Today I was reunited with the mathematical phenomenon known as the Singapore Bar.
I have always been a firm believer in using pictures and representations to aid mathematical thinking and the bar is a prime example of this. To be honest, it’s nothing Earth shattering – if you’ve ever used a number line to explore your thinking, it’s much the same.
Take this problem for example:
Jake is 3 years older than Lucy and 2 years younger than Pete.
The total of their ages is 41 years old.
Find Jake’s age. What else can you find?
My brain leaped immediately to creating an algebraic equation. The bar is a step between a trial and error approach and the leap to sticking letters inside numbers.
Let me show you.
From this diagram, you can see that the common link is Lucy’s age. Rewording the question is essentially the key, but creating the image in stages helps a lot too.
Removing the additional years (shown as squares above), gives us 41-8, which is 33. From that point, it isn’t a great leap to get to 33 ÷ 3 = 11, so Lucy is 11, Jake is 14 and Pete is 16.
Adding their ages up is a final additional stage to ensure your answer makes sense, of course.
When I was presented with the question, I did this:
L = J-3; P = J+2; J = J
41 = 3J-3+2
41 = 3J-1
42 = 3J
42 ÷ 3 = J
J = 14
I did miss a few steps out by doing them in my head though.
If you want to try a further example, I’ll leave this one here for you:
Abe, Ben and Ceri scored a total of 4,665 points playing a computer game.
Ben scored 311 points fewer than Abe. Ben scored 3 times as many points as Ceri.
How many points did Ceri score?
To be honest, thinking like this is far from natural, but I can see how it would close the gap and potentially, once children are comfortable with it, reduce the fear of algebra for children.
The other major revelation was more a confirmation of one of my long held beliefs. I was told today, by two separate people, that we should be spending a lot longer on breaking down our teaching mathematical topics than we currently are. Finally, I don’t feel like a lone voice…
If we, as a profession, can continue to think like this, then maybe, just maybe, some good changes are ahead of us.
