If I were to be asked the most important skill associated with passing external examinations at age 16 or thereabouts, I would say without any shadow of a doubt it is a good knowledge of times tables. During the 30 years of my teaching career, I have come across so many students (both in schools and as private students) who do not know their times tables at age 16 well enough to be able to calculate such things as a fifth of 45 or the total length of 8 ropes, each 4.5 metres long.
I write as a teacher in the UK, so my examples relate specifically to this country, but the points I make have universal relevance across the whole world. We have a system of examinations now in which there is nearly always a calculator examination paper and a non-calculator paper at every level from age twelve. So a good knowledge of tables is definitely needed in the non-calculator paper, but is of great benefit in the calculator paper too, as knowing that seven eights is fifty six is much less time consuming than having to press the appropriate buttons on a calculator. In an examination, seconds count.
A moment’s thought will reveal many of the instances where times tables are used. Every money problem in any currency involving a multiplication ($12.67 x 9) or division (Find the average of $34.50, $33.60, $59.90 and $46.80) uses times tables. Percentages (Find 17% of 12.50), fractions (cancel 45/75 to its lowest terms), geometry (find the internal angles of a regular octagon), algebra (expand 7a(3a + 6b + 9c)) and speed problems (find the average speed of a car that travelled 960 kilometres in 8 hours) are just a few of the many more examples to be found on examination papers.
One way of practising times tables is to complete random tables squares, i.e. tables squares in which the numbers 1-10 are distributed randomly across the top of the table and down the left hand side. I am currently working with a group of 8 and 9 year olds in a local primary school, several of whom can already complete such a table correctly in about five minutes. At sixteen years old, the great majority of students should be able to easily beat that time – and get them all correct, of course.
The question of whether times tables from 1 to 10 is sufficient often crops up. Should youngsters know the eleven and twelve times tables? If you live in a mostly metric country, 1 to 10 is sufficient for all examination work and I would then concentrate on learning the square numbers up to 20 x 20 as these are very useful for Pythagoras’ Theorem. If you live in a country still using feet and inches for everyday measurements, then you will probably need to learn tables up to 12 x 12.
So, if you or your youngsters are taking external examination some time soon, the one thing you could do to improve your performance more than anything else is to get those tables well and truly in the old brain box!