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?
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. . . .
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?
How much peel does an apple have?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
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
This spreadsheet highlights multiples of numbers up to 20 in
Pascal's triangle. What patterns can you see?
Learn how to use Excel to create triangular arrays.
A ribbon is nailed down with a small amount of slack. What is the
largest cube that can pass under the ribbon ?
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
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 lookup functions to create exciting interactive
This investigation uses Excel to optimise a characteristic of
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?
With access to weather station data, what interesting questions can you investigate?
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 ?
Learn how to use advanced pasting techniques to create interactive
If a sum invested gains 10% each year how long before it has
doubled its value?
Learn how to use composite bar charts in Excel.
Learn how to use conditional formatting to create attractive
interactive spreadsheets in Excel.
Use an Excel spreadsheet to approximate a decimal using trial and
Investigate factors and multiples using this interactive Excel
spreadsheet. Use the increment buttons for experimentation and
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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.
When is 7^n + 3^n a multiple of 10? Use Excel to investigate, and
try to explain what you find out.
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 make a simple table using Excel.
Learn how to use the Excel functions LCM and GCD.
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?
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.
Use Excel to investigate digit sums of multiples of three. Can you
explain your findings?
Use Excel to investigate remainders and divisors. Was your result
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.
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.
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
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
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 ?.
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 explore multiplication of fractions.
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?
It's like 'Peaches Today, Peaches Tomorrow' but interestingly
What day of the week were you born on? Do you know? Here's a way to
An Excel spreadsheet with an investigation.