Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
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?
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.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
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.
If the answer's 2010, what could the question be?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
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?
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 all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
Investigate what happens when you add house numbers along a street in different ways.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
How many different sets of numbers with at least four members can you find in the numbers in this box?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
An investigation that gives you the opportunity to make and justify predictions.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
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?
How many tiles do we need to tile these patios?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
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?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
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?
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?
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?
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!
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?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
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.
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.
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
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?
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?
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.
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?
Why does the tower look a different size in each of these pictures?
In how many ways can you stack these rods, following the rules?