Maths: Flexibility = efficiency= speed

I have previously written about the importance of understanding as the foundation of applying mathematical methods. Working with a Year 6 child on finding percentages of numbers, and having taught her different methods to apply to various types of problem – you can imagine my surprise, and frustration, on hearing that her teacher insists on the ‘chunking’ method only for solving percentage problems. Furthermore, this particular child does not understand ‘chunking’ and prefers others. My logical approach to this issue is that not all problems are the same – therefore, in the interests of efficiency and speed, the same method cannot be applied to all problems. Consider some examples of percentage problems:
1. 10% of 30 or 25% of 60: these can be done in most Year 6 heads, often by converting to a fraction equivalent (30 divided by 10 is 3 and 60 divided by 4 is 15). A division made comparatively simple because of the zeroes.
2. 73% of 261: demands long multiplication, followed by decimal point adjustment (back two places to divide by 100).
3. 26% of 30: simple multiplication (26 x 3 = 78) add zero (780), decimalise (7.8).
4. 99% of 245: could be a simple subtraction of 1% from the whole. Short cuts can be useful.

Schools also teach chunking as a method for solving these types of problems, for example, 45% of 60: 10% = 6 so 40% = 4 x 6 = 24. 5% is 3. So 24 + 3 = 27. Simple enough. But how does this chunking method work for problems such as the second one above: 73% of 261? By the time a child has worked out 10% (26.1), multiplied this by 7, then worked out 1% and multiplied this by 3, then added the two answers together, this chunking method is no more efficient than long multiplication, followed by a simple decimal point adjustment.

My point is simple: in the interests of efficiency, different problems surely demand different methods. When speed matters, for example in exams, choosing the method that best suits a particular problem, is surely what we want young people to do. So when it comes to mathematical problem-solving, flexibility = efficiency = speed: the key to success.

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