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

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

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

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

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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?

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

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?

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?

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

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?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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...

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

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?

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

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

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

Can you beat the computer in the challenging strategy game?

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?

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

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?

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?

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

Can you find triangles on a 9-point circle? Can you work out their angles?

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.

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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. . . .

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.

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

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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

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

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