Rearranging Formulae

Teachers' notes

The programme aims to provide additional content by taking a fresh look at the topic and relating it to real-life examples. The contexts have been chosen to demonstrate the application of simple algebra in situations that should appeal to a teenage audience. It is hoped that follow-up work in the classroom can draw on and extend the examples given.

For each formula shown we see why a change of subject may be needed and how to perform the necessary algebra. Throughout the programme the chosen method is to ‘do the same to both sides’ and we see the working on both sides of the formulae. Some substitution of values is included as appropriate, but the focus is on rearrangement. Each step is discussed in detail, supported by clear visual and graphic images that allow the student to track the algebra as it is performed. The formulae become more complex throughout the programme so that there is a progression from a simple one-step rearrangement through to a formula that contains four variables.

The programme could be used as an introduction to the topic, as revision or viewed in stages as classroom work progresses alongside the content. Some preparatory work on the order of operations and inverses would be useful prior to viewing. It is expected that after viewing, students will need to look in more detail at the formulae and rearrangements that featured in the programme. These were:

S = d/t make d the subject
T = W/100 make W the subject
C = 140 + 0.6m make m the subject
F = 9/5C + 32 make C the subject
C = (O – F)/t make F the subject

The final step (to make F positive) in the rearrangement of the last formula was deliberately left for classroom discussion. It was felt that there were several possible methods and that television could not provide the depth of discussion necessary to cover this point. As stated earlier, the programme consistently shows a single method having rejected others (for example using flow diagrams). This decision rests on the ability to provide sufficient depth for examples to be followed within a short programme.