Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
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?
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 find all the different triangles on these peg boards, and find their angles?
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?
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?
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
A train building game for 2 players.
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....?
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 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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
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!
A card pairing game involving knowledge of simple ratio.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Granma T?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
An environment which simulates working with Cuisenaire rods.
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of this junk?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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
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?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
How many different triangles can you make on a circular pegboard that has nine pegs?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?