What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Can you explain the strategy for winning this game with any target?
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.
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?
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?
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 make a right-angled triangle on this peg-board by joining up three points round the edge?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle 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
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
A metal puzzle which led to some mathematical questions.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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?
Can you find all the 4-ball shuffles?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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. . . .
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal 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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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?
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.
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?
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.
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?
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.
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.
Match the cards of the same value.
Here is a chance to play a version of the classic Countdown Game.
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?
A group of interactive resources to support work on percentages Key Stage 4.
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?
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
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?
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 be the first to complete a row of three?
Here is a chance to play a fractions version of the classic Countdown Game.
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.
How good are you at estimating angles?
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.
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. . . .
Cellular is an animation that helps you make geometric sequences composed of square cells.
Practise your skills of proportional reasoning with this interactive haemocytometer.