Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Can you find ways of joining cubes together so that 28 faces are visible?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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 shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Have a go at this 3D extension to the Pebbles problem.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Can you fit the tangram pieces into the outline of the child walking home from school?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Exploring and predicting folding, cutting and punching holes and making spirals.
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outlines of these people?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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?
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?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of Granma T?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Can you fit the tangram pieces into the outline of Little Ming?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Here's a simple way to make a Tangram without any measuring or ruling lines.