# Exploring relationships

Having just finished some work with my year 10s on forming and solving equations (see this great resource they made), we have turned our attention to looking at rearranging formulae. As an introduction to this, I have used an idea that I first explored when doing my PGCE all those years ago. The idea is to take a simple everyday situation as a hook and use it to explore mathematical relationships. I created this excel spreadsheet a few years ago that adds some interactivity to the idea.

There are three different situations to explore with the one above looking at a helicopter rescue. We had a whole class discussion on how I could work out the hidden value and what calculations would be involved. I then asked them to come up with a formula to work out the time taken for the helicopter to arrive at the scene of the accident. We tested the formula they came up with and convinced ourselves it would always work. We then ‘changed the subject’ by hiding a different value and they came up with the calculations they would need to carry out in order to work that out. I then asked them to come up with 3 different formulae using each of the variables as the subject and got them to convince each other by testing using numbers. This was then followed up by using two other situations where they engaged with the numbers first to get a ‘feel’ for the relationships and then came up with formulae with each of the variables as a subject.

The level of engagement of the students was absolutely fantastic and although we haven’t yet formalised methods of changing the subject of formulae, I feel that they will have a much deeper understanding of what they are doing when we do this next lesson. It also gives us concrete examples to refer back to over the next couple of lessons.