How to: Learn how to solve a simple equation…in one hour!

The task is to plan a one hour lesson to teach 'one-on-one' someone (a 16 year old girl), who is at an F grade in maths, how to solve a simple equation like

$$0.24 = \frac{1}{x}$$

I have done this successfully many times (I have a PhD in maths), though there must be an agreed method which you guys think is the most clear and penetrating for a young girl who understands fractions, variables, multiplication and very elementary techniques. Any advice?

If by the end, we could tackle problems like solving

$$4x-1 = 2x + 4(x+4) - 5$$

that would be a successful lesson I think. I'm looking for the optimal technique here, any discussion of why you think this works would be advantageous....

• There is no single "optimal technique". The outcome depends on both ability and how information is received - which is not wholly captured by ability (which you emphasise with reference to the F grade). Are you able to furnish your question with an example of how you have approached it, or are thinking about approaching it? I think this would improve the focus of the question, reduce the possibility of answers telling you things you have already tried - and result in more useful and plentiful answers. – Rusan Kax Jan 7 '15 at 23:09
• A similar question has been broached before on this site here. The answers there should provide a start for some of the issues that may arise. – Andrew Sanfratello Jan 7 '15 at 23:42
• The issue is we don't know the source of the F. When dealing one on one with students, I try to get to the bottom of what they don't understand, and then try to fill in the gaps to full problem solving expertise. Your second example - would she know the first step can be distribute and combine like terms? There are a few skills needed for quick isolation of the variable. Tough to know where she's lost. – JTP - Apologise to Monica Jan 8 '15 at 2:10
• In my experience "who understands fractions" is a MUCH higher level skill than the essentially mechanical task that you're trying to accomplish. – Dave L Renfro Jan 8 '15 at 16:37