If you have only four weights, where could you place them in order to balance this equaliser?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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!
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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.
A collection of resources to support work on Factors and Multiples at Secondary level.
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
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. . . .
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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 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.
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.
Can you complete this jigsaw of the multiplication square?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Choose a symbol to put into the number sentence.
Work out how to light up the single light. What's the rule?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you explain the strategy for winning this game with any target?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Here is a chance to play a version of the classic Countdown Game.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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. . . .
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
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 interactive activity for one to experiment with a tricky tessellation
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
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?
A generic circular pegboard resource.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
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.