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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...

Summing Consecutive Numbers

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

Paving Paths

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

Seven Squares

Age 11 to 14
Challenge Level


How did Phoebe group the matchsticks that she drew?
How did Alice and Luke group their matchsticks?


For the follow-up activities, draw them out for yourself and notice how YOUR drawings develop.
Always begin with simple cases and try to PREDICT what will happen.

Look for patterns.
How can you describe the lines? Horizontal? Vertical?
Try to understand why the patterns develop in the ways that they do.