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

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?

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

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

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

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?

Investigate what happens when you add house numbers along a street in different ways.

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?

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

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?

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

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

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

"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?

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

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

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

This activity creates an opportunity to explore all kinds of number-related patterns.

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.

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

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

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.

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

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

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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

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

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

Investigate these hexagons drawn from different sized equilateral triangles.

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

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?

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?

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

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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

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

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

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.

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When did July 1st fall on a Monday again?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.