Click on the calendar and a 'T' will appear.

Add together the numbers in the left and right cells of the top of the T.

Add together the two numbers in the base of the T.

Find the difference between your two answer and make a note of it.

Move the T to another position on the calendar and repeat the instructions above.

Do it a few more times, what do you notice?

If you do this activity using a different month what results would you get? Investigate.

If you had multiplied instead of added what results would you get? Investigate.

If you had used a different shape instead of a T what results would you get? Investigate.

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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.