I inherit every possible method for teaching fractions under the sun. My learners come from every school across the city and all have their own way of doing things. Kiss and flick, kris kross, X marks the spot and so on are all ways for multiplying and dividing fractions. Like I always say, if you have a way that works consistently for you then use that way. I never unteach a method unless it is incorrect. Often methods have become incorrect because the learner has become confused with the method shown to them. In my experience students are more likely to become confused if they lack knowledge of the basics. One of the ‘wins’ I enjoy teaching is product of primes, prime numbers, simplifying fractions and divisibility checks.
I like to start with prime factor decomposition. I like to call it this in my intentions on the board. I like to discuss the anxieties the learners have when they see the title and then experience the joy on their faces when they crack it in the end! There’s no fancy trick in what I am teaching, this one I am afraid requires singing and dancing as it is all about the presentation. I am not above making a fool of myself to help a concept stick in the learners minds. It all starts with some audience participation. I write up 2, 3, 5, 7, 11 on the board. We spend a few minutes shouting it as loud as we can. We play finish my sentence and I will call out 2, 3 and pick a learner to finish it off. Then we move onto questions of what is the third prime number? What is the fifth? We spend quality time recalling the first 5 prime numbers.
I don’t think I am doing anything out of the ordinary at this point for the learners. Everyone I have ever seen teach the topic as well has started by spending quality time on the first 5 primes. I tend to just stick to 2 3 5 7 11 for these early stages. An old favourite from my cover supervisor days on my PGCE was the 10 x 10 grid and playing in pairs to find all the primes up to 100. I will, if we have time, move onto games like this but in the first instance I stick to the first 5 primes.
Here comes the singing and dancing…
“If you like it then you should have put on a ring on it”
Here is an example of the prime factor decomposition of 420:
We begin with writing our first 5 primes. We then use these as divisibility checks. I am aware that learners can find the highest prime factor and solve this problem quicker. I am not aiming for speed here. I am aiming for a consistently correct method. We always begin by seeing if 2 goes into the number. We keep the primes on the left as well.
I am aware that it may be obvious for some learners to use 5 as the prime when breaking down 105. I have no problem with this, actually in making these images that’s what I did and had to start again! Once we have broken the number down. I will then sing a bit of Beyonce or show an image of her on my board. (Beyonce also sits on my wall as well as Terry Pratchett!) The blue writing is purely for the example here, we verablise this in class but don’t write it.
Once we have really solidly grasped these divisibility checks, we can use them in a variety of ways. We can then look at simplifying fractions.
Yes this is a long way round but it ensures a consistent approach and reinforces the use of 2, 3, 5, 7, 11. It's a nice introduction in a stepping-stone to unpicking that initial knowledge that's needed to tackle a wide range of questions. Like I always say if you have your own with working things out please use your own way, but for those who struggle 2, 3, 5, 7 11 may just help with developing those core divisibility skills.
