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.

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.

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?

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

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

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

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 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.

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.

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

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

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

Can you complete this jigsaw of the multiplication square?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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

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....?

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

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

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

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

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

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

Explore displacement/time and velocity/time graphs with this mouse motion sensor.

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!

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

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

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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

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?

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?

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 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.

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. . . .

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

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

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.

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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?

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.

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. . . .

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

An interactive activity for one to experiment with a tricky tessellation

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

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.