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I made the icon using multiple creative commons svg resources, the banner is this.
You can't take three from two,
Two is less than three,
So you look at the four in the tens place.
Now that's really four tens,
So you make it three tens,
Regroup, and you change a ten to ten ones,
And you add them to the two and get twelve,
And you take away three, that's nine.
Is that clear?
Common core made an effort to teach kids to think about numbers this way and people flipped the fuck out because that wasn't how they were taught. Still mad about that.
The problem with common core math was not that they taught these techniques. It's that they taught exclusively these techniques. These techniques are born from the meta manipulation of the numbers which comes when you have an understanding of the logic of arithmetic and see the patterns and how they can be manipulated. You need to understand why you can you "borrow" 1 from the 7 or the 9 to the other number and get the same answer, for example. It makes arithmetic easier for those who do it, yes, but only because we understand why you are doing it that way.
When you just teach the meta manipulation, the technique, without the reason, you are teaching a process that has no foundation. The smarter kids may learn to understand the foundational logic from that, but many will only memorize the rules they are taught without that understanding of why and then struggle to build more knowledge without that foundation later.
Math is a subject where each successive lesson is built on the previous lessons. Without being solid on your understanding, it is a house of cards waiting to fall.
To add to this, people come up with math tricks all the time but you then have to check it against the manual method, and often multiple times with different numbers, before you can connect the manual process to the trick for later use.
In my opinion I don't think you can teach just the trick side of it, if thats what common core is.
When I was tutoring, i had a few elementary-school aged kids. They'd have homework where they had to do the problems three or so different ways, using each of the methods that they were taught (one of which was always the way I was taught when I was their age). I actually feel like I learned a lot from them, as there were some interesting tricks that I didn't know before helping with the homework. I think that's a really good way to approach it, because a kid may struggle with some of the methods but generally was able to "get it" with one of them, and which method was "the best" was entirely dependent on the kid. For me, being able to see which methods clicked and which ones didn't helped me be more effective as a tutor, too, since it showed me a bit more about how their individual little brains were working.
But I agree, if you're not also at least trying to explain why the different methods get you the same answer, it can lead to problems down the line. Some of them saw the "why" for themselves after enough time working at it, and some needed a bit more external guidance (which, considering they were coming to me for tuturoing, I guess they weren't getting at school). My argument would be that no one really taught me "why" when I was in school learning The One Way to do math either. I still had to figure out little tricks that worked for me on my own, since my brain is kinda weird. It may not have taken me so long to believe that i'm actually pretty damn good at math if I'd done those kids' homework when I was their age, as i would have had more tools in the toolbox to draw from.
There's ~~people~~aliens who would add 9+7 instead of 10+6 or 8+8 in their heads?
I do, because 9 plus anything is just a 1 in front of the other digit minus 1.
Weirdly enough, I just thought about using the methods here for the first time in my life earlier today. Weird.
9 plus anything is just a 1 in front of the other digit minus 1
This is also how it works in my head, but isn't it the same as the other guy was saying, 10+6?
The difference would just be how you think of the process. I sometimes shuffle around the numbers to make math easier, but the shortcut for adding 9s just feels different. Instead of 9+7 = 10 + 6, it's more like 9+7 = 17-1. It feels less like solving it with math and more like using a cool trick, since you didn't really use addition to solve the addition problem.
Mental arithmetic is all little tricks and shortcuts. If the answer is right then there's no wrong way to do it, and maths is one of the few places where answers are right or wrong with no damn maybes!
Well, there are certainly wrong ways to arrive at the answer, e.g. calculating 2+2 by multiplying both numbers still gets you 4 but that is the wrong way to get there. That doesn't apply to any of the methods in the post though.
Unsolved problems do not all fall into binary outcomes. They can be independent of axioms (the set of assumptions used to construct a proof).
I like your funny words, mathemagic man
What does adhd have to do with anything?
ADHD is sometimes used as a catchall to mean a set of behaviors that does not coincide with the majority at school or work. Ive met a bunch of people on ADHD medicine, but it was usually because they wanted to force themselves to be good at or like something they didnt want to do normally.
In this case its called ADHD because the student has found their own way to solve it despite the method the teacher is teaching and that the rest of the class uses.
Nothing, it has become quite common to say ADHD causes every little odd behavior. I'm not sure if all those people are even actually diagnosed and not just lying for internet points...
I assume people with actual ADHD find it offensive their condition is made fun of by "quirky" idiots online.
Yep. Just because you do something in a nonsensical, stupid way doesn't mean you have ADHD or that is what someone with ADHD would do. People with ADHD are also "intellectual."
For me, this is how I'd solve 9+7:
Day 1: Fuck it, I'll do it tomorrow
Day 2: Alright gotta do that problem now! Just gonna eat and take a walk to prepare my mind
Day 3: okay for real this time
Day 4: staring intently at problem for half an hour before getting incredibly inspired to do anything else
Day 5: anxiety
Day 6: paralyzed but anxiety
Day 7: Either I actually try to do it and it takes 30 seconds or I give up entirely and flunk the class
Not "hehe quirky look at me I'm so stupid because my brain does things differently, ur so smart I wish I was like you and not so dumb! x3"
Has nothing to do with ADHD.
Wouldn't say nothing to do with.
Many neurodivergent students find themselves in situations where they haven't fully absorbed the taught material. Many of them end up figuring problems out themselves, with varying degrees of creativity and success
Neurotypical students do the same thing. It’s not like every neurotypical will internalize every piece of material they are taught.
I would have done 10+6, but that's effectively the same thing as the OP.
Aside from literally counting, what other way is there to arrive at 16? You either memorize it, batch the numbers into something else you have memorized, or you count.
Am I missing some obvious 'natural' way?
I'd argue memorizing it is the natural way, at least if you work with numbers a lot. Think about how a typist can type a seven letter word faster than a string of seven random characters. Is that not good proof that we have pathways in our brain that short circuit simpler procedural steps?
Why is everything ADHD?
Yeah, this has nothing to do with ADHD.
The "ADHD way" is literally what they are teaching in school.
Yup, this is what parents are complaining about when they say math has changed. Before, math was primarily about rote memorization. You just memorized that 9+7 is 16. There were multiplication tables you were expected to memorize and regurgitate ad nauseam. Sure you could count it out on your fingers, but that only works for numbers under 11. For anything above that, you just referred to your memorized addition, subtraction, multiplication, or division tables. But this also meant that numbers outside of those tables were really difficult to do in your head, because you were poorly equipped to actually calculate them out.
Common core math is attempting to make math easier to do in your head, by teaching the concepts (rather than promoting rote memorization) and helping students learn shortcuts to avoid getting lost. 9+7 is 16, but it’s also 10+6 or 8*2, which are much easier to visualize in your head without counting on your fingers.
Admittedly I was in school multiple decades ago, but our teachers wanted us to memorize addition and multiplication tables. Which of course made anything outside the tables hard to do. I (and others apparently) thought it would be a great idea to use shortcuts like this.
So many failed tests. So many. When teachers saw us write down that we took the 21 apples multiplied by 7 bushels and just did 2x7, and tack a 7 on the end, they broke out the red pen.
Why are these posts always shitting on teachers? I don't know what teachers you're seeing, but I've never seen any teacher of any subject / age-group ever discourage anyone for thinking about something a different way. Quite the contrary, different ways of approaching problems are always encouraged.
My math teacher (at a private school) was just a random students' mom. She had no higher degree and only taught the book. If you got the right answer by using a method not included in the book, it was marked half-credit because she didn't understand and wasn't interested in hearing your logic, because "that's not what the book says".
Being taught by people who have no drive for knowledge and just want to teach the standardized test answers SUCKS.
You're old school, like me. You're literally describing the "new math" that boomers hate. Teachers are finally teaching kids to do it the way we've always done it in our head.
"8 + 7 is awkward, but if you take two from seven and give it to eight, now you have 10 + 5 and that's easy mental math."
And the reason they teach it that way is because it’s what the people who are good at math were already doing. Math isn’t about memorization it’s about understanding how numbers work and that’s how numbers work
If your teacher gets mad about breaking an addition problem into easier problems, then that teacher should be fired. Phony tale.
If anything, these are exactly the techniques that "New Math" was supposed to teach. Your brain doesn't work math the same way as a computer. People who are good at math tend to break the whole thing down into simple pieces like this. New Math was developed by studying what they did and then teaching that to everyone.
I tend to add 9 to things by bumping the tens digit up by one (7 becomes 17) and then subtracting 1 (17 becomes 16).
Most of the arguments against New Math tended to prove the point; our mathematical education was in dire need of fixing.
No no no 10+7 = 17 and 9 is always one less so 16
Let's make that 9 a 10 because it's good enough, it's smart enough, and goshdarnit people like it. Also, I don't wanna add with a 9. So 10 + 7 would be 17, but we added 1 to the 9 to make it 10 so now we take 1 away, 17 - 1 = 16.
ezpz
Whatever number is closest to 10 steals enough to make itself 10. Same goes for hundreds, thousands, whatever. Get your round numbers first, add in the others later. All numbers must become 10. In a pinch, a number may become a 5, but if so, it's really just become a half-10, and it should feel bad about itself that isn't a full 10 yet.
10 is just easier for me to work with so...
9+1=10 10+7=17 17-1=16
The second method is very chemistry-like. I do that too naturally
So do I! When I saw that 9 stealing a 1 and becoming a 10, I thought "Wait... These are electrons. This is chemistry. That 9 is a halogen!"
I thought that too, 9 is like a halogen, it wants to resolve to 10 anyway it can like fluorine wants one last electron. So allow the 9 to rip one off of the neighboring numbers and then perform the calculation.
It took me 3 years to pass HS algebra because the coaches/part-time math teachers didn't like the way I solved problems. I got the right answers. But the way I got them was wrong apparently.
No no no. Adding nine is just subtracting one, but adding to the front digit. 9 + 7 is actually 7 - 1=6, then add that 1 to the front. 16. Let's not make more complicated than it needs to be.
this is a false story. everybody knows 7 ate 9
Yo but hear me out. Because 7 ate(8) 9, 7 + 9 = 7
I realized something. I relate so much to ADHD memes not because i have it but because they simply do a lot of things that they think only people with ADHD do. In my school they encouraged you to come up with techniques like this. Often 9 is hungry in different ways. Another exmple is multiplication. 5099 is 50100-50 which is much easier to calculate.
In my school they encouraged you to come up with techniques like this.
You’re either very lucky and were in a school that went against established norms, or you’re young enough that you were taught the “new” math that boomers hate. Because this is the new math.
Boomers, GenX, and elder millennials were primarily taught via rote memorization. You simply memorized the times tables, and committed “8*3=24” to memory. You didn’t calculate it every time. You just memorized the tables, regurgitated them ad nauseam to appease the teachers, and then referred to those memorized tables for any multiplication you needed to do.
For reference, this is the times table I’m referring to. Our quizzes/tests required you to fill out the entire thing in less than 5 minutes:
We had to fill this out multiple times per week. The goal of the time limit was to force you to memorize it, instead of calculating it out every time. You simply didn’t have time to calculate each one out. Then once you had it memorized, if you ever had to do 8*3, you would just refer to your memorized times tables for it.
But the issue with this is that it doesn’t teach you how to actually do the math in your head, it just teaches you the times tables. You aren’t calculating it out each time, so you don’t develop any shortcuts or methods to make it easier. If a teacher ever saw you turn 9+7 into 10+6, they would bust out the red pen and start slashing. Even though 10+6 is undeniably easier to do in your head, the teachers weren’t concerned with that; They wanted to know that you had memorized what 9+7 is. These memes are primarily aimed at the millennials and GenX with ADHD, because they were the ones who got bored of rote memorization and started coming up with shortcuts (which then got docked points on their quizzes.)
9 is 3+3+3, 7+3 is 10, 3+3 is 6, 6+10 is 16. I'm also a fucking heathen.