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.

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

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 Excel to investigate the effect of translations around a number grid.

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?

Use Excel to practise adding and subtracting fractions.

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

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

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

An Excel spreadsheet with an investigation.

Use an interactive Excel spreadsheet to explore number in this exciting game!

Use an interactive Excel spreadsheet to investigate factors and multiples.

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?

Use an Excel spreadsheet to explore long multiplication.

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Use Excel to explore multiplication of fractions.

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?

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

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

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?

A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?

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 ?.

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.

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

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.

Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?

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.

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?

This investigation uses Excel to optimise a characteristic of interest.

Learn how to use composite bar charts in Excel.

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?

How much peel does an apple have?

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

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 make a simple table using Excel.

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?

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.

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.

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

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.

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