Aaah, Multiplication Facts

There are few things mathematical guaranteed to stir the emotions more than the multiplication facts. Over the centuries just about everything has been tried to help students, round about the age of ten, memorize or remember their multiplication facts. Traditionally, they have been presented in the format in the image to the left. For example for the 'fives' the 5s came first followed by x1,x2,x3,x4 etc. This format is still frequently used which is really unfortunate because it would be so much more efficient if the 1x,  2x, 3x, 4x, etc came first (as in 1 x 5 = 5). This would allow students to use the repeated addition concept of multiplication to learn the sequence of the multiples of 5 more efficiently and effectively as in one 5 is 5, two 5s are 10, 3 5s are 15 and so on. Here an additional 5 is being added each time; something that does not work when the 5 is presented before the x1, x2 etc.

More recently, we have started using the multiplication square as a way of learning and remembering the facts. This method has the added advantage that each fact makes an array (rectangle or square)which helps the student visualize the fact as they are learning it. For example 5 x 4 can be visualized as a rectangle with side 5 and 4. Square numbers can also be idenfied as squares such as 36 or 6 x 6. Prime numbers make only one array (e.g. 13 only makes 1 x 13) but that's another story.

Today, in my Teaching Math to ELL students class we interviewed students from different countries around the world to find out about the way they learned math. Interestingly, most learned their multiplication facts to 9 x 9 while some learned to 10 x 10 and one student from Saudi Arabia learned up to 19 x 19. No-one seemed to learn to 12 x 12.

10 x 10 is the usual limit for remembering the facts but I always have wondered why it was, traditionally, 12 x 12. Perhaps it was because 12 figures so large in our Western culture (12 Apostles, 12 months in a year, 12 hours in a day, 12 in a dozen, twelfth day of Christmas, 12 inches in a foot etc). Perhaps there is a more logical reason? I can't find an answer on Google, yet.