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

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?

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

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?

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

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

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

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?

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

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

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

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

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

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?

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.

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

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

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

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

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?

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

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?

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

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

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

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?

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

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

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

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.

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

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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

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.

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

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

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

Can you find the connections between linear and quadratic patterns?

"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?

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?