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'Time to Evolve' printed from http://nrich.maths.org/
Why do this problem?
will give practice in making sensible estimates,
approximations and making a prediction based on a range of possible
values. Although the content is relatively simple, answers could be
given to this question at a range of levels and the problem would
suit both Stage 3 and Stage 5 students as an exercise in
There are various ways in which approximations can be made and
it might be good to let students attempt to make their own
approximations before opening up to group discussion. As they work
on the problem, various decisions will need to be made and various
uncertainties will arise (for example: at what stage between
maturity and death of a parent was a particular offspring in the
chain of descendants produced?). Students should be encouraged to
take notes of these points, as discussion of these forms a key part
of the evaluation process.
It is interesting to ask students first to give a
guess/estimate of the number of descendants without doing any
calculation. Students could then work on the problem in pairs to
come up with an estimate and then share their ideas with other
groups. Whose estimations seem best? Can students justify clearly
their estimations to each other? Do any students wish to revise
their estimates in light of such interaction?
Once estimations have been constructed and discussed it would
be worth relating the estimates back to the original question: how
reliable might we consider our estimates of the number of
generations to be? What questions would this raise? What
information might lead to better estimates?
Finally, how did the students' initial guesses/estimates fit
in with the calculated estimates? This allows students to reflect
on the size of the final answers. Were they much larger or smaller
Key questions should be used as appropriate to help students
find their way into the question:
- Can you make a start to the question by giving a very rough
estimate of the numbers that go into the table? How could you use
these numbers to work out the number of generations?
- When you fill in the table, what sensible range of choices do
you have for each entry?
- When you calculate the number of descendants from a filled-in
table, what uncertainties are there?
- How could you use a filled-in table to calculate the maximum or
minimum number of descendants?
The fullest solution to this task/main extension involves a
careful investigation of the minimum and maximum possible number of
descendants. For those with a knowledge of statistics, you might
refer them to Time
to Evolve 2
As a very general extension discussion point, it is worth
mentioning that the evolution from one species to another occurs
through gene mutation. Can students get any sense of the rate at
which the genes would have to mutate to account for the required
genetic change over the given time period? This activitiy would, of
course, be research intensive.
Some students might feel uncomfortable that there are no
'right' numbers to fill into the table and no 'right' answer to the
estimation question. Encourage them that it is OK to make a rough
estimate to begin with and then to refine that estimate later. Give
them some concrete estimates of time to maturity/death if