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And that’s basically it!
Reading through these comments thinking, "Did nobody ever learn how to multiply by nine on their fingers?"
Hold up your hands, fingers out.
9x4? Put down your 4th finger. Note there are three fingers to the left of it and six fingers to the right. 36.
9x8? Put down your 8th finger. Note there are seven fingers on the left, two on the right. 72.
9x17? Put down your 17th finger. Zoo called. Time to go home, buddy.
Why not just count by threes three at a time?
Huh, nines are the hardest to grasp?
That sounds... very wrong.
I mean, it's definitely 7s, right? Like no contest, hands down, it's 7s for everybody isn't it?
I never learned my times tables past x5. I have to math it out every time.
Yeah, that's fair. I mean I always liked math for the most part, but learning times tables was definitely an annoying phase. But for me, finding those patterns was always going to be preferable to rote memorization, and 9s had a nice easy pattern. All the even numbers have some useful patterns too, and I still think about those patterns when I help my kids with homework, but none are of them are as simple and useful as the 9s pattern.
I mean, after doing the math for each time table over and over again, you do eventually just remember it.
7, 14, ...21? uhhhhhhhhhhhhhhhhhhhhhhhhhhhh
10x8 is 80. Minus 8. Is 72.
That's how I do it. I actually struggle a lot with 7x and 8x.
Still don't know 6x7 7x8 8x8 8x6
1-9 by 9 is easy though.
Take the first number, subtract 1 from it, and that will be your 10's place. Your 1's place with be whatever that first number needs added to it to get to nine.
Example... 7x9. 7-1= 6, so 60. 9-6=3. Answer is 63.
Another fun math trick while we're at it. If you want to know if a number is divisible by 3, just add up all the digits, and if that number is divisible by 3, then so is your original number. 3135...3+1+3+5=12, so 3135 is divisible by 3.
8x8 = 16x4 = 32x2 = 64
OR
play minecraft for 3 years straight
That's a nice little trick. Let's see if I can remember it. 😅
The nine timestable was one of the easier ones for me to learn as a child because I recognized the pattern in the numbers:
First row of digits go 0123456789 while the second row goes 9876543210. Idk, I thought it was cool that they did that.
The timestables that I had the most difficulty with were 7 and 8.
That is how I learned it way back when.
8 isn't bad if you do x2 x2 x2. It sounds like a lot of steps but it's fast.
For 7... Just use the trick for the other number 😋
The trick I was taught is that the sum of all two digit multiples of nine add up to nine. Then you just take the number you want to multiply times none and subtract 1.
For example if you want to multiply times 8, the tens place is 7 and the ones place must add up to 9, so 2. 7+2=9, so 9x8=72.
Isn't it easier to just do 80 - 8
not for me. I do the "adds up to 9" trick to this day.
The method I'm talking about only adds/subtracts single digit numbers, which is easier for kids.
The niner table is one of the easier ones. Add first and second digit, and you'll get a nine.
What kids are really struggling with regularly are the seveners.
"Cheats" like this is why critical thinking is fucked...
Kids are supposed to learn:
Times 10 adds a zero, minus one from that is times 9
And different steps for different rows/columns.
We shouldn't "memorize" the times tables, because that's just memorization. These cheats learn a process, but it dead ends at this, it can't be used as a foundation to build on the real skill it should be developing: doing multiple math steps in your head.
If done right it "times tables" are the most important building block in being good at math. But for decades teachers just care if the right answer is spit out.
I use my memorized times tables in my head a lot more often than many other math skills. But maybe I'm just weird, I'm certainly no math whiz. Yet.
Edit: I realize this may just be because I don't have many other math skills, to your point.
We shouldn't "memorize" the times tables,
While I agree with your sentiment, times table memorization is necessary to build a skill that will be needed later in math. It's good to teach the basis of the times table but if you don't have it memorized, every later math problem will be slower to solve because you will be focusing on the principles of how a times table works instead of the new concept like how to multiply long number with carry.
This is related to my pet peeve, that despite it being 40 years ago is still burned into my memory. I had many Physics professors who would talk about not needing to memorize formulas for exams because they could be derived from first principles. Those same professors were always the ones who would give exams that if you didn't have formulas memorized, there wouldn't be time to finish.
I agree the the number-theoretic shortcuts for multiplication (and division!) based on the factors of 9, 10, and 11 should be taught.
I disagree that single-digit sums and products shouldn't be memorized. Neither students nor practitioners derive formulae from first principles each and every time, and breaking down a single-digit sum or product into "simpler" ones is a very similar ask.
Neither students nor practitioners derive formulae from first principles each and every time,
If they have it memorized, it's from years of usage, they didn't need to practice moroizing the things theyd use every day. Because it would happen anyways.
Math class isn't applied Math, it's just Math. Giving credit for memorizing someone else's equation is a way to push people thru who can't do the math.
And even in a hypothetical world where someone needs to apply an existing mathematical formula that they don't use constantly, they're not gonna just risk it to save 2 seconds checking.
I understand why you have the opinion you have, but that doesn't mean our education system was blinded in the pursuit of metrics generations ago, hell, it's ancedotal evidence it did...
If you try to do that for all multiplication you might end up with something like 10*6 = 60 - 6 = 54 - 6 = 48 - 6 = 42 - 6 = 36 and even then the subtractions are going to involve some memorization unless you are counting down or something.
You kinda need to have the basic operations involving the 10 digits in our common number system memorized to then start building algorithms for more complicated problems like multi digit numbers.
you might end up with something
Literally the point I was trying to get thru to people.
The thing is there's a lot of human variation, and if I wrote it out enough for everyone to understand, no one would read it.
So I end up with shit like your reply.
You don't understand the goal, so you don't understand why it's being taught
And after (maybe) reading the other comments, you come in completely sincerely with "just memorize it".
I know you're trying to help, and legitimately don't see the problem here. But fucking come on man, at least ask questions and people may explain it
I taught it this way for 20 years. It works.
Oh. Haha, this was how I was actually taught to do the 9s. I think it was meant as just a "you can also do the lower ones this way" and wasn't suppose to be "the only way you'll remember, Rebekah" but it was the second one!