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?
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 triangles can you make on the 3 by 3 pegboard?
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?
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 dice stairs using the rules stated? How do you know you have all the possible stairs?
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.
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?
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 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
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
How many models can you find which obey these rules?
These practical challenges are all about making a 'tray' and covering it with paper.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Make a cube out of straws and have a go at this practical
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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 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 make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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.
Explore the triangles that can be made with seven sticks of the
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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 fit the tangram pieces into the outline of this junk?
In this activity focusing on capacity, you will need a collection of different jars and bottles.
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you see which tile is the odd one out in this design? Using the
basic tile, can you make a repeating pattern to decorate our wall?
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 lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
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?
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 these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this telephone?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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 outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?