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?

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

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?

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?

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 reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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.

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

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. . . .

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

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

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?

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

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

Work out how to light up the single light. What's the rule?

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

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.

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

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

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

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.

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

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.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

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

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?

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.

Use Excel to explore multiplication of fractions.

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

Have you seen this way of doing multiplication ?

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.

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?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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.

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

A collection of our favourite pictorial problems, one for each day of Advent.

A metal puzzle which led to some mathematical questions.

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?

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

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.

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

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .