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.
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?
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?
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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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....?
Can you find all the different ways of lining up these Cuisenaire
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find out what a "fault-free" rectangle is and try to make some of
An environment which simulates working with 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?
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Here is a chance to play a version of the classic Countdown Game.
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?
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?
Choose a symbol to put into the number sentence.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
A generic circular pegboard resource.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you complete this jigsaw of the multiplication square?
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?
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?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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!
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this telephone?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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 fit the tangram pieces into the outline of Little Fung at the table?