Pressure - a rich new vein for compound measures and proportionality

First off - apologies for the lack of post in the last week. A combination of mounds of marking, open evening, and of course preparing for the session at #mathsconf5, has left me a little short on time! Nonetheless I am slowly getting back into the swing, and thought I would talk about my teaching of compound measures this week.

Typically, teaching compound measures at GCSE has meant teaching kids how to calculate speed, distance and time and then looking at density as mass over volume. Throw in a bit of time as a decimal hour and having to find volume from given lengths and that was that. However the new GCSE has provided a new rich source of teaching for compound measures that can highlight much more strongly the proportional and inversely proportional relationships - the calculation of pressure.

Having downloaded a solid exam question worksheet resource from mrbuckton4maths on TES to give the pupils an opportunity for consolidation, I felt the need for a final top end question to challenge the best and brightest in the class - and came up with this:

The box below exerts a pressure of 2.5 Pascals when in the orientation pictured. Calculate the pressure when the box is turned onto the shaded side.

………………………… Pascals

[2]

 I am sure I have seen a similar question in one of the SAMs (I am sure I got the inspiration from somewhere), however what I particularly like about this question is that despite 1 Pascal being the pressure exerted by a force of 1 N when spread over 1 metre squared, there is no need to convert the cm into metres to solve this problem. The inverse proportionality between area and pressure is all that is needed, as the start and end units are both Pascals. Simply multiplying 2.5 by 8 (=20) and then dividing 20 by 6 (= 3⅔) is enough to solve the problem correctly (hence only 2 marks), without considering the units of measure themselves. Although some won't like this approach I do really like the exploitation of the inverse proportion as an abstract process. What I also like is that the area of this block in contact with the surface changes depending on its orientation, unlike the volume which is fixed for each shape (in this case 24 cm2) which means that questions like the one above can be asked for pressure where they cannot be asked for density.

Now pressure is not a quantity that lots of maths teachers will have an in-depth knowledge of, but take my advice and talk to your science department colleagues about getting some questions about pressure into your lessons.