Explore the relationships between different paper sizes.

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

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

There are lots of different methods to find out what the shapes are worth - how many can you find?

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

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

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?

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

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?

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

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

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

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

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?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

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

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

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

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...

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?

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

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

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

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

Which countries have the most naturally athletic populations?

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

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

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

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

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".

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

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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

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?

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?

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

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

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

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

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?

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?

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

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

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

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

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