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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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 triangles can you make on the 3 by 3 pegboard?
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 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.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 many models can you find which obey these rules?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
It's hard to make a snowflake with six perfect lines of symmetry,
but it's fun to try!
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.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Follow these instructions to make a five-pointed snowflake from a
square of paper.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
This activity investigates how you might make squares and pentominoes from Polydron.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Can you make the birds from the egg tangram?
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.
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?
Here is a version of the game 'Happy Families' for you to make and
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you create more models that follow these rules?
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?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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?
Can you fit the tangram pieces into the outline of Granma T?
Here's a simple way to make a Tangram without any measuring or
This practical activity involves measuring length/distance.
Ideas for practical ways of representing data such as Venn and
Can you fit the tangram pieces into the outline of the rocket?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Exploring and predicting folding, cutting and punching holes and
Make a cube out of straws and have a go at this practical
How do you know if your set of dominoes is complete?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.