Can you find all the different triangles on these peg boards, and
find their angles?
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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....?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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 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?
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 find all the different ways of lining up these Cuisenaire
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?
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?
Find out what a "fault-free" rectangle is and try to make some of
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?
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 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
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
A generic circular pegboard resource.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
How many different triangles can you make which consist of the
centre point and two of the points on the edge? Can you work out
each of their angles?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
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 this shape. How would you describe it?
A train building game for 2 players.
A simulation of target archery practice
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!
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?
Exchange the positions of the two sets of counters in the least possible number of moves
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Train game for an adult and child. Who will be the first to make the train?
Can you fit the tangram pieces into the outlines of the workmen?
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?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
If you have only four weights, where could you place them in order
to balance this equaliser?