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 a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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 birds from the egg tangram?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
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?
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.
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.
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?
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?
Can you create more models that follow these rules?
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?
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.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
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.
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?
Explore the triangles that can be made with seven sticks of the
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?
These practical challenges are all about making a 'tray' and covering it with paper.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
We have a box of cubes, triangular prisms, cones, cuboids,
cylinders and tetrahedrons. Which of the buildings would fall down
if we tried to make them?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
These pictures show squares split into halves. Can you find other ways?
Can you fit the tangram pieces into the outlines of the chairs?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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 this junk?
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 shape. How would you describe it?
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 brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
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 Little Ming playing the board game?
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 this telephone?
Can you fit the tangram pieces into the outline of the child walking home from school?