Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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?
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.
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.
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
An interactive activity for one to experiment with a tricky tessellation
Using angular.js to bind inputs to outputs
Exchange the positions of the two sets of counters in the least possible number of moves
Train game for an adult and child. Who will be the first to make the train?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
A card pairing game involving knowledge of simple ratio.
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.
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
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Can you be the first to complete a row of three?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
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. . . .
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.
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?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
A generic circular pegboard resource.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Here is a chance to play a version of the classic Countdown Game.
A train building game for 2 players.
Find out what a "fault-free" rectangle is and try to make some of
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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. . . .
Ahmed has some wooden planks to use for three sides of a rabbit run
against the shed. What quadrilaterals would he be able to make with
the planks of different lengths?
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?
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...