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.

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

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?

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?

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

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

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.

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?

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?

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

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?

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

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?

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

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. . . .

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...

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

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

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

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

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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.

Can you see how to build a harmonic triangle? Can you work out the next two rows?

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

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

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?

Explore the effect of reflecting in two parallel mirror lines.

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .

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

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

Use the differences to find the solution to this Sudoku.

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

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

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

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. . . .

Explore the effect of combining enlargements.

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

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

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

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?