pulse beats for 30 seconds. Record the number in the third line of your table.
D Rest for a further 30 seconds. Your partner must then take your pulse again for 30 seconds and record the number.
E Repeat step D.
F Work out your fitness index For further investigations: do those with the high scores make the best runners in terms of speed and stamina? Or do the best runners have the greatest lung capacity?
Further factors for success Do the tallest people make the best runners and jumpers? Is leg length a factor? A simple table or graph can be made showing the relationship between leg length and height. Does the fastest runner in the class have the longest legs or the longest legs in proportion to hisher body? (See graph, figure 5) The children can work out what fraction their legs are of their total height. The fraction of Nilesh's legs to his height is 80130 or 813. Expressed as a decimal this is 0.62. The fraction of Jane's legs to her height is 86146 or 4373, which expressed as a decimal is 0.59. Thus Jane has longer legs, but Nilesh's legs are a greater proportion to his height.
It is also interesting to find out whether there is any correlation between the best throwers and the length of their arms.
Data gathered can also be expressed in Venn diagrams and Carroll diagrams: for example, the top ten long jumpers in the class against the top ten pupils with the longest legs; or the top 25 per cent of long jumpers against the topo 25 per cent of pupils with the longest legs.
Venn diagram (figure 3) Venn diagram (figure 4) Gender differences can be highlighted by Venn and Carroll diagrams for the fastest and slowest runners in the class.
Carroll diagram (see figure 8); Venn diagram (see figure 9) Similar work can come from other running, throwing and jumping events, where pupils can compare times and distances; find averages; and work out their own speeds.
Here are some more suggested correlations for running which can be expressed in the form of Venn diagrams: fastest (top ten, to 25 per cent) and those pupils with the longest legs; fastest with the lowest pulse rate; fastest with the best recovery rate; fastest with largest lung capacity; fastest with those who can complete most squat thrusts in a minute; fastest with those with the quickest reaction times.
World and Olympic records Statistics from secondary sources such as the Guinness Book of Records, and various athletics magazines, provide a wealth of material to study, and are particularly good for work on decimalsplace value, and rounding updown to the nearest tenth of a secondsecondminutetenth of a metremetre. Here are some suggestions from information found in the Guinness Book of Records: * compare times and distances for world records in track and field events between men and women. Show difference in timedistance on a graph * compare times and distances between world records and UK records for both men and women. Show difference in timedistance on a graph * what is the difference in time between the men's 100m and the men's 200m?
* compare differences between your own performance and various world records in the 100m; 400m; the long jump; triple jump etc (see figure 10) * round up or down world records to the nearest tenth of a second; second; minute (for track events) and to the nearest metre (for field events) * the men's world record for the high jump is 2.45m: how far is this above your head? Can you reach 2.45 with a spring jump?
* the women's world record long jump record is 7.52m; how many of your standing jumping would fit into this length?
You can work out someone's speed if you know the time it takes to cover a certain distance.
Speed = Distance Time The UK record time for the men's 100m is 9.87 set by Linford Christie in 1993. 100m = 10.13 9.87 so Linford ran at 10.13 metres by 3600 (seconds in an hour). 10.13 x 3600 = 36468 metres per hour. To know how many kilometres he would run in an hour, divide 36468 by 1000 (metres in a kilometre). 36468 V by 1000 = 36.4: so, Linford ran his 100m in 1993 at a speed of 36.4 kmhour. Following these procedures allows you to work out the speeds of other record holders in other events.
These are just a few of the endless possibilities of finding maths in athletics; there's only one half term of summer left, so I suggest you'd better get going.
Jon Swain is deputy head and maths co-ordinator at White Bridge Junior School in Essex