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

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

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.

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

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

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

How did the the rotation robot make these patterns?

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

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

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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?

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

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

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

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Can you work out what step size to take to ensure you visit all the dots on the circle?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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

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

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

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

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

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

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

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

Can you work out which drink has the stronger flavour?

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

In each of these games, you will need a little bit of luck and your knowledge of place value to develop a winning strategy.

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

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

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?

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

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

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Are these games fair? How can you tell?

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

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

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

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.

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?

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

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

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

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

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

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