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.
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Find out what a "fault-free" rectangle is and try to make some of
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 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?
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
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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....?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
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.
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Can you fit the tangram pieces into the outline of Granma T?
Choose a symbol to put into the number sentence.
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!
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
A card pairing game involving knowledge of simple ratio.
Can you complete this jigsaw of the multiplication square?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you fit the tangram pieces into the outline of this telephone?
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?
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 make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
Use the blue spot to help you move the yellow spot from one star to
the other. How are the trails of the blue and yellow spots related?