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?

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.

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?

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

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?

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.

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

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

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. . . .

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 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?

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?

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. . . .

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.

How many winning lines can you make in a three-dimensional version of noughts and crosses?

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

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...

Is there an efficient way to work out how many factors a large number has?

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

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

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

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

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

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

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

If you move the tiles around, can you make squares with different coloured edges?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

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

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

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

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.

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

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

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

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

Explore the effect of combining enlargements.