Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
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
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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?
Work out the fractions to match the cards with the same amount of
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. . . .
An environment which simulates working with Cuisenaire rods.
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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 article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
Here is a chance to play a version of the classic Countdown Game.
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.
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 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.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Work out how to light up the single light. What's the rule?
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?
A generic circular pegboard resource.
A card pairing game involving knowledge of simple ratio.
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. . . .
An interactive activity for one to experiment with a tricky tessellation
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 complete this jigsaw of the multiplication square?
Using angular.js to bind inputs to outputs
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Exchange the positions of the two sets of counters in the least possible number of moves
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Train game for an adult and child. Who will be the first to make the train?
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.
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?
Can you find all the 4-ball shuffles?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Find out what a "fault-free" rectangle is and try to make some of
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
A train building game for 2 players.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?