It's easy to work out the areas of most squares that we meet, but what if they were tilted?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
A metal puzzle which led to some mathematical questions.
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.
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
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.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
Use an Excel spreadsheet to explore long multiplication.
Use an interactive Excel spreadsheet to investigate factors and multiples.
Use an interactive Excel spreadsheet to explore number in this exciting game!
Use Excel to investigate the effect of translations around a number grid.
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.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Use Excel to explore multiplication of fractions.
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.
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?
Match the cards of the same value.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
An animation that helps you understand the game of Nim.
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.
Can you explain the strategy for winning this game with any target?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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?
What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?
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?
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.
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
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. . . .
Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?
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 game for 1 person to play on screen. Practise your number bonds whilst improving your memory
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
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.
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
Can you find triangles on a 9-point circle? Can you work out their angles?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?