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?

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

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

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?

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

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

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

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?

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

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

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 logic tests to create interactive resources using Excel.

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

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

How much peel does an apple have?

This investigation uses Excel to optimise a characteristic of interest.

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

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 ?

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

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

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

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

Learn how to make a simple table using Excel.

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. . . .

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.

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.

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

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

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?

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.

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 the Excel functions LCM and GCD.

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

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

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

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?

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.

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?

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 ?.

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

Use Excel to explore multiplication of fractions.

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

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