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 make a right-angled triangle on this peg-board by joining up three points round the edge?

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

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 explain the strategy for winning this game with any target?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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?

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

A game in which players take it in turns to choose a number. Can you block your opponent?

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

A collection of resources to support work on Factors and Multiples at Secondary level.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Here is a chance to play a version of the classic Countdown Game.

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

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

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?