There are **82** NRICH Mathematical resources connected to **Describing patterns and sequences**, you may find related items under Patterns, Sequences and Structure.

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

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

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

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

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

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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?

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

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

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An environment which simulates working with Cuisenaire rods.

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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?

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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?

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

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

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

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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?

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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?

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

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

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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?

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

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

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

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

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

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

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Can you find the connections between linear and quadratic patterns?

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

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

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

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.

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

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

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

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

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

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

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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?

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This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?

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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?

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

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

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.

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Investigate these hexagons drawn from different sized equilateral triangles.