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.

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

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.

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

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?

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

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

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

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

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?

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.

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

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

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

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 Excel to create triangular arrays.

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

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

Learn how to use composite bar charts in Excel.

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.

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 ?

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?

How much peel does an apple have?

This investigation uses Excel to optimise a characteristic of interest.

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

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

Use an Excel spreadsheet to explore long multiplication.

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. . . .

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

An Excel spreadsheet with an investigation.

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 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.

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

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?

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

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

Use Excel to explore multiplication of fractions.

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.

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. . . .

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

Use Excel to practise adding and subtracting fractions.

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

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

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