This article is intended for parents and mathematics teachers who are involved in teaching multiplication tables to students. The usual approach to teaching tables is by rote learning but, unfortunately, there is always a proportion of students who struggle to commit them to memory. Those who fail are disadvantaged for the rest of their school mathematics career. Here, a simple and original system is developed which allows students to calculate results of multiplications using fingers. Although applicable for tables 1 to 9, it turns out that it is easiest to use on the 7, 8 and 9 times tables, the ones that students traditionally have the greatest problem with.
NINE TIMES TABLE. Raise both hands and hold them together with palms facing you (see right). We shall calculate the result of 7 x 9. As with all calculations with this method, it is important to remember the position in the multiplication table we are interested in. Here it is 7. Now jumping in ones, count seven from the left and drop the seventh finger. The units digit of the result is simply the number of fingers raised to the right of the seventh, that is, 3. The tens digit of the result is the position in the multiplication table (7) minus the number of the pass along the ten fingers (1) to give 7 - 1 = 6. So the result is 63. We note that for other tables, we start a second pass through the ten fingers on reaching the end, however, for the nines, only one pass is required. nine times table
There is another well-known method, which only applies to the nine times table, that simply counts the number of fingers raised to the left of the dropped finger (6) to give the tens digit more directly. However, as we shall see, the method developed here also applies to other tables and for consistency it is better to keep to one method of calculation. Let us look at the eight times table.
eight times table

EIGHT TIMES TABLE. Let us suppose we are interested in 9 x 8 (see left). Remember, we must keep in mind the position in the eight times table (9). With the eight times table, we jump in twos from the left, performing a second pass through the fingers on reaching the end. The ninth finger we reach in this way is dropped. As before, the units digit is the number of fingers raised to the right of the one dropped (2). The tens digit is calculated from the position in the table (9) minus the number of the pass along the ten fingers and since we drop the finger on the second time round, this is 2. So the tens digit calculation is 9 - 2 = 7. This gives the result 9 x 8 = 72.

Whereas the number of passes for the nine times table cannot exceed one, for the eight times table, it cannot exceed two. Also the size of jump used in counting is given by the calculation ten minus the number of the table we are using. So for the six times table, we have 10 - 6 = 4, that is, we jump in fours. Clearly, the method becomes more troublesome the lower the number of the table but is easier to use on the higher tables which are usually the ones that students have the most trouble with. In my own one-to-one mathematics teaching, I have discovered that a reasonably intelligent ten year old can master this method after only a few trials and that those who have been left behind through lack of tables learning have found this method a great relief. Not only does it open up avenues into other calculations that the student previously could not access but it also encourages concentration and spatial thinking.

eight times table
Okay, now its your turn! Using finger multiplication with the seven times table (jumps of three) calculate the result of 8 x 7. To make things easy, the diagrams for the calculation are shown below.

WHY IT WORKS. If we take our earlier calculation for 9 x 8 for the eight times table we can rewrite it as follows :

9 x 8 = 9 x (10 - 2) = 90 - 18 = 90 - 20 + 20 -18 = (9 - 2) x 10 + 2 = 72

Notice that the jumps of two appear with (10 - 2) and our nine jumps of two (18) is counted on the fingers. When this is subtracted from the next highest ten (20) we get the units digit (2) and when the number of the pass is subtracted from the position in the multiplication table (9 - 2) we get the tens digit (7).