Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
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?
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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.
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 many triangles can you make on the 3 by 3 pegboard?
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?
How many models can you find which obey these rules?
These practical challenges are all about making a 'tray' and covering it with paper.
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
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?
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 dice stairs using the rules stated? How do you know you have all the possible stairs?
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.
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
This activity investigates how you might make squares and pentominoes from Polydron.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
This practical activity involves measuring length/distance.
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
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?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
In this article for teachers, Bernard uses some problems to suggest
that once a numerical pattern has been spotted from a practical
starting point, going back to the practical can help explain. . . .
It's hard to make a snowflake with six perfect lines of symmetry,
but it's fun to try!
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
Have you noticed that triangles are used in manmade structures?
Perhaps there is a good reason for this? 'Test a Triangle' and see
how rigid triangles are.
Make a mobius band and investigate its properties.
Surprise your friends with this magic square trick.
Galileo, a famous inventor who lived about 400 years ago, came up
with an idea similar to this for making a time measuring
instrument. Can you turn your pendulum into an accurate minute
Follow these instructions to make a five-pointed snowflake from a
square of paper.
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
How can you make a curve from straight strips of paper?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
What shapes can you make by folding an A4 piece of paper?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
Can you create more models that follow these rules?
Can you make the birds from the egg tangram?
Here's a simple way to make a Tangram without any measuring or