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Why do this problem ?

Use of units is a critical skill in the sciences, and one which often leads to confusion. This problem will encourage students to understand the relationships between various types of units, as well as possibly introducing them to new important scientific units. It will also help to embed the important skill of checking numerical answers to see if they make sense in terms of orders of magnitude, along with a sense of where units are of relevance in science.

Possible approach

This question works well through discussion in pairs. Remind the students that common sense works well when dealing with units: for example, a cubic mm is clearly far smaller than the volume of a bathtub.

Key questions

What suggestions for units are possible in each case?

Possible extension

Continue the question for other, more exotic units of measure (such as those given in New units for Old )

Possible support

Remind students the formulae for the compound measures, such as volume.

Students might also struggle with the reasonably open nature of the question. Remind them that there is no 'correct' answer and common sense approximations will help.