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

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

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

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

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

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

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

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

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

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?

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

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

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?

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?

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

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

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

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?

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?

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?

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...

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

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

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

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

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

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

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?

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?

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

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

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

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

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

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

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?

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

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

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?

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...

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?

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

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?