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

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

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

With access to weather station data, what interesting questions can you investigate?

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?

If a sum invested gains 10% each year how long before it has doubled its value?

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?

How much peel does an apple have?

Can you make sense of information about trees in order to maximise the profits of a forestry company?

Choose four numbers and make two fractions. Use an Excel spreadsheet to investigate their properties. Can you generalise?

This investigation uses Excel to optimise a characteristic of interest.

Learn how to use composite bar charts in Excel.

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 ?

Learn how to use conditional formatting to create attractive interactive spreadsheets in Excel.

Use Excel to create some number pyramids. How are the numbers in the base line related to each other? Investigate using the spreadsheet.

This spreadsheet highlights multiples of numbers up to 20 in Pascal's triangle. What patterns can you see?

Learn how to use Excel to create triangular arrays.

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.

Learn how to use lookup functions to create exciting interactive Excel spreadsheets.

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

Learn how to use logic tests to create interactive resources using Excel.

Use an Excel spreadsheet to approximate a decimal using trial and improvement.

Investigate factors and multiples using this interactive Excel spreadsheet. Use the increment buttons for experimentation and feedback.

Learn how to make a simple table using Excel.

Learn how to use advanced pasting techniques to create interactive spreadsheets.

Use an Excel spreadsheet to investigate differences between four numbers. Which set of start numbers give the longest run before becoming 0 0 0 0?

When is 7^n + 3^n a multiple of 10? Use Excel to investigate, and try to explain what you find out.

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

If you take two integers and look at the difference between the square of each value, there is a nice relationship between the original numbers and that difference. Can you find the pattern using. . . .

A number of useful techniques that can extend your use of Excel.

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

I have an unlimited supply of planks, of lengths 7 and 9 units. Putting planks end to end, what total lengths can be achieved? Use Excel to investigate.

Use Excel to find sets of three numbers so that the sum of the squares of the first two is equal to the square of the third.

A heap of beads was shared out by a professional bead sharer. Use the information given to find out how many beads there were at the start.

Use Excel to investigate digit sums of multiples of three. Can you explain your findings?

Use Excel to investigate remainders and divisors. Was your result predictable?

Learn how to use increment buttons and scroll bars to create interactive Excel resources.

Learn how to use the Excel functions LCM and GCD.

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.

Use Excel to practise adding and subtracting fractions.

It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.

What day of the week were you born on? Do you know? Here's a way to find out.

Use Excel to explore multiplication of fractions.

In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.