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?

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

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?

Have you seen this way of doing multiplication ?

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?

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

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

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?

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

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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

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.

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

Can you fill in the mixed up numbers in this dilution calculation?

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

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

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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

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

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.

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.

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

Can you break down this conversion process into logical steps?

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 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?

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

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.

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.

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. . . .

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

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.

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

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

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

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.

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. . . .

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

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

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.

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.

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. . . .

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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. . . .

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.

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.

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?