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. . . .

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

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

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.

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...

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

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?

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

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

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.

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

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?

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

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?

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

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

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

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

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?

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?

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

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?

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

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

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

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.

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?

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

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?

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

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. . . .

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

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

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

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

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

Explore the effect of combining enlargements.

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

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

What is the same and what is different about these circle questions? What connections can you make?

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

Explore the effect of reflecting in two parallel mirror lines.

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?

Use the differences to find the solution to this Sudoku.

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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?

Start with two numbers. This is the start of a sequence. The next number is the average of the last two numbers. Continue the sequence. What will happen if you carry on for ever?

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".