Football Scores

If you know the final score of a football match, what might the half time score have been?

For example:

Somewhere City 5 - 3 Fiction FC

Write down all of the possible scores at half time.

Is there a quick way to figure out how many possibilities there are?

Investigate

Football Scores Trophy Challenge

You can earn a Transum Trophy for the work you do for this investigation. If you can complete the table below then a virtual trophy will be awarded to you.

How many different half-time scores could there have been if the final score was 3 - 3?
How many different half-time scores could there have been if the final score was 3 - 5?
How many different half-time scores could there have been if the final score was 4 - 3?
How many different half-time scores could there have been if the final score was 6 - 9?
How many different half-time scores could there have been if the final score was 9 - 11?
How many different half-time scores could there have been if the final score was 7 - 13?
How many different half-time scores could there have been if the final score was 9 - 15?
How many different half-time scores could there have been if the final score was 17 - 15?
How many different half-time scores could there have been if the final score was 19 - 14?
When he found out the final score of the United vs City game he calculated that there could have been 20 different half-time scores. If United scored 3 goals how many did City score?

Try some other activities that apply systematic listing strategies.

Investigations Home

A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is closed. Investigations can always be extended by varying the initial instructions or asking the question 'what if...?'. Sometimes students point out that the instructions are ambiguous and can be interpreted in different ways. This is fine and the students are encouraged to explain how they interpreted the instructions in their report.

Some students may benefit from a writing frame when producing the reports of their investigations. Teachers may suggest sections or headings such as Introduction, Interpretation, Research, Working and Conclusion or something similar.