Choose your units
Which units would you choose best to fit these situations?
Age
14 to 16
Challenge level
Problem
Some units are particularly well suited to a given measurement because they turn out to give a small, whole number of units. Understanding this concept gives you a feel for the order of magnitude of the quantities.
What units would you measure these quantities in to make an approximation which was a reasonably small whole number?
- The volume of a bacterium
- The mass of an oak tree
- The area of a leaf
- The half-life of Uranium-235
- The area of a football pitch
- The average lifespan of a human
- The volume of a bath tub
Can you reverse the process? For the following units, what physical phenomena might naturally be measured to be around 1 unit?
- Millimetre
- Newton
- Angstrom
- Joule
- Volt
- Microgram
- Micrometre
- Hertz
- Parsec
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Student Solutions
Phenomena to units
Volume of a bacterium - Cubic micrometres $\mathrm{\mu m}^3$Mass of an oak tree - Tonnes $(10^3\textrm{ kg})$
Area of a leaf - Square centimetres $(\textrm{cm}^2)$
Half-life of Uranium-235 - Millions of years
Area of a football pitch - Hectares
Average life-span of a human -Years
Volume of a bath tub - Cubic metres $(\textrm{m}^3)$
Units to phenomena
Millimetre - size of an amoebaNewton - weight of an apple
Angstrom - atomic diameter of a hydrogen atom
Joule - kinetic energy of a table tennis ball travelling at $100\textrm{ km h}^{-1}$
Volt - voltage across an AA cell
Microgram - mass of $1\textrm{ mm}^3$ of air
Micrometre - mitochondrion
Hertz - frequency of tick-tock on a clock
Parsec - distance to Proxima Centauri (closest star other than the Sun)
Teachers' Resources
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.