Explore the relationships between different paper sizes.

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

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?

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

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

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?

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

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

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

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?

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

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

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

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

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

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

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

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?

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

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?

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.

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

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

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

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

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?

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

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

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?

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

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".

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?

Which countries have the most naturally athletic populations?

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

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

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?

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

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

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?

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

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

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

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?