Here is a chance to play a version of the classic Countdown Game.
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you explain the strategy for winning this game with any target?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use the interactivities to complete these Venn diagrams.
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!
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?
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.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Can you complete this jigsaw of the multiplication square?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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.
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
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?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Choose a symbol to put into the number sentence.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
A generic circular pegboard resource.
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?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
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 tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
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 find all the different ways of lining up these Cuisenaire rods?
An animation that helps you understand the game of Nim.
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
A simulation of target archery practice
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
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?