This activity lies on a cross-curricular basis, linking number exponentiation to biological processes. According to this approach, it is appropriate to collaborate with the biology teacher in order to handle precise and correct information, as well as to take his or her advice.
We begin with a question to connect with student's existing knowledge, which can consist of something like the following:
"What do all living beings have in common?"
The teacher will write on the board all the ideas brought up by students, among which we expect to find the three basic processes defining life: nutrition, interaction and reproduction. Discussion will be driven towards them; more precisely, we want to stress on the reproduction one.
based on this lesson by Khan Academy.
Right after this warming-up, some copies are handed to students. This material shows some text about reproduction processes: it focuses on two types of reproduction that can be distinguished: sexual and asexual. It is advisable to highlight key vocabulary (sexual, asexual, organism, offspring, parents, etc.) and structures (split into, give rise to, etc.), so as to give students some facilities to express themselves.
Some volunteer reads the text. Afterwards, students will take part in a game with questions of the kind:
-"How would you reproduce if you were a ...?"
The teacher sets off giving an answer for some sample question, and then asks somebody else. After giving an answer, each student thinks of a living being and asks the corresponding question to another partner. Students will write down their whole answer. For example:
-"If I were an apple tree, I would wait for a bee to spread my pollen."
This is also an opportunity to introduce new vocabulary, as well as practising with the one previously shown.
The teacher will draw students' attention to two particular cases: we (humans) and bacteria.
In the same text sheet, they will be asked to draw and iterate two phenomena (for instance, in a graph-like shape):
- The proliferation of a bacteria which duplicates in every step of reproduction (asexual reproduction). That is, to describe how a population of bacteria grows towards the future.
- Their family tree, including only parents, grandparents, etc. This also grows, but towards the past.
In each case, the task consists in noticing how the number (of bacteria in the first case, and of ancestors belonging to some generation in the second) appears to grow exponentially, following powers of two.
To this extent, some intermediate questions can be included:
-"How many ancestors did you have [whatever number] generations ago?"
-"How many bacteria are there after [whatever number] steps?"
-"Can you tell some pattern?"
Conclusions are shared in the big group. It is interesting to emphasize some facts and to put forward extra problems to extend the activity and/or make it more interesting and challenging (the language and expressions may be adapted depending on the level):
- Funny fact:
"Over two hundred years ago, more than a hundred strangers agreed in order for you to be here!"
- Stop the mistake (rather subtle):
"According to the funny fact, the number of ancestors you had seven generations ago was greater than a hundred. One generation earlier there were more than two hundred of them, and previously the number must had been greater and greater. Therefore, we can be absolutely sure that sometime in the past the number of humans on Earth was close to infinity."
- Solve a classic problem:
"There is a species of bacteria which doubles its number at every minute. At 11:00 a.m., we place one individual of this species in a closed, glass-made jar. At 13:00 a.m. the jar is already full of bacteria. At which time was it half-full?"
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