A fraction fanatical
Football matches are played almost every Saturday between mid-August and mid-May, and the results and associated league tables provide a rich source of statistical data for the junior school teacher looking to take advantage of pupils' own interest, and to use mathematics in a meaningful and relevant way. The suggested activities and questions can be adapted to suit pupils working from level 3 to 5.
Judging from the experience of my own school, with the on-going collection of magazines and the swapping of stickers, interest in the game of football has never been so high, both for boys and girls.
The football results and league tables are published in the Sunday, Monday, and midweek newspapers, and differ both in format, and in the amount of detail provided. For example, The Sunday Times and The Times provide some of the most comprehensive detail, even including goal differences and the number of goals scored.
However, sometimes it may be more desirable to have a simpler form of league table which can generally be found in the Monday and midweek papers.The example in Figure 1 is from the Guardian. These results are simpler to read and interpret, and there is also more information for the pupils to find out for themselves.
It is important to check that the results show both the full attendance figures, and the times when goals were scored. Figure 2 gives one example from the matches played on Saturday and Sunday March 1 and 2.
The main areas of the mathematics curriculum covered are mental calculation, paper and pencil, and calculator work in addition and subtraction; negative numbers; fractions; percentages; graphical representation; measurement to scale in cm and/or mm.
There are four league tables in England and Wales, and a different four in Scotland. Most interest is obviously focused on the Premiership league where the biggest clubs compete.
The following set of questions and activities are divided into three parts. They are based on the football results; the associated league tables; and the football clubs.
It will be obvious that many of the questions and activities are included as examples, and are transferable to any set of results, or division, or set of football teams.
Specific questions on the results in the Carling Premiership 1. How many games were played last Saturday?
2. How many were home wins; away wins; scoring draws; no-score draws?
3. What fraction (or percentage) of total games played were home wins; away wins; draws?(see Figure 3 and Figure 4) 4. How many goals were scored?
5. What was the difference between the number of goals scored at half-time and full-time?
6. After how many minutes was the first goal scored? Who scored it, and for which team ?
7. When was the last goal scored? Who scored it, and for which team?
8. How may goals had been scored after 60 minutes of football?
9. How many penalties were scored?
10. Express this as a fraction (or percentage) of the total number of goals scored.
11. Which player, or players, scored the most goals?
12. What was the total number of people that watched the games?
13. Where was the highest attendance?
14. Where was the lowest attendance?
15. Round the attendance figures up or down to the nearest thousand, five thousand, ten thousand.
16. What was the difference in attendance between the games played at Manchester Utd and Wimbledon etc?
* Make a graph of attendance for the Premiership (see Figure 5) Questions comparing all four divisions 1. Add up the total number of goals scored. Which division had the most number of goals scored; the fewest number of goals scored?
2. What was the total attendance for each division? Where was the highest? Where was the second highest? Where was the lowest?
3. Express the total attendance of the Premiership as a fraction (or percentage) of the total attendance of all four divisions 4. In which division was the first goal scored; the last goal scored?
* Make a graph of top attendance in each of the four divisions.
Questions on specific league tables eg, Carling Premiership For some of the question below, pupils will need league tables showing the results from both home and away.
1. Which team has won the most matches? Lost the most matches? Drawn the most matches?
2. How many points are Nottingham Forest behind Liverpool? Newcastle in front of Coventry?
3. How many games would Coventry have to win to catch up with Manchester United?
4. Which team has the best home record? The best away record?
5. Which team has the worst home record? The worst away record?
6. There are 40 games played in the Premiership each season. If a team was to win all its matches, how many points would it get? (3 points for a win, 1 for a draw).
7. What is the average numbers of goals scored, and goals conceded in the Premiership?
(Hint: divide totals by number of teams which is 20.) 8. Which team has the best goal difference? The worst goal difference?
* Make a graph of goal differences. (This involves working with negative numbers, see Figure 6.) Questions on teams involved in the Carling Premiership 1. How may London teams (or say, Midlands teams) are there?
2. What is the fraction (or percentage) of London teams?
3. Which team has the longest name? The shortest name?
4. How many teams are Utd? How many City etc?
5. Which is the most northerly team? The most westerly team?
6. Make a Venn diagram showing the sets of: a) London teams; teams that have a positive goal difference b) London teams; teams in the top half of the table; teams which have red shirts (see Figure 7) 7. How far do Chelsea have to travel to their away matches each season? This involves finding the towns and cities in the atlas, and calculating the distance between the chosen team and the rest of the teams in the division.
Pupils will need to know that Aston Villa is in Birmingham, and Everton in Liverpool. For London teams, you could suggest a standard distance of say, 30 kilometres round trip (see Figure 8).
Jon Swain is deputy head and maths co-ordinator at White Bridge junior school, Essex
TEAM PLACE VISITED DISTANCE ROUND TRIP IN CM/MM IN KMS
Chelsea Manchester 7cm 320 km 640 km
Coventry 3.5 cm 160 km 320 km
Newcastle 10 cm 450 km 900 km
Tottenham - 15 km 30 km
all other 19 teams
Total distance travelled in one season
DERBY (0) 3 CHELSEA (1) 2
Minto 51 (og) Minto 16
Asanovic 62 (pen) Leboeuf 54
Ward 90 18,039
Sent off: F Leboeuf (Chelsea) 61
Derby County: R Hoult, L Carsley, G Rowett, J Laursen, D Powell, I Stimac, R van der Laan, A Asanovic, C Dailly, A Ward, D Slurridge
Chelsea: F Grodas, F Leboeuf, S Clarke, A Myers, G Vialli (sub: R Gullit, 62 min, sub: M Nicholls, 79 min), M Hughes, D Wise, R Di Matteo, S Minto, F Sinclair, P Hughes (sub J Morris, 76 min)
Booked: Minto, Di Matteo. Referee: A Wilkie
THE FRACTION AND PERCENTAGE OF HOME WINS, AWAY WINS AND DRAWS IN THE PREMIERSHIP, MARCH 1 & 2
Blackburn v Sunderland Home win
Derby v Chelsea Home win
Everton v Arsenal Away win
Leeds v West Ham Home win
Man United v Coventry Home win
Newcastle v Southampton Away win
Sheffield Wed v Middlesbro Home win
Tottenham v Nottm Forrest Away win
Wimbledon v Leicester Away win
Aston Villa v Liverpool Home win
Fraction Percentage of total of total results results
6 Home wins
6/10 60 % 0 Draws 0/10 0 %
4 Away wins 4/10 40 %
They don't always work out so nicely. Pupils may need to round the percentage figures up or down to make sure figures come to 100%
P W D L F A Pts
Man Utd 28 16 9 3 56 31 57
Liverpool 28 15 8 5 46 21 53
Arsenal 29 14 9 6 47 26 51
Newcastle 27 14 6 7 51 31 48
Aston Villa 28 13 7 8 35 26 46
Wimbledon 27 12 8 7 39 32 44
Chelsea 26 11 9 6 41 37 42
Sheffield Wed 27 10 12 5 34 32 42
Leeds 28 10 6 12 23 31 36
Leicester 26 9 6 11 32 38 33
Everton 27 8 8 11 34 40 32
Derby 28 7 11 10 30 38 32
Tottenham 27 9 5 13 3O 38 32
Blackburn 26 7 10 9 27 25 31
Sunderland 27 7 8 12 23 34 29
Coventry 29 6 11 12 26 39 29
Nottm Forest 27 6 9 12 24 40 27
West Ham 27 6 7 14 24 37 25
Southampton 26 6 6 14 35 44 24
Middlesbrough 26 5 7 14 31 48 19