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?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you find all the different ways of lining up these Cuisenaire rods?
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....?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
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?
Can you find all the different triangles on these peg boards, and find their angles?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
An environment which simulates working with Cuisenaire rods.
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!
Here is a chance to play a version of the classic Countdown Game.
If you have only four weights, where could you place them in order to balance this equaliser?
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?
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?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
How many different triangles can you make on a circular pegboard that has nine pegs?
A generic circular pegboard resource.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
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.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Can you explain the strategy for winning this game with any target?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Can you fit the tangram pieces into the outline of Little Fung at the table?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you use the interactive to complete the tangrams in the shape of butterflies?
How good are you at estimating angles?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you complete this jigsaw of the multiplication square?
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?
Can you fit the tangram pieces into the outline of this telephone?