Maths and the Euro 2020 tournament
This year Euro 2020 is happening in 2021, a full year late because of the pandemic - remember this fact for pub quizzes in years to come!
With the twenty four of the best football teams in Europe battling it out to lift the trophy, put your maths skills to the test to see if you really understand how the competition works.
Kids aged 5 to 11 will enjoy finding out about the Euros, and you can tackle these little maths puzzles as you go along - just see how many you can do!
The Tournament - group stage
The first round of the European Championships is called the group stage. Here are all the teams in the group stage this year.
If there are six groups - how many teams are in each group?
For younger children, you can introduce the concept of dividing by printing and cutting out the flag of each team, and then physically divide them into groups. Older kids can figure out the calculation they need to do, and then try it in their heads or on paper.
24 teams in total divided by 6 groups: 24 ÷ 6 = 4, so there are four teams in each group.
In every group, each of the teams play each other once.
How many games does each team play?
Three - there are four teams in a group, but you can't play against yourself, so each team plays three other teams.
If a team wins a game, they get three points and their opponents get none. If there's a draw, each team gets one point.
What's the most points each team can get in the group stage?
9 (They play three matches each, and 3 points are awarded for a win: 3 x 3 = 9)
Next, we have the knockout stages. The top two teams in each group go through to the knockout rounds, and the four highest ranking teams in third place also make it through.
Can you work out how many teams will go through to the knockout round?
Two teams from each group 6 x 2 = 12,
plus the four highest third place teams: 12 + 4 = 16
In the knockout stages, the winner of each match goes through to the next round, and the loser is out.
Here's UEFA's planner showing all the competition stages.
This means that in each round from here on in, half of the teams playing go through to the next round. In numbers this looks as follows (look carefully for the pattern):
16 teams in the first knockout round, half will win and half will lose, leaving
8 teams in the quarter final (or third round), half of which will go through, meaning
4 teams in the semi final, leaving
2 teams to battle it out in the final!
How many matches does the winning team have to play altogether?
7 - (3 group stage matches, first knockout, quarter final, semi final then the final)
Here's a tricky one - can you work out how many games are played in the whole tournament? First you need to calculate how many games are played in the group stage. Be careful, as this one might catch you out!
We calculated previously that each team plays three games, and there are four teams in each group, so you might just do the calculation 3 x 4 = 12 But don't stop there - because each match involves two teams, we need to divide this by 2 to get the number of matches played: 12 ÷ 2 = 6. Then we multiply that by the number of groups: 6 × 6 = 36
Then you need to work out how many teams are played in the knockout stages.
There are 8 + 4 + 2 + 1 = 15 games in the knock-out stages. (You can also reason that each knock-out game gets rid of one team, and you start with 16, so you need 15 games to find a winner!)
Then you need to add the two totals together to get your answer!
36 + 15 = 51
There's a load more maths in the group tables, with goal differences and points to take into account, but we'll save that for another day!
Until then, we'll leave you with a final question - a really hard one! This one is a bit of fun, and will pose a challenge to the keenest of maths whizzes and football fans alike - but might give some hope if your team of choice is languishing with no wins!
How could a team get through the group stages to the knockout rounds with only one point?
Let's call our team C. To get one point, C must have lost two games (against teams A and B) and drawn one (against D). A and B have at least three points, so must finish higher than C (with one point) - so it's not possible for C to be in the top two. Could they qualify in third? Team D have at least one point (from drawing with C), but they could finish below C if they also lost to A and B, and ended up with a worse goal difference than C. In addition, at least two teams in other groups would have to finish third with one point and a worse goal difference. It's not likely, but it's possible!
We hope you enjoyed this trip through the maths of Euro 2020 - remember to keep finding the maths in the world around you!
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