How many triangles can you make on the 3 by 3 pegboard?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
How many models can you find which obey these rules?
These practical challenges are all about making a 'tray' and covering it with paper.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Here is a version of the game 'Happy Families' for you to make and
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you make the birds from the egg tangram?
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Mai Ling?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Here's a simple way to make a Tangram without any measuring or
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Can you fit the tangram pieces into the outline of this plaque design?
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outlines of these people?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Can you fit the tangram pieces into the outline of these rabbits?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you create more models that follow these rules?
Can you fit the tangram pieces into the outline of Granma T?
This activity investigates how you might make squares and pentominoes from Polydron.