A challenging activity focusing on finding all possible ways of stacking rods.

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

This challenge extends the Plants investigation so now four or more children are involved.

Can you find ways of joining cubes together so that 28 faces are visible?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

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 these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

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.

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

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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

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?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

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

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

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?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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. . . .

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 shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

This article for teachers suggests ideas for activities built around 10 and 2010.

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

How many models can you find which obey these rules?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

It starts quite simple but great opportunities for number discoveries and patterns!

A follow-up activity to Tiles in the Garden.

Which way of flipping over and/or turning this grid will give you the highest total? You'll need to imagine where the numbers will go in this tricky task!

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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

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

An investigation that gives you the opportunity to make and justify predictions.

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