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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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.
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 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?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Here is a version of the game 'Happy Families' for you to make and
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?
Can you make the birds from the egg tangram?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
These practical challenges are all about making a 'tray' and covering it with paper.
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
An activity making various patterns with 2 x 1 rectangular tiles.
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 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 fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you split each of the shapes below in half so that the two parts are exactly the same?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
Can you fit the tangram pieces into the outline of these rabbits?
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?
Make a chair and table out of interlocking cubes, making sure that
the chair fits under the table!
Can you put these shapes in order of size? Start with the smallest.
These pictures show squares split into halves. Can you find other ways?
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?
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this junk?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Here's a simple way to make a Tangram without any measuring or
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
Can you fit the tangram pieces into the outline of this telephone?
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 the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?