Learning multiplication facts is a challenge because it’s the first math operation where your child needs to contend with relatively large numbers. Two digit addition and subtraction is squarely in the realm of numbers less than 20, which is familiar territory. There’s something concrete about 12 or 15 or similar numbers countable on fingers and toes, but 73 really is a big step out of the pond.
There’s two ways to approach this. One is just brute force memorization. I remember endless flash card drills after school, the timed tests in the classroom and the gradual accumulation of resentment towards anything with that little ‘x’ attached to it. While we love the Rocket Math program the schools use here, it is largely just memorization and could use something to back it up.
The other alternative is to make multiplication something of a game, with systems for some of the numbers. There still an inevitable amount of memorization that goes on, but by getting 90% of the multiplication table down to a few simple rules, the goal is suddenly within everyone’s reach. Split second, memorized results are still going to come, but having some means to reach incremental (albeit slower) success takes the fear and dread out of the process.
The place to start is understanding that multiplication is just repeated addition, and then using a few tricks to make the addition go faster. For example, if we need to multiply 4×6, an easy explanation is that this is just four copies of six added together, or six doubled twice. This “Double-Double” rule works for anything multiplied by four, and is easy to apply if basic addition has already been covered. A handful of these rules cuts 90% of the multiplication table away so that memorization is only required for ten facts.
Even if you ignore the ‘tricks’ in the rules below, the brute force way of multiplying by breaking it out into a bigger addition problem may seem like more work than just memorizing the facts, but it helps build some understanding of what multiplication actually means and provides a way to find the answers if they haven’t been memorized. Knowing what multiplication is, how multiplication works and (worst case, without any other tricks) how to solve a multiplication problem makes the whole process tangible. Also, this builds up some of the thinking processes used to multiply larger numbers where memorization isn’t possible.
Our focus for now is the core, so we’ll start with the 100 basic math facts (1×1 all the way through 10×10) and cut them down to size. The rules are ordered so that the easiest ones to memorize and use take the biggest chunks out of the table. If you learn them in this order, you cover the facts in the table in the fastest possible way.