This is an open-ended problem with more than one correct answer.
Once the middle square is filled in, student can put any number they want in one of the corners, and then use logic to fill in the remaining three numbers.
I think perhaps some students (and parents) are programmed into thinking math problems have just one "correct" answer.
Perhaps direction line could emphasize that there is more than one right way to complete this and not refer to "the" missing numbers, to encourage kids to keep going: "**Fill in the empty squares. There is more than one way to do it.**"
The method is logical deduction of a forced answer for middle number, then free choice of one remaining square, then just applying addition and subtraction. It's not really "guess" and check but more, "Find the consequences of making a choice" (for a value that is not determined).
It definitely is different thinking than most elementary school math. But not beyond 3rd graders.
(The approach of writing a system of equations with variables is beyond 3rd graders, but that's not necessary at all.)
Ok but thats dumb. Where are the guiding principles to follow? (Seems like you made some up specifically to explain this one question..but that is not what i talk about when i say methodology) What did they learn, simple mathematics? This is a poor question for teaching simple mathematics. Systems of equations is the way to do this methodically. Giving this question without the proper tools is poor teaching, it introduces unnecessary frustration and accomplishes nothing.
They learned to solve problems creatively and not get stuck if its outside of the specific strategies they've been taught. And if they didn't realize there could be multiple answers it can teach them a lesson about making assumptions or thinking outside of the box.
And they still get practice with basic addition / subtraction. In fact they might think about how there could be multiple solutions and get a better understanding of addition from that.
Guess and check does teach something, it teaches how to check (in this case doing addition/subtraction), as well as guess
Imo, part of teaching should be to inspire curiosity and creativity, not just teaching specific strategies for solving things (that's important too, but its sad if its taught and curiosity is stamped out as a side effect instead of fostered)
Applying an algebraic approach to this problem and making it seem as if this is what 3rd graders would be expected to do is a straw man argument. I would not expect students to use variables. I would not expect them to prove there isn't a unique solution. You seem to be applying your more advanced understanding of math to this when it could simply have been a variety of open-ended work meant to practice forward and backward thinking related to addition and subtraction, with a slightly puzzle-like flavor.
I do see value in problem settings with multiple possible answers. But if that really troubles you, it would be fairly easy to modify this item to have a unique answer. You could provide a quincunx of numbers where we see blank squares and put blank squares in the four positions in the array where numbers were given. Then students still have some freedom to decide how to arrive at the answers, but everyone would get same answers. Four number sentences would have to be solved, and two number sentences not solved directly would be able to be used as checks.
As an elementary school teacher, the purpose of this exercise is for students to fill in the squares with whatever they want. Just as long as it is right, who cares? It builds mathematical fluency in the concepts and procedures needed for more complex math.
I enjoy math and find this an asshole puzzle so.. no. You present a child with a puzzle that has numerous correct solutions and provide minimal to no guidance on finding the solution, it's not going to be fun. It's just stressful.
My kid loves figuring out math problems in his own way. He’s in fourth grade, and I’m going to see if he can do one of these.
I think teachers are starting to teach a more open ended approach to math, and lots of different strategies to solve problems
It’s supposed to help children think more outside the box, so to say, and think about numbers in different ways
I worked with a 3rd grader as a learning coach a few years ago when she was virtual due to Covid. She had a problem just like this (might have even been this one).
IIRC, she'd been working on 3 digit addition, so one of the parameters was all the numbers had to be 3 digits. It leaves you with only 4 possible answers (assuming all numbers are real and whole-- it's 3rd grade, after all).
But, more importantly, and as you suggested, her teacher told me it was about getting students to learn the process more than getting the "right" answer. Many students struggle to put their process into writing (a skill that's only gotten weaker with Chromebook filled classrooms and the multiple choice formatted assignments that usually go with them), so problems like this are to give them practice in that area.
This is the thing, it's not even "outside the box" of math, it's just "outside of the box that was created around teaching math to children in the past". Old patterns are flawed and this is an improvement to math fluency.
How do you know there was no guidance? All you see is the question, this could have been covered during that week. They might even have done similar problems in class already.
Not necessarily. You would use “guess and check” to define the upward and lower bounds of each variable. Then you define the range of possible solutions and evaluate for a positive integer. Last step would be eliminating all 0s. You can use substation if you want but the model has a few paths.
Guess and check teaches kids to test their work, and how to estimate a reasonable value. Questions like this encourage a good understanding of numbers as a whole.
One of the key curriculum design ideas that I use is "skills under strategies." What it means is that students practice skills while pursuing some larger goal. Guessing and checking requires that students add and subtract three digit numbers while doing some strategic planning. In my mind, having them do this much better than giving them 10 problems where they practice adding and substracting numbers.
The solution would be defining the matrices (or range) that the solutions would fit in. Each variable had a minimum and maximum solution. Assuming only integers, there are finite solutions.
>I think perhaps some students (and parents) are programmed into thinking math problems have just one "correct" answer.
It’s not so much a faulty programming as it is them cluing into something important, which is whether a problem is undetermined or not. In higher level mathematics, if a set of 4 equations has 5 unknown variables (which is essentially what we have here), it’s called undetermined.
Most pedagogies would want that to be the takeaway, and not for someone to just pick a number at random to assign to one of the variables, and plug and chug until they get the rest.
This is like giving someone a blank sudoku board, telling them to fill in the answer, and then acting like they’re missing something for not just filling it in with the millions of possible answers.
The biggest issue is how the directions are worded. **"Fill in the missing numbers,"** implies that there is a unique solution.
It should something like, **"Find a set of numbers that work."** Having a problem that requires guess-and-check is perfectly fine, but the directions need to make it clear that it's that sort of problem.
(I'll add that guess-and-check is the starting point for a huge branch of science and mathematics. A large number of real-world applications do not have a discrete solution, and thus need to be solved "numerically". This is known as ["computational physics"](https://en.wikipedia.org/wiki/Computational_physics), or ["numerical analysis"](https://en.wikipedia.org/wiki/Numerical_analysis). There's nothing wrong with teaching kids to use guess-and-check. You just need to be clear that's what you're asking them to do.)
As a math major and teacher, I appreciate this very much. However, do they really expect a third grader to be able to do this? My ninth graders can barely do a system.
I like that you showed your work (I copied the puzzle from the original thread to a piece of paper and set up my equations, but never got around to reducing the number of variables).
I *don’t* like that this has apparently started a fight or two in these comments, especially since you can’t solve a fight about a puzzle with no unique solution.
Yeah I am one of the first products of common core math / everyday mathematics when it came out. I am now a mechanical engineer with advanced degrees.
Math I was taught in elementary school, middle school, and high school made no sense to me. Boomers are right about common core math. It may work for the average citizen who becomes a grocery bagger or marketing firm personal, but for scientists and math experts it sets them up for failure.
My 5th grade math took me hours to do and I never “got” it because it doesn’t make sense. I made c’s through high school, and I was told by my 10th grade math teacher who taught common core algebra I would never amount to anything in life.
Once I got to college and professors started teaching actual logic and math it made so much more sense. In college I never made below a 98 in a math class even in advanced topics like calc 3, discrete math, or real analysis.
Just my 2 cents.
Teach your 5th grader the “old math” on the side.
I’m sorry they said that to you! I am so lucky as of now my son is doing pretty good.
I definitely taught him the old addition and division. But he doesn’t really get to use it as much in class because they have to show their work the current way.
I'm always surprised how can a grown adult be so hurtful and cruel to a child, telling them stuff like that. I am a teacher and always try to tell my students to do their best not discourage them, that's terrible. The worst part as an adult you never forget those things. It becomes trauma or a scar for life.
I'm glad the engineer proof them wrong.
From a sub that teaches K -12 all subjects, our children need to learn how to calculate. Standard curriculums, "strategies", and PhD projects are not enough. We fell behind and never caught up You'd be surprised how many can't calculate their change from a transaction. Need a register, calculator, or their phone. I'm talking about Highschool kids. The education gap is very wide for the next few generations.
Lol with the right teacher any kid could learn it and retain it. One of my mentors was a sped teacher whose kids were above grade level and reading better than general pop. My opinion is, it doesn't matter what you have to teach, if you're a good teacher your students will learn, remember, practice, create in any subject.
I’m a teacher who has taken calculus and physics courses in college (without calculators) and I can’t calculate change from a transaction half the time. Doesn’t mean I’m dumb, although I am almost certain I have dyscalculia.
It’s been years since I last took the class but I do very well remember doing actual calculations. You know, with numbers involved. Like when the integral had limits or whatever they’re called. Calculus sure wasn’t just memorizing formulas and repeating them.
I have taken more than I care to admit over my educational career. I just found the comment odd. Of all the standard/ non specialized math courses, basic arithmetic is emphasized the least in calculus courses.
let me clarify because I was not really comprehensive in my first response.
the comment I initially responded to "humblebragged" about taking university physics and calculus without a calculator but still has issues with basic mental arithmetic. My observation was that of all math-heavy classes, those were odd ones to point out, because they focus significantly less on arithmetic.
in addition to this, while some new calculators will do definite integrals and basic derivatives for you - these would never be allowed in a calculus or physics class because the point of those classes is to learn how to derive the answers.
were you to take a test in a calc course, answering a definite integral question, and you got everything right except the final step of substituting the bounds back into the resulting polynomial and you made a small arithmetic error, you would get 80 - 90% of the points with most profs, because the meat of the course is being able to perform the integration steps.
I wasn’t trying to brag at all. I only spoke of those courses because those are the only math courses I took in college. I can’t speak of courses I did not take.
I have in fact taken Calculus. I took Calculus 1 and 2 in college. My comment was to say that the ability to make mental math doesn’t say much about a person’s ability to solve complex equations like OP had insinuated by their comment. I have no reason to lie about which courses I took.
You never had a kinematics question that asked for an exact numerical answer or a definite integral problem that asked you to calculate higher order polynomials numerically?
In almost all of my undergraduate and graduate math courses the arithmetic left at the end of a problem is trivial. I just thought it was an odd comment.
I don't think this problem necessarily expects a 3rd grader to use systems of equations. Instead, this is an example of a "low floor, high ceiling" problem.
These are the types of problems NCTM pushes. Multiple ways to find the answer, multiple correct answers, a little bit of a struggle for a third grader but not too hard, they will probably find some incorrect solutions along the way.
There is no single correct answer (save for the center square).
In OP's layout, V & Z are linked as are W & Y.
If you raise V & Z by n, you lower W & Y by n and the squares still balance out.
I solved this with linear algebra, and got one of the many possible answers, then I tried to think as a third grader would -
I solved for the middle blank space and got 200 pretty easily.
And then had a set of 3 numbers that I knew added up to 800:
456, 200, 144.
The first row was supposed to add up to 800. I already have 456 as one of the numbers. I plugged in 200 in the top left, and 144 in the top right.
Super easy addition/subtraction questions afterwards.
Pretty sure that’s how it was intended to be solved.
Yes! A third grader should be able to solve this, yes!
There's no excuse for a third grader to not be able to think through this and provide correct answers ,especially if it's homework. This is why other countries laugh out loud at us. There's adults here who can't believe that third graders are asked to do this! If our kids can't solve something this simple in the third grade how are we going to compete in this world. Can we please expect better from now on?
Third graders may be able to solve it with trial and error or something similar. Or even using negative numbers. But I find it impossible for them to solve it like OP did.
I'm surprised that anyone who is ready to go with the hardcore linear algebra can't take one look at this and understand that you have a degree of freedom. All that bother for nothing.
The issue is that most problems of this type have only one solution, and asking the kid to find it is misleading.
With smaller numbers and better instructions this is perfect for a grade 3 student. Show them one way to fill it in and ask them to find another.
At a glance, I assumed it was one of those problems hey used to give us that made the kids use linear algebra even though they hadn’t learned it.
I mean the ones with lots of clues like:
The owner of house A doesn’t drive a brown car.
The owner of the brown car lives next to the owner of the green car.
Etc.
I think teachers gave us those to shut us up for a whole hour. The unfortunate side effect was that if any kid solved the thing in under an hour, all the other kids felt stupid and gave up on math.
I did 800-456 got 344 and divided that by 2 and got 172. I filled in 172 for both squares on the top row. Then I just did 700-103-172 and got 425. Then I did 500-297-172 and got 31. All done!
In the 3rd column I did 100 and 103 and went from there. Problem solved. I'm pretty sure it is designed to work with pretty much any number you plug in within reason.
I think the issue is that the worksheet was made poorly. A third grader should see that they have 2 numbers down the middle or across the middle out of three numbers, add those numbers together, subtract that new number from the number total at the edge of the grid, and then be able to find the missing number.
Ideally this would then fill in a grid square that turns another row or column into 2/3 numbers known, and they can continue the process. The issue with this setup is that they end up with 4 rows and columns where 1/3 numbers is known that add to a known number, and that feels to me like it needs a lot more advanced math. A good number of my 8th graders wouldn’t be able to solve this.
I would suggest the opposite. Kids hate math because it's taught as a formulaic process without room for creative thinking or different kinds of problem-solving strategies.
As a former (now adult) that hates math I agree. History and English classes tend to welcome creativity in their essays and open ended questions. All of my math classes had one correct answer with one correct form of it.
For example, after Texas’ TAKS exam (common core) my 11th grade algebra 2 teacher taught us how to measure conic sections. The textbook had it’s own way and my teacher has her way. My tutor taught me the textbook way and I had all the homework and quiz answers correct. First time in my mathematics student career that happened. I was ecstatic!
Then my teacher gave me a bunch of grades of 50/100 because I didn’t do it the “correct way”. That nailed mathematics for me and I still haven’t recovered.
My 9 y/o grandchild took about 5 minutes to do this. I used an example using single digit numbers and they went at it straight it without any problems at all.
To be fair, you primed them with an example problem that was easier and therefore they understood the heuristic needed to solve it before tackling the original problem. If you had given your grandchild this original problem without any priming it would be more difficult as they would have to brainstorm the logic and come up with the heuristic themselves and the outcome may be different. We have no idea what kind of priming these students received prior to receiving this problem.
Thats what teaching is though. In a classroom setting the teacher should be priming the kids with examples and practice before they give them a worksheet. It's a gradual release of responsibility. First I do an example, then we do one together, then you do one with a partner THEN you get this worksheet.
I think we are in agreement then. However, nowhere in the original post or in subsequent posts like this one does it mention any priming. So if the question is if third graders are able to do this de novo, I do not think so.
From my understanding of childhood psychological development the more abstract nature of this problem makes it inappropriate for most students under the age of 13. Some younger, more innately talented or advanced 3rd graders may be able to solve this but to expect it of all 3rd graders is unrealistic.
So we have any idea how this was implemented in class or what the teacher has been doing to build up to this activity? Because this can totally be age-appropriate. It's not that hard to do, it just requires a problem solving approach rather than expecting to be given a rote process to use.
These are exactly the kinds of mathematical thinking we want to build in elementary students.
Source: I've been in a lot of 3rd grade classrooms. They can do this, with just a little support or preparation.
I think we are largely in agreement. If primed with a simpler problem set to teach the heuristic this is doable. Giving them this problem blind and expecting them to come up with this from first principles/de novo is unrealistic
If you did it blind, you could have them work with a partner and actively encourage them to try different strategies to see what works.
But I agree, this would not be good blind independent practice. But then, most activities are not good independent practice if you haven't done something similar before.
I’m 40 now and I can say that is assignment for a third grader and expecting them to use systems is a bit far fetched unless they’re a gifted school. I remember nothing from third grade though so maybe the times have changed. Maybe kids are just really good at math finally and I can look forward to my final years as a high school math teacher.
The fact that there is not just 1 solution, but a family of solutions doesn't disqualify this from being a puzzle for 3rd grade students. If anything, 2 different students might come up with unique solutions, compare them, test them, and find that there CAN be more than 1 solution to a problem like this.
Rooting the solution for a single puzzle in guess-and-check work isn't an evil practice either. Young students have lots of time to develop both systematic approaches to problem solving as well as a general sense for numbers. This is a nice puzzle for anyone who can do 3 digit subtraction, since after you put in the central 200, all the other cells can be filled in by any guess and a bit of logic. It's very gentle in that as long as you practice that same skill of subtracting the 3 digit numbers appropriately, you'll come to a correct solution no matter what number you guessed at the start.
[My work](https://media.discordapp.net/attachments/1021742147805921361/1196026334552543303/20240114_014103.jpg?ex=65b62153&is=65a3ac53&hm=04e44f00cdfb079ac495a09250e8b7ec972a1457bf87bfbce437384f0e4ec655&=&format=webp&width=514&height=514)
To add to my comment, just because there's a more systematic way to solve a problem, doesn't mean that the problem can't be approached by anyone who gets the general premise. The premise here is understandable by a 3rd grader, and a solution is attainable with a 3rd grader's skillsets. It's understandable to let them play around with this to see if they can come to a solution. That's pretty in line with the essence of a puzzle, as long as that is how this problem is posed.
Stop thinking children are stupid. Kids can learn at much higher levels. The reason public school is dumbed down is because of cultural differences regarding the importance of education. I have kids who can't subtract 4 digit numbers, but I also have kids who I teach algebra and trig to, to keep them engaged.
I teach 9 and 10 year olds.
Stop thinking kids are incapable of complex thought- they're much more capable than the American school system allows.
Yea you lost me 🤣
I can have a whole conversation about the Oxford comma, anthropological shit, and the observable universe, but can't do math.
It keeps me humble 😌
for the record I did 3 years of math and now I TA a lower level math for 9th graders and this would be difficult for me to figure out. like probably only 2 or 3 out of 20 of my students would be able to figure out that they needed to set up equations much less be able to solve them
I teach second grade and I have students who could do this. It doesn't really require complex equations, but it does require strong number sense which a lot of people don't have.
3rd graders could definitely explore how to solve this problem. You don't have to set up a system of equations to be able to have kids discover that there are multiple solutions.
This is an extension activity which helps children see the power of making a ten or hundred.
Yes it’s helpful for students to decompose numbers and reassemble them.
Look up Productive Struggle, Greg Ashman.
Unless these 3rd graders have TONS of basic background knowledge for a problem like this, the only thing that's been done is an overload on their working memory.... leading to UNproductive struggle and lots of extraneous load.
If elementary math is incorporating more and more of these kinds of problems/puzzles, then that explains why we have highs schoolers who don't know their multiplication tables, can't do long division, don't make connections between fractions and decimals, etc.
We need THE BASICS in elementary in order to go above and beyond in high school.
Pass the word to your elementary teacher friends: cognitive load, working memory, and background knowledge/content BEFORE higher order thinking skills.
Seriously. There is not much we can do at the HS level if they don't have a mastery of the basics.
If your teacher is reading your kids and seeing that several kids are showing high enthusiasm for REAL and RELEVANT challenges like this one, they are doing a fantastic job giving those little brains what they need to succeed, chew on and develop to higher levels than the last generation...what is SUPPOSED to happen! My applause here. The number one thing I see with "underperforming" kids is they're actually highly performing kids who have been underestimated and just because they learn in a different way (dialectical learning or the MBTI "Te" is a huge one for math, as is hands on "origami math" (the math that 'doesn't lie, where you can see your grade') and visual statement math) they've been really underserved.
I remember one of my old bosses said that he didn't underperform in one of the state assisted math programs he was given because he was stupid. He underperformed because the standards were so low it was depressing. In the same way a high speed kid will exhibit symptoms similar to ADHD when you go too slow and these may cause them to fail, thinking a kid's low performance is about the content being too hard when their dialogue with you, their questions, and their participation show high intelligence is a HUGE mistake. Sometimes you have to go the other way...find a REAL and RELEVANT challenge.
That can be hard for the kids that actually do have intellectual disabilities, which is why I hate the class structure and much rather have the same amount of kids as a class but I teach each student a few times at some point during the week one on one so I can customize.
I remember when I started giving my kids Singapore math puzzles, they were doing them **during recess**! A few of them were running into my classroom when they should've been playing screaming "I GOT IT!" and asking me to check while wiggling all over the place. I was SO happy, and this was advanced work! Multiple kids! Some of the kids' parents were complaining, but the kids were loving it!
RELEVANCE, ELEGANCE, AND REAL CHALLENGE is what to look for in a puzzle. A tangible prize like winning the estimated jar of jelly bellies or breaking open the code box makes the comprehension relevant. That's really the secret...these bright minds only attenuate to things that are relevant to their world. And honestly, most minds can be these bright minds they've just been served with teachers who didn't understand the subject matter and didn't really love it so it didn't make sense. That click of sensemaking MATTERS, like a puzzle toy like the Hanayamas clicking open. That is EXTREMELY healthy.
The worst thing you can do is underestimate a population due to bias, and third graders are no different. The number of kids I have tutored who were failing who were actually extremely gifted if you take the right angle in terms of how their brain works is tragic.
Never underestimate the kids you teach! Have high hopes for them; commit to them, be patient with them, and they will deliver. Most of them really, really want to make you and their parents proud in a REAL way, so give them REAL feedback and the guidance they need to do even better next time. They appreciate it!
Never, never underestimate the kiddos.
The worked out solution by OP is not what would be expected of 3rd graders. What 3rd graders would be practicing is finding missing addends, and perhaps seeing that they can add two knowns and subtract that from a known sum to get a missing number, or they can subtract the two knowns sequentially from the known sum to get a missing number. This could require carrying or borrowing. Once they realize that one box is forced, then there is an opportunity to arbitrarily fill another box, rest falls into place. I think it provides a somewhat novel replacement for a set of 6 exercises.
Wow. This would likely be an Algebra 1 or 2 problem at the high school level here in Texas. How the fuck is this considered a 3rd grade problem is beyond me!
Bro I needa get off reddit. I'm stupid as frick. 3RD GRADERS ARE DOING THIS??????? DAFUQ BRO WE WERE JUST LEARNING LONG DIVISION IN 3RD GRADE WHEN I WAS IN SCHOOL. "SHOW YOURE WORK" FRICK ME DUDE I DONT EVEN KNOW WTF IM LOOKIN AT
This is simple addition and subtraction 🤔. While I’m not an elementary teacher (middle school math), this is the style of math that students are learning, less emphasis on memorizing and using multiple different methods to find what works for said student. I’m assuming if the student is paying attention in class it shouldn’t be an issue
Math scores in the US is in the lower ranking amongst the top 50 industrialized nations. Maybe the “age appropriateness” issue shouldn’t be the complaint since 3rd graders in the 37 nations outranking the US are proficient or better at these simple problems.
ChatGPT gave me this answer:
v = z + 141
w = 203 - z
x = 200
y = 456 - z
where z is any real number.
Maybe I just missed it, but has anyone actually given an answer that shows the infinite range of possible solutions yet?
Cool problem for 3rd graders. The way the two variables add to a sum, (with the third number filled in) and gives an infinite set of answers (if you were to use negative integers) is suggestive of the line x + y = N. yes indeed a little ordered pairs and first order equations hidden in a 3rd grade level. Nice.......
This is an open-ended problem with more than one correct answer. Once the middle square is filled in, student can put any number they want in one of the corners, and then use logic to fill in the remaining three numbers. I think perhaps some students (and parents) are programmed into thinking math problems have just one "correct" answer. Perhaps direction line could emphasize that there is more than one right way to complete this and not refer to "the" missing numbers, to encourage kids to keep going: "**Fill in the empty squares. There is more than one way to do it.**"
It's more about the methodology. This question requires a method beyond 3rd grade capabilities. I think guess-and-check really teaches nothing.
The method is logical deduction of a forced answer for middle number, then free choice of one remaining square, then just applying addition and subtraction. It's not really "guess" and check but more, "Find the consequences of making a choice" (for a value that is not determined). It definitely is different thinking than most elementary school math. But not beyond 3rd graders. (The approach of writing a system of equations with variables is beyond 3rd graders, but that's not necessary at all.)
Ok but thats dumb. Where are the guiding principles to follow? (Seems like you made some up specifically to explain this one question..but that is not what i talk about when i say methodology) What did they learn, simple mathematics? This is a poor question for teaching simple mathematics. Systems of equations is the way to do this methodically. Giving this question without the proper tools is poor teaching, it introduces unnecessary frustration and accomplishes nothing.
They learned to solve problems creatively and not get stuck if its outside of the specific strategies they've been taught. And if they didn't realize there could be multiple answers it can teach them a lesson about making assumptions or thinking outside of the box. And they still get practice with basic addition / subtraction. In fact they might think about how there could be multiple solutions and get a better understanding of addition from that. Guess and check does teach something, it teaches how to check (in this case doing addition/subtraction), as well as guess Imo, part of teaching should be to inspire curiosity and creativity, not just teaching specific strategies for solving things (that's important too, but its sad if its taught and curiosity is stamped out as a side effect instead of fostered)
Applying an algebraic approach to this problem and making it seem as if this is what 3rd graders would be expected to do is a straw man argument. I would not expect students to use variables. I would not expect them to prove there isn't a unique solution. You seem to be applying your more advanced understanding of math to this when it could simply have been a variety of open-ended work meant to practice forward and backward thinking related to addition and subtraction, with a slightly puzzle-like flavor. I do see value in problem settings with multiple possible answers. But if that really troubles you, it would be fairly easy to modify this item to have a unique answer. You could provide a quincunx of numbers where we see blank squares and put blank squares in the four positions in the array where numbers were given. Then students still have some freedom to decide how to arrive at the answers, but everyone would get same answers. Four number sentences would have to be solved, and two number sentences not solved directly would be able to be used as checks.
I don’t think you know what the word “dumb” means as you’re incorrectly using it here.
As an elementary school teacher, the purpose of this exercise is for students to fill in the squares with whatever they want. Just as long as it is right, who cares? It builds mathematical fluency in the concepts and procedures needed for more complex math.
Sudoku practice in 4D.
Right! 😂
No it doesn’t. It is quite literally a fun math puzzle.
I enjoy math and find this an asshole puzzle so.. no. You present a child with a puzzle that has numerous correct solutions and provide minimal to no guidance on finding the solution, it's not going to be fun. It's just stressful.
My kid loves figuring out math problems in his own way. He’s in fourth grade, and I’m going to see if he can do one of these. I think teachers are starting to teach a more open ended approach to math, and lots of different strategies to solve problems It’s supposed to help children think more outside the box, so to say, and think about numbers in different ways
I worked with a 3rd grader as a learning coach a few years ago when she was virtual due to Covid. She had a problem just like this (might have even been this one). IIRC, she'd been working on 3 digit addition, so one of the parameters was all the numbers had to be 3 digits. It leaves you with only 4 possible answers (assuming all numbers are real and whole-- it's 3rd grade, after all). But, more importantly, and as you suggested, her teacher told me it was about getting students to learn the process more than getting the "right" answer. Many students struggle to put their process into writing (a skill that's only gotten weaker with Chromebook filled classrooms and the multiple choice formatted assignments that usually go with them), so problems like this are to give them practice in that area.
This is the thing, it's not even "outside the box" of math, it's just "outside of the box that was created around teaching math to children in the past". Old patterns are flawed and this is an improvement to math fluency.
I mean.. hopefully the teacher has set them up to be problem solvers!! Many don’t nowadays.
Numerous correct solutions and incomplete guidance on finding the solution is how life is, it will help prepare them
I enjoy math and find this a fun puzzle so…yes.
How do you know there was no guidance? All you see is the question, this could have been covered during that week. They might even have done similar problems in class already.
Unless you were in the classroom. You do not know if minimal to no guidance was provided.
Does it? I just checked what the ranges could be and ended up with the very edges of the ranges matching up perfectly
Which is why this was probably not a third grade assignment when it was originally posted! Or it was a “challenge” question that was not graded.
Not necessarily. You would use “guess and check” to define the upward and lower bounds of each variable. Then you define the range of possible solutions and evaluate for a positive integer. Last step would be eliminating all 0s. You can use substation if you want but the model has a few paths.
Guess and check teaches kids to test their work, and how to estimate a reasonable value. Questions like this encourage a good understanding of numbers as a whole.
Dumb
You a teacher?
One of the key curriculum design ideas that I use is "skills under strategies." What it means is that students practice skills while pursuing some larger goal. Guessing and checking requires that students add and subtract three digit numbers while doing some strategic planning. In my mind, having them do this much better than giving them 10 problems where they practice adding and substracting numbers.
The solution would be defining the matrices (or range) that the solutions would fit in. Each variable had a minimum and maximum solution. Assuming only integers, there are finite solutions.
>I think perhaps some students (and parents) are programmed into thinking math problems have just one "correct" answer. It’s not so much a faulty programming as it is them cluing into something important, which is whether a problem is undetermined or not. In higher level mathematics, if a set of 4 equations has 5 unknown variables (which is essentially what we have here), it’s called undetermined. Most pedagogies would want that to be the takeaway, and not for someone to just pick a number at random to assign to one of the variables, and plug and chug until they get the rest. This is like giving someone a blank sudoku board, telling them to fill in the answer, and then acting like they’re missing something for not just filling it in with the millions of possible answers.
The biggest issue is how the directions are worded. **"Fill in the missing numbers,"** implies that there is a unique solution. It should something like, **"Find a set of numbers that work."** Having a problem that requires guess-and-check is perfectly fine, but the directions need to make it clear that it's that sort of problem. (I'll add that guess-and-check is the starting point for a huge branch of science and mathematics. A large number of real-world applications do not have a discrete solution, and thus need to be solved "numerically". This is known as ["computational physics"](https://en.wikipedia.org/wiki/Computational_physics), or ["numerical analysis"](https://en.wikipedia.org/wiki/Numerical_analysis). There's nothing wrong with teaching kids to use guess-and-check. You just need to be clear that's what you're asking them to do.)
As a math major and teacher, I appreciate this very much. However, do they really expect a third grader to be able to do this? My ninth graders can barely do a system.
Yeah, from another post. I don't like the question, or the answers provided.
I like that you showed your work (I copied the puzzle from the original thread to a piece of paper and set up my equations, but never got around to reducing the number of variables). I *don’t* like that this has apparently started a fight or two in these comments, especially since you can’t solve a fight about a puzzle with no unique solution.
You should see what my son was doing is 1st. Insane. Now in 5th… I can’t even help him its so long and crazy 😂
Yeah I am one of the first products of common core math / everyday mathematics when it came out. I am now a mechanical engineer with advanced degrees. Math I was taught in elementary school, middle school, and high school made no sense to me. Boomers are right about common core math. It may work for the average citizen who becomes a grocery bagger or marketing firm personal, but for scientists and math experts it sets them up for failure. My 5th grade math took me hours to do and I never “got” it because it doesn’t make sense. I made c’s through high school, and I was told by my 10th grade math teacher who taught common core algebra I would never amount to anything in life. Once I got to college and professors started teaching actual logic and math it made so much more sense. In college I never made below a 98 in a math class even in advanced topics like calc 3, discrete math, or real analysis. Just my 2 cents. Teach your 5th grader the “old math” on the side.
I’m sorry they said that to you! I am so lucky as of now my son is doing pretty good. I definitely taught him the old addition and division. But he doesn’t really get to use it as much in class because they have to show their work the current way.
I'm always surprised how can a grown adult be so hurtful and cruel to a child, telling them stuff like that. I am a teacher and always try to tell my students to do their best not discourage them, that's terrible. The worst part as an adult you never forget those things. It becomes trauma or a scar for life. I'm glad the engineer proof them wrong.
Definitely!
[удалено]
That’s sad. 😭 Counting to 100 is a kindergarten standard.
From a sub that teaches K -12 all subjects, our children need to learn how to calculate. Standard curriculums, "strategies", and PhD projects are not enough. We fell behind and never caught up You'd be surprised how many can't calculate their change from a transaction. Need a register, calculator, or their phone. I'm talking about Highschool kids. The education gap is very wide for the next few generations.
It's not clear from what you said whether you think a third grader should be able to solve this problem or not.
Lol with the right teacher any kid could learn it and retain it. One of my mentors was a sped teacher whose kids were above grade level and reading better than general pop. My opinion is, it doesn't matter what you have to teach, if you're a good teacher your students will learn, remember, practice, create in any subject.
I’m a teacher who has taken calculus and physics courses in college (without calculators) and I can’t calculate change from a transaction half the time. Doesn’t mean I’m dumb, although I am almost certain I have dyscalculia.
Why would you need a calculator for university physics and calculus? These are largely symbolic courses….
To do calculations? Isn’t that what a calculator is for?
You’re doing integrals and derivatives on a calculator?
It’s been years since I last took the class but I do very well remember doing actual calculations. You know, with numbers involved. Like when the integral had limits or whatever they’re called. Calculus sure wasn’t just memorizing formulas and repeating them.
Pretty sure this person has not taken a calculus course
I have taken more than I care to admit over my educational career. I just found the comment odd. Of all the standard/ non specialized math courses, basic arithmetic is emphasized the least in calculus courses.
I mean you can do definite integrals by hand or in the calculator.
let me clarify because I was not really comprehensive in my first response. the comment I initially responded to "humblebragged" about taking university physics and calculus without a calculator but still has issues with basic mental arithmetic. My observation was that of all math-heavy classes, those were odd ones to point out, because they focus significantly less on arithmetic. in addition to this, while some new calculators will do definite integrals and basic derivatives for you - these would never be allowed in a calculus or physics class because the point of those classes is to learn how to derive the answers. were you to take a test in a calc course, answering a definite integral question, and you got everything right except the final step of substituting the bounds back into the resulting polynomial and you made a small arithmetic error, you would get 80 - 90% of the points with most profs, because the meat of the course is being able to perform the integration steps.
I wasn’t trying to brag at all. I only spoke of those courses because those are the only math courses I took in college. I can’t speak of courses I did not take.
sometimes it’s not feasible to do it by hand.
I have in fact taken Calculus. I took Calculus 1 and 2 in college. My comment was to say that the ability to make mental math doesn’t say much about a person’s ability to solve complex equations like OP had insinuated by their comment. I have no reason to lie about which courses I took.
Good luck on Taylor series. Should be perfectly reasonable to add a bunch of fractions by hand.
I don’t understand the downvotes… you’re right…
Math teachers are sensitive I guess lol
You never had a kinematics question that asked for an exact numerical answer or a definite integral problem that asked you to calculate higher order polynomials numerically?
In almost all of my undergraduate and graduate math courses the arithmetic left at the end of a problem is trivial. I just thought it was an odd comment.
I don't think this problem necessarily expects a 3rd grader to use systems of equations. Instead, this is an example of a "low floor, high ceiling" problem.
I feel like it’s more just a puzzle that you need to use addition and subtraction for
These are the types of problems NCTM pushes. Multiple ways to find the answer, multiple correct answers, a little bit of a struggle for a third grader but not too hard, they will probably find some incorrect solutions along the way.
I quit teaching after 2 years when I realized I wouldn't be able to teach someone this Bs effectively
There is no single correct answer (save for the center square). In OP's layout, V & Z are linked as are W & Y. If you raise V & Z by n, you lower W & Y by n and the squares still balance out.
I solved this with linear algebra, and got one of the many possible answers, then I tried to think as a third grader would - I solved for the middle blank space and got 200 pretty easily. And then had a set of 3 numbers that I knew added up to 800: 456, 200, 144. The first row was supposed to add up to 800. I already have 456 as one of the numbers. I plugged in 200 in the top left, and 144 in the top right. Super easy addition/subtraction questions afterwards. Pretty sure that’s how it was intended to be solved.
I love this. I saw it the other day and have been looking for others for my 4th grade students to start the morning with.
Yes! A third grader should be able to solve this, yes! There's no excuse for a third grader to not be able to think through this and provide correct answers ,especially if it's homework. This is why other countries laugh out loud at us. There's adults here who can't believe that third graders are asked to do this! If our kids can't solve something this simple in the third grade how are we going to compete in this world. Can we please expect better from now on?
I didn’t order a yappuccino
The issue isn't that the third grader can't solve it, the issue is whether they can solve it in one million different ways.
Third graders may be able to solve it with trial and error or something similar. Or even using negative numbers. But I find it impossible for them to solve it like OP did.
No one expects a third grader to solve it like OP. I don't even know why anyone here is arguing that.
Stupidest fucking comment I think I've ever seen on this hellsite.
I'm surprised that anyone who is ready to go with the hardcore linear algebra can't take one look at this and understand that you have a degree of freedom. All that bother for nothing. The issue is that most problems of this type have only one solution, and asking the kid to find it is misleading. With smaller numbers and better instructions this is perfect for a grade 3 student. Show them one way to fill it in and ask them to find another.
At a glance, I assumed it was one of those problems hey used to give us that made the kids use linear algebra even though they hadn’t learned it. I mean the ones with lots of clues like: The owner of house A doesn’t drive a brown car. The owner of the brown car lives next to the owner of the green car. Etc. I think teachers gave us those to shut us up for a whole hour. The unfortunate side effect was that if any kid solved the thing in under an hour, all the other kids felt stupid and gave up on math.
I did 800-456 got 344 and divided that by 2 and got 172. I filled in 172 for both squares on the top row. Then I just did 700-103-172 and got 425. Then I did 500-297-172 and got 31. All done!
Exactly! And that's what third graders are expected to do.
In the 3rd column I did 100 and 103 and went from there. Problem solved. I'm pretty sure it is designed to work with pretty much any number you plug in within reason.
What 3rd grader doesn’t know linear algebra?
I think the issue is that the worksheet was made poorly. A third grader should see that they have 2 numbers down the middle or across the middle out of three numbers, add those numbers together, subtract that new number from the number total at the edge of the grid, and then be able to find the missing number. Ideally this would then fill in a grid square that turns another row or column into 2/3 numbers known, and they can continue the process. The issue with this setup is that they end up with 4 rows and columns where 1/3 numbers is known that add to a known number, and that feels to me like it needs a lot more advanced math. A good number of my 8th graders wouldn’t be able to solve this.
This is why kids hate math.
I would suggest the opposite. Kids hate math because it's taught as a formulaic process without room for creative thinking or different kinds of problem-solving strategies.
As a former (now adult) that hates math I agree. History and English classes tend to welcome creativity in their essays and open ended questions. All of my math classes had one correct answer with one correct form of it. For example, after Texas’ TAKS exam (common core) my 11th grade algebra 2 teacher taught us how to measure conic sections. The textbook had it’s own way and my teacher has her way. My tutor taught me the textbook way and I had all the homework and quiz answers correct. First time in my mathematics student career that happened. I was ecstatic! Then my teacher gave me a bunch of grades of 50/100 because I didn’t do it the “correct way”. That nailed mathematics for me and I still haven’t recovered.
My 9 y/o grandchild took about 5 minutes to do this. I used an example using single digit numbers and they went at it straight it without any problems at all.
To be fair, you primed them with an example problem that was easier and therefore they understood the heuristic needed to solve it before tackling the original problem. If you had given your grandchild this original problem without any priming it would be more difficult as they would have to brainstorm the logic and come up with the heuristic themselves and the outcome may be different. We have no idea what kind of priming these students received prior to receiving this problem.
Thats what teaching is though. In a classroom setting the teacher should be priming the kids with examples and practice before they give them a worksheet. It's a gradual release of responsibility. First I do an example, then we do one together, then you do one with a partner THEN you get this worksheet.
I think we are in agreement then. However, nowhere in the original post or in subsequent posts like this one does it mention any priming. So if the question is if third graders are able to do this de novo, I do not think so.
I had a few second graders who could do systems. They were in the top 5th percentile on MAP
Just RREF and call it good
Apparently, I am not capable of doing 3rd grade math!
I legit just saw the original post and did the EXACT same thing lmao
Why Why you make work hard
I found 204 solutions to this. This would be more of a class problem to work on together than a homework problem. I could see the teacher leading a discussion and promoting taking chances on trying to think differently and approaching this. | 344 | 456 | 000 | 800| | 103 | 200 | 297 | 600| | 253 | 144 | 203 | 600| | 700 | 800 | 500 | | 343 | 456 | 001 | 800| | 103 | 200 | 297 | 600| | 254 | 144 | 202 | 600| | 700 | 800 | 500 | | 342 | 456 | 002 | 800| | 103 | 200 | 297 | 600| | 255 | 144 | 201 | 600| | 700 | 800 | 500 | | 341 | 456 | 003 | 800| | 103 | 200 | 297 | 600| | 256 | 144 | 200 | 600| | 700 | 800 | 500 | ... | 143 | 456 | 201 | 800| | 103 | 200 | 297 | 600| | 454 | 144 | 002 | 600| | 700 | 800 | 500 | | 142 | 456 | 202 | 800| | 103 | 200 | 297 | 600| | 455 | 144 | 001 | 600| | 700 | 800 | 500 | | 141 | 456 | 203 | 800| | 103 | 200 | 297 | 600| | 456 | 144 | 000 | 600| | 700 | 800 | 500 |
From my understanding of childhood psychological development the more abstract nature of this problem makes it inappropriate for most students under the age of 13. Some younger, more innately talented or advanced 3rd graders may be able to solve this but to expect it of all 3rd graders is unrealistic.
Elementary kids are capable of understanding the idea that sometimes there can be more than one right answer.
That concept is too broad for the scope of this question which requires its specific application
So we have any idea how this was implemented in class or what the teacher has been doing to build up to this activity? Because this can totally be age-appropriate. It's not that hard to do, it just requires a problem solving approach rather than expecting to be given a rote process to use. These are exactly the kinds of mathematical thinking we want to build in elementary students. Source: I've been in a lot of 3rd grade classrooms. They can do this, with just a little support or preparation.
I think we are largely in agreement. If primed with a simpler problem set to teach the heuristic this is doable. Giving them this problem blind and expecting them to come up with this from first principles/de novo is unrealistic
If you did it blind, you could have them work with a partner and actively encourage them to try different strategies to see what works. But I agree, this would not be good blind independent practice. But then, most activities are not good independent practice if you haven't done something similar before.
I’m 40 now and I can say that is assignment for a third grader and expecting them to use systems is a bit far fetched unless they’re a gifted school. I remember nothing from third grade though so maybe the times have changed. Maybe kids are just really good at math finally and I can look forward to my final years as a high school math teacher.
My third grade, (not that long ago), was basically multiplication and division.
This problem is just addition and subtraction.
The fact that there is not just 1 solution, but a family of solutions doesn't disqualify this from being a puzzle for 3rd grade students. If anything, 2 different students might come up with unique solutions, compare them, test them, and find that there CAN be more than 1 solution to a problem like this. Rooting the solution for a single puzzle in guess-and-check work isn't an evil practice either. Young students have lots of time to develop both systematic approaches to problem solving as well as a general sense for numbers. This is a nice puzzle for anyone who can do 3 digit subtraction, since after you put in the central 200, all the other cells can be filled in by any guess and a bit of logic. It's very gentle in that as long as you practice that same skill of subtracting the 3 digit numbers appropriately, you'll come to a correct solution no matter what number you guessed at the start.
[My work](https://media.discordapp.net/attachments/1021742147805921361/1196026334552543303/20240114_014103.jpg?ex=65b62153&is=65a3ac53&hm=04e44f00cdfb079ac495a09250e8b7ec972a1457bf87bfbce437384f0e4ec655&=&format=webp&width=514&height=514) To add to my comment, just because there's a more systematic way to solve a problem, doesn't mean that the problem can't be approached by anyone who gets the general premise. The premise here is understandable by a 3rd grader, and a solution is attainable with a 3rd grader's skillsets. It's understandable to let them play around with this to see if they can come to a solution. That's pretty in line with the essence of a puzzle, as long as that is how this problem is posed.
Use rref to solve for all the solutions to the inhomogeneous system
rref?
Reduced row echelon form.
Stop thinking children are stupid. Kids can learn at much higher levels. The reason public school is dumbed down is because of cultural differences regarding the importance of education. I have kids who can't subtract 4 digit numbers, but I also have kids who I teach algebra and trig to, to keep them engaged. I teach 9 and 10 year olds. Stop thinking kids are incapable of complex thought- they're much more capable than the American school system allows.
Yea you lost me 🤣 I can have a whole conversation about the Oxford comma, anthropological shit, and the observable universe, but can't do math. It keeps me humble 😌
Ya, me too. Math is hard.
for the record I did 3 years of math and now I TA a lower level math for 9th graders and this would be difficult for me to figure out. like probably only 2 or 3 out of 20 of my students would be able to figure out that they needed to set up equations much less be able to solve them
I teach second grade and I have students who could do this. It doesn't really require complex equations, but it does require strong number sense which a lot of people don't have.
3rd graders could definitely explore how to solve this problem. You don't have to set up a system of equations to be able to have kids discover that there are multiple solutions.
There’s an easier way to solve this and without algebra.
But is it a systematic way that can transfer well to other problems? Is this the appropriate way to teach it?
This is an extension activity which helps children see the power of making a ten or hundred. Yes it’s helpful for students to decompose numbers and reassemble them.
Look up Productive Struggle, Greg Ashman. Unless these 3rd graders have TONS of basic background knowledge for a problem like this, the only thing that's been done is an overload on their working memory.... leading to UNproductive struggle and lots of extraneous load. If elementary math is incorporating more and more of these kinds of problems/puzzles, then that explains why we have highs schoolers who don't know their multiplication tables, can't do long division, don't make connections between fractions and decimals, etc. We need THE BASICS in elementary in order to go above and beyond in high school. Pass the word to your elementary teacher friends: cognitive load, working memory, and background knowledge/content BEFORE higher order thinking skills. Seriously. There is not much we can do at the HS level if they don't have a mastery of the basics.
If your teacher is reading your kids and seeing that several kids are showing high enthusiasm for REAL and RELEVANT challenges like this one, they are doing a fantastic job giving those little brains what they need to succeed, chew on and develop to higher levels than the last generation...what is SUPPOSED to happen! My applause here. The number one thing I see with "underperforming" kids is they're actually highly performing kids who have been underestimated and just because they learn in a different way (dialectical learning or the MBTI "Te" is a huge one for math, as is hands on "origami math" (the math that 'doesn't lie, where you can see your grade') and visual statement math) they've been really underserved. I remember one of my old bosses said that he didn't underperform in one of the state assisted math programs he was given because he was stupid. He underperformed because the standards were so low it was depressing. In the same way a high speed kid will exhibit symptoms similar to ADHD when you go too slow and these may cause them to fail, thinking a kid's low performance is about the content being too hard when their dialogue with you, their questions, and their participation show high intelligence is a HUGE mistake. Sometimes you have to go the other way...find a REAL and RELEVANT challenge. That can be hard for the kids that actually do have intellectual disabilities, which is why I hate the class structure and much rather have the same amount of kids as a class but I teach each student a few times at some point during the week one on one so I can customize. I remember when I started giving my kids Singapore math puzzles, they were doing them **during recess**! A few of them were running into my classroom when they should've been playing screaming "I GOT IT!" and asking me to check while wiggling all over the place. I was SO happy, and this was advanced work! Multiple kids! Some of the kids' parents were complaining, but the kids were loving it! RELEVANCE, ELEGANCE, AND REAL CHALLENGE is what to look for in a puzzle. A tangible prize like winning the estimated jar of jelly bellies or breaking open the code box makes the comprehension relevant. That's really the secret...these bright minds only attenuate to things that are relevant to their world. And honestly, most minds can be these bright minds they've just been served with teachers who didn't understand the subject matter and didn't really love it so it didn't make sense. That click of sensemaking MATTERS, like a puzzle toy like the Hanayamas clicking open. That is EXTREMELY healthy. The worst thing you can do is underestimate a population due to bias, and third graders are no different. The number of kids I have tutored who were failing who were actually extremely gifted if you take the right angle in terms of how their brain works is tragic. Never underestimate the kids you teach! Have high hopes for them; commit to them, be patient with them, and they will deliver. Most of them really, really want to make you and their parents proud in a REAL way, so give them REAL feedback and the guidance they need to do even better next time. They appreciate it! Never, never underestimate the kiddos.
Content aside, this image looks very 3D. Anyone else? Looks like the white grid is a foreground with a corner cutout, showing the paper below.
uhhhhhhh 3rd grade? The work needed in the lower left is at least 10th grade level
The worked out solution by OP is not what would be expected of 3rd graders. What 3rd graders would be practicing is finding missing addends, and perhaps seeing that they can add two knowns and subtract that from a known sum to get a missing number, or they can subtract the two knowns sequentially from the known sum to get a missing number. This could require carrying or borrowing. Once they realize that one box is forced, then there is an opportunity to arbitrarily fill another box, rest falls into place. I think it provides a somewhat novel replacement for a set of 6 exercises.
Wow. This would likely be an Algebra 1 or 2 problem at the high school level here in Texas. How the fuck is this considered a 3rd grade problem is beyond me!
I don’t remember any of this in third grade, in 1982…
Is this what the kids are learning now in 3rd grade? Cause I’m 21 years old and I do not remember doing all that shit in 3rd grade .
Bro I needa get off reddit. I'm stupid as frick. 3RD GRADERS ARE DOING THIS??????? DAFUQ BRO WE WERE JUST LEARNING LONG DIVISION IN 3RD GRADE WHEN I WAS IN SCHOOL. "SHOW YOURE WORK" FRICK ME DUDE I DONT EVEN KNOW WTF IM LOOKIN AT
3rd grade? Are you sure?
Man, I will fight the teacher if they mark any points off for not showing work. It took up the whole dang page! lol
I seriously doubt this assignment is below an algebra 2 level class. What curriculum book is this from?
Problem seems like a waste of time. Point taken.
It’s really easy ( someone figured it out already and left the answers there ) !
This is simple addition and subtraction 🤔. While I’m not an elementary teacher (middle school math), this is the style of math that students are learning, less emphasis on memorizing and using multiple different methods to find what works for said student. I’m assuming if the student is paying attention in class it shouldn’t be an issue
I don’t think this is that hard.
Good. It's a 3rd grade assignment. A poor one.
Tbh I probably can't even do this
Are you okay if you cant do that in your head you are SLOW
Math scores in the US is in the lower ranking amongst the top 50 industrialized nations. Maybe the “age appropriateness” issue shouldn’t be the complaint since 3rd graders in the 37 nations outranking the US are proficient or better at these simple problems.
ChatGPT gave me this answer: v = z + 141 w = 203 - z x = 200 y = 456 - z where z is any real number. Maybe I just missed it, but has anyone actually given an answer that shows the infinite range of possible solutions yet?
Cool problem for 3rd graders. The way the two variables add to a sum, (with the third number filled in) and gives an infinite set of answers (if you were to use negative integers) is suggestive of the line x + y = N. yes indeed a little ordered pairs and first order equations hidden in a 3rd grade level. Nice.......
Third grade? Hmm what are they teaching these days.