How many trains can you make which are the same length as Matt's,
using rods that are identical?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many different rhythms can you make by putting two drums on the
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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 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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
How many different triangles can you make on a circular pegboard
that has nine pegs?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal 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?
Use the clues to colour each square.
Find out what a "fault-free" rectangle is and try to make some of
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
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you find all the different ways of lining up these Cuisenaire
A train building game for 2 players.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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....?
Match the halves.
A generic circular pegboard resource.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Can you find all the different triangles on these peg boards, and
find their angles?
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Use the interactivity to find out how many quarter turns the man
must rotate through to look like each of the pictures.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Move just three of the circles so that the triangle faces in the
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
An interactive activity for one to experiment with a tricky tessellation
Complete the squares - but be warned some are trickier than they
Can you make a train the same length as Laura's but using three
differently coloured rods? Is there only one way of doing it?