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

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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

Sort the houses in my street into different groups. Can you do it in any other ways?

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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 your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

This problem is intended to get children to look really hard at something they will see many times in the next few months.

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?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they 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!

Investigate what happens when you add house numbers along a street in different ways.

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

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

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?

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.

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at 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.

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.

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

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

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. . . .

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

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

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

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

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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

These pictures show squares split into halves. Can you find other ways?

Investigate the number of faces you can see when you arrange three cubes in different ways.

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?

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

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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?