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 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?
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.
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 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
This spreadsheet highlights multiples of numbers up to 20 in
Pascal's triangle. What patterns can you see?
Learn how to use advanced pasting techniques to create interactive
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
Learn how to use the Excel functions LCM and GCD.
Learn how to use lookup functions to create exciting interactive
Learn how to use conditional formatting to create attractive
interactive spreadsheets in Excel.
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?
With access to weather station data, what interesting questions can you investigate?
This investigation uses Excel to optimise a characteristic of
Learn how to use composite bar charts in Excel.
Use Excel to investigate remainders and divisors. Was your result
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 create some number pyramids. How are the numbers in the base line related to each other? Investigate using the spreadsheet.
Use an Excel spreadsheet to approximate a decimal using trial and
Use Excel to investigate digit sums of multiples of three. Can you
explain your findings?
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.
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?
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 use increment buttons and scroll bars to create
interactive Excel resources.
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
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 number of useful techniques that can extend your use of 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. . . .
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.
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 ?
How much peel does an apple have?
It's like 'Peaches Today, Peaches Tomorrow' but interestingly
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 explore multiplication of fractions.
However did we manage before calculators? Is there an efficient way
to do a square root if you have to do the work yourself?
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. . . .
What day of the week were you born on? Do you know? Here's a way to
If a sum invested gains 10% each year how long before it has
doubled its value?
Use an Excel spreadsheet to explore long multiplication.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
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 an interactive Excel spreadsheet to investigate factors and
Use Excel to practise adding and subtracting fractions.