Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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 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?
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.
Here is a version of the game 'Happy Families' for you to make and
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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.
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
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?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
How many triangles can you make on the 3 by 3 pegboard?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
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
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
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?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
How many models can you find which obey these rules?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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 the chairs?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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 this goat and giraffe?
Can you fit the tangram pieces into the outline of this plaque design?
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 the telescope and microscope?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of the child walking home from school?
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 split each of the shapes below in half so that the two
parts are exactly the same?
These pictures show squares split into halves. Can you find other
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
We can cut a small triangle off the corner of a square and then fit
the two pieces together. Can you work out how these shapes are made
from the two pieces?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?