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?

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

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. . . .

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?

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?

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

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

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

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?

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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?

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....?

An environment which simulates working with Cuisenaire rods.

Can you complete this jigsaw of the multiplication square?

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

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

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

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

Use the interactivities to complete these Venn diagrams.

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

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

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.

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!

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

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

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?

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.

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

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

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

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.

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?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outline of the child walking home from school?

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?

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

Can you fit the tangram pieces into the outlines of these clocks?

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.

Can you fit the tangram pieces into the outline of Little Fung at the table?

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

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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

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?

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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 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?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?