10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
What is the best way to shunt these carriages so that each train can continue its journey?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
What happens when you try and fit the triomino pieces into these two grids?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
How will you go about finding all the jigsaw pieces that have one peg and one hole?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Can you cover the camel with these pieces?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Reasoning about the number of matches needed to build squares that share their sides.
What is the greatest number of squares you can make by overlapping three squares?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
Can you make a 3x3 cube with these shapes made from small cubes?
Make a cube out of straws and have a go at this practical challenge.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
Can you find ways of joining cubes together so that 28 faces are visible?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
How many different triangles can you make on a circular pegboard that has nine pegs?
Have a go at this 3D extension to the Pebbles problem.
Exploring and predicting folding, cutting and punching holes and making spirals.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Move just three of the circles so that the triangle faces in the opposite direction.
Can you cut up a square in the way shown and make the pieces into a triangle?
Make one big triangle so the numbers that touch on the small triangles add to 10.
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?