This problem solving activity has a number (multiplication and division) focus.
Mr Greenwill looked out on his Otago farm and saw rabbits everywhere.
"I reckon there are about 1280 rabbits in that paddock.
They’ve been doubling in number each year for the last seven years", he said.
How many rabbits were in the paddock seven years ago?
This problem is about recognising that if the rabbit numbers doubled this year, then to find the number of rabbits last year, you have to halve the present number.
This ‘undoing’ is an important theme in mathematics. At all levels we look for operations that will take us back to the original position. An operation that will undo another operation is called its inverse. The inverse of doubling is halving, and the inverse of halving is doubling. Similarly the inverse of multiplying by 3 is dividing by 3. Multiplying by anything can be undone by dividing by the same amount, so these are the inverses of each other.
It’s often not so easy to see the inverse of a more complicated operation. Suppose that we double a number and add 1. The inverse of this is subtracting 1 and halving.
You might like to discuss, with the class, the other operations and what their inverses might be. What is the inverse of adding 5? What is the inverse of multiplying by a half? What is the inverse of rotating about 90 degrees?
Because this is an inverse or undoing problem, a good strategy is to work backwards.
Estimating (half), then using a calculator to check is one approach. Some calculators will repeat an operation with the touch of just one button.
Mr Greenwill looked out on his Otago farm and saw rabbits every where. "I reckon there are about 1280 rabbits in that paddock. They’ve been doubling in number for the last seven years", he said.
How many rabbits were in the paddock seven years ago?
If now there are 1280 rabbits, then a year ago there were 640, two years ago there were 320, three years ago there were 160, four years ago there were 80, five years ago there were 40, six years ago there were 20 and seven years ago there were 10.
So seven years ago there were only 10 rabbits in Mr Greenwill’s paddock.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/rabbits at 8:56pm on the 26th February 2024