Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
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?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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 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?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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.
What is the best way to shunt these carriages so that each train can continue its journey?
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 triangles can you make on a circular pegboard that has nine pegs?
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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 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?
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?
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 ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of these rabbits?
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 this plaque design?
Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Here's a simple way to make a Tangram without any measuring or ruling lines.
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Mai Ling?
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?
Can you cut up a square in the way shown and make the pieces into a triangle?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of this sports car?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of this telephone?
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 the rocket?
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 this goat and giraffe?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of Little Ming?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?