Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
An activity making various patterns with 2 x 1 rectangular tiles.
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
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
These practical challenges are all about making a 'tray' and covering it with paper.
How many models can you find which obey these rules?
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?
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?
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.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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 many triangles can you make on the 3 by 3 pegboard?
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?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
This activity investigates how you might make squares and pentominoes from Polydron.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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 activity involves measuring length/distance.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Make a mobius band and investigate its properties.
Ideas for practical ways of representing data such as Venn and
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
How is it possible to predict the card?
Here is a version of the game 'Happy Families' for you to make and
Follow these instructions to make a three-piece and/or seven-piece
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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.
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?
Kaia is sure that her father has worn a particular tie twice a week
in at least five of the last ten weeks, but her father disagrees.
Who do you think is right?
Can you make the birds from the egg tangram?
Here's a simple way to make a Tangram without any measuring or
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. . . .
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
It's hard to make a snowflake with six perfect lines of symmetry,
but it's fun to try!
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Follow these instructions to make a five-pointed snowflake from a
square of paper.
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
Surprise your friends with this magic square trick.
Make a cube with three strips of paper. Colour three faces or use
the numbers 1 to 6 to make a die.
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.
Here are some ideas to try in the classroom for using counters to investigate number patterns.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular