Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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.

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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?

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

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

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

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

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Can you complete this jigsaw of the multiplication square?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

A game in which players take it in turns to choose a number. Can you block your opponent?

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?

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

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?

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?

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

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.

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

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.

An environment which simulates working with Cuisenaire rods.

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?

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Use the interactivity or play this dice game yourself. How could you make it fair?

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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

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?

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?

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?

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.

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...

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

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

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

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

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?