This is a two-part article on Times Tables and Number Facts, terms used by mathematics teachers to refer to facts to be learned by students.

For many generations, the name used for multiplication facts (the results of multiplying two small numbers) has been "times tables". This term is used by most ordinary folks, including parents, children and many teachers. The fact that most people learned the term at an early age means that they don't often stop to consider if it is the best term for what teachers expect children to learn as part of their mathematics education.

## "Tables" of Facts

"Times Tables" probably got its name from the "tables" of facts familiar to students of mathematics over many, many generations. Multiplication facts learned by students are quite sensibly laid out in vertical columns, with each set of facts in a "table", showing each family of facts in order, usually from zero times to twelve times. For example, the "3 Times Table":

- 3 x 0 = 0
- 3 x 1 = 3
- 3 x 2 = 6
- 3 x 3 = 9
- ...
- 3 x 12 = 36

A set or family of facts such as the above, with a single multiplier, clearly illustrates key patterns in this set of facts. Apart from the first and last facts, each fact is between two other facts which differ by the value of the multiplier. The products, or results of multiplying, are on the right hand side in a vertical column which shows all the multiples in order. Students need to become familiar with each of these sequences of numbers, so that when necessary any one of these facts can be recalled quickly, and when needed the two multiples either side can also be recalled at the same time. This is essential knowledge when dividing, for example. When dividing 254 by 3, for example, you would first need to find the multiple of 3 closest to, but no greater than, 25: in this case, 3 x 8 = 24. With one ten left over, you then need to find the closest multiple of 3 to 14, which is 3 x 4 = 12.

(As an aside: if you have children aged between around 7 to 16 and they are learning their multiplication facts, a poster showing all the multiplication facts on their bedroom wall can be one of the best investments you can make in their mathematical education. Just having the lists of multiples on display at all times of the day and night will help to make your child familiar with them, with minimal conscious effort on their part.)

## "Times" means Multiplication

The other part of the term "times tables" is the word "times", being used to refer to multiplication. The word "multiplication" is the formal term, used by mathematicians and mathematics teachers to refer to this most vital and useful of operations. However, the word is not familiar to young children, and its multisyllabic form makes it difficult for a young child to remember and say. For these and other good reasons, the operation is usually called "times". This has both benefits and disadvantages.

On the positive side, the word "times" is often used to refer to repetition, a key concept around this operation. For example, if there were 7 pairs of shoes by the back door to the house, we could say that a pair of shoes had been left there 7 times in all by members of the family; and 7 x 2 = 14. Multiplication may be thought of as repeated addition; for example, "6 times 4" is the same as "6 added 4 times", or 6 + 6 + 6 + 6 = 24.

On the negative side of the ledger, "times" is now often used by children and some adults as a verb. "What do I get if I times 7 by 5?", they may say. This is really a misuse of the word "times", and while I suspect it will soon appear in dictionaries, for now at least this is not correct English. Once we start to accept "times" as a verb, it is quickly joined by other awkward and incorrect constructions such as "timesing" and "timesed". My recommendation to teachers is to patiently correct students who use "times" in this way, and either use other available correct verbs with young children, such as "grouping", and with older students use the standard term "multiplying".

This article is continued in Part 2: "Times Tables: Better Called Number Facts"

michael pannSeptember 23, 2012 at 6:38 AMIs it possible to fill in a few of the missing work sheets? For whatever reason I am missing 15, 18, 19, 20, & 23. My system for working on stuff at home is clombersome and i deleted them by accident.