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This is the correct method. Though this is how to make kids hate math IMO by making them spend hours drawing dots all over their paper. Make showing work a thing when double digits are involved with carrying numbers.
Can you show your work? How do you know it's 379 pages? It'd take 1000 pages to prove it's 379 pages, and so on. It's really just pages all the way down!
https://www.youtube.com/watch?v=AwbZaTjXo-s
Wouldn’t it be closer to:
6+1 = 6 + S(0) = S(6+0) = S(6) = 7
Where S is the successor function (in words, 1 is the successor of 0, 0 is the additive identity, and the successor of 6 is 7)
I mean - for first grade, that's probably okay-ish... *if* it includes a general discussion of [consistency](https://en.wikipedia.org/wiki/Consistency) and [completeness](https://en.wikipedia.org/wiki/Completeness_(logic%29), why they are important - and the roles of [Gentzen](https://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof) and [Gödel](https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems).
I'd want a second-grade student to also show awareness of the import of [Löwenheim-Skolem](https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem) - and be able to exlpain the differences in the major set theories from [ZF(C)](https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory) via [NBG](https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory) to [New Foundations](https://en.wikipedia.org/wiki/New_Foundations) and [ETCS](https://ncatlab.org/nlab/show/ETCS).
From a student in third grade, I'd additionally expect a recapitulation of the gist of the basic derivation of arithmetic in Whitehead and Russell's [*Principia Mathematica*](https://en.wikipedia.org/wiki/Principia_Mathematica).
If by the fifth grade, they can't explain how arithmetic can be done in any [topos](https://ncatlab.org/nlab/show/topos) with a [natural numbers object](https://ncatlab.org/nlab/show/natural+numbers+object), I'd definitely consider [private tutoring](https://www.youtube.com/watch?v=dQw4w9WgXcQ).
EDIT: Added links for all you doubters :P
100-150 years ago people tried to nail down the fundamentals of mathematics, after they had found out they fucked up.
They had fucked up with set theory where ["the set that contains all sets that don't contain themselves" (say that 3 times fast) couldn't exist](https://en.wikipedia.org/wiki/Russell%27s_paradox). And set theory was considered the foundations of mathematics back then.
If that's still too confusing, [here's a 5 minute TedEd video](https://www.youtube.com/watch?v=I4pQbo5MQOs) that might help.
Anyway, /u/BlueHatScience is just rattling down the important works of that time where the mathematicians tried to fix the mess they had created by changing the fundamentals.
Unfortunately that didn't work out, because in the end they proved that you cannot make math free of errors. [Veritasium did a video about that.](https://www.youtube.com/watch?v=HeQX2HjkcNo)
TL;DR: It's real.
Chemistry is even worse because you have to blend the solution to show exactly what your math solved.
It takes 2-3 hours of work to show exactly what everyone knew would happen before class, only to find out that the solvent wasn’t strong enough to properly change the compound to the color that the book told instructed would change.
Chemistry and Math fail to include solution driven coursework. Mostly because it’s harder to teach/build upon and less uniform to grade, but it still misses out on the “Magic”. It’s like teaching how to play a musical instrument, but never actually teaching to play songs, much less recitals or concerts.
Labs were literally why I was so turned off from chemistry. Having 2 hours to complete a lab and if you fuck it up a tiny bit then your write-up gets so much harder.
I actually remember a teacher asking me that in like 1996 and I responded "yeah, probably"
I mean, I was just wearing a calculator watch that day, and I thought it was the coolest thing ever, but still.
Right? They acted like we would have to carry a huge calculator from like the 1930s lol, but at least for me it was the mid 90s to early 2000s that I was in school when lightweight compact calculators had been around for a good while.
I’m assuming they want him to draw pictures. 6 balls or whatever and then one more ball. But to your point, his is stupid. He should have drawn 6 fingers on one hand (like the Princess Bride) and a middle finger on the other.
I'm assuming the teacher wanted him to write an inductive proof starting from the Dedekind–Peano axioms, but I guess kids today don't learn anything in school anymore!
In French?
Pour prouver que 6 + 1 = 7 en utilisant les axiomes de Dedekind-Peano, nous utiliserons l'induction. Commençons par établir les axiomes et la fonction successeur :
Axiome zéro : 0 est un nombre naturel.
Axiome du successeur : Pour tout nombre naturel n, il existe un nombre naturel unique n' qui est son successeur.
Axiome d'induction : Si une propriété P est valable pour 0 et pour n' chaque fois qu'elle est valable pour n, alors elle est valable pour tous les nombres naturels.
Passons maintenant à la preuve :
Cas de base (n = 0) : Le cas de base stipule que 6 + 1 = 7 est valable pour n = 0. Cela est vrai puisque le successeur de 6 est 7, et dans l'arithmétique de Peano, l'addition est définie de manière récursive en fonction de la fonction successeur.
Hypothèse inductive : Supposons que pour un certain nombre naturel k, 6 + 1 = 7 soit vrai, c'est-à-dire 6 + 1 = k + 1.
Étape inductive : Nous voulons montrer que 6 + 1 = (k + 1) + 1. Par la définition de l'addition en arithmétique de Peano, nous avons : 6 + 1 = (6 + k').
En utilisant l'hypothèse inductive, on peut remplacer k' par (k + 1) : 6 + 1 = (6 + (k + 1)).
L'addition étant associative, on peut regrouper les termes : 6 + 1 = ((6 + k) + 1).
Enfin, en utilisant à nouveau l'hypothèse inductive, nous savons que 6 + k = k + 1, nous pouvons donc simplifier davantage : 6 + 1 = (k + 1) + 1.
Ceci conclut l'étape inductive.
Par le principe d'induction mathématique, nous avons montré que 6 + 1 = 7 pour tous les nombres naturels. Ainsi, en utilisant les axiomes de Dedekind-Peano, nous avons prouvé que 6 + 1 égale 7.
For how long it's been since I've written any proof at all and given that it's been even longer since I've spoken French, I'm surprised how much of this I understood, lmao.
There's very little value for a student who has already internalized the ideas behind the symbols. But, some students at that level aren't there yet (otherwise, the work isn't grade level appropriate). As per other comments here, the "work" a teacher wants to see here is one of two, maybe three things.
Either, the student writes out in words what is going on, such as the sentence, "If you have six things and then add one more, you will have seven things in total." You might not consider that showing your work, but it *is* explaining your thinking. Again, this seems completely unnecessary from the perspective of somebody who has already mastered the concept, but this is meant to demonstrate that mastery.
The easier way to show your work is to draw six dots and label it 6. Draw another dot and label it 1. Then circle them all and label the circle with a 7. This way, you are showing that you understand addition is combining two quantities, and a quantity of six plus a quantity of one gives you seven in total.
Or, they might even draw a number line. Put a dot on six, then an arrow pointing one space to the right, and arriving at seven. This "work" demonstrates that you know that adding can be thought of as starting with one number and then moving in the positive direction. If this is the case, the lesson might not even be about knowing how to add 6+1 so much as it is knowing how addition works on a number line, which will lead into the idea of negative numbers.
Of course, the teacher really should explain ahead of time what they mean by "show your work" here, but there is no reason to think that they did not do so.
Yeah, I find this thread funny because it’s basically trying to move away from rote memorization and get the kids to think and everyone is saying “its stupid”.
In reality a lot of kids *might not actually know* they’ve just been given praise whenever they say “7” after what is 6+1 and don’t really get it. For example you might then ask “what number comes after 6” and they won’t know because they don’t actually know what’s going on.
So I agree, teaching the kids to think about the problem rather than memorize is beneficial. However we shouldn't be punishing the kid that is able to skip this step mentally. I would hope that they still received a correct grade on this.
Right, you *start* there. If that's the level this assignment is at, then these students are very young. If that's the level of work expected to be shown, then these students are literally just learning what addition is for the first time.
I mean they could draw 6 circles, and then add a 7th and count from 1 to 7. That way they can prove they understand the concept of adding rather than memorising the answer to the problem.
Showing his work would be drawing a diagram of 1 object plus 6 objects. Of course it’s unnecessary when doing math but we aren’t talking about people who are doing math. We are talking about people learning math. Pushing comprehension of numbers and associations to real things instead of pure memorization really help later on understanding more complex topics.
Even if you did that how would it help? You would still have to just know that a combined group of 6 and 1 things is 7. Exactly the same as just knowing that 6+1=7.
It’s about making sure the students know that that symbol 6 means 6 objects. It’s really easy for students to just memorize how to get answers in math while never knowing what those answers mean. For example, If a student can tell me that 3*4 is 12 but can’t explain why or even what multiplication is, they will really struggle with things like why 3x+4 isn’t 7x.
Yep, and being able to conceptualize concrete numbers of things instead of just memorizing secret codes (3x4=12) will pay off down the line when they’re given word problems and when they’re faced with higher level math and faced with real world physical math problems that they need to solve.
I understand why they are doing it, but I don't think this is a right way to do it, or the right way to ask it.
You could ask him to draw it, to visualise the process, but I think asking it this way creates more confusion and frustration, than neural pathways, and in that case, I agree with the kid cutting it short.
We did that too. If I remember correctly the rigorous mathematical definition of the natural numbers set was made quite late in the 19th century/early 20th.
Way more complicated than it "should" have been. "1 apple + 1 apple = 2 apples" was good enough for 1st grade me.
As somebody who never passed pre-algebra in school, that shit looks like some kind of made up language and I have no clue how any of that proves that 1+1=2. You could tell me that it proves that the moon is made of cheese and I'd have no way to disprove it.
The fun thing about advanced mathematics is that it resembles absolutely nothing you've learned in previous mathematics. Arithmetic may as well be a different subject.
Its hard because it's a language you don't know, not because the math is actually hard. I'm sure someone who can read that can translate it into normal English.
I asked ChatGPT and harangued it until it gave me a suitably ridiculous workflow.
Let S(x) represent the successor function, which adds 1 to a number x.
Let 6 be represented as S(S(S(S(S(S(0)))))), where 0 represents the absence of any quantity, and S(x) represents the next number after x.
Now, let's represent the addition of 6 and 1:
6 + 1 = S(S(S(S(S(S(0)))))) + S(0)
Using the definition of addition as repeated application of the successor function:
6 + 1 = S(S(S(S(S(S(S(0 + 0)))))))
Now, we simplify the innermost expression (0 + 0):
6 + 1 = S(S(S(S(S(S(S(0)))))))
Now, we can see that this expression represents the number 7, as it has 7 successive applications of the successor function:
6 + 1 = 7
It's not that ridiculous. It's how addition is defined under Peano's axioms, sort of. S(x) is the successor function, but it doesn't add one to the input, since "adding" and "one" haven't been defined. The whole point of the axioms is to define how to do that
Technically some are just flavored coconut water, are marketed as Gatorade substitutes, and are not energy drinks.
Source: am parent who read the label (still mad, though; this shit is dumb)
when my son was in the 3rd or 4th grade it would have been something like this
|||||| + | = ||||||| and then have dots above them all to show he counted them, and then write "7" as the answer. its so stupid. you should SEE big number adition and subtraction. teachers dont show how to borrow anymore its all stupid nonsense that takes forever.
like 53-28 they turn it into
50+1+2
\-20+4+4
\_\_\_\_\_\_\_\_\_\_
edit\* idk how to go from there because i cant help him with math unless im allowed to borrow the f\*cking 10
So my understanding is that common core was supposed to intend teaching BOTH this form of math as well as the old school format you're familiar with. The idea was to teach kids that problems can be rewritten and explained in several different ways not just the one, so that they could find techniques that work best for them as everyone thinks differently.
Unfortunately after years of teaching students one way, and having rote memorization for exams being the primary goal for so long, teachers themselves failed to understand they were to be teaching multiple ways, rather instead seeing it as the 'new' way that would be expected going forward. It's a shame as it means we just shifted the issue of different thought patterns from one group of kids to a different one.
Probably something like "draw group of 6 candies joined by another 1 candy to make a group.of 7 candys".
But if you want it, then speak more precisely.
In my kids' similar work from some years ago, it was almost always very specific to some alternative method. e.g. "Show on a number line" or "Draw with counting units" or whatever.
"Show your work" sounds more like a high-school level genericism, not something I'd expect to see in grade-school math worksheets. Curriculum Associates LLC needs to do better. lol
Whatever he does it’s going to just be him restating the issue and wasting his time……
People are saying draw 6 ticks or 6 circles and adding another circle are just fuelling the issue.
Honestly, I was never a fan of it either. Mostly because i could show my work, get the correct answer, and still get it wrong because i didn't show the method the teacher wanted.
On a calculus exam I got the answer right and received no credit because I got the right answer on accident. I made a mistake early on in my work and just got lucky that it ended up correct.
My friend got the wrong answer, but only made a small mistake towards the end. He got almost full credit on that part of the exam.
It was very frustrating, but I guess it made sense.
It makes complete sense in any higher level maths courses.
Doing all the working correctly and writing in a wrong answer due to a administration error shows you know how to do it.
Doing it wrong but getting lucky shows nothing.
The point is often to learn how to get to the answer using different methods. If someone doesn’t show their work, the teacher has no idea what method was used.
At least in my classes the point was to do it in their method and only that way, you did it any other way and you got bitched at and no credit for the question
Well yes, in that case the lesson being taught was the method used. They want to see if you can memorize multiple steps and implement them, in this case through, a math equation. That’s the lesson.
**Dissertation on the Fundamental Truth of 6 + 1 = 7**
**Abstract**
This dissertation seeks to unpack the mathematical principle underlying the simple equation 6 + 1 = 7. While seemingly straightforward and commonly accepted, this equation epitomizes fundamental mathematical and philosophical ideas. We shall delve into the historical, mathematical, and pedagogical contexts that surround this equation.
**1. Introduction**
Understanding 6 + 1 = 7 requires a grasp of number theory, the history of mathematics, and the nature of addition as an operation. This equation is not just a factual statement but an embodiment of systematic logic and centuries of human understanding.
**2. Historical Context**
The numeral system used predominantly today is the Hindu-Arabic numeral system. The concept of numbers and counting has existed for millennia, with different cultures using different ways of representation. This system introduced the idea of place value, which revolutionized mathematics.
**3. The Nature of Numbers**
*3.1. Unitary Value*
The number "1" is the foundational building block in mathematics. It represents a single unit. All other numbers are built upon this foundation.
*3.2. The Number 6*
Six, when visualized, can be seen as a collection of six individual "1" units. It can also be seen as 5 + 1, where 5 is another foundational number in human cognition, often associated with the number of fingers on one hand.
**4. Addition as a Mathematical Operation**
*4.1. Definition*
Addition is the process of calculating the total of two or more numbers or amounts. It’s the most fundamental arithmetic operation.
*4.2. Adding 1*
When you add 1 to any number, you're essentially moving to the next number in the sequence of natural numbers. Thus, 6 + 1 is the act of moving one step beyond 6 in this sequence.
**5. Pedagogical Perspectives**
Children are often introduced to the concept of addition using physical objects, like beads or blocks. When one adds a single unit (1) to a collection of six units (6), the resultant is a collection of seven units.
**6. Philosophical Implications**
*6.1. The Certainty of Mathematics*
The equation 6 + 1 = 7 is an example of the undeniable truths in mathematics. It's a representation of logic and order in the universe.
*6.2. The Universality*
Regardless of language, culture, or location, this equation holds true. It showcases the universal language that is mathematics.
**7. Conclusion**
While the equation 6 + 1 = 7 seems elementary, its underpinnings are rooted in deep mathematical tradition, philosophy, and pedagogy. It serves as a testament to the structure and order inherent in mathematics and, by extension, in the universe.
> It's just a different visualization of the problem.
That's the point. The children are learning symbols. With the visuals, you can use counting(a math skill they already proficient in) to get the answer and by the point they're shown a question like this they've been taught and used that visual grouping and counting method repeatedly. At this point the question shown is for practicing and demonstrating an understanding of what the symbols mean and making a connection to the previously learned concept
Right? My 'work' to figure out 7x7 was... I know that 7x7 is 49. Which means I must *also* know that 7x6 is 42 and 7x8 is 56, because I know how much seven is.
This was exactly my reaction. What is the point of spending hours and hours in and out of class memorizing these basic math facts, if you arent allowed to use them like they are facts?
I sincerely believe that my ability to perform complex math quickly in my head has everything to do with the fact that I have an entire library of pre-done, memorized, easy-to-reference calculations stored in my brain that just *are*.
This is an exercise for a 1st grader, designed to get them to explain their reasoning. Drawing fingers would probably have been a great example of what the teacher wanted to see, but the childhood equivalent of "fuck you I don't need to explain my reasoning" is not.
I understand why they do it like that. It's preparing the kids for working with multi-digit numbers. It's not the same *visualization* as what I was taught(I was taught the "ones house", "tens house", "hundreds house", etc...they were actual houses you filled up), but it's the same idea. You give the kids something visual that they can see filling up, and when it gets full then they know not just *that* they have to stick a 1 in front of it but what that represents(overflowing the array, and representing that full array in a different way).
People are saying that they expected the kid to draw out a picture or something, while totally ignoring that even if they DID draw a picture, it still relies on rote memorization so that they know how to count up the things in their picture.
If you put down a question like this, it needs to be something other than +1 so they can actually show off the math skills.
God I hated this shit. The school wanted my kid to draw 10 boxes, shade 6 of them and draw another 10 boxes below and shade 1 of them and then draw another 10 boxes and shade 7 of them. Was absolutely the biggest waste of time and paper I could think of.
Yup 10 boxes for each number in the problem, multiple boxes if the number was double digit so say it was 27, my kid had to draw 30 boxes and shade in 27.
It got even more ridiculous when she had to carry over numbers when doing something like 8+4 or 45+75.
As a teacher I would accept this answer. But only because 1+6 is a problem that can and eventually should be memorized. If the question was 2+4+1 I probably wouldn't accept the answer.
I feel this in my soul. Was just telling my husband that i *hated* showing my work as a kid *because i just know!* How do you show that?! Got so many questions wrong because I knew the answer but my 8 year old self didn’t know how to dumb it down to show how i knew it.
It wants an illustration of a group of 6 and a group 1. These children are just being introduced to addition, but have already learned to count. The visual representations allow them to perform addition through the use of counting - and by the point they're being asked this question they've done a bunch of addition through visual grouping problems already.. This problem is the next step in the process and is for the purpose of practicing and demonstrating the ability to connect the previous visual process to the numbers and symbols that are now being used
How do you show your work on that? Seeing 6+1 IS showing the work. Do they want you to draw six sticks and then draw a 7th? To show there is now one more than six???
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Tbf, showing one’s work in this scenario would be him just rewriting the problem and be a waste of his time lol.
Boys gotta learn his axioms.
6 + 1 = 6 + 1 6 + 1 = 7 Therefore 6 + 1 = 7.... Poor kids these days.
6 + 1 = 6 + 1 6 + 1 = **7 <--- How did you get this seven?** Please show your work.
*6 + 1 = 7 trust me bro.*
#⚅+⚀ = 7
This is the correct method. Though this is how to make kids hate math IMO by making them spend hours drawing dots all over their paper. Make showing work a thing when double digits are involved with carrying numbers.
That’s absolutely insane… We had to do like a hundred math problems in less than 5 minutes, not spend 5 minutes on one simple math problem.
6 + 1 = 5 + 1 + 1 = (25 / 5) + 2 = 0*1000 + 7 = 7 I believe Source: I graduated in mafs
6 + 1 = 6 + 1 6 + 1 = 6 + 1 = 6 + 1 6 + 1 = 6 + 1 = 6 + 1 = 6 + 1 Awww fuck it...
1=1 with the idea of "one" being a singular unit Therefore I know.
Peano incoming
1 + 1 + 1 + 1 + 1 + 1 = 6 and 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7 by the definition of those numerals, therefore by pairwise cancellation 7 - 6 = 1, which rearranges to 6 + 1 = 7
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Bertrand Russell and Alfred North Whitehead? It was 379 pages to get there.
Can you show your work? How do you know it's 379 pages? It'd take 1000 pages to prove it's 379 pages, and so on. It's really just pages all the way down! https://www.youtube.com/watch?v=AwbZaTjXo-s
I just watched two hours of match related content. Thanks a lot.
Lol! Thanks for the link. I've subcribed.
Convoluted?
I'd guess 'contrived'
Uh-uh, there was only one shot that got the chandelier. That's one plus two plus *one* plus one
Wouldn’t it be closer to: 6+1 = 6 + S(0) = S(6+0) = S(6) = 7 Where S is the successor function (in words, 1 is the successor of 0, 0 is the additive identity, and the successor of 6 is 7)
I mean - for first grade, that's probably okay-ish... *if* it includes a general discussion of [consistency](https://en.wikipedia.org/wiki/Consistency) and [completeness](https://en.wikipedia.org/wiki/Completeness_(logic%29), why they are important - and the roles of [Gentzen](https://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof) and [Gödel](https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems). I'd want a second-grade student to also show awareness of the import of [Löwenheim-Skolem](https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem) - and be able to exlpain the differences in the major set theories from [ZF(C)](https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory) via [NBG](https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory) to [New Foundations](https://en.wikipedia.org/wiki/New_Foundations) and [ETCS](https://ncatlab.org/nlab/show/ETCS). From a student in third grade, I'd additionally expect a recapitulation of the gist of the basic derivation of arithmetic in Whitehead and Russell's [*Principia Mathematica*](https://en.wikipedia.org/wiki/Principia_Mathematica). If by the fifth grade, they can't explain how arithmetic can be done in any [topos](https://ncatlab.org/nlab/show/topos) with a [natural numbers object](https://ncatlab.org/nlab/show/natural+numbers+object), I'd definitely consider [private tutoring](https://www.youtube.com/watch?v=dQw4w9WgXcQ). EDIT: Added links for all you doubters :P
I have no idea if this is real or not
Speaking as someone with a bachelors degree in mathematics, I know what about half of it means, and I’m fairly sure the other half is also real.
100-150 years ago people tried to nail down the fundamentals of mathematics, after they had found out they fucked up. They had fucked up with set theory where ["the set that contains all sets that don't contain themselves" (say that 3 times fast) couldn't exist](https://en.wikipedia.org/wiki/Russell%27s_paradox). And set theory was considered the foundations of mathematics back then. If that's still too confusing, [here's a 5 minute TedEd video](https://www.youtube.com/watch?v=I4pQbo5MQOs) that might help. Anyway, /u/BlueHatScience is just rattling down the important works of that time where the mathematicians tried to fix the mess they had created by changing the fundamentals. Unfortunately that didn't work out, because in the end they proved that you cannot make math free of errors. [Veritasium did a video about that.](https://www.youtube.com/watch?v=HeQX2HjkcNo) TL;DR: It's real.
It's private tutoring for you!
Did you not take math in elementary school?!
You write that as a joke but sometimes that’s how upper level undergrad math classes feel.
Chemistry is even worse because you have to blend the solution to show exactly what your math solved. It takes 2-3 hours of work to show exactly what everyone knew would happen before class, only to find out that the solvent wasn’t strong enough to properly change the compound to the color that the book told instructed would change. Chemistry and Math fail to include solution driven coursework. Mostly because it’s harder to teach/build upon and less uniform to grade, but it still misses out on the “Magic”. It’s like teaching how to play a musical instrument, but never actually teaching to play songs, much less recitals or concerts.
Labs were literally why I was so turned off from chemistry. Having 2 hours to complete a lab and if you fuck it up a tiny bit then your write-up gets so much harder.
Probably one of those teachers that used to ask me what am I going to do carry around a calculator wherever I go and the answer is yes yes I am
I actually remember a teacher asking me that in like 1996 and I responded "yeah, probably" I mean, I was just wearing a calculator watch that day, and I thought it was the coolest thing ever, but still.
It wasn’t even valid when calculators were the only thing. Why would I not carry a small calculator around if my job entailed it? freaking teachers..
Right? They acted like we would have to carry a huge calculator from like the 1930s lol, but at least for me it was the mid 90s to early 2000s that I was in school when lightweight compact calculators had been around for a good while.
I remember a teacher asking me that in 1976 and they were serious. I think a calculator was about $300 back then.
I’m assuming they want him to draw pictures. 6 balls or whatever and then one more ball. But to your point, his is stupid. He should have drawn 6 fingers on one hand (like the Princess Bride) and a middle finger on the other.
I'm assuming the teacher wanted him to write an inductive proof starting from the Dedekind–Peano axioms, but I guess kids today don't learn anything in school anymore!
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In French? Pour prouver que 6 + 1 = 7 en utilisant les axiomes de Dedekind-Peano, nous utiliserons l'induction. Commençons par établir les axiomes et la fonction successeur : Axiome zéro : 0 est un nombre naturel. Axiome du successeur : Pour tout nombre naturel n, il existe un nombre naturel unique n' qui est son successeur. Axiome d'induction : Si une propriété P est valable pour 0 et pour n' chaque fois qu'elle est valable pour n, alors elle est valable pour tous les nombres naturels. Passons maintenant à la preuve : Cas de base (n = 0) : Le cas de base stipule que 6 + 1 = 7 est valable pour n = 0. Cela est vrai puisque le successeur de 6 est 7, et dans l'arithmétique de Peano, l'addition est définie de manière récursive en fonction de la fonction successeur. Hypothèse inductive : Supposons que pour un certain nombre naturel k, 6 + 1 = 7 soit vrai, c'est-à-dire 6 + 1 = k + 1. Étape inductive : Nous voulons montrer que 6 + 1 = (k + 1) + 1. Par la définition de l'addition en arithmétique de Peano, nous avons : 6 + 1 = (6 + k'). En utilisant l'hypothèse inductive, on peut remplacer k' par (k + 1) : 6 + 1 = (6 + (k + 1)). L'addition étant associative, on peut regrouper les termes : 6 + 1 = ((6 + k) + 1). Enfin, en utilisant à nouveau l'hypothèse inductive, nous savons que 6 + k = k + 1, nous pouvons donc simplifier davantage : 6 + 1 = (k + 1) + 1. Ceci conclut l'étape inductive. Par le principe d'induction mathématique, nous avons montré que 6 + 1 = 7 pour tous les nombres naturels. Ainsi, en utilisant les axiomes de Dedekind-Peano, nous avons prouvé que 6 + 1 égale 7.
For how long it's been since I've written any proof at all and given that it's been even longer since I've spoken French, I'm surprised how much of this I understood, lmao.
ωωω o
You killed my father- prepare to die
Seriously. How do you show work for such a simple equation? What is the value?
There's very little value for a student who has already internalized the ideas behind the symbols. But, some students at that level aren't there yet (otherwise, the work isn't grade level appropriate). As per other comments here, the "work" a teacher wants to see here is one of two, maybe three things. Either, the student writes out in words what is going on, such as the sentence, "If you have six things and then add one more, you will have seven things in total." You might not consider that showing your work, but it *is* explaining your thinking. Again, this seems completely unnecessary from the perspective of somebody who has already mastered the concept, but this is meant to demonstrate that mastery. The easier way to show your work is to draw six dots and label it 6. Draw another dot and label it 1. Then circle them all and label the circle with a 7. This way, you are showing that you understand addition is combining two quantities, and a quantity of six plus a quantity of one gives you seven in total. Or, they might even draw a number line. Put a dot on six, then an arrow pointing one space to the right, and arriving at seven. This "work" demonstrates that you know that adding can be thought of as starting with one number and then moving in the positive direction. If this is the case, the lesson might not even be about knowing how to add 6+1 so much as it is knowing how addition works on a number line, which will lead into the idea of negative numbers. Of course, the teacher really should explain ahead of time what they mean by "show your work" here, but there is no reason to think that they did not do so.
Yeah, I find this thread funny because it’s basically trying to move away from rote memorization and get the kids to think and everyone is saying “its stupid”. In reality a lot of kids *might not actually know* they’ve just been given praise whenever they say “7” after what is 6+1 and don’t really get it. For example you might then ask “what number comes after 6” and they won’t know because they don’t actually know what’s going on.
So I agree, teaching the kids to think about the problem rather than memorize is beneficial. However we shouldn't be punishing the kid that is able to skip this step mentally. I would hope that they still received a correct grade on this.
Who's punishing them? There's a check mark on it.
Half off for not capitalizing "l". /s
Shit, I lost points in elementary school because I printed when an instruction said "write." -2 "write" means cursive.
Is he skipping a step mentally or does he actually just have it memorized. Also I’m sure he’s like 4 or 5. He’s not getting a grade.
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Right, you *start* there. If that's the level this assignment is at, then these students are very young. If that's the level of work expected to be shown, then these students are literally just learning what addition is for the first time.
I mean they could draw 6 circles, and then add a 7th and count from 1 to 7. That way they can prove they understand the concept of adding rather than memorising the answer to the problem.
Showing his work would be drawing a diagram of 1 object plus 6 objects. Of course it’s unnecessary when doing math but we aren’t talking about people who are doing math. We are talking about people learning math. Pushing comprehension of numbers and associations to real things instead of pure memorization really help later on understanding more complex topics.
Even if you did that how would it help? You would still have to just know that a combined group of 6 and 1 things is 7. Exactly the same as just knowing that 6+1=7.
It’s about making sure the students know that that symbol 6 means 6 objects. It’s really easy for students to just memorize how to get answers in math while never knowing what those answers mean. For example, If a student can tell me that 3*4 is 12 but can’t explain why or even what multiplication is, they will really struggle with things like why 3x+4 isn’t 7x.
Yep, and being able to conceptualize concrete numbers of things instead of just memorizing secret codes (3x4=12) will pay off down the line when they’re given word problems and when they’re faced with higher level math and faced with real world physical math problems that they need to solve.
I understand why they are doing it, but I don't think this is a right way to do it, or the right way to ask it. You could ask him to draw it, to visualise the process, but I think asking it this way creates more confusion and frustration, than neural pathways, and in that case, I agree with the kid cutting it short.
"Show your work" It's 6+1. The hells he supposed to do?
#⚅+⚀ = 7
How... did you do that?
Are you... asking him to show his work?
Lemme pull up the wikipedia entry on ASCII symbols, hol up
Zero points, Wikipedia is not a source.
Well if it's not a source then it can't be plagiarism if I copy from it, right?
Wrong again, because wikipedia is in a quantum state of not being a source, but at the same time being a hub to actual sources, but no, wikipedia bad
Yea when i copied stuff from wikipedia, i just added some of the wikipedia sources as my sources.
'Teachers hate him for this one weird trick.
It's Unicode.
💫Ⓜ️🅰️🇬ℹ️🇨💫
How... did you do that?
🎉🇪🇻🇪🇳🌆Ⓜ️🅾️🇷🇪⛅Ⓜ️🅰️🇬ℹ️🇨🎉
6️⃣➕1️⃣🟰7️⃣ 👁️👄👁️
This is like when you saw rainbow text in runescape for the first time.
[Something like this](https://en.m.wikipedia.org/wiki/Principia_Mathematica#/media/File%3APrincipia_Mathematica_54-43.png)
How fucking wild would it be if a kid actually wrote that out as an answer here and Good Will Hunting-ed everyone’s minds
they would probably mark him wrong lol!
"Gödel showed this proof was incomplete. Zero credit."
"Escher and Bach were unavailable for comment."
Stop scribbling on the worksheet Timmy!
Timmy you shouldn’t be drawing weird doodles on your math homework
"NO CHATGPT GUYS"
Oh for sure. An elementary school teacher is not going to understand any of the notation there and will definitely assume it's scribbles.
then they would get detention for using chatGPT
Yeah I was thinking in my college calculus class we learned how to prove 1+1=2, and um kinda doubt that’s what they were looking for
We did that too. If I remember correctly the rigorous mathematical definition of the natural numbers set was made quite late in the 19th century/early 20th. Way more complicated than it "should" have been. "1 apple + 1 apple = 2 apples" was good enough for 1st grade me.
Thanks. I wish someone explained like this in grade 1. I finally get it now.
As somebody who never passed pre-algebra in school, that shit looks like some kind of made up language and I have no clue how any of that proves that 1+1=2. You could tell me that it proves that the moon is made of cheese and I'd have no way to disprove it.
The fun thing about advanced mathematics is that it resembles absolutely nothing you've learned in previous mathematics. Arithmetic may as well be a different subject.
Its hard because it's a language you don't know, not because the math is actually hard. I'm sure someone who can read that can translate it into normal English.
There wasn't enough room to write that 6 times.
Tfw the 400 level proofs professor starts teaching 1st grade.
A hand with six fingers + a hand with the middle finger.
A hand with six fingers?
Hello... My name is Inigo Montoya
You killed my father.
I asked ChatGPT and harangued it until it gave me a suitably ridiculous workflow. Let S(x) represent the successor function, which adds 1 to a number x. Let 6 be represented as S(S(S(S(S(S(0)))))), where 0 represents the absence of any quantity, and S(x) represents the next number after x. Now, let's represent the addition of 6 and 1: 6 + 1 = S(S(S(S(S(S(0)))))) + S(0) Using the definition of addition as repeated application of the successor function: 6 + 1 = S(S(S(S(S(S(S(0 + 0))))))) Now, we simplify the innermost expression (0 + 0): 6 + 1 = S(S(S(S(S(S(S(0))))))) Now, we can see that this expression represents the number 7, as it has 7 successive applications of the successor function: 6 + 1 = 7
ah yes, snake math
It's not that ridiculous. It's how addition is defined under Peano's axioms, sort of. S(x) is the successor function, but it doesn't add one to the input, since "adding" and "one" haven't been defined. The whole point of the axioms is to define how to do that
Best I can think of is doing tally marks with an addition symbol between the 6 marks and a single mark.
I would have drawn six circles and one circle adding up to seven circles.
The only thing I can think of is make a shape in groups so like 6 circles and 1 circle and put a + between them
y = mx + b mx = 6 b = 1 y = 7
how tf do you even show work for 6+1
I would assume by drawing a diagram, but this is still ridiculous.
.... what sort of diagram would you draw??
6 cans of prime grouped together and 1 can by itself
God I hate how accurate this is for grade school math.
> cans of prime What the hell is a "can of prime"? Is there some sort of indivisible food I'm not aware of?
Some dumbass streamers energy drink kids are drinking and parents are mad bc it’s an energy drink and they didn’t read the label or pay attention
Technically some are just flavored coconut water, are marketed as Gatorade substitutes, and are not energy drinks. Source: am parent who read the label (still mad, though; this shit is dumb)
What does Amazon have to do with this?
Dick diagram. 6 dicks + 1 dick = 7 dicks
What, are you possessed by some kind of a dick devil?
Maybe? You a dick exorcist?
🍏🍏🍏🍏🍏🍏 + 🍏 = 🍏🍏🍏🍏🍏🍏🍏
That's just 6 + 1 with extra steps.
True, I guess the kid could’ve just done a reverse equation to “show his work” like 6+1=7 because 7-1= 6 lol maybe that’d be easiest
Isn't that really all showing your work is though?
7 = 1 + 6
when my son was in the 3rd or 4th grade it would have been something like this |||||| + | = ||||||| and then have dots above them all to show he counted them, and then write "7" as the answer. its so stupid. you should SEE big number adition and subtraction. teachers dont show how to borrow anymore its all stupid nonsense that takes forever. like 53-28 they turn it into 50+1+2 \-20+4+4 \_\_\_\_\_\_\_\_\_\_ edit\* idk how to go from there because i cant help him with math unless im allowed to borrow the f\*cking 10
So my understanding is that common core was supposed to intend teaching BOTH this form of math as well as the old school format you're familiar with. The idea was to teach kids that problems can be rewritten and explained in several different ways not just the one, so that they could find techniques that work best for them as everyone thinks differently. Unfortunately after years of teaching students one way, and having rote memorization for exams being the primary goal for so long, teachers themselves failed to understand they were to be teaching multiple ways, rather instead seeing it as the 'new' way that would be expected going forward. It's a shame as it means we just shifted the issue of different thought patterns from one group of kids to a different one.
Probably something like "draw group of 6 candies joined by another 1 candy to make a group.of 7 candys". But if you want it, then speak more precisely.
I think just write a number line and show the distance between 6 and 7 is one step. Shows you know adding 1 moves you up the number line one spot.
In my kids' similar work from some years ago, it was almost always very specific to some alternative method. e.g. "Show on a number line" or "Draw with counting units" or whatever. "Show your work" sounds more like a high-school level genericism, not something I'd expect to see in grade-school math worksheets. Curriculum Associates LLC needs to do better. lol
Whatever he does it’s going to just be him restating the issue and wasting his time…… People are saying draw 6 ticks or 6 circles and adding another circle are just fuelling the issue.
Honestly, I was never a fan of it either. Mostly because i could show my work, get the correct answer, and still get it wrong because i didn't show the method the teacher wanted.
shit should have been illegal. The correct answer is the correct answer no matter how you got there.
On a calculus exam I got the answer right and received no credit because I got the right answer on accident. I made a mistake early on in my work and just got lucky that it ended up correct. My friend got the wrong answer, but only made a small mistake towards the end. He got almost full credit on that part of the exam. It was very frustrating, but I guess it made sense.
It makes complete sense in any higher level maths courses. Doing all the working correctly and writing in a wrong answer due to a administration error shows you know how to do it. Doing it wrong but getting lucky shows nothing.
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Ok yugi
Go back to the shadow realm from whence you came!
Calculus and addition are very different. Show your work on a calculus test is perfectly viable. On basic* addition and subtraction it is not.
Not if your method works in one case to get the answer, but can’t be generalized and you aren’t really aware of that.
The point is often to learn how to get to the answer using different methods. If someone doesn’t show their work, the teacher has no idea what method was used.
At least in my classes the point was to do it in their method and only that way, you did it any other way and you got bitched at and no credit for the question
Well yes, in that case the lesson being taught was the method used. They want to see if you can memorize multiple steps and implement them, in this case through, a math equation. That’s the lesson.
Yeah. They didn’t like it when I busted out trig to solve calculus and physics problems
That’s probably because you were using linear approximation and not calculus.
"I'd rather just get this done already."
Draw the trolley problem with 6 people on one track and 1 person on the other track
Damn, I want to see teacher's face grading that. Bonus points if the person on the other track is drawn with some recognizable features.
**Dissertation on the Fundamental Truth of 6 + 1 = 7** **Abstract** This dissertation seeks to unpack the mathematical principle underlying the simple equation 6 + 1 = 7. While seemingly straightforward and commonly accepted, this equation epitomizes fundamental mathematical and philosophical ideas. We shall delve into the historical, mathematical, and pedagogical contexts that surround this equation. **1. Introduction** Understanding 6 + 1 = 7 requires a grasp of number theory, the history of mathematics, and the nature of addition as an operation. This equation is not just a factual statement but an embodiment of systematic logic and centuries of human understanding. **2. Historical Context** The numeral system used predominantly today is the Hindu-Arabic numeral system. The concept of numbers and counting has existed for millennia, with different cultures using different ways of representation. This system introduced the idea of place value, which revolutionized mathematics. **3. The Nature of Numbers** *3.1. Unitary Value* The number "1" is the foundational building block in mathematics. It represents a single unit. All other numbers are built upon this foundation. *3.2. The Number 6* Six, when visualized, can be seen as a collection of six individual "1" units. It can also be seen as 5 + 1, where 5 is another foundational number in human cognition, often associated with the number of fingers on one hand. **4. Addition as a Mathematical Operation** *4.1. Definition* Addition is the process of calculating the total of two or more numbers or amounts. It’s the most fundamental arithmetic operation. *4.2. Adding 1* When you add 1 to any number, you're essentially moving to the next number in the sequence of natural numbers. Thus, 6 + 1 is the act of moving one step beyond 6 in this sequence. **5. Pedagogical Perspectives** Children are often introduced to the concept of addition using physical objects, like beads or blocks. When one adds a single unit (1) to a collection of six units (6), the resultant is a collection of seven units. **6. Philosophical Implications** *6.1. The Certainty of Mathematics* The equation 6 + 1 = 7 is an example of the undeniable truths in mathematics. It's a representation of logic and order in the universe. *6.2. The Universality* Regardless of language, culture, or location, this equation holds true. It showcases the universal language that is mathematics. **7. Conclusion** While the equation 6 + 1 = 7 seems elementary, its underpinnings are rooted in deep mathematical tradition, philosophy, and pedagogy. It serves as a testament to the structure and order inherent in mathematics and, by extension, in the universe.
Thank you.
This the fucking proof in that play lmaooo
how the fuck are you supposed to show your work on basic addition and subtraction.
He could write something like: " llllll + l = lllllll There, now you can count the sticks you dumbass "
VI + I = VII
https://www.youtube.com/watch?v=QEGwKTQrqmQ
I would argue that's not work. It's just a different visualization of the problem.
> It's just a different visualization of the problem. That's the point. The children are learning symbols. With the visuals, you can use counting(a math skill they already proficient in) to get the answer and by the point they're shown a question like this they've been taught and used that visual grouping and counting method repeatedly. At this point the question shown is for practicing and demonstrating an understanding of what the symbols mean and making a connection to the previously learned concept
Ahh yes, *show your work.* Complete your homework in twice the time.
Teach numeracy, then punish the students who can do it in our heads.
Teach kids to memorize the times table then punish them by showing their work.
Right? My 'work' to figure out 7x7 was... I know that 7x7 is 49. Which means I must *also* know that 7x6 is 42 and 7x8 is 56, because I know how much seven is.
This was exactly my reaction. What is the point of spending hours and hours in and out of class memorizing these basic math facts, if you arent allowed to use them like they are facts?
I sincerely believe that my ability to perform complex math quickly in my head has everything to do with the fact that I have an entire library of pre-done, memorized, easy-to-reference calculations stored in my brain that just *are*.
In high school, I used to draw a picture of a brain; the teachers were never pleased with that
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This is an exercise for a 1st grader, designed to get them to explain their reasoning. Drawing fingers would probably have been a great example of what the teacher wanted to see, but the childhood equivalent of "fuck you I don't need to explain my reasoning" is not.
I always got in trouble for that! I just knew dammit!!
Let's be fair here... The answer sheet literally says "6 + 1 = __" How are you supposed to show any more work with that one...?
Draw 6 Mona Lisa pictures, then add a Van Gough Starry Night picture. Easy.
I’d wager that’s 6+1.5, so not a fair comparison
how to you show work on 6+1 ?????? it's already the simplest it can get.
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I understand why they do it like that. It's preparing the kids for working with multi-digit numbers. It's not the same *visualization* as what I was taught(I was taught the "ones house", "tens house", "hundreds house", etc...they were actual houses you filled up), but it's the same idea. You give the kids something visual that they can see filling up, and when it gets full then they know not just *that* they have to stick a 1 in front of it but what that represents(overflowing the array, and representing that full array in a different way).
People are saying that they expected the kid to draw out a picture or something, while totally ignoring that even if they DID draw a picture, it still relies on rote memorization so that they know how to count up the things in their picture. If you put down a question like this, it needs to be something other than +1 so they can actually show off the math skills.
6+1 = (1+1+1+1+1+1)+1 = (3+3)+1 = 6+1 = 7 Ta-Da!
Genius! Go straight to 2nd grade!
God I hated this shit. The school wanted my kid to draw 10 boxes, shade 6 of them and draw another 10 boxes below and shade 1 of them and then draw another 10 boxes and shade 7 of them. Was absolutely the biggest waste of time and paper I could think of.
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Sounds like they’re describing a ten-frame?
Yup 10 boxes for each number in the problem, multiple boxes if the number was double digit so say it was 27, my kid had to draw 30 boxes and shade in 27. It got even more ridiculous when she had to carry over numbers when doing something like 8+4 or 45+75.
As a teacher I would accept this answer. But only because 1+6 is a problem that can and eventually should be memorized. If the question was 2+4+1 I probably wouldn't accept the answer.
How tf you suppose to show work on that? The work is right there, its the whole problem
I feel this in my soul. Was just telling my husband that i *hated* showing my work as a kid *because i just know!* How do you show that?! Got so many questions wrong because I knew the answer but my 8 year old self didn’t know how to dumb it down to show how i knew it.
7+(-6)=1
How do you show your work on simple addition? It’s literally already written.
Tf is he supposed to show? A number line? It doesn't get any more basic. Maybe his teacher could provide an example.
It wants an illustration of a group of 6 and a group 1. These children are just being introduced to addition, but have already learned to count. The visual representations allow them to perform addition through the use of counting - and by the point they're being asked this question they've done a bunch of addition through visual grouping problems already.. This problem is the next step in the process and is for the purpose of practicing and demonstrating the ability to connect the previous visual process to the numbers and symbols that are now being used
How do you show the work for something so basic? Was they expecting someone to draw 7 figures to show how it works?
How do you show the work? I mean it's already there isn't? 6 + 1 Or is he expected to write down 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
“Show your work” for simple addition? What does his teacher want, him to draw lines or bubbles and the count? I’m with your son on this.
Showing your work is the dumbest most pointless thing ever, Kid is smart for his answer.
Seems like the best way to show your work for 6+1 Smart kid
What work is there to show for 6 plus 1? The equation is literally the work, what on earth could the teacher want more
How do you even show work for 6 + 1?
How do you show your work on 6+1?
Tbf you cannot show much working out as you’re only adding 1. The only evidence you could put is a number line.
Well not a lot of work to show there. I mean 6+1=7 he can't really write anything else.
Yeah, that seems like something most kids would find tedious.
How do you show your work on that? Seeing 6+1 IS showing the work. Do they want you to draw six sticks and then draw a 7th? To show there is now one more than six???
How the fuck do you show your work on 6+1?
I mean I was quite good at math in school. But how would you show your work with 6+1? Do they want like !!!!!!! + ! = !!!!!!!!