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Why do this problem?
To give students an opportunity to work with large numbers.
To give students an opportunity to work on problems that require
more than one simple step.
- Discuss the kinds of thinking required for these types of
"If I were to ask you to work out answers to these questions,
what information would you need to know?"
Make a list on the board.
"Some of these things you can work out from things you already
know, some of them need an estimate."
- Let pairs/groups of students select the questions they want to
do, and then work together, on paper.
"You're going to be comparing answers with other groups, so
make sure that you have written your final thinking carefully, to
make it easier to spot differences."
"Each question should be done on a separate sheet of
- Students stick finished questions on the board, next to other
solutions to the same problem, they can check whether theirs is the
same/different to what other groups have done.
"If two groups work on the same question and get different
answers, it may be because their estimates are different, or it may
be because one method is wrong."
- Teacher to monitor board and organise "case conferences" where
answers or methods are different - i.e. representatives from the
different groups come together and troubleshoot each others'
working, then feed back to their own group.
How can I ensure that I make reasonable estimates?
How can I set out my working most clearly?
Which of these questions is the hardest, and why? Have a go at
Suggest 10 more questions using large numbers, decide whether they
are one star, two star or three star in difficulty. What do you
think comprises a three star answer? Solve a couple, or swap with
another fast student and solve some of theirs.
The process of adapting difficult problems, "making sense" of
them in simpler cases, is a powerful technique for dealing with
hard questions. This may be an appropriate moment at which to
Pick one question to work on as a class task.
Ask the students to pose related, smaller questions that they
can answer, and build up a body of work (display work?) around the
theme, for example:
Your age if you are 100 seconds
old, 1000 seconds old, 10000 seconds old, etc.
The age in
months/days/hours/minutes or seconds of people in the class, their
The time since key moments in
history (or sport, etc) measured in different units.
Then encourage students to work towards the original