Thursday, 1 June 2017

Learn Times Tables in 90min!

Multiplication chart
Times tables are the cornerstone of mathematics and are a lifetime investment for every one. We used to learn them since the early years in primary school. Still I am always surprised to see so many children (and adults...) not mastering this very basic knowledge.

There is a common misunderstanding in considering the times tables as a long list of multiplications difficult to memorise. Well, this is wrong. Actually, there are only 36 unique combinations to learn, and most of them can be deduced from the easiest ones. For example, if you know 2×5=10, you definitely know 8×5 which is simply 4×(2×5)=4×10=40. And if you know 8×5, you know 5×8 as well by symmetry. Additionally, most people know already the times tables up to 5×5 - this is 25% of all times tables - without even noticing!

Convinced? Let's have a look at the multiplication chart above. The numbers in the top row and the left column are called factors. All the others numbers are the products of the multiplication of these factors. You can easily notice that the shaded numbers are symmetric to the coloured ones. Because of this multiplication fact: a×b=b×a. It means you need to learn only haft of the times tables. If you don't know a×b, just try b×a. The 36 unique combinations I mentioned before are represented by the coloured area in the chart.

Lesson plan
Now, the question is: 36 combinations, are they to much to memorise? You must believe in the extraordinary capacity of the brain. Do you know that children from grade 3 onward learn 2000-3000 new words a year (ref. Biemiller; Nagy & Anderson)? That is 6-8 new words a day in average. By comparison, if you learn 36 combinations in 9 days, it is like learning 4 new words a day. By practising 10min a day for 9 days, you can master all the times tables in 90min. How easy it is!

You can find the full lesson plan in the illustration. Times tables are arranged by difficulty level to optimise their memorisation. They are incremental, i.e. only a few new combinations are introduced in each one: no wasting time with the symmetric forms that will be assimilated naturally by practising the daily worksheets.

The full method package including a complete set of daily worksheets to practise at home or at school is available for download.

MathEngines Founder