The Maths Question of the Year 2016!

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Here is a question which has intrigued me for a few years now, but this year it seems most pertinent!

2016 is the product of two 2-digit numbers. 
What are they?
Can you find all the possibilities?

The Brute Force method

2016The interesting aspect to the question is the way it is worded. It suggests to many pupils, particularly those trained in calculations, that they should begin to try lots of multiplication calculations. They begin a trial and improvement method, often starting with 44 x 54 (as 40 x 50 = 2000 and 4 x 4 = 16). They will often come up with one answer after some furious pencil scribblings, and then struggle on to find some more.
When questioned about how they will know when they have got them all, there is normally a silence or blank face. If not, a lot of ‘ums’ and ‘ers’.

Stepping Back

It is usually the less trained student that will step back from the question and think about what they actually can do. Sometimes those among the least able in the class will say, well I know 2016 = 2 x 1008… This simple step leads them on a journey of discovery to their first answer, and it doesn’t take too long to discover some more. Clearly using factorising to prime factors is the best approach to a complete solution, and it is often less confident pupils who will happen upon this.

The Lesson

So why use this sort of question? Firstly, it teaches children that a question is not always asking you to do what it seems. It teaches children that Maths is about connections as much as calculations. This type of open ended question often requires curiosity and perseverance in order to achieve. It links to division and factors, and opens up lots of discussion about how seemingly difficult multiplication or division problems can be simplified.