Instead of talking about fractions, it is all about wholes. I have not seen the whole fraction (eg showing £60/£60) emphasised in any math book or video.

The course consists of:

• Seeing Decimals, Percentages, Ratio and Fractions as all being Fractions: why we use 1/2 and 0.5 and 50%; how ratio and fractions are different ways of looking at the same thing; fractions in how we look; fractions as relationship, not a number.
• Equivalent fractions: converting one fraction to another, multiplying by 1 using different ratios; writing whole amounts as a fraction.
• Using three methods (factors and multiples, unitary multiplier, algebra) on any FDP question; translating any FDP question into an equivalent fraction.

I learned to teach algebra in one lesson at the very start of my PGCE teaching qualification degree. Only when I came back to teaching after a decade did a way to teach fractions, decimals, percentages appear. It’s about emphasising the ‘whole’ whenever tackling any kind of FDP or Ratio question.

When in a chemistry class while the students were dutifully doing some sheet work since I wasn’t qualified nor was I interested in conducting experiments with various acids, I assembled the plastic baubles which are customarily used to model chemicals. I think I created CO2 though it could have been for H2O. I still carry around the model. At the end of the lesson, I lifted up the model and gave the students an alternative way of thinking about the model; that it was a model of concepts. Like algebra: it consisted of three concepts, no more no less. However, there were some conceptual structures that were more complicated than the three concept model I showed them, and Fractions appeared to be of this nature. Over the years I have shown that little three-part model, but nothing has come to me which unlocks the simplicity of fractions. It took me two decades before it revealed itself.