3) How many games would there be if there were six teams?
If there were six teams there will be five matches each and thirty games in total. The rule is to count in extra girds; such as if there was five girds count in an extra ten matches. The gird below simplifies this answer-
So you count in this extra girds on the right and you count the extra grids at the bottom and this is how you get you answer. It is very simple.
4)
5) Can you spot any patterns? If you can the write them down clearly?
In the chart above I found a pattern. The pattern is to add on the next even number to the number of games. This way you will get the correct answer.
Example- Teams two = games two = + four you just keep on
Teams three = games six = + six adding even
Teams six = games twelve = + eight numbers to the
Teams five = games twenty = + ten number of games.
6) Can you find a rule that could predict the number of games from the number of teams?
The way you can predict the answer is by guessing. The rule is to add on four if there are two teams to get the answer six for if there were three teams. You carry on like this. It does not matter how many teams you have you just keep on adding on the next even number. This was one of the ways of predicting.
Example-
7) By extending the table or using the rule you have found, predict the number of games that seven teams would have to play?
For this question I predict that seven teams would play six matches each and forty-two games in total. I know this answer is correct since I followed the rule (just add the next even number to the answer of six teams). The grid below explains it all-
Add this side with the right side and you will get twelve. Add twelve to the other gird of six teams and you get the answer is forty-two game in total.
8) If you have found a rule, check it is correct by comparing it with the values you already have in your table.
The rule I have found works hundred percent correctly.
Example-RULE-Add on an even number to the column with the number
of games each time to get the answer.
To check, if your answer is correct take away the answer you got and if you end up with the number you started with your answer is correct.
Example-Two teams = two games = two + f our (Works even
Three teams = games? Two + four = six games if you have
To Check-Three teams = six games = six – four eighty teams.)
Two teams = six games – four = two ----------------
9) In the first division of the football league there are twenty-two teams. Each club plays each other twice, (once at home And once away). How many matches will this involve?
If twenty-two teams played each other twice it will equal to forty-four games in total.
Example-twenty-two x two = forty-four
Each team plays twice.
10) The organisers of the European Football decide that they want to have a ‘Mega League’ involving the top eighty clubs in Europe and played over three years. How many matches would this involve?
If there were eighty teams and they played over three years time, there should be two hundred and forty games in total.
Example-eighty x three = two hundred and forty.
To Check-two hundred and forty / three = eighty.
11) The organisers wish to be able to calculate the number of matches for any number of teams. If the number of teams is ‘n’ find a formula in terms of ‘n’ for the number of games.
The formula for this question is simple, all it is, that you do the same as question ten, but instead of numbers you add letters. So if the organisers wish to organise any number of teams for any number of games, the formula would be- N x M = T
Total number of games.
Number of
Teams. Time period for
total amounts
of matches.
Example-Eighty x Four = three hundred and twenty.
N M T
This is the simplest rule to do this question.
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