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

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Can you find the values at the vertices when you know the values on the edges?

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

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

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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?

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.

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 parallelogram.

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 rhombus.

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

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 arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

The Number Jumbler can always work out your chosen symbol. Can you work out how?

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Can you select the missing digit(s) to find the largest multiple?

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 use the clues to complete these 4 by 4 Mathematical Sudokus?

Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

Can you use the clues to complete these 6 by 6 Mathematical Sudokus?

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

How did the the rotation robot make these patterns?

Can you find the hidden factors which multiply together to produce each quadratic expression?

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Can you find a way to identify times tables after they have been shifted up or down?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Can you work out which drink has the stronger flavour?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

How well can you estimate 10 seconds? Investigate with our timing tool.

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

Can you work out which spinners were used to generate the frequency charts?

Are these games fair? How can you tell?

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

Use your knowledge of place value to try to win this game. How will you maximise your score?

Use these four dominoes to make a square that has the same number of dots on each side.

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