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?

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

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

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...

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

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

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

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

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

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.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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

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.

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?

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

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.

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

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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.

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?

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

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

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

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?

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

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?

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.

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.

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.

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

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

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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

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

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