Ten Green Bottles
Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?
Problem
Ten green bottles hanging on the wall,
Ten green bottles hanging on the wall,
And if one green bottle should accidentally fall,
There'd be nine green bottles hanging on the wall.
Nine green bottles...
If the first bottle fell at ten past five in the morning ($5.10$ a.m.) and the others fell down at $5$ minute intervals, what would the time be when the last bottle fell down?
Getting Started
You could use a real or model clock and count.
Think how many $5$ minutes are there between the first and tenth bottles falling.
Student Solutions
We had very clearly explained solutions to Ten Green Bottles. David from Tithe Barn Primary School, Stockport wrote:
The answer is that the last bottle fell at five minutes to six. I worked this out by writing down the numbers 1-10 and by the first number I put the time when it fell. Then, I added 5 minute intervals and put them at the next number down i.e. 5:10, 5:15, 5:20 etc.
Jeff from Kelly Elementary School in Carlsbad, California agreed with the answer of 5.55.
Airlangga from St Joseph's Catholic Primary School wrote:
5.10 + (5minx9) = 5.55
Alistair from Histon and Impington Infant School used a similar way of working it out to David, but then generalises, leading nicely on from Airlangga's response:
I have spotted that the equation for the nth bottle is 5 x(n-1) minutes after 5.10
Very well thought out all of you.
Teachers' Resources
Why do this problem?
This problem is one which could be done quickly as an introduction when extending or revising work on time and clocks.
Key questions
Possible extension
Learners could find the equation for the $nth$ bottle falling.
Possible support
Suggest using a real or model clock and counting.