Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

If you have only four weights, where could you place them in order to balance this equaliser?

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Can you find all the different triangles on these peg boards, and find their angles?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

An interactive activity for one to experiment with a tricky tessellation

An environment which simulates working with Cuisenaire rods.

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

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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?

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?

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?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

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.

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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!

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. . . .

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you complete this jigsaw of the multiplication square?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Try out the lottery that is played in a far-away land. What is the chance of winning?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Work out the fractions to match the cards with the same amount of money.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?