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

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.

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points for mathematical investigations or comments about the investigations we have presented here?

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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.