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?

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

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?

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 fit the tangram pieces into the outline of these rabbits?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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!

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?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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?

Can you fit the tangram pieces into the outline of Mai Ling?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you fit the tangram pieces into the outline of the telescope and microscope?

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?

Can you fit the tangram pieces into the outline of the rocket?

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?

Can you fit the tangram pieces into the outline of this plaque design?

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?

What is the best way to shunt these carriages so that each train can continue its journey?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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 Little Ming playing the board game?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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 fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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?

Exchange the positions of the two sets of counters in the least possible number of moves

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Granma T?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outlines of these clocks?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Can you fit the tangram pieces into the outline of these convex shapes?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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 fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outlines of the chairs?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Can you fit the tangram pieces into the outline of this junk?

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 outlines of Mai Ling and Chi Wing?

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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.

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?