When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

What is the largest cuboid you can wrap in an A3 sheet of paper?

All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .

This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

An activity making various patterns with 2 x 1 rectangular tiles.

What do these two triangles have in common? How are they related?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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 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?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

Here are many ideas for you to investigate - all linked with the number 2000.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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.

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Investigate the different ways you could split up these rooms so that you have double the number.

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?

Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

How many models can you find which obey these rules?

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

Why does the tower look a different size in each of these pictures?

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Formulate and investigate a simple mathematical model for the design of a table mat.

In how many ways can you stack these rods, following the rules?

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

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

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

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?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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?

Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.