Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

How many different symmetrical shapes can you make by shading triangles or squares?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

There are lots of different methods to find out what the shapes are worth - how many can you find?

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

The clues for this Sudoku are the product of the numbers in adjacent squares.

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

Explore the effect of reflecting in two parallel mirror lines.

Can you describe this route to infinity? Where will the arrows take you next?