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?

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

Can you explain the strategy for winning this game with any target?

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?

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

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

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

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

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?

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

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

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

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

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. . . .

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

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

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

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

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.

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

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?

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

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

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...

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.

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

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?

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 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.

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.

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.

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?

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

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

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 solitaire type environment for you to experiment with. Which targets can you reach?

Can you find triangles on a 9-point circle? Can you work out their angles?

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.

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

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 game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

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?

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