What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
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?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
There are lots of different methods to find out what the shapes are worth - how many can you find?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Can you draw a square in which the perimeter is numerically equal to the area?
An investigation that gives you the opportunity to make and justify predictions.
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!
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
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?
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.
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
This task follows on from Build it Up and takes the ideas into three dimensions!
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
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?
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.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Can you use this information to work out Charlie's house number?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
These practical challenges are all about making a 'tray' and covering it with paper.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?