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?

Can you explain the strategy for winning this game with any target?

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

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

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.

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 make a right-angled triangle on this peg-board by joining up three points round the edge?

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?

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?

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

Can you complete this jigsaw of the multiplication square?

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?

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 this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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

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

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

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

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!

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

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.

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

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

An interactive activity for one to experiment with a tricky tessellation

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.

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

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible 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.

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.

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

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?

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.

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

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?

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?

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

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?

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. . . .

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?

An environment which simulates working with Cuisenaire rods.

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

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