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

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?

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

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

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?

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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.

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

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

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Discover a handy way to describe reorderings and solve our anagram in the process.

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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.

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. . . .

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?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

Have you seen this way of doing multiplication ?

Could games evolve by natural selection? Take part in this web experiment to find out!

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?

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

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.

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.

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. . . .

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

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

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.

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.

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

This resource contains interactive problems to support work on number sequences at Key Stage 4.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Square It game for an adult and child. Can you come up with a way of always winning this game?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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 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?

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

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

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.

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.

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...

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. . . .