Why do this problem?
The ability to work with big and small numbers is a very important
scientific skill. These
provide a variety of contexts where handling such numbers is
necessary, while offering practice at identifying key information
and making decisions about estimates and assumptions. It is
suitable as a look-forward to A-level for students finishing GCSEs,
or as a look back revision task for more advanced students.
These questions could be used individually as starters or
fillers within lessons. Alternatively, a class could work on
different questions in small groups and then present their answers
with reasoning to the rest of the class to stimulate discussion.
Some questions can be tackled with little specialist knowledge;
others may require research and additional information, as well as
some assumptions, in order to come up with an answer.
It is important to stress that there is no "correct" answer
for some of these questions - the value of this task comes from
having a go at estimating and calculating with big and small
numbers, and discussing assumptions that need to be made and extra
data that needs to be sought in order to find a solution.
What assumptions have you made?
What other information do you need?
Are there any questions which give an exact answer? Can you say
anything about the accuracy of those answers which aren't
This problem could be done in conjunction with
Big and Small
Numbers in Physics
. Similar questions could be created and
shared within the class.
Start with those questions which have familiar content, and
encourage whole class discussion of the ideas in them, before
tackling any of the questions which require extra information. It
is well worth suggesting that students read the article
Student Guide to Getting Started with Rich Tasks
tackling a very open problem like this one.