Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Investigate what happens when you add house numbers along a street in different ways.
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?
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.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
If the answer's 2010, what could the question be?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
How many different sets of numbers with at least four members can you find in the numbers in this box?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
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.
Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.
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?
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?
An activity making various patterns with 2 x 1 rectangular tiles.
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
Bernard Bagnall describes how to get more out of some favourite NRICH investigations.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Investigate the different ways you could split up these rooms so that you have double the number.
Here are many ideas for you to investigate - all linked with the number 2000.
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
This problem is intended to get children to look really hard at something they will see many times in the next few months.
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?
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?