You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Can you make the birds from the egg tangram?
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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
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.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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 fit the tangram pieces into the outline of Little Ming?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
Here is a version of the game 'Happy Families' for you to make and
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Explore the triangles that can be made with seven sticks of the
Can you make five differently sized squares from the tangram
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?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you put these shapes in order of size? Start with the smallest.
Can you deduce the pattern that has been used to lay out these
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
These practical challenges are all about making a 'tray' and covering it with paper.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Make a cube out of straws and have a go at this practical
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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?
Have you ever noticed the patterns in car wheel trims? These
questions will make you look at car wheels in a different way!
Exploring and predicting folding, cutting and punching holes and
We can cut a small triangle off the corner of a square and then fit
the two pieces together. Can you work out how these shapes are made
from the two pieces?
Ideas for practical ways of representing data such as Venn and
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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?
Can you fit the tangram pieces into the outline of this junk?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?