This is a post about the importance of knowing the multiplication table BY HEART. The intended audience is adults: primarily, parents, caregivers, teachers.
Back in my elementary school years, we spent grade 1 and 2 on addition and subtraction, grade 3 on multiplication and division, and grade 4 on fractions and decimals. Perfectly feasible, if all taught well and in good measure. Upon entering grade 5, most of us could operate with simple algebraic concepts. I’ll come back to this in another post.
There was no way you could go into the next grade unless you knew how to operate at a medium level on those – so yes, you could fail grade 1, or 2, or 3, or 4 just for that. There was also no way you would not do your homework - you would have to present your notebook at the beginning of every class and if you had chosen not to complete your homework, you’d get a “4 (four)” (FAIL) on the big book of marks. In a system where marks were taken very seriously and ranged from 1 to 10, this would directly affect your average mark at the end of the term and, conversely, the end of the year report. Yes, we learned what a “mean” is (no pun intended!) BEFORE learning multiplication and division – how crazy is that?
Still, it worked, and actually very well. Fear is a great motivator.
The current society claims children are not to be forced into anything. They should come to learning led by their curiosity. This is fine and dandy, but hardly anyone does homework just because they love it – and that’s valid for any kind of society.
I absolutely loathe learning things by heart. Never liked it. I need a reason to do something, it’s the only thing which motivates me. So of course, I didn’t get it when they said: you need to learn the multiplication table by heart. What, ALL OF IT? Yeah, pretty much. But why? Just do it or else, came the answer. Reluctantly, I wrote down all the tables a good few times, said them aloud, whatever worked... and they stuck. Much later on, I used the same method on my kids, no mercy.
All this preamble, to get to the point which I discovered as perfectly valid later on: you cannot do any further math properly if you don’t know your multiplication tables really well. And you can't understand what the multiplication table is good for because that knowledge comes AFTER in the logic of math learning. Now come (some of) those reasons as to why:
1. Long division is the inverse operation of multiplication. It provides you with a quotient (the result of the division) which is a whole number only in very rare cases (for example, 30 ÷ 5 = 6). In MOST long divisions, you get a little extra: that is called a remainder. You can write a division in many ways, say:
34 ÷ 5 = 34/5 (improper fraction) = 6 4/5 (mixed number made of 6 wholes and 4/5 proper fraction) = 6.8 (decimal) = 680 % (percentage)
Out of these, when you punch in the division into a calculator, it will only give you the result as a decimal (see underlined answer in the sequence above.)
2. If you need to transform a mixed number into an improper fraction, you need multiplication.
3. All numbers are made of factors. These are smaller numbers “included” in the big number.
For instance: 12 is made of 12 x 1; or 2 x 6; or 3 x 4; or 2 x 2 x 3
1, 2, 3, 4, 6 and 12 are all factors of 12.
Sometimes, the bigger the number, the more factors (but not always! Enroll in my course to get when and why.)
Knowing how to decompose a big number into factors is crucial to be able to add and subtract fractions which have different denominators (there’s a whole process and I won’t go into that lesson here). Again, the calculator won’t add and subtract those fractions.
4. It’s a fact that our brains do not like big numbers, for the very reason it’s easier to operate with smaller ones. Those factors help tremendously when attempting to simplify fractions or algebraic expressions:
(36x + 42y) divided by 6z = 6 (6x + 7y) / 6z (because 6/6 = 1 you can strike the two sixes) = (6x + 7y) /z
So there, you have a smaller fraction!
5. Needless to say, math is just FULL of fractions. You can’t avoid them. Fractions are in the money we use, in the distances we cover, in the areas calculated to change the flooring in our houses or how much paint we need for a new colour on the walls, in the statistics you’d preferably be able to read yourself so some government won’t trick you into believing their propaganda, in how big of a mortgage you can afford or how to stay out of debt so the banks or credit card companies don't trick you either. Handy stuff, right?
As you can probably gather, the most interesting - and I dare say wonderful! - thing about knowing your multiplication tables is that it really helps multiplying your math knowledge. You can’t do much without multiplication, can you? You get stuck at that level. So why wouldn’t you learn those tables and get unstuck? Here’s a few strategies:
- Get a notebook and a pencil. Write down BY HAND all tables 1 to 10 daily, for as long as it takes to know them.
- Recite them aloud, one table at a time.
- Get a bunch of post-it notes, preferably different colours. Write down those multiplications you have more trouble remembering: one multiplication per post-it note. Place the post-it notes around the house in areas where you can see them daily. By the bathroom or kitchen sink, near your bedside table, above your dresser etc.
- Sing them in the shower: the sillier the song, the more fun you have and the quicker you retain it (laughter helps memorization)
- Associate some multiplications with familiar concepts: for me, multiplying any number with 25 means that many quarters (cents), for example it’s really quickly to know that 11 x 25 = 275 (think 2$ and 75c). Or 15 is a quarter of an hour, so I visualize the clock and count the quarters around it when I need to multiply with 15. This goes for 30, or 45, or 60. Yes, I’m rather old-fashioned with clocks too – I like analogue ones! By the way, clocks really help in trigonometry too – but that’s another blog post.
So there, a few reasons to not only make friends with, but also love your multiplication tables.
One last word for parents: don’t let this slip. You need to make sure your kids know their multiplication tables. The schools are not diligent these days (at least, in Canada that’s a fact.) And the vast majority of kids won’t learn them out of good will.