Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
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?
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?
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?
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?
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?
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?
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
In how many ways can you fit all three pieces together to make shapes with line symmetry?
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 find ways of joining cubes together so that 28 faces are visible?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Can you work out what kind of rotation produced this pattern of pegs in our pegboard?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Try this interactive strategy game for 2
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
How many different triangles can you make on a circular pegboard that has nine pegs?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you picture where this letter "F" will be on the grid if you flip it in these different ways?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Can you fit the tangram pieces into the outline of this telephone?
Exploring and predicting folding, cutting and punching holes and making spirals.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you fit the tangram pieces into the outline of Little Ming?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Make a cube out of straws and have a go at this practical challenge.
Can you fit the tangram pieces into the outline of Granma T?
Can you cut up a square in the way shown and make the pieces into a triangle?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Can you make a 3x3 cube with these shapes made from small cubes?
Can you fit the tangram pieces into the outline of Mai Ling?