Or search by topic
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?
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?
Can you find a way to identify times tables after they have been shifted up or down?
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?
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
There are nasty versions of this dice game but we'll start with the nice ones...
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
What's the largest volume of box you can make from a square of paper?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
Can you work out which spinners were used to generate the frequency charts?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
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?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Can you find the values at the vertices when you know the values on the edges?
Can you work out what step size to take to ensure you visit all the dots on the circle?
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?
Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
If you move the tiles around, can you make squares with different coloured edges?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
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?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
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.
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Which set of numbers that add to 100 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?
There are lots of different methods to find out what the shapes are worth - how many can you find?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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".
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
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?
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?
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.