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. . . .
If a sum invested gains 10% each year how long before it has
doubled its value?
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.
However did we manage before calculators? Is there an efficient way
to do a square root if you have to do the work yourself?
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an Excel spreadsheet to explore long multiplication.
Use Excel to practise adding and subtracting fractions.
Use an interactive Excel spreadsheet to explore number in this
A group of interactive resources to support work on percentages Key
What day of the week were you born on? Do you know? Here's a way to
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
An Excel spreadsheet with an investigation.
Use Excel to investigate the effect of translations around a number
Use an interactive Excel spreadsheet to investigate factors and
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 Excel to explore multiplication of fractions.
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. 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?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
A ribbon is nailed down with a small amount of slack. What is the
largest cube that can pass under the ribbon ?
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?
It's like 'Peaches Today, Peaches Tomorrow' but interestingly
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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. . . .
Learn how to use composite bar charts in Excel.
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
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
This investigation uses Excel to optimise a characteristic of
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.
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?
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?
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 increment buttons and scroll bars to create
interactive Excel resources.
Learn how to use conditional formatting to create attractive
interactive spreadsheets in Excel.
How much peel does an apple have?
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 ?.
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 ?
This spreadsheet highlights multiples of numbers up to 20 in
Pascal's triangle. What patterns can you see?
Learn how to use the Excel functions LCM and GCD.
Learn how to use advanced pasting techniques to create interactive
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.
Use Excel to investigate remainders and divisors. Was your result
Use Excel to investigate digit sums of multiples of three. Can you
explain your findings?
A number of useful techniques that can extend your use of Excel.
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.
Choose four numbers and make two fractions. Use an Excel
spreadsheet to investigate their properties. Can you generalise?