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You can teach old dogs new tricks: bar modelling in maths


Reading time: 3 minutes. Relevant programme: SSAT Lead Practitioner Accreditation


A student comment prompted David Newburn, SSAT LP at Excelsior Academy, to change his long-standing approach

A student asked me the other day, ‘Sir, do you not get bored teaching the same thing every year?’ It took me a little by surprise, but frankly I thought, yes I do. So why not try something new?

As a secondary school maths teacher I continually see staff banging their heads against a brick wall with particular subject content year in year out. I hear comments like ‘our kids are rubbish at this topic’, and ‘I hate teaching (insert boring, bland, dry subject matter)’. Is it the topic? Or are the conventional approaches we were taught and are hence delivering failing to provide the necessary understanding to the masses?

With this at the forefront of my mind, I started to reflect on a training course I took a couple of years earlier, based on the Singapore bar model (essentially a consistent pictorial layout of maths). If I am being honest, it is a course I went on, enjoyed somewhat, dwelled on, thought it too onerous a task to implement, ignored, shelved and forgot. My thought process went along the well-trodden path of ‘This will mean I will have to rewrite all of my collated resources. Anyway, my methods work too!’

But this is where I was deceiving myself. Yes, my methods work for some, but every year I can predict which topics students will struggle with, what the misconceptions will be. I watch them fall at these hurdles, time and time again.

With the constant changing seas of the teaching world, fad initiatives, and continual reinvention of the wheel, I was very aware that a departmental directive to change approaches could be met with reluctance and cynicism among the old guard. For this reason I chose only one topic, ratio, and embarked on an experiment with two of my classes. Why ratio? Mistakes are so predictable, all questions are completed in exactly the same manner ‘add, divide, times’, despite the multitude of different circumstances and questions.

The Singapore bar model

Like all good ideas, it seems so simple. The Singapore bar model breaks down the numerical content into a pictorial representation. When I taught it for the first time in a lesson I couldn’t believe that I could have been so blinded by my own stubbornness not to try this before. Just look at this example yourself (trying your best to ignore any preconceived ideas about the infallibility and correctness of the way you were taught … and your ego).

Like all good ideas, it seems so simple: break down the numerical content into a pictorial representation

Basic ratio question: 25 sweets are divided between Cheryl and Simon in the ratio 2:3. How many sweets does each get?

Old teaching method:
2+3=5
25/5=5
2×5=10
3×5=15.

Yes, this works. However, you can clearly see that, if you are not confident with the method, this may just look like a bunch of random numbers on a page with operators inserted.

New approach :

For a ratio of 2:3, the students draw 2 boxes alongside 3 boxes of the same size and share the 25 sweets out, leaving 5 in each box. It may not seem revolutionary to draw this out and many people may be shouting at the screen that this pictorial based style of mathematical teaching has been carried out for years … but for the teachers and students that I have since discussed this with, it has been the breakthrough they were looking for.

What if the question was a ratio of 65:42? I hear you cry. A great thing about it is that when mastered it can then be dropped and used solely as a support strategy. But the best thing about it is that it provides concrete understanding of the problem at hand that can be transferred to an array of different scenarios rather than just learning a trick that offers no thought process. See the next tricky example for a demonstration of a concept all of my students previously struggled with (trying to apply the old teachings from the earlier question).

More challenging ratio question: Mary and Peter share money in the ratio 3:7. Peter gets £20 more than Mary. How much does Mary get?

Old teaching method:
7 – 3 = 4
20/4 = 5
5 x 3 = 15

Again a method that works for some, but doesn’t allow the simplicity of the question at hand to be presented in a clear manner for all to see.

New teaching method :

In this case, the picture from the previous example can be continued here, meaning that we aren’t always learning new tricks for new questions.

The results were quite remarkable. Ratios, from being one of the most derided topics when the students saw the lesson title on the board, started to be one of their favourites.

The thing that surprised me most, however, was the uptake by staff. Unfamiliarity can be a scary thing, so after demonstrating the impact in the classroom I made them have a go at some questions in the new style themselves. To my astonishment all of the department favoured the change. Turns out you can teach old dogs new tricks after all!

Fancy a go yourself? Try these with the bar model…

Question 1: 45 sweets are shared between Anne and Bob in the ratio 2:7. How many sweets does each get?

Question 2: A fruit drink is made by mixing lemon squash with water in the ratio 4:5. How much water needs to be added to 28cl of lemon squash to make the drink?

Question 3: Ahmed and Sandra are sharing a prize in the ratio 3:7. Sandra got £16 more than Ahmed. What was the prize initially worth?

Do you believe that the greatest drivers of professionalism in your school are the practitioners who always aspire to improve, nurture and lead colleagues, and develop the next generation? Lead Practitioner (LP) Accreditation will help empower and develop your best practitioners, to reward and inspire them to make a difference where it really counts – in the classroom. Find out more.


Read on the SSAT blog: How we ensure the KS3 English curriculum makes pupils KS4-ready


 David Newburn, SSAT Lead Practitioner, Excelsior Academy

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