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?

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.

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?

Have you seen this way of doing multiplication ?

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

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

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

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

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?

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

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 explain the strategy for winning this game with any target?

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

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

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. . . .

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. . . .

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.

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

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

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

Triangle 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?

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

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

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

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

To avoid losing think of another very well known game where the patterns of play are similar.

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.

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?

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

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

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?

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

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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?

Prove Pythagoras' Theorem using enlargements and scale factors.

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?

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.

There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

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...

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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