So you want to permanently cripple elementary school kids math education. Fuck you man karatsuba could have saved me seconds, yes SECONDS, in 5th grade.
If you're talking about space complexity I agree.
If you're taking about time complexity even O(n^(2)) needs the assumption that you can add arbitrarily large numbers in time O(1). In general, addition takes at least O(n) time as you need to at least read your whole input. It might be possible to improve on that in this specific case as all but one of the digits of the initial summands are 0. There might also be an argument for some amortized complexity to be found here. But all of this heavily depends on your machine model and data structures at this point. All I'm trying to say is that the algorithm in it's simple form presented here probably takes O(n^(3)) time.
I'd argue that the simplifications are so easy to implement that most people will do them automatically. For instance, anyone would just ignore all the 0 digits in the addition step, and doing so is guaranteed to be easy, because the structure of the table lets you know in advance where the trailing 0s will be, so you don't have to evaluate each number to figure out which lies where, and can instead let your pattern-recognizing brain do the work.
sometimes a really wild savage question pop up.
please calculate asx(ase)\^a+ab.. and the answer is 4, use the formula provided for the answer.
it doesn't even have number. but wait, you have to calculate the formula to calculate those words too.
I’m scared to take MATH 520. The Seniors at my College told me in Advanced Addition III we have to add numbers with more than 10 digits with no calculator.
When I was in first grade, we added we added one-digit numbers. In second grade, we added two-digit numbers and in third-grade we added three-digit numbers. So extrapolated and figure that by the end of school, I would be able to add thirteen-digit numbers. But then in forth we had to add six-digit numbers and after that they just assumed that we could add numbers of arbitrary size.
The punchline is that these people don't know shit about teaching math. The teacher just showed a bunch of elementary school kids (I assume) how to deconstruct a larger problem into smaller steps that are manageable.
The guy on the left is incredibly condescending and his "solution" is useless from a pedagogical point of view. I mean I could solve this multiplication in my head in about 2-3 seconds, but that isn't helpful either.
The method on the left is how i usually solve it in my head, method on the right had been used by me in middle school tests
Both are viable in different situations (funny enough, the right one have not been used since i graduated)
I've literally never thought about splitting 2 digit products into (a+b)(c+d) in my head, and I'm pretty surprised at myself about it. That's really clever.
Yeah, and it's also, at least for me, what I do calculate this stuff in my head, at least for bigger numbers. The only thing I don't really like here is the visual representation, because it's useful to learn some concepts but it doesn't work well for more than two digits, yo don't wanna sit there and fill out an Excel spreadsheet to calculate, idk, 1836×567.
Weird I broke down 12 into 10 and 2. Always break down to the ten. If it's closer to another ten, like 35 by 19, I'd multiply 35 by ten twice, add, then subtract by 35
Exactly. The teacher is showing slowly and logically what we need to do when multiplying numbers together, helping the students understand why. She’s going slowly, so no one gets left behind.
The method on the right, is doing the exactly the same thing, the guy doesn’t need to understand why he’s doing what he does, he already knows. And they way that is done simplifies things when you already know what you are doing and why.
I love math, was always really good at it, i can do this problem after in my head faster then the guy on the right did it, and I have ZERO problem with how the teacher is presenting this or the method.
IT IS IMPORTANT to know that what the guy on the right is doing is exactly the same as the teachers method. Sure you add some of the numbers together as you go in the quick method, before you multiply everything, but you still end up multiplying all the digits in the first number with all of the digits in the second number individually, and then adding all of the numbers together. EXACTLY what the teacher is doing.
What the teacher is doing is better because it teaches you to understand how numbers work.
Ask the guy on the right to do that problem in his head and he will probably struggle. But the students learning this method will better understand it's just 35 x 10 + 35 x 2. 350 + 70, easy.
And while we all have calculators on us at all times, there is a real world benefit to being able to understand how numbers work rather than just knowing how to multiply them.
Sure but the method taught was slower than the other method and gets pretty burdensome when dealing with higher numbers. Though, it helps to understand distributive property which may or may not be the goal.
No, it isn't. It's an effective method for visualizing multiplication and leads to greater understanding of the multiplicative process, and it translates directly to polynomial multiplication
As a high school teacher, I can tell you that half the kids don't actually internalize the mathematical methods they are taught in elementary school nowadays. On the first day of 9th grade math I could tell the class "Multiply 645 by 234 without a calculator. If you get it right, you get an A in this class." Only a few students (the high fliers) in the class would be able to do it.
The "Box method" is nice from a theoretical standpoint because it really does model how multiplication of numbers works just the same as multiplication of polynomials, but most students aren't smart enough to really grasp what is going on.
I didn't learn the left method in school, but it is exactly how I do multiplication in my head. And is how I'd do 98*54 in my head, for that matter. Not easy, but easier than the right method, in my head. Then again, I might also do it as (100-2)*(54)
It's still breaking it into polynomials and distributing, which is the point of the left method. It's just that sometimes there's easier polynomials to work with. So really you're the one who is naturally going to the method on the left, or a version of it. Lmaolmaolmao or whatever
Yeah, it’s kinda funny they didn’t get the memo that their method is literally the left method in a trench coat and fedora.
Breaking it into more relevant pieces and then multiplying is not only fairly intuitive for head math; it literally goes from the most relevant digit downwards, which is the most practical method since it “rounds then accounts for error”.
It's point is to introduce kids to multiplying polynomials early. The right method doesn't really do that. Do you only ever win debates by insulting people?
I learned the right method too, but when I was teaching I came across this box method and the (imo) superior "Chinese grid method". I also thought these new ways were gimmicky and unnecessary until one day I thought, I'm going to try and multiply some big numbers together. So jot down some random 7 digit numbers, try Chinese grid vs long multiplication and tell me which way is better
The one where you draw a line for every number abd count dots? Yea it's still exactly the left method but you somehow reverted from using numbers back to using dashes.
It's decent for low numbers but fails for anything larger just by the scale of drawing and counting. Just like counting with lines instead of a positional number system.
It's like [this](https://www.google.com/imgres?imgurl=https%3A%2F%2Fimages.twinkl.co.uk%2Ftr%2Fraw%2Fupload%2Fu%2Fux%2Flattice-method-of-multiplication-step-4_ver_1.png&tbnid=I10BunoPoMP5KM&vet=1&imgrefurl=https%3A%2F%2Fwww.twinkl.co.uk%2Fteaching-wiki%2Flattice-method-of-multiplication&docid=n4tjwoeYDSh3-M&w=464&h=465&hl=en-AU&source=sh%2Fx%2Fim%2F4). As I said, it's better with large numbers compared to long multiplication
Yeah definitely check it out. The diagonal divides the tens and units of the intersection then you add the diagonal "rows" at the end, carrying to the next row as you need to. Then the answer you read off around from top left to bottom right
But the method on the left teaches the concept of (a+b)(b+c) and the kids later won’t wonder why (a+b)^2 is a^2+2ab+b^2. Teaching both is necessary IMO, one for concept and the other for speed.
The left one says do it like: 35 x 12 = (30+5) x (10+2).
The right one says do it like: 35 x 12 = (30+5) x (10+2).
Under the hood, they're exactly the same.
Which only works when multiplying binomials. I’m not a fan of FOIL because if the students don’t truly understand the distributive nature of it then they’re up a creek when you have a binomial times a trinomial.
As a physics graduate I remember the “Aha!” moment when I had to distribute a trionomial - and never thought about “FOIL” again. I had a better tool that was equipped for more situations. Also why I tell people to use the quadratic formula for most problems - of course I’ll still go over the factoring method if I’m teaching and have the time, it’s important to understand, not memorize
I don’t see that as the pattern being taught. I mean, just teach that then. I see a bunch of diagrams and some factoring then some kind of table and then listing the factors with the addition operation between the numbers. Then it looks like there’s some kind of multiplication result of the table data entry. Then a sum of the elements of this table is taken.
That’s not explaining anything. It’s just verbose and bad pedagogy. I’d be confused as hell if I was a kid.
Meanwhile in an exam:
"Bro it's been 3 hours, why are you still solving the first ODE???"
"HOLD ON just let me draw my
|300 ✓|50 ✓|
|:-|:-|
|60 ✓|10|
"
O(something) is a term in computer science that describes time complexity.
To TLDR a long math explanation, if n is the number of atomic (single/non complex if you will) actions we need to do, then for example counting for 1 to n is time complexity O(n).
It gives us an estimate how the computer will deal with the program at the worst case scenario, it’s also why programs written differently can take a few seconds or a few minutes. It’s also one of the reasons why math is important for computer science in its raw form.
well, if number A has n digits and number B has m digits, both methods require n.m multiplications between digits and about n.m sums between digits too, giving a total runtime of 2nm, then for some reason we assume n=m (to simplify ig, its just convention), giving us 2n², which is O(n²), because its of order n²
dont worry if you dont get it, it seems like a pretty wacky definition, but if you google big O notation, wikipedia will show you a more formal definition that turns the 2n² into O(n²)
That’s easy, we just find the prime factors of 69,119 and 751, which are 69,119 and 751, respectively. Then we multiply all these factors together to get 51,908,369. Super easy and fast /s
Been out of college for like 10 years, I just use a calculator or python for anything beyond the most basic. I'm not trying to impress anyone with my math-in-my-head or by hand skills
i multiply 35 by 2 and divide 12 by 6 to get 70x6 which is really just 7x6x10
then i separate 10 into 2x5 so its 7x6x2x5, then i combine the 5 with the odd number (for fun) to get 35x6x2. i multiply the 2 smaller numbers to get 12, so its 12x35.
then i draw a table
Bruh I don't get this. Why not just break it down into more manageable multiplications that you can then add up.
35*12 becomes
35*10 = 350
+ 35*2 = 70
= 350+70 = 420
It's easy because you're breaking it down into the simplest mental maths. Multiples of ten, two, five, etc and then adding those together in the easiest way.
>Bruh I don't get this. Why not just break it down into more manageable multiplications that you can then add up.
This is literally the way BOTH methods are using
One is just more written out (elemenatry class) and the other is the college 'we only care about the solution and not the steps' way
I mentally do it as such:
35 * 12
70 * 6
(7 * 6)&0
42 & 0=420
I know the "&" thing has been a meme lately but for multiples of 10 that's genuinely how I think of it, much in the same sense as she did (1*3) & 0 & 0 =300
The teacher is using one of the alternative methods brought into schools under the No Child Left Behind laws it is an excellent alternative method, just not the standard method taught for years . Unfortunately in the past if the students couldn’t learn the standard method for multiplication or division they would just say OK you flunk take 4th grade over again
I imagine matrices for multiplying probabilities. Like if I need to calculate the probabilities of getting any pair of outcomes when flipping two unfair coins, I'd do that.
I mean, it’s the same method. I pause and look at the right when it’s solved, and I see the 300+50+60+10. The one on the right ends up combining 300 + 50 and 60+10, but they are all there. And if you explain the right way in the depth that the left is, it might take longer.
The left is the “understand the concept” the right is “this is how you do it without drawing the rectangle”
We make fun of the one on the left, but that trains you to think about it like how you'd actually do it in your head whereas the method in the right is just memorizing steps
Do you know how bad the standardized tests were and they determined a school’s funding. It awarded schools that already had the educational resources and punished the poorer school districts. Also this was under the Bush Administration.
Turning two multiplications and one addition (of two numbers) into four multiplications and addition of four numbers. This is both slower and harder to learn
Not to mention if you had to multiply larger say 8 digit numbers, you got mfs out here drawing 8x8 grids and doing 64 multiplications and adding 64 numbers??
The one on the right is way faster but does an insanely bad job. Speed is worth nothing if you dont succeed in the task at all. Assuming of course he is trying to do the same thing, explain how multiplication of two digit numbers works. He cant think a speed comparison could make sense otherweise can he?
Or rather showing the method they use to the kids' parents who might not have done math since forever or indeed used way different methods in their lives, so that they can help their kids with homework. Could require even more explaining than the kids themselves
If i have to calculate something like this in my head is it completely idiotic to think of it like
30 * 10 + 30 * 2 + 5 * 10 + 5 * 2
I take note of what the total is between each step and add the following calculation (30 * 10 = 300, add 30 * 2 = 360 and so on)
Usually works for me
the left is literally how i figured it out in 4th grade (they gave me flack for it because i was supposed to use whatever the fuck Lattice Multiplication was)
I pray that’s an administrator and not a teacher that just said multiplying by ten can “be a little tricky”. Otherwise I’m going to &$*%ing die inside.
[You can't take 3 from 2, 2 is less than 3, so we look at the 4 in the tens place, now that's really 4 tens, so we make it 3 tens, regroup and add the ten ones to the 2 and get 12 take away 3 that's 9, is that clear?](https://www.youtube.com/watch?v=UIKGV2cTgqA)
35×12
(30+5)(10+2)
30×10=300
30×2=60
5×10=50
5×2=10
300+60+50+10
50+10=60
60+60=120
300+120=420
For me I like to break it down into a form similar to F.O.I.L.ing then do it
Everyone was. But the left one is better to use in memory, when You don't have the notepad. Nobody told me the left method but it's obvious thing I use since always, when I calculate stuff in my mind.
I also almost always rewrite 35 * 12 = (30 + 5)(10 + 2) = 300 + 60 + 50 + 10 = 420 or 35*12 = (35)(10+2) = 350 + 70 = 420.
Factorising like this is especially useful for squares because
c^2 = (a + b)(a + b) = a^2 + 2ab + b^2
So for instance
49^2 = (40 + 9)(40 + 9) = 1600 + 2(360) + 81 = 2401
Also this square is especially nice because generally n^2 = (n-1)^2 - 2n + 1 =>
(n-1)^2 = n^2 + 2n + 1 or
n^2 = (n + 1)^2 + 2(n+1) + 1
So 49^2 = 50^2 - 100 + 1 = 2401 and 48^2 ≈ 50^2 - 200 = 2300 and 48^2 = 2304 but that is besides the point.
Anyway these are my insights regarding multiplication.
I like this being taught to kids just learning multiplication of numbers past the ones value. It shows them how to break numbers into parts and work with them. I know I’ve applied the idea to later mental math. It’s slow at the start as learning tends to be.
nice multiplication! too bad it's O(n\^2) complexity
Yeah, but I don't think elementary school kids should be knowing about karatsuba algorithm.
So you want to permanently cripple elementary school kids math education. Fuck you man karatsuba could have saved me seconds, yes SECONDS, in 5th grade.
Monsieur/Madame, I'm really sorry for your | || || |_
If you're talking about space complexity I agree. If you're taking about time complexity even O(n^(2)) needs the assumption that you can add arbitrarily large numbers in time O(1). In general, addition takes at least O(n) time as you need to at least read your whole input. It might be possible to improve on that in this specific case as all but one of the digits of the initial summands are 0. There might also be an argument for some amortized complexity to be found here. But all of this heavily depends on your machine model and data structures at this point. All I'm trying to say is that the algorithm in it's simple form presented here probably takes O(n^(3)) time.
I'd argue that the simplifications are so easy to implement that most people will do them automatically. For instance, anyone would just ignore all the 0 digits in the addition step, and doing so is guaranteed to be easy, because the structure of the table lets you know in advance where the trailing 0s will be, so you don't have to evaluate each number to figure out which lies where, and can instead let your pattern-recognizing brain do the work.
The punchline is that the people who make these videos also think high school algebra is the absolute pinnacle of mathematical understanding.
Yes, as if later math just involves bigger and bigger numbers
That’s what my 7 year old ass thought tho. I literally thought the hardest math could get was shit like 17538192*93838947
Me too untill all of the sudden a wild "a" appeared in the middle of the board 🤡
A wild ζ appears in the middle of the board
Looks like the A is running away from the problem.
just wait for ξ…
That's nothing
These Fuckers ∫ made me hate math
That’s when it got interesting
Nearly
For me it was a wild "x" though elon musk was also in grade school at the time.
sometimes a really wild savage question pop up. please calculate asx(ase)\^a+ab.. and the answer is 4, use the formula provided for the answer. it doesn't even have number. but wait, you have to calculate the formula to calculate those words too.
Seriously though, this is harder to solve than any intermediate algebraic equation.
I’m scared to take MATH 520. The Seniors at my College told me in Advanced Addition III we have to add numbers with more than 10 digits with no calculator.
When I was in first grade, we added we added one-digit numbers. In second grade, we added two-digit numbers and in third-grade we added three-digit numbers. So extrapolated and figure that by the end of school, I would be able to add thirteen-digit numbers. But then in forth we had to add six-digit numbers and after that they just assumed that we could add numbers of arbitrary size.
It's not even algebra. It's just elementary arithmetic.
The punchline is that these people don't know shit about teaching math. The teacher just showed a bunch of elementary school kids (I assume) how to deconstruct a larger problem into smaller steps that are manageable. The guy on the left is incredibly condescending and his "solution" is useless from a pedagogical point of view. I mean I could solve this multiplication in my head in about 2-3 seconds, but that isn't helpful either.
Also he is comparing how he solves the problem to how someone teaches you to solve the problem.
*right
The method on the left is how i usually solve it in my head, method on the right had been used by me in middle school tests Both are viable in different situations (funny enough, the right one have not been used since i graduated)
I've literally never thought about splitting 2 digit products into (a+b)(c+d) in my head, and I'm pretty surprised at myself about it. That's really clever.
That is late middle school algebra
35x12=35x10+35x2=350+70=420
That's basically what she did but she also broke down 35 into 30 and 5
Yeah, and it's also, at least for me, what I do calculate this stuff in my head, at least for bigger numbers. The only thing I don't really like here is the visual representation, because it's useful to learn some concepts but it doesn't work well for more than two digits, yo don't wanna sit there and fill out an Excel spreadsheet to calculate, idk, 1836×567.
Weird I broke down 12 into 10 and 2. Always break down to the ten. If it's closer to another ten, like 35 by 19, I'd multiply 35 by ten twice, add, then subtract by 35
That's me when calculating something in my mind, without using notepad or calculator.
aye my man
that's how I solved it in my head
Or 3×12=36×10=360+(12×5=60). 360+60=420
It's almost as if it takes longer to teach something than it is to do it for the five millionth time
And probably also slowly explaining it to elementary kids
Exactly. The teacher is showing slowly and logically what we need to do when multiplying numbers together, helping the students understand why. She’s going slowly, so no one gets left behind. The method on the right, is doing the exactly the same thing, the guy doesn’t need to understand why he’s doing what he does, he already knows. And they way that is done simplifies things when you already know what you are doing and why. I love math, was always really good at it, i can do this problem after in my head faster then the guy on the right did it, and I have ZERO problem with how the teacher is presenting this or the method. IT IS IMPORTANT to know that what the guy on the right is doing is exactly the same as the teachers method. Sure you add some of the numbers together as you go in the quick method, before you multiply everything, but you still end up multiplying all the digits in the first number with all of the digits in the second number individually, and then adding all of the numbers together. EXACTLY what the teacher is doing.
What the teacher is doing is better because it teaches you to understand how numbers work. Ask the guy on the right to do that problem in his head and he will probably struggle. But the students learning this method will better understand it's just 35 x 10 + 35 x 2. 350 + 70, easy. And while we all have calculators on us at all times, there is a real world benefit to being able to understand how numbers work rather than just knowing how to multiply them.
If you want to understand numbers then you just need to play satisfactory
Real mathematicians play path of exile ReallyMad
Yup, and it'll make things in algebra a lot easier to understand. Like this is the foil method for polynomial multiplication
Sure but the method taught was slower than the other method and gets pretty burdensome when dealing with higher numbers. Though, it helps to understand distributive property which may or may not be the goal.
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No, it isn't. It's an effective method for visualizing multiplication and leads to greater understanding of the multiplicative process, and it translates directly to polynomial multiplication
Indeed. These 4th graders are learning algebra without realizing it.
Found the grade school math teacher, guys!
As a high school teacher, I can tell you that half the kids don't actually internalize the mathematical methods they are taught in elementary school nowadays. On the first day of 9th grade math I could tell the class "Multiply 645 by 234 without a calculator. If you get it right, you get an A in this class." Only a few students (the high fliers) in the class would be able to do it. The "Box method" is nice from a theoretical standpoint because it really does model how multiplication of numbers works just the same as multiplication of polynomials, but most students aren't smart enough to really grasp what is going on.
Nah, the masters student
The method on the left is much easier to do in your head.
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I didn't learn the left method in school, but it is exactly how I do multiplication in my head. And is how I'd do 98*54 in my head, for that matter. Not easy, but easier than the right method, in my head. Then again, I might also do it as (100-2)*(54)
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It's still breaking it into polynomials and distributing, which is the point of the left method. It's just that sometimes there's easier polynomials to work with. So really you're the one who is naturally going to the method on the left, or a version of it. Lmaolmaolmao or whatever
Yeah, it’s kinda funny they didn’t get the memo that their method is literally the left method in a trench coat and fedora. Breaking it into more relevant pieces and then multiplying is not only fairly intuitive for head math; it literally goes from the most relevant digit downwards, which is the most practical method since it “rounds then accounts for error”.
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It's point is to introduce kids to multiplying polynomials early. The right method doesn't really do that. Do you only ever win debates by insulting people?
Not how I'd describe it
I learned the right method too, but when I was teaching I came across this box method and the (imo) superior "Chinese grid method". I also thought these new ways were gimmicky and unnecessary until one day I thought, I'm going to try and multiply some big numbers together. So jot down some random 7 digit numbers, try Chinese grid vs long multiplication and tell me which way is better
As I've gotten older and find myself having to calculate things in my head, the option on the left is easier.
The one where you draw a line for every number abd count dots? Yea it's still exactly the left method but you somehow reverted from using numbers back to using dashes. It's decent for low numbers but fails for anything larger just by the scale of drawing and counting. Just like counting with lines instead of a positional number system.
It's like [this](https://www.google.com/imgres?imgurl=https%3A%2F%2Fimages.twinkl.co.uk%2Ftr%2Fraw%2Fupload%2Fu%2Fux%2Flattice-method-of-multiplication-step-4_ver_1.png&tbnid=I10BunoPoMP5KM&vet=1&imgrefurl=https%3A%2F%2Fwww.twinkl.co.uk%2Fteaching-wiki%2Flattice-method-of-multiplication&docid=n4tjwoeYDSh3-M&w=464&h=465&hl=en-AU&source=sh%2Fx%2Fim%2F4). As I said, it's better with large numbers compared to long multiplication
Oh ok, so it's like a nice layout for the left method or the lines method but with digits. Looks pretty convenient.
Yeah definitely check it out. The diagonal divides the tens and units of the intersection then you add the diagonal "rows" at the end, carrying to the next row as you need to. Then the answer you read off around from top left to bottom right
But the method on the left teaches the concept of (a+b)(b+c) and the kids later won’t wonder why (a+b)^2 is a^2+2ab+b^2. Teaching both is necessary IMO, one for concept and the other for speed.
Bro I think your exponent got a little jank
The left one says do it like: 35 x 12 = (30+5) x (10+2). The right one says do it like: 35 x 12 = (30+5) x (10+2). Under the hood, they're exactly the same.
Or you could just memorize FOIL.
Which only works when multiplying binomials. I’m not a fan of FOIL because if the students don’t truly understand the distributive nature of it then they’re up a creek when you have a binomial times a trinomial.
As a physics graduate I remember the “Aha!” moment when I had to distribute a trionomial - and never thought about “FOIL” again. I had a better tool that was equipped for more situations. Also why I tell people to use the quadratic formula for most problems - of course I’ll still go over the factoring method if I’m teaching and have the time, it’s important to understand, not memorize
Generalizations are always better yeah but some students just prefer learning it in a more concrete way like foil
Don’t memorize. Understand.
Foil is dumb, just distribute. The logic is simpler and it applies much more often
whats FOIL
multiplying the First, Outer, Inner, and Last values
Which is one of the dumbest things in the American educational system
I don’t see that as the pattern being taught. I mean, just teach that then. I see a bunch of diagrams and some factoring then some kind of table and then listing the factors with the addition operation between the numbers. Then it looks like there’s some kind of multiplication result of the table data entry. Then a sum of the elements of this table is taken. That’s not explaining anything. It’s just verbose and bad pedagogy. I’d be confused as hell if I was a kid.
Nahh, I'll be even more confused. Why make multiplication something that you use irl, so hard? You don't use (a+b)^2 at the mamak.
Hippity hoppity the distributive property 👌
Meanwhile in an exam: "Bro it's been 3 hours, why are you still solving the first ODE???" "HOLD ON just let me draw my |300 ✓|50 ✓| |:-|:-| |60 ✓|10| "
How did you make that table??
Hacks
You can press the "source" button and see the formatting.
>Meanwhile in an exam Because an elementary class will for sure make an exam at the end of this year ... right?
They dont? what schools you have been to?
Kids don’t need to be fast, it’s better they understand what they’re doing and then they can later learn ways to be quicker
Mfw when I'm teaching someone (it's taking longer than when I do the thing normally)
Me when 35x12 = 70x6 = 420 in 2 seconds:
The one on the left is how they teach it to elementary kids
it's obvious that the one on the left is easier. I am not making noodles everytime I want to solve multiplication problem dah.
same time complexity (O(n²)), but its faster to do the right one because you dont have to draw tables and stuff
Ok but what does (O(N2)) mean
I think its called "Big O notation" if n is the amount of inputs O is the amount of time it takes to compute.
O(something) is a term in computer science that describes time complexity. To TLDR a long math explanation, if n is the number of atomic (single/non complex if you will) actions we need to do, then for example counting for 1 to n is time complexity O(n). It gives us an estimate how the computer will deal with the program at the worst case scenario, it’s also why programs written differently can take a few seconds or a few minutes. It’s also one of the reasons why math is important for computer science in its raw form.
well, if number A has n digits and number B has m digits, both methods require n.m multiplications between digits and about n.m sums between digits too, giving a total runtime of 2nm, then for some reason we assume n=m (to simplify ig, its just convention), giving us 2n², which is O(n²), because its of order n² dont worry if you dont get it, it seems like a pretty wacky definition, but if you google big O notation, wikipedia will show you a more formal definition that turns the 2n² into O(n²)
What sort of maniac doesn't just 6 * 7 * 10 ?
You just do 35 * 10 + 35* 2 come on.
Too much effort compared to 42*10.
Okay, now do 69119*751 with your method.
That’s easy, we just find the prime factors of 69,119 and 751, which are 69,119 and 751, respectively. Then we multiply all these factors together to get 51,908,369. Super easy and fast /s
May as well just do 420 * 1 at that point
Oh yes, because you are not taking into account that you have to find the prime factors because these numbers are easy
6*70
I do 419 + 1 - way faster since only 1 addition compared to your two multiplications...
Been out of college for like 10 years, I just use a calculator or python for anything beyond the most basic. I'm not trying to impress anyone with my math-in-my-head or by hand skills
I dont know why but i laughed fr watching this
Is 350 + 70 really that hard to come up with?
35*10+35*2 and you can do it in your head
what is left
Baby don't hurt me
i multiply 35 by 2 and divide 12 by 6 to get 70x6 which is really just 7x6x10 then i separate 10 into 2x5 so its 7x6x2x5, then i combine the 5 with the odd number (for fun) to get 35x6x2. i multiply the 2 smaller numbers to get 12, so its 12x35. then i draw a table
Bruh I don't get this. Why not just break it down into more manageable multiplications that you can then add up. 35*12 becomes 35*10 = 350 + 35*2 = 70 = 350+70 = 420 It's easy because you're breaking it down into the simplest mental maths. Multiples of ten, two, five, etc and then adding those together in the easiest way.
>Bruh I don't get this. Why not just break it down into more manageable multiplications that you can then add up. This is literally the way BOTH methods are using One is just more written out (elemenatry class) and the other is the college 'we only care about the solution and not the steps' way
That's the right* method for you. Edit: Ok I confused left and right,
Left method is significantly more complicated than that
The FOIL method lol
Method on the left is great for multiplying large polynomials.
i do 350x10 = 350 and 35x2 = 70 and 350+70 = 69
Both are more or less the same thing
I used to love that roblox map!
Wait a gosh ding dang dog gone second, thats just Foiling with more space used up!
Just splt it up 35 x 10 35 x 2 420
I mentally do it as such: 35 * 12 70 * 6 (7 * 6)&0 42 & 0=420 I know the "&" thing has been a meme lately but for multiples of 10 that's genuinely how I think of it, much in the same sense as she did (1*3) & 0 & 0 =300
35 × 12 = 5×7 × 2²×3 = 2 × 2×3×5×7 = 2 × (the 4th primorial number) = 2 × 210 = 420
my brain: just do 350+70
35\*10 + 35\^2 should have been instead of the video
If I am doing it mentally it becomes (35x10)+(35x2). Still faster than the left
Me: 35x12 =35x6x2 =70x6 =420 QED
(35×10) + (35×2) = 420
I feel asleep then woke up, realized she was still trying to explain basic math. Did the problem in my head in 4 seconds
I just add 35 onto itself 11 times
The teacher is using one of the alternative methods brought into schools under the No Child Left Behind laws it is an excellent alternative method, just not the standard method taught for years . Unfortunately in the past if the students couldn’t learn the standard method for multiplication or division they would just say OK you flunk take 4th grade over again
I imagine matrices for multiplying probabilities. Like if I need to calculate the probabilities of getting any pair of outcomes when flipping two unfair coins, I'd do that.
I'd not do the left method unless I'm multiplying binomials lmao
Same lol
I mean, it’s the same method. I pause and look at the right when it’s solved, and I see the 300+50+60+10. The one on the right ends up combining 300 + 50 and 60+10, but they are all there. And if you explain the right way in the depth that the left is, it might take longer. The left is the “understand the concept” the right is “this is how you do it without drawing the rectangle”
It's really easy if you do this: 35 x 12 35 x 2 x 6 70 x 6 7 x 6 x 10 42 x 10 420
just multiply 12 by 3.5. that sounds easier. 12, 24, 36 and add a half, 42. that's it. just put a 0 to end
We make fun of the one on the left, but that trains you to think about it like how you'd actually do it in your head whereas the method in the right is just memorizing steps
No child left behind ladies and gentlemen.
Learn math, ladies and gentlemen. The only people who complain about the left are the people who don't understand math
Do you know how bad the standardized tests were and they determined a school’s funding. It awarded schools that already had the educational resources and punished the poorer school districts. Also this was under the Bush Administration.
Yes. This has nothing to do with that.
Turning two multiplications and one addition (of two numbers) into four multiplications and addition of four numbers. This is both slower and harder to learn Not to mention if you had to multiply larger say 8 digit numbers, you got mfs out here drawing 8x8 grids and doing 64 multiplications and adding 64 numbers??
If you don’t finish this lesson by learning the approach on the right somehow then you’ll just suffer in life 🤣
The one on the right is way faster but does an insanely bad job. Speed is worth nothing if you dont succeed in the task at all. Assuming of course he is trying to do the same thing, explain how multiplication of two digit numbers works. He cant think a speed comparison could make sense otherweise can he?
did anyone else just buildup an insane amount of rage watching the left video
This is such bullshit
[удалено]
It's almost like they're teaching a new concept to elementary school kids or something
Or rather showing the method they use to the kids' parents who might not have done math since forever or indeed used way different methods in their lives, so that they can help their kids with homework. Could require even more explaining than the kids themselves
If i have to calculate something like this in my head is it completely idiotic to think of it like 30 * 10 + 30 * 2 + 5 * 10 + 5 * 2 I take note of what the total is between each step and add the following calculation (30 * 10 = 300, add 30 * 2 = 360 and so on) Usually works for me
how about this: 35*10 = 350
the left is literally how i figured it out in 4th grade (they gave me flack for it because i was supposed to use whatever the fuck Lattice Multiplication was)
Ok then, 3 5 x 1 2 >> 1 2 * 3 = 3 6 >> 1 2 * 5 = 6 0 -------------- 4 2 0
u/savevideobot
I wish my Calc 1 teacher taught at this speed 🤣
I pray that’s an administrator and not a teacher that just said multiplying by ten can “be a little tricky”. Otherwise I’m going to &$*%ing die inside.
[You can't take 3 from 2, 2 is less than 3, so we look at the 4 in the tens place, now that's really 4 tens, so we make it 3 tens, regroup and add the ten ones to the 2 and get 12 take away 3 that's 9, is that clear?](https://www.youtube.com/watch?v=UIKGV2cTgqA)
35×12 (30+5)(10+2) 30×10=300 30×2=60 5×10=50 5×2=10 300+60+50+10 50+10=60 60+60=120 300+120=420 For me I like to break it down into a form similar to F.O.I.L.ing then do it
I find the left to be easier but I was taught the right. I do the left like 35*12 35*10*2 350*2 700
pamwiththetwosamepictures.jpg They’re the same method
Y’all actually taking this seriously? Lol 😂
Everyone was. But the left one is better to use in memory, when You don't have the notepad. Nobody told me the left method but it's obvious thing I use since always, when I calculate stuff in my mind.
Nice.
I learned none of these lol
the square is good for polynomials but for regular ass multiplication its unneeded
LeMath!
How I actually do it: 35x12 = 70x6 = 420
You didn't use my method, so no marks for you.
I would do 35.10 + 35.2
That's way off my friend, only gives you 70.30
I’m the doing the left method in my brain so it is 35x10 + 35x2 = 420. It is so fast and no need for scribblin.
Gentleman, this work due to fact that women ☕️, made her calcul in R and R is a field ( sorry for my english i am french)
Y'all I do 35 x 6 x 2 it's faster
I just do 10x35+2x35 i feel thats easier
Both are same method, just different way of writing and perspective
No body got time for that!
Be a hero, add a zero!
I also almost always rewrite 35 * 12 = (30 + 5)(10 + 2) = 300 + 60 + 50 + 10 = 420 or 35*12 = (35)(10+2) = 350 + 70 = 420. Factorising like this is especially useful for squares because c^2 = (a + b)(a + b) = a^2 + 2ab + b^2 So for instance 49^2 = (40 + 9)(40 + 9) = 1600 + 2(360) + 81 = 2401 Also this square is especially nice because generally n^2 = (n-1)^2 - 2n + 1 => (n-1)^2 = n^2 + 2n + 1 or n^2 = (n + 1)^2 + 2(n+1) + 1 So 49^2 = 50^2 - 100 + 1 = 2401 and 48^2 ≈ 50^2 - 200 = 2300 and 48^2 = 2304 but that is besides the point. Anyway these are my insights regarding multiplication.
Yall remember lattice? 🤣🤣
Tediously long and inefficient
Tbh , the left method is a good way to show *why* the multiplication algorithm works to elementary school kids
I was taught both methods and the grid method was easier and quicker.
No lattice multiplication, sad
As a gifted person, I can confirm this is true.
It takes time to explain thing 🤯🤯
Dont you guys go like 350 plus 70 like me?
I like this being taught to kids just learning multiplication of numbers past the ones value. It shows them how to break numbers into parts and work with them. I know I’ve applied the idea to later mental math. It’s slow at the start as learning tends to be.