Describing patterns and sequences

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Train spotters' paradise

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
problem
Magic letters

Age

11 to 14

Challenge level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
problem
Steps to the podium

Age

7 to 14

Challenge level

It starts quite simple but great opportunities for number discoveries and patterns!
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Polygonals

Age

7 to 11

Challenge level

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
problem
Summing consecutive numbers

Age

11 to 14

Challenge level

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?
problem
Poly plug pattern

Age

5 to 7

Challenge level

Create a pattern on the small grid. How could you extend your pattern on the larger grid?
problem
Attractive tablecloths

Age

14 to 16

Challenge level

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem
Odds, evens and more evens

Age

11 to 14

Challenge level

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
problem
Seven squares

Age

11 to 14

Challenge level

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
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What numbers can we make?

Age

11 to 14

Challenge level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?