Why do this problem ?
gives practice with the use of estimating numbers and making choices about the information to use in a question. These are crucial mathematical skills in the sciences. These interesting questions will allow students to practise these skills whilst developing awareness of orders of magnitude in scientific
contexts. As with any problems involving approximation, they offer opportunity for classroom discussion and justification.
There are several parts to this question, arranged in approximate order of difficulty. The individual pieces could be used as starters or filler activities for students who finish classwork early. Enthusiastic students might work through them in their own time. Since there is no absolutely 'correct' answer to many of these questions, they might productively be used for discussion: students
create their own answers and then explain them to the rest of the class. Does the class agree? Disagree? Is there an obvious best 'collective' answer?
- What assumptions will you need to make in this question?
- What formulae will you need to use?
- How accurate do you think the answer is?
- What 'order of magnitude' checks could you make to test that your answer is sensible?
Can students make up similar questions? Can they put any upper or lower bounds on the actual numbers that would arise from a detailed calculation?
Students might struggle with the 'open' nature of the questions. To begin, they might like to read the Student Guide to Getting Started.