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Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Pick's Theorem

Age 11 to 14 Challenge Level:

* How many different figures can be described as $(4, 0)$?

* What do you notice about $(4,0)$ figures?

* Choose another particular value for $(p,i)$ and explore different shapes.

* Have you tried drawing shapes with the same area?

* What do you notice about those figures whose areas are the same?

* What ways are there of increasing the area by $1$ unit?

* Draw more figures; tabulate the information about their perimeter points ($p$), interior points ($i$) and their areas ($A$).