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.

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?

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?

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

A square patio was tiled with square tiles all the same size. Some of the tiles were removed from the middle of the patio in order to make a square flower bed, but the number of the remaining tiles. . . .

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square. Three of the numbers that he found are a = 18530, b=65570, c=45986. Find the fourth number, x. You. . . .

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?

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

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

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

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

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 investigate the effect of translations around a number grid.

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

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.

A group of interactive resources to support work on percentages Key Stage 4.

Use an Excel spreadsheet to explore long multiplication.

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

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 ?.

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 ?

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

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

Use Excel to explore multiplication of fractions.

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?

An Excel spreadsheet with an investigation.

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

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

Learn how to use composite bar charts in Excel.

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

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?

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

How much peel does an apple have?

This investigation uses Excel to optimise a characteristic of interest.

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

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.

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

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

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.

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.