Choose Your Units
Which units would you choose best to fit these situations?
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
- Millimetre
- Newton
- Angstrom
- Joule
- Volt
- Microgram
- Micrometre
- Hertz
- Parsec
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 amoeba
Newton - 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
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
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
Key questions
Possible extension
Continue the question for other, more exotic units of measure (such as those given in New units for Old )
Possible support