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.
Use an interactive Excel spreadsheet to investigate factors and multiples.
A metal puzzle which led to some mathematical questions.
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
An Excel spreadsheet with an investigation.
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?
Use an Excel spreadsheet to explore long multiplication.
Use Excel to practise adding and subtracting fractions.
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
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.
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. . . .
A group of interactive resources to support work on percentages Key Stage 4.
Use Excel to investigate the effect of translations around a number grid.
Use an interactive Excel spreadsheet to explore number in this exciting game!
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Use Excel to explore multiplication of fractions.
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?
Prove Pythagoras' Theorem using enlargements and scale factors.
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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?
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.
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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.
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.
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.
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?
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. . . .
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. . . .
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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.
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?
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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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. . . .
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
To avoid losing think of another very well known game where the patterns of play are similar.
A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
Work out how to light up the single light. What's the rule?
A tool for generating random integers.
A collection of our favourite pictorial problems, one for each day of Advent.
Here is a chance to play a fractions version of the classic Countdown Game.