Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
An activity making various patterns with 2 x 1 rectangular tiles.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Can you make the birds from the egg tangram?
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?
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.
How many triangles can you make on the 3 by 3 pegboard?
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?
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?
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?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
How many models can you find which obey these rules?
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
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
Here is a version of the game 'Happy Families' for you to make and
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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 outlines of the chairs?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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 Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Here's a simple way to make a Tangram without any measuring or
Can you create more models that follow these rules?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Use the tangram pieces to make our pictures, or to design some of
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?