One way to check whether a model is valid is to consider whether it’s units are valid. Consider speed, which a distance divided by a time. The units are speed are something like “miles per hour”, “metres per second”, in other words, a distance over time.
An invalid model might not have consistent units. If I write A = B x C, where A is a speed (m/s), B is a distance (m) and C is a volume (cubic metres), this model can not be correct.
Tasks/Ideas – Higher Apps Consistent Units
- Leckie Higher Applications Student Book, Chapter 2 Exercises 2A and 2B.
- Does it have consistent units? – Bryn Jones – This resource asks students to consider a series of formulae and work out whether each formula could model area.
- A good source of discussion can be looking at formulae from Physics. For example, this website lists several: https://www.cyberphysics.co.uk/general_pages/equations.html. If you know the units that most of the variables are measured in, can you work out the units of the variable you don’t know?
- A fantastic video showing the power of units and mathematical modelling: Numberphile
- A slightly silly, but mathematically interesting example of mathematical modelling and unit cancelation. The brilliant What If? from Randall Munroe (XKCD) perfectly demonstrates what can be done with consistent units.