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?

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?

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.

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?

Can you make the birds from the egg tangram?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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?

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?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Use the tangram pieces to make our pictures, or to design some of your own!

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Can you fit the tangram pieces into the outline of Little Ming?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Here is a version of the game 'Happy Families' for you to make and play.

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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?

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?

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?

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 it up?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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.

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

Explore the triangles that can be made with seven sticks of the same length.

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Can you make five differently sized squares from the tangram pieces?

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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?

Make a cube out of straws and have a go at this practical challenge.

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?

Can you deduce the pattern that has been used to lay out these bottle tops?

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?

Exploring and predicting folding, cutting and punching holes and making spirals.

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?