Times Tables
Times tables
If I were to be asked the most important ability related to passing external examinations at age 16 or thereabouts, I might say without the shadow of a doubt it is a superb understanding of times tables. During the 30 years of my teaching career, I've come across numerous students (both in schools and as private pupils) who don't know their times tables at age 16 well enough in order to calculate such things as a fifth of 45 or the total length of 8 ropes, each 4.5 metres long.
Times tables songs
I write as a teacher in the UK, so my examples relate especially to the country, but the points have worldwide relevance across the whole world. We've got a system of examinations now in which there's almost always a calculator examination paper and a non-calculator paper at each level from age twelve. So an excellent knowledge of tables is undoubtedly needed in the non-calculator paper, but is of great benefit in the calculator paper too, as understanding that seven eights is fifty six is much less time consuming than having to press the right buttons. In a assessment, seconds count.
A minute's thought will reveal several of the instances where times tables are employed. Every money issue in almost any currency involving a multiplication ($12.67 x 9) or division (Locate the average of $34.50, $33.60, $59.90 and $46.80) uses times tables. Percents (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 rate difficulties (find the typical rate 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 finish random tables squares, i.e. tables squares in which the amounts 1-10 are distributed at random across the highest part of the table and down the left hand side. I'm currently working using a group in an area primary school, several of whom can already complete this type of table right in about five full minutes. At sixteen years-old, the great majority of students should be able to easily conquer that time - and get them all right, needless to say.
The inquiry of whether times tables from 1 to 10 is adequate often crops up. Should youngsters understand the eleven and twelve times tables? If you reside in a largely metric state, 1 to 10 is adequate for all examination work and I might then concentrate on learning the square numbers up to 20 x 20 as all these are extremely useful for Pythagoras' Theorem. If you reside in a nation still using feet and inches for regular measurements, then you will most likely have to learn tables up to 12 x 12.
Accordingly, in case you or your children are taking outside assessment some time soon, the one thing you can do to enhance your operation more than anything would be to get those tables nicely and actually in the old brain box!
Alan Young has been a teacher of mathematics for thirty years and high schools. He's been employed in the private together with the public sector and coached a lot of private students in this area.