Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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

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

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 work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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,. . . .

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

An activity centred around observations of dots and how we visualise number arrangement patterns.

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 happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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.

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

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 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 each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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?

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?

Watch this animation. What do you see? Can you explain why this happens?

Have a look at these photos of different fruit. How many do you see? How did you count?

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

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?

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

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.

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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!

Which of these dice are right-handed and which are left-handed?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

How many different symmetrical shapes can you make by shading triangles or squares?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?