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...

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.

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

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

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

Can you complete this jigsaw of the multiplication square?

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.

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.

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.

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

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?

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

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

An environment which simulates working with Cuisenaire rods.

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

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

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

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

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.

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

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

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?

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!

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

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?

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

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

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

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

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?

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.

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.

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. . . .

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

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

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

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

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

An interactive activity for one to experiment with a tricky tessellation

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

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?

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.

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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....?