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

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

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?

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

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

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?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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?

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!

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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?

Can you complete this jigsaw of the multiplication square?

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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

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

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?

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?

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

Work out how to light up the single light. What's the rule?

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

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

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

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

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

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

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...

Can you find all the different ways of lining up these Cuisenaire rods?

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

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?

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....?

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

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

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

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?

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 activity for one to experiment with a tricky tessellation

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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?