A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Can you explain the strategy for winning this game with any target?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

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.

Can you complete this jigsaw of the multiplication square?

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Here is a chance to play a version of the classic Countdown Game.

A game in which players take it in turns to choose a number. Can you block your opponent?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Use the interactivities to complete these Venn diagrams.

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

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

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?