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

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

Which countries have the most naturally athletic populations?

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

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?

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?

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

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

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

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

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

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

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

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

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?

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

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

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

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.

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

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?

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

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?

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

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

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

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

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

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

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?

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

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

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

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

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

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

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

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

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

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?

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?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

What's the largest volume of box you can make from a square of paper?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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