There are 100 NRICH Mathematical resources connected to Describing patterns and sequences, you may find related items under Patterns, Sequences and Structure.Broad Topics > Patterns, Sequences and Structure > Describing patterns and sequences
What patterns can you make with a set of dominoes?
How do you know if your set of dominoes is complete?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you find a way to identify times tables after they have been shifted up or down?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
An environment which simulates working with Cuisenaire rods.
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
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?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
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?
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?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
There are lots of ideas to explore in these sequences of ordered fractions.
What is the last digit of the number 1 / 5^903 ?
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
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?
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?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
Can you find examples of magic crosses? Can you find all the possibilities?
How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Which of these pocket money systems would you rather have?
This activity creates an opportunity to explore all kinds of number-related patterns.
Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
What's the greatest number of sides a polygon on a dotty grid could have?
Can you find the connections between linear and quadratic patterns?
Play around with the Fibonacci sequence and discover some surprising results!
Just because a problem is impossible doesn't mean it's difficult...
Surprising numerical patterns can be explained using algebra and diagrams...
Can you figure out how sequences of beach huts are generated?
Here are some more lower primary number pattern tasks for you to try.
These upper primary activities offer opportunities for children to recognise, extend and explain number patterns.
These lower primary activities offer opportunities for children to create, recognise and extend 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.
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.
It starts quite simple but great opportunities for number discoveries and patterns!