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?

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

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

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

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?

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

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

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?

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?

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

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

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?

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?

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

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?

Can you complete this jigsaw of the multiplication square?

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

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

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

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. . . .

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

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

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?

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

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

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.

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.

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?

An interactive activity for one to experiment with a tricky tessellation

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....?

Use the interactivities to complete these Venn diagrams.

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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

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

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

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