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?
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.
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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.
This challenge extends the Plants investigation so now four or more children are involved.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
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 possibilities that could come up?
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 to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
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?
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
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!
An activity making various patterns with 2 x 1 rectangular tiles.
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
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?
Investigate the different ways you could split up these rooms so that you have double the number.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
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?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
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?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
How many models can you find which obey these rules?
Have a go at this 3D extension to the Pebbles problem.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
A challenging activity focusing on finding all possible ways of stacking rods.
In how many ways can you stack these rods, following the rules?
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?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
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?
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 investigation that gives you the opportunity to make and justify predictions.
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
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?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.