This entry gives some detail about the aspects and issues you may need to think about to help pupils understand what a fraction is, how to operate with fractions and the links between fractions and other numbers.
Fractions is a large and very complexly interconnected topic. It is possible to begin teaching fractions to pupils in many different ways. When one arrives in the topic it is also possible to travel through it by many different roads. Before beginning to teach, think about where you are coming from, what you will cover and how you will go back to follow up on questions that pupils have raised.
For example the following route may be useful as one route: The first block of teaching: Start with what a fraction is and how a fraction is different from a ratio.
Make sure students understand a fraction as a number and a fraction as a measure.
Look at different representations of different families of fractions. There is a worksheet you can use that covers this first stage click here to view.
Then progress onto how to link fractions to decimals and decimals to fractions. Then progress onto fractions of quantities moving from the diagrams you created to represent fractions to calculating fractions of quantities.
Another ‘block’ of teaching could be about the family of 1, connected with the impact of multiplying and dividing any number by 1, (mathematical identities) connected with equivalent fractions and writing fractions in their lowest terms.
When pupils are familiar and confident with equivalent fractions and cancelling fractions it is possible to move onto the teaching block about adding and subtracting fractions.
At this stage it is also important to think about where to put top heavy fractions and mixed number into the process.
Last and not least in this series of blocks I would look at multiplication and division of fractions to round off the four operations.
This leaves the possibility of revisiting fractions when you tackle another teaching block which looks at the equivalence between fractions, decimals and percentages. Because all the operations in fractions are quite challenging it is important to revisit them in a variety of different guises to give pupils plenty of confidence to tackle any question.
For example, if students fully understand fractions and are also confident in trying to solve difficult problems they may like to try the Ben's Game problem on the NRICH site.
N.B. this really thorough way of proceeding through stages of complexity towards deep understanding of fractions lends itself really well to adult learners too. It is great if you can instill a thirst for knowledge of this kind through exploration.
However, the really discorncerting thing for a teacher of adults can be when you think you are working systematically and then the adult comes up with a piece of knowledge or a skill (often out of context) that you didn't realise they already have, e.g. knowing lots about percentage through looking for discounts in shops, but not realising how this relates to fractions and decimals.
The other disconcerting thing can be the "grasshopper" thinking style that gets impatient with systematic learning, and wants to leap on to the next stage. Some learners will struggle for ages with what we may thing is an easy stage, and then take a big leap of understanding that seems more like intuition than learning. Learners with dyslexia or dyscalcuia may experience this.