There’s Too Many!!
Times tables up to 12 can be so horrible to learn, memorise and recite. There just seems to be so many of them. Let’s look at exactly how many multiples there are to learn.
We’ll only go up to 12. Any further than that, and they start getting really difficult to learn. It might be good to learn the square numbers up to 16², or even 20² or 25², but we’ll get to those.
If we learn all 12 times tables up to 12×12, then that’s 144 multiples to learn altogether. That’s a lot! But twelve of those are the one times tables, and those are dead easy! So let’s not count them. That’s over 8% of the times tables dealt with, only 132 to go. Wohoo!
Next after the one times tables is the two times tables. Now maybe we can skip this one too, but first, think to yourself “can I really instantly recall any number multiplied by 2, all the way up to 12?” maybe commit a day or two reciting them, just to really be sure. It seems trivial, but it’s one less obstacle to trip you up when you’re trying to multiply bigger numbers together, for example, 22×17. You need to recall 2×7 whilst retaining the rest of your working out in order to calculate something like that.
Now that the ones and twos are out of the way, that’s 24 of our 144 times tables done, bringing the total down to a measly 120. The 10’s are straightforward enough to discount, since you just add a 0 on the end move each digit one space to the left, and keep the decimal point where it was. So that’s another 12 down, 108 to go!
While we’re at it, the 11’s up to 99 are probably straightforward enough to discount too, so that’s another 9 down, from 108, so 99 to go. Just 99 multiples left to memorise, less than 100, and we’ve barely even started!
Since the ones, two’s, ten’s and eleven’s can be ignored (up to 9×11 (wait, up to 10×11, because that’s in the 10’s)) then we can take those ones out of the remaining times tables too, so when we learn the three’s, we don’t need to learn 1×3, 2×3, 10×3 & 11×3. Same for the fours, fives and so on. That means there’s a grand total of 67 multiples left to learn. Still quite a few, but we can bring that number down even further.
When we learn something like 3×4, the answer is the same if we switch the question around and say 4×3. This means we can drop 29 more off our list, bringing the total number of times tables facts to memorise down to 38. Now, to cut the fives, or not to cut the fives. That is the question.
If you can instantly recall 5×3, 5×4, 5×5, 5×6, 5×7, 5×8, 5×9 and 5×12, then we can drop those from our list. That’s 8 less, meaning we now only need to memorise 30 times tables facts to proudly be able to announce to the world that we know all of our times tables. And here they are:
3×3=9
3×4=12
3×6=18
3×7=21
3×8=24
3×9=27
3×12=36
4×4=16
4×6=24
4×7=28
4×8=32
4×9=36
4×12=48
6×6=36
6×7=42
6×8=48
6×9=54
6×12=72
7×7=49
7×8=56
7×9=63
7×12=84
8×8=64
8×9=72
8×12=96
9×9=81
9×12=108
11×11=121
11×12=132
12×12=144
Square numbers!
I often teach my students square numbers up to 16². The reason for this is because it’s surprisingly easy, and comes up a lot in maths.
All the square numbers up to 12² are covered in the times tables. There’s only four more. That’s it. Not only that, but the remaining four are quite easy to remember with a small bit of effort. 13² and 14² are 169 and 196. You just swap the 6 and the 9 around! Easy, right?
15² is 225. That’s 3²×5², or 9×25, and the product of two square numbers is definitely worth memorising. Especially because 225 ends in 25, which is 5².
Finally, 16²=256. That’s worth remembering because it’s what you get if you double 16 four times, or if you double 2 seven times.
I would recommend putting a bit of extra effort in and going up to 20², and learning the cubed numbers up to 10³, but you really don’t have to. It’s just fun.
I hope this blog post helps you to realise how small the daunting times tables actually are, and brings some reassurement that there is an end to them eventually.