Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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

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

Can you figure out how sequences of beach huts are generated?

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

Play around with the Fibonacci sequence and discover some surprising results!

How many moves does it take to swap over some red and blue frogs? Do you have a method?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

Surprising numerical patterns can be explained using algebra and diagrams...

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?

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

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?

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

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

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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

In this article for teachers, Bernard Bagnall describes how to find digital roots and suggests that they can be worth exploring when confronted by a sequence of numbers.

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Can you find examples of magic crosses? Can you find all the possibilities?

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?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Can you find the connections between linear and quadratic patterns?

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

An environment which simulates working with Cuisenaire rods.

Just because a problem is impossible doesn't mean it's difficult...

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

Can you find a way to identify times tables after they have been shifted up or down?

What's the greatest number of sides a polygon on a dotty grid could have?

There are lots of ideas to explore in these sequences of ordered fractions.

Which of these pocket money systems would you rather have?