Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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 find all the different ways of lining up these Cuisenaire rods?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
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?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Use the clues to colour each square.
How many different rhythms can you make by putting two drums on the wheel?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
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....?
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 work out how to balance this equaliser? You can put more than one weight on a hook.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
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.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Sort the houses in my street into different groups. Can you do it in any other ways?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Investigate the different sounds you can make by putting the owls and donkeys on the wheel.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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. . . .
A variant on the game Alquerque
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.
Using angular.js to bind inputs to outputs
Complete the squares - but be warned some are trickier than they look!
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?