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?
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?
This number has 903 digits. What is the sum of all 903 digits?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
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.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Look at the squares in this problem. What does the next square look
like? I draw a square with 81 little squares inside it. How long
and how wide is my square?
Investigate the numbers that come up on a die as you roll it in the
direction of north, south, east and west, without going over the
path it's already made.
Using only the red and white rods, how many different ways are there to make up the other colours of rod?
Investigate and explain the patterns that you see from recording
just the units digits of numbers in the times tables.
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?
Make an estimate of how many light fittings you can see. Was your
estimate a good one? How can you decide?
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 find any perfect numbers? Read this article to find out more...
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
Here are some ideas to try in the classroom for using counters to investigate number patterns.
How do you know if your set of dominoes is complete?
A case is found with a combination lock. There is one clue about the number needed to open the case. Can you find the number and open the case?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
What are the coordinates of this shape after it has been
transformed in the ways described? Compare these with the original
coordinates. What do you notice about the numbers?
Use the interactivity to sort these numbers into sets. Can you give
each set a name?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Libby Jared helped to set up NRICH and this is one of her favourite
problems. It's a problem suitable for a wide age range and best
This article for teachers describes the exchanges on an email talk list about ideas for an investigation which has the sum of the squares as its solution.