Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

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

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

You'll need to know your number properties to win a game of Statement Snap...

Where should you start, if you want to finish back where you started?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

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

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?

There are nasty versions of this dice game but we'll start with the nice ones...

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

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

Play around with sets of five numbers and see what you can discover about different types of average...

If you move the tiles around, can you make squares with different coloured edges?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

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

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

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

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

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

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 country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

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

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

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

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Which set of numbers that add to 10 have the largest product?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Can you find any two-digit numbers that satisfy all of these statements?

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

Use your skill and judgement to match the sets of random data.

Which countries have the most naturally athletic populations?

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

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?