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

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

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

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

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

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

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

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

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

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?

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?

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

Can you find the connections between linear and quadratic patterns?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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

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?

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?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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

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

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.

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

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...

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?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

Which of these pocket money systems would you rather have?

This article for primary teachers outlines how we can encourage children to create, identify, extend and explain number patterns and why being able to do so is useful.

These upper primary activities offer opportunities for children to recognise, extend and explain number patterns.

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

An environment which simulates working with Cuisenaire rods.

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?

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

Here are some ideas to try in the classroom for using counters to investigate number patterns.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

How many different sets of numbers with at least four members can you find in the numbers in this box?