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

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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?

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?

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?

What happens when you try and fit the triomino pieces into these two grids?

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?

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

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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

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 make a 3x3 cube with these shapes made from small cubes?

Move just three of the circles so that the triangle faces in the opposite direction.

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 does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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?

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?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

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

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?

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?

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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?

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!

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?

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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?

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?

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 outlines of the candle and sundial?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Can you find ways of joining cubes together so that 28 faces are visible?

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?

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.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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

Here are shadows of some 3D shapes. What shapes could have made them?