I genuinely don’t understand how people go on living adult lives without understanding basic concepts about fractions. It’s one of the few things from math class I actually regularly use even as a non math person
@@dlp7377 When I first read it, I thought it wanted remaining pages, and it had missing info. The question isn't hard, but that doesn't mean it's not normal to have problems understanding them. That's why schools teach word problems to begin with. Much easier to solve a given equation than to figure out what equation you need to solve the problem.
Although the book is quite short, the beginning shows a lot of promise and it seems like you can't put it down, but after the 5/8 mark, unfortunately, it turns into a slog.
I mean seriously, if you can blitz through 30 pages in a day but then you need full day to make it through 6 pages and another full day to push through the final 12, the ending must be AWFUL.
@@pablorosada9788 They’re not disputing the amount of pages, they’re saying it didn’t have to take the whole day. Maybe it had a riveting ending, and he was done by 10 am. That still counts as reading the last 1/4 on Wednesday.
I spent 30 seconds doing this in my head. Honestly, the hardest part of word problems is reading and understanding the problem itself. Edit: 400+ likes?? Thanks everyone!
Yeah, I didn't catch "remaining" when reading the thumbnail, but easy solve once I saw that. I have a feeling that when I was in primary school key words like that would be underlined so it's hard to miss, you can't give a kid all of that text as it all hinges on a single word
That's very true. Just like in the real world, numbers are not picked out of nowhere, they are attached to real things, and the hardest part is assigning the numbers to real quantities and coming up with a meaningful answer from those conditions.
You are right: READING a question is the true key to doing word problems. Help students all the time, and I daresay whenever a student has a serious issue, it's because they didn't read and understand the problem. 👍
@nmappraiser9926 Plus the real world seldom lays out all the details in a well-formulated word problem. A real-world word problem would be like, "Your back fence needs to be replaced. It is 6' tall and 90' long, and made from dogeared cedar boards. How much will it cost?" You can't put that on a test, but that's how they come IRL.
That's why it's a crime how little value the math curriculum (at least in my country, Austria) places on mathematical modeling. The way you solve any real life math problem is first modeling it in a formal system (like algebra), then solving it in that system according to its rules, then interpreting the formal answer into a real life answer. Exactly the second part seems to be the only one the curriculum is interested in, when it is entirely useless without the others.
1/8 + 1/4 = 3/8, 1-3/8 = 5/8, so 30 pages is 5/8 [of the book]. From there, I just divided 30 by 5 to get 1/8 of the book and multiplied by 8. Took a minute to solve
You would get 48 pages. If 30 is 5/8 of the book, then 1/8 of the book is 6. I added 30 and 6, and then 12 to get 48. I know I was in the AGP program in 5th grade, but I don't think a regular 5th grader would be able to do this. It took me about a minute to do this as a HS Sophmore. Whatever the kids are learning today is rather unnecessarily complicated.
YES! At 66yo that's exactly how I did it, and I'm pretty sure we were solving similar problems in that way when I was 10yo. As another commentator has said, people are making primary school maths look far more complicated than it needs to be.
Well, many (if not most) adults don't regularly deal with math that's more difficult than basic addition and subtraction. And no one would encounter something as strangely worded as this problem in their daily lives.
Same here. It hardly took me 2 minutes to calculate while sitting on my toilet seat. I was suprised and opened the video link simply to check what is so challenging about it.
The question is badly worded. It should say that Klein began reading the book on Monday. If someone told you they read two chapters of a book yesterday, you can't assume they started reading it yesterday & those were the first two.
@@DavidZ4-gg3dmNo, it doesn't need to say that. Have you forgotten the context? This is a question for 10 year olds. We should therefore presume it is not meant to be a trick question requiring an outside-the-box assumption that some information could be missing. We should presume that all necessary and sufficient information is given to us. It would be irrational to presume otherwise, given the context. Being able to apply this sort of pedantry is a useful skill when it's appropriate. But being unable to recognise when it isn't appropriate shows a weakness in someone's logical reasoning ability.
@@gavindeane3670just the anti-sociality and autism of these times that people can't humor a problem in a kids' math textbook despite the ambiguity (moreso as it's unsolvable otherwise.) Though I imagine many became like this from all the times they tried to meet someone or some thing halfway, only to be bitten in the - many people's model for all interactions and whether they assume good faith is squabbles on sm
@@gavindeane3670 Exactly my thoughts. I think it's because there are often "solve this riddle" items on the internet. These are also fun, but we get used to reading between the lines, and looking for hidden meaning in words, and other items of sneakiness. A maths problem given to 10yo kids isn't going to have this, at least not intentionally.
1:22 This is not a creative writing assignment where you get to add your own ideas to the prompt or a detective mystery where you're trying find the missing clues. This is a math problem and you work with the premise given to you. I solved it by setting up an algebraic equation or as you described it "The Old Way"
No, Presh is saying the issue is like being asked to find the numeric value of x + 1, without being given any info about x, key words being *the* and *numeric* .
Incorrect. The premise given to you requires an additional unstated assumption that the 30 pages read on Monday were the FIRST pages read. It's a very reasonable and natural assumption to make (especially for a 5th grader who probably won't have had their basic assumption that "questions I am given will contain all the information needed to get an answer" challenged yet) but for the sake of completeness and pure logic this point is worth making on a channel like this.
Exactly. These sort of things always attract a bunch of commenters who are really impressed with their own ability to apply maximal pedantry, despite having no ability whatsoever to know when that is and isn't appropriate.
Of course, which is what the video shows, but the language in the question should be more precise and state “read the first 30 pages on Monday” so it’s clearer that’s when he started
For me its like this: concepts like square roots, prime numbers, fractions and long division I literally do not understand. But when it comes to googology I DO understand it. I guess it depends on what you are most interested in. Also, me doing algebra is like godzilla in his most powerful form vs a coughing baby.
the main reason i belive is when mixed units are presented (as in us) wich adds an extra layer of complexity 1/5 inch + 1/8 feet + 1/35 yard = ?? ofc the solution is to convert everything to a common factor 1 yard = 3 feet = 36 inch -> 1/5 + 12/8 + 36/35 inch -> 1/5 + ( (12*35) / (8 * 35) ) + ( (36 * 8) / (35 *8) -> 1/5 + 420/280 + 288/280 -> 280/1400 + 2100/1400 + 1440/1400 -> (280+2100+1440)/1400 -> 3820/1400 = 382/140 = 191/70 = 2 + 51/70 inch OR 2 + 5/7 + 1/70 inch This is the primary reason US students struggle so much .. and even scientists actually has to work with this nightmare of a system called imperial-/customary-/freedom- units curiosa: 19028/7000 is aproximately equal to e
Eh, I learned the "old way", which is Algebra I for me, in 9th grade in... 1973? And there a lot of people in my class (the college prep course) who had lots of trouble with word problems. These were considered the hardest part of the class, at least to them. So I wouldn't be quite so quick to say that this demonstrates anything (though I think there is a strong likelihood that math and science skills are lessening).
@@Patrik6920what do you mean, struggle? fractions are easy to work with, certainly far more so than decimals. i always convert to fractions when doing mental math.
30 pages + 1/4 of the book + 1/8 of the book = whole book 30 pages + 3/8 of the book = whole book 30 pages = whole book - 3/8 of the book 30 pages = 5/8 of the book So if N is the number of pages then: 30 = N * (5/8) , divide both sides by 5/8 to get N by itself. 30 / (5/8) = N, dividing by a fraction is the same as multiplying by its reciprocal, so: 30 x (8/5) = N, so: 240 / 5 = N, so: 48 = N. There are 48 pages in the book. Double checking against the problem, 1/8 of 48 is 6, and 1/4 of 48 is 12. 30 + 6 + 12 = 48. Everything checks out.
I got 48 in my head. p=number of pages in the book p=30+(1/8)p+(1/4)p p=30+(1/8)p+(2/8)p p=30+(3/8)p p-(3/8)p=30 p(1-3/8)=30 p(5/8)=30 p=(30/5)*8 p=(6)*8 p=48
Yikes, overly complicated (or should I say simplified?) I just saw 30 + 1/8 = 3/4 = 6/8, therefore 30/5 = # of pages in 1/8 (which is 6), then 6 * 8 = 48. Guess I'll finish watching to see Presh's derivation.
Because of the way the problem is presented, with "Klein" reading a certain amount per day, my mind immediately latched onto the _rate_ of reading and I tried figure that out, which was completely pointless and impossible. After a few seconds, I realized that the reading rate and the days he read on weren't even relevant and solved the problem easily, but I can imagine someone being lead down the wrong path and getting very confused. It's kind of a weird problem and strangely presented in my opinion. It feels like an overcomplicated mess for such a simple idea, which maybe leads one to dismissing the obvious and simple answer because it seems _too_ simple to be worth asking about in such a complicated way.
so he read 1/8 on Tuesday and 1/4 was left for him to read on Wednesday so Tuesday + Wednesday combined is 1/4 + 1/8 = 2/8 + 1/8 = 3/8. so the rest (what he read on Monday) is the rest of the full thing, meaning 8/8 - 3/8 = 5/8 5/8 = 30, so 1/8 = 30/5 = 6. so the full book is 8/8 = 1/8 * 8 = 6 * 8 = 48 pages.
This is the kind of problem my 69yo autistic brain can solve almost instantly. I don’t know why that is, but it works for me. I had the answer to this problem before you finished reading the question. I’m glad you’re good at explaining math problems, it saves me from trying and failing to explain it to my friends and family! 😎❤️
I was so lucky when I first started learning arithmetic back in the early 50s because I felt like this was a class where I got to play puzzles. It was fun. It was cool to be able to figure out these things. I never once had this fear and dread of mathematics. And I never once fell into that. When are we gonna need this after school mentality because I found myself using it in thewoodshop, and the projects I did as a graphic designer, and even sometimes in music. It was fun!
I hate to be the old fogey, but… While visual intuition is useful on its own right, algebra is the master tool that opens the world. Kids don’t need to learn how to get-by on a grade school test with toy problems; they need to learn how to harness algebra for future complex problem solving in school and life. That’s how you train people to become engineers and scientists. And if you are not going to need algebra in your adult life these approaches are just as useless to you as algebra would be anyway.
Stumped me for a few seconds until I re-read it and saw the word 'remaining'. Then it was easy. Assuming, of course, he didn't read any pages before Monday.
You also need to assume that he read all the pages in order. And that the book is only full of readable pages. And that he didn't read any page twice. And that he's not in Congress giving a Tarot reading to a Congressional page.
There has to be a level of trust between the people making the test and those taking the test. While being unsolvable if you assume the test maker was purposely leaving out key details, this is bad business. This is why I do not like trickery of any kind on a test unless, they tell the students ahead of time they will be purposely ask misleading questions. The rest of the world outside of school will provide plenty enough opportunities to learn of the dishonesty of others.
That is not a good reason not to set a rigorous question. I solved this in about 10 seconds as I knew to make assumptions. I am pretty sure my ten year old self would have crossed it out as unsolvable. I was a precocious brat and often knew more about maths and science than my teachers who tended to be arts graduates. One tried to ridicule me when I said not all infinities were the same size - I had read a book* which covered such stuff at a basic level. * more accurately it was probably an article by Isaac Asimov "varieties of the Infinite" in an SF magazine my older brother had. Amazing what you can remember from nearly 60 years ago when you turn your mind to it!
@@matthewryan9323Yes, I think that's a very good way to put it. I think what happens is that people have seen occasions when someone pointed out a genuine, problematic flaw in a logic or mathematics question, been impressed by what they saw, and concluded that that's the only way a clever person should ever respond to these things. People who try and show how clever they think they are by pointing out all the holes they can find, are often actually showing how clever they aren't.
@@Llanchlo To me it is not about any specific question but more about the long-term benefits of students trusting the system. Many people get caught up in the here and now and ignore the accumulated distrust these kinds of questions build in many students over time. Clever tests don't teach students, clever teachers teaching the right way teaches students.
I did it the old way. I find it amusing that one of the first answers is always “it’s unsolvable” and an assumption that something is left out. ‘I’m not wrong, it’s the problem that sucks.’
1:14 NO Presh, the question AS STATED IS SOLVABLE. Adding UNSTATED "details" to the problem makes it "unsolvable" and is intellectually DISHONEST! You should KNOW BETTER!
Exactly. There are times when a maximal approach to pedantry, to identify unwritten assumptions, is appropriate. Solving a homework question for 10 year olds is not one of those times.
And just for completeness, if you wanted to actually TEACH something useful, you COULD solve the equation for "starting 1 day earlier than stated". Then solve for "two days earlier", and so on until you discovered a pattern. THEN you would have a function to calculate the pages based on when Klein stated reading. But I guess that's just too much work for you.
@@ThorsHammer1 He added that assumption because the problem can't in any way be solved without making that assumption in which case there would be nothing more to say about it, and he later specifically said that it's reasonable to assume that the question meant for you to make that assumption given that it's a question for 10 year olds and was probably not intended to be some kind of trick question. There is no formula for how many days earlier he started, you need to know how many pages he already read, not how many days he started earlier. And it would be completely and utterly trivial if you had that information, you'd just replace 30 with (30+previously read pages) and perform the exact same steps as he did, so there's really not much point mentioning it (the days of the week never had any relevance, the only thing that matters is that you know that all of the numbers added together will equal the total number of pages in the book, which requires him to make the assumption he did).
The possible _What If's_ have to be ignored, if the exam question doesn't give all relevant info then it can't be done properly (like about what day starting).
This demonstrates how phrasing can affect maths problems stated in a textual format. I agree that, if you take it as stated, where it doesn't *explicitly* state that Klein started the book on the Monday that he read the 30 pages, it is unsolvable. If you assume that it's not meant to be a trick question and that we have all of the information we need and it's implied that Klein did indeed start on Monday, it's just a matter of choosing the right method to plug the numbers into. There will of course be those who will still try to "outsmart" the question, whether because they legitimately feel that it should be interpreted in the unsolvable way due to the lack of explicit details, they enjoy exploring different interpretations of these sort of things and exploring more deeply, or just have a weird need to "prove" how smart they are to randoms on the internet.
You must NEVER assume that it isn't a trick question, because usually they are. Not in this case, I admit. But these questions usually do not only give the needed information (which you would have in a non-textual math problem, in this case: solve 5/8x=30 for x), but a plethora of misleading "clues" to derail the normal student. This is done to trick and outsmart those who know the maths but may lose time to eliminate all the junk information. I find this ethically reprehensible, but that's how maths education works in many places.
Edit: I’m just gonna use a philosophical razor and say he started reading the book on monday, as there used to be no other information provided that would state otherwise. the creator of the problem could have assumed that it was clear that he started Monday without explicitly stating it. First find the fraction of the book the first 30 pages were. I will use p and b as units for pages and books respectively. 30p + 1/8b + 1/4b = 1b 30p + 3/8b = 1 b 30p = 5/8b so 30 pages is 5/8ths of a book. to find out how many pages is 1 whole book, multiply each side by 8/5ths to get 48p = 1 book. Checking the math, 1/8 of the book would be 6 pages, and 1/4 of the book would be 12 pages. 30+6+12 = 48
I had this in a slightly different way. I basically saw a 1/4 and 1/8, saw that that was 3/8 because quarters and eights are fairly intuitive common denominators, and just solved for what would make 5/8x=30. Which is basically the old way with mental shortcuts that could resemble common core if put on paper.
This one was an easier to solve. Did variation of equation, but by multiply everything with 8 beforehand, so the numbers wouls be whole instead of 3/8 fraction.
You can do this one in your head if you can add simple fractions and factor small numbers. Here's how: Tuesday and Wednesday combined are three eights of the total book. That means that the 30 pages read on Monday were five eights of the total book. To see what one eighth of the total book is, therefore, divide 30 by 5. That means that 6 pages is one eighth of the total book, so EIGHT eighths of the total book would be 6 times 8. That comes out to 48 pages for the entire book. Word problems are all about setting it up as simply as it can be expressed. This is easier when the word problems deal with real-world situations involving whole numbers like this one. Usually in these types of word problems the factors stand out quite visibly, and the fractions have simple common denominators. Perfect for head math.
Problem reads very straight forward, so no need to complicate 30 + 1/8book + 2/8book = book 30 = book - 1/8book - 2/8book 30 = 5/8book book = 30*8/5 book = 48 You don't need blocks or squares.
That IS the blocks and squares solution. It's just that you already know how to do it so you don't need the thought process illustrated step by step to show you how it works.
It took about 1 second to see what needed to be done. Then about 30 seconds to write it down. I probably could have just done it in my head. But if I had tried it the "common core" way, it would have taken a lot longer.
It isn't even algebra. If you don't throw X in there, it can be solved with basic third grade math skills (at least, the skills we were taught back in the 1970s-80s). back then, first grade math was addition and subtraction, second was multiplication and division, third was fractions and decimals. Mind you, we also didn't have preschool or head start when I was a kid and kindergarten was half a day. With as much school as kids get these days, a first grader SHOULD have the skills to solve this, second at worst. And yet this was given to a fifth grader.
@@ValosiTiamata But it IS algebra. You may not be throwing an explicit "x" in there, but 30 + 1/8*(book) + 1/4*(book) = book is basically the same thing with "book" being the unknown.
To echo the sentiments of others here before finishing the video: the combined reading of Wednesday and Friday is 3/8. Ergo, Monday's reading of 30pp must equal 5/8 of the book, making 1/8 of the book equal to 6 pp. 6*8=48. QED.
From a pedagogical point of view, problems assigned in elementary school math classes should have a numerical solution within the understanding of the students. Thus assigning a problem for which the answer is "not enough information" is not worthwhile, and we are justified in making the assumption that Klein started the book on Monday. Any parent who recognized the error in the statement of the problem should also be wise enough to see that answering the question as "unanswerable" would defeat the purpose of the question, identify and make the missing assumption and help the child arrive at the numerical solution the problem setter expected.
@@gavindeane3670 The question may be originally for a 5th grader but the audience for this video are people enthusiastic about logic and problem solving. It's not a homework channel just about helping kids get the answer the teacher is looking for. This level of pedantry very much IS appropriate to give a complete answer to this audience. Assumptions about what the intended/ correct answer should be can massively trip you up in other more complex problems this channel frequently deals with.
@@theomegajuice8660I don't know about you, but I am not impressed at all by people who only know how to apply pedantry and have no idea when to apply it. It's juvenile.
@@gavindeane3670 How do you agree with a nit-picking comment that uses the term "pedagogical" and think you're somehow the down to earth working-class hero in this scenario?
If Klein had read a pages before Monday, then the equation would be: a + 30 + 1/8 * x + 1/4 * x = x, which gives: x = 8/5 * a + 48 So if a=0 (as assumed in the solution), the book would have 48 pages. If a=20, for example, then x=80. Saying that problem is unsolvable if the value of some constant is unknown, doesn't sound very mathematical.
The 1/4 and 1/8 immediately stood out to me, so my first step was Tue = 1/8 and Wed = 2/8. Add the two together for 3/8, so Monday must be 5/8. Monday was 30 pages, so (30/5)*8 to get the total number of pages = 48.
I know you're joking, but plenty of books for elementary school aged children (especially early grades when they're in the "starting to read for real" stage) would be that thin.
I don't think 5th graders (in the US) would be using algebra. The first line of reasoning seems more aligned with the normal curriculum (even in the "old" days). But, as usual, there are multiple valid lines of reasoning. 👍
I don't get the ideas behind common core but maybe I am stuck in my "old" ways. I just hope all these young people who are learning common core grow up to be able to have the flexible reasoning to solve all the engineering and science problems they will face.
Common core is basically trying to teach math on an abacus (highly effective) without giving the child an abacus. It also relies heavily upon the exact grammar of a problem without allowing for basic mathematical principles such as 5x3 = 3x5 (commutative property), so the child has to learn ADDITIONAL terminology to explain how they went from 5x3 to 3x5 as an additional step in the problem to avoid their solution being marked wrong. In other words, someone saw what China was doing and decided to copy it without investing in an abacus for every student, then decided to do their best to remove the math aspect (because "math is racist") and turn them into grammatical problems that you have to solve by making an illustration representing an abacus and explaining in detail each step of using that abacus. It's substituting art class and grammar class for math class and expecting better results as someone teaching just simple math.
My approach was sort of a hybrid. I didn't try to set up an equation, but I also didn't try to match up blocks. 1/8 + 1/4 = 3/8 So Klein read 30 pages on Monday, and the remaining 3/8 on Tuesday and Wednesday. So... 30 pages = 5/8 6 pages = 1/8 And 6 × 8 = 48 Just step by step deduction and hardly any "math".
@@briant7265That IS the matching up blocks method. It's just that you already know how to do it, so you don't need someone to draw diagrams to illustrate how the thought process works.
@@briant7265That's exactly the solution he illustrates with rectangles and blocks in the video. Obviously those of us who already know how to think of it like that do not need a bunch of diagrams to illustrate the thought process.
(30/x)+(1/8)+(1/4)=1 [Multiply by 8x] 240+x+2x=8x [Subtract 3x] 240=5x [Divide by 5] x=48 Figured 30 over the total pages plus the two fractional portions of the book had to equal 1 book.
This is one of those that makes me wonder how these people passed school. I'm one of the worst exampled of a student and I did this instantly in my head, it's like 3rd or 4th grade math.
30+x/8+x/4=x 240+3x=8x x=240/5 48 pages The book must've been hella boring by the end for the kid to take 2 days to read 18 pages when he could read 30 on one day
1/4 of book was read on Wednesday that means 30+1/8 = 75% of the remaining book. 1/8 is 12.5% and since the total is 75% it implies: 75%-12.5% 62.5% Which means 30 pages are 62.5% of the total pages. So we can find total like this: 62.5%(x) = 30
For me, the "old way" was introduced later. For my 5th grade level, we would have taken 1/4 to be 2/8, and used 30=5/8 as a basis for converting the others in a table. While we would have variables at the time, it wouldn't be until year 6 that we'd do complex equations like that, and probably year 7 or 8 when we'd bring it all together for solving problems this way.
It's been a long time since I've been in school so I haven't done stuff like this in a long time. Still, from the comments, I knew I was on the right track when I figured out 3/8 for Tuesday+Wednesday, so 30 pages is 5/8 of the book. I admit I stumbled next, but I'd like to think that's more from not doing this sort of thing in a long time then anything. Once I read the comments and got my brain to co-operate, just divide 30 by 5/8 to get the number of pages in the book.
To be fair, Presh, you learned to solve this type of problem algebraically (variables and equations) when you were in middle school (for me, it was “junior high”). This problem, as you say, was given to a 10yo. I taught 4th/5th graders math for many years; I introduced them to algebraic thinking/solving via the “Singapore Math” bar model strategy on display here. I regularly teach/tutor middle (even high) schoolers to understand algebra through pictures and models when the variables and equations don’t make any sense to them. I can’t tell you how many students wonder why, for example, they don’t understand functions yet can’t begin to tell you what a particular function might look like if/when graphed (some don’t even know such a possibility exists) let alone whether/how it relates to real life
You gave 2 ways. There is a 3rd that is similar to both combined. 1 = 30/x+1/4+1/8 where x is the total number of pages and the number 1 stands for one whole book. So, 30/x is the fraction of pages read on Monday, then add Tuesday & Wednesday to it.
Word problems can be extremely tricky, especially for those out of practice, because you need to be able to pick all the relevant info, then figure out how it all fits together. For example, if the problem were 30 + x / 8 = (3 / 4) * x Or 30 + x / 8 + x / 4 = x I bet most parents who remember even a little algebra would know to solve for x and may know you need to isolate x. However, trying to pick the info for these equations from a word problem is a skill of its own that is entirely different from solving algebra equations.
I was stuck for about a minute because I forgot to think of "the book" as the unknown variable. But then after that point, it was essentially just the equation 30 + x/8 + x/4 = x.
I was falling asleep waiting for you to get through the problem the first time. No kid would have the patience to turn a simple math problem into art school like that. And then you said "kids today" and I realised you were doing common core instead of proper math. Mind you, your algebraic answer was still a bit long-form, but at least I could wrap my head around it. Using basic math, I solved the problem completely in my head in about 20-30 seconds: 1/4 and 1/8 are basic fractions, so common denominator makes it 1/8 + 2/8 = 3/8. So 30=5/8. 30/5 is 6, 6x8=48 Common core makes this problem feel like something out of early calculus when I had learned everything I needed to solve this problem in third grade and my three year old will probably be able to solve this problem in about two more years because he's learning proper math. I feel so bad for Gen Alpha, knowing they're going to leave school with next to zero education because of stuff like this.
Another question of overthinking it that would make it difficult to solve, how do we know the 1/8ths of the book didn't include any rereading? The question doesn't say he read "the next 1/8th of the book"
We don’t know whether there was any overlap between Monday and Tuesday’s pages. If he’s anything like me, he probably had to turn back a couple of pages to refresh his memory!
I can understand a ten-year-old having to dig deep for this but adults baffled by it, really? It's a simple mental arithmetic problem. If 1/8 + 1/4 (3/8) is the remainder of the book after Monday then 30 is 5/8 of the book, so 1/8 is 6 and 8/8 is 48!
So as I read it 30 pages are 5/8 of the book because the rest of the book he reads over two days is 1/8 and 1/4 of the book to finish it. So the first 30 pages he read must have been 5/8 of the book. So you multiply 30 x 8 and divide it by 5 to get a book with 48 pages. So he read 30 , then an 8th (so six more pages) taking him to 36 and then a quarter of the book, 12/48 to get to the full 48 page read.
At 2:28 on, you could improve the graphics, by colouring the segments in the order they were read. Don't colour the first 1/8 segment green, colour the 5th one! It's still 1/8th, but it's in the right time position. Similarly, don't colour the first 1/4 segment green, colour the last one. It's the last 1/4 of the book that was read on Wednesday. _ _ _ _ _ _ _ _
I went with the equation x-30-x/8-x/4=0 because on Wednesday there are 0 pages left, and we start with x pages. This quickly resolves to the same path as the second solve. The question as stated needs two assumptions: a) the reading starts on Monday, and b) no pages have to be re-read.
If the remaining 1/4 completes it, it means that 30+1/8=3/4 of the book. Pages= 30+1/8+1/4 which is equal to 30+3/8 so 30 is the remaining 5/8. So to find the pages we can do 30•8/5=48
My method of solving this was to look at the question and yell 48. It's sad that there is at least one person in the world who is not able to solve these kind of equations in mere seconds.
Similar to the old way, I just converted Monday's reading to a fraction: 30/x. Then added the other two fractions to it and set the sum equal to 1 for the whole book. Solve for x.
After watching this video I understood why this question might have stumped many people. It might be due to the fact they were just overthinking by focusing on the part of the missing "starting point" which in a maths question for 10 years olds or for that matter any school grade will be like an inherent assumption.
The issue with the first method is that you don't build abstract intuition by doing it this way, most of the time learning the algorithm first and then deconstructing it helps you learn it better. The black box method basically. Don't understand something? Think of it like a black box. Once you know how to use the black box, disassemble it, you will find smaller black boxes inside, and you will have an intuition on how the larger one works, repeat process until you understand the whole thing. The new method is kinda backwards.
What??? The second method in the video goes to the concurred lengths of constructing, manipulating, and solving an algebraic equation. That's massive overkill compared to the first method, which simply and clearly visualises the problem. The first method is how I solved it. Intuitively. With a few seconds of mental arithmetic.
You know, to be fair I learned it the "old way" too... but I'm pretty sure this was in Algebra I which was 9th grade. So if this is really 5th grade, that's actually fairly advanced for that age. I still think the old way is more general since algebra is pretty fundamental, but I think it works for 5th grade math.
Fractions are like kryptonite for some people.
I genuinely don’t understand how people go on living adult lives without understanding basic concepts about fractions. It’s one of the few things from math class I actually regularly use even as a non math person
Did you know? 4 out of 3 people don't understand fractions
Most people couldn’t count change from a $5 bill on a $3.77 purchase without a machine telling them the number.
@@luisfilipe2023 Its just hard to understand ok. I can't explain why, but fractions are just hard to understand.
@@luccafortestoledo1300116% of people would say that you're wrong
It genuinely took me longer to understand the question than it took me to answer it.
Facts 😂
nothing hard about the question
Had to read it twice as well cause i thought there was information missing.
@@meinacco Yeah, I went in with the expectation of it being hard and kept thinking I missed something.
@@dlp7377 When I first read it, I thought it wanted remaining pages, and it had missing info. The question isn't hard, but that doesn't mean it's not normal to have problems understanding them. That's why schools teach word problems to begin with. Much easier to solve a given equation than to figure out what equation you need to solve the problem.
Although the book is quite short, the beginning shows a lot of promise and it seems like you can't put it down, but after the 5/8 mark, unfortunately, it turns into a slog.
I mean seriously, if you can blitz through 30 pages in a day but then you need full day to make it through 6 pages and another full day to push through the final 12, the ending must be AWFUL.
@@pablorosada9788 who said Klein spent entire 3rd day on the rest 12 pages tho?
@@asdbanz316 1/4 48 is 12
That's when the book starts using formulas.
@@pablorosada9788 They’re not disputing the amount of pages, they’re saying it didn’t have to take the whole day. Maybe it had a riveting ending, and he was done by 10 am. That still counts as reading the last 1/4 on Wednesday.
I spent 30 seconds doing this in my head. Honestly, the hardest part of word problems is reading and understanding the problem itself.
Edit: 400+ likes?? Thanks everyone!
Yeah, I didn't catch "remaining" when reading the thumbnail, but easy solve once I saw that. I have a feeling that when I was in primary school key words like that would be underlined so it's hard to miss, you can't give a kid all of that text as it all hinges on a single word
That's very true. Just like in the real world, numbers are not picked out of nowhere, they are attached to real things, and the hardest part is assigning the numbers to real quantities and coming up with a meaningful answer from those conditions.
You are right: READING a question is the true key to doing word problems. Help students all the time, and I daresay whenever a student has a serious issue, it's because they didn't read and understand the problem. 👍
@nmappraiser9926 Plus the real world seldom lays out all the details in a well-formulated word problem. A real-world word problem would be like,
"Your back fence needs to be replaced. It is 6' tall and 90' long, and made from dogeared cedar boards. How much will it cost?"
You can't put that on a test, but that's how they come IRL.
That's why it's a crime how little value the math curriculum (at least in my country, Austria) places on mathematical modeling. The way you solve any real life math problem is first modeling it in a formal system (like algebra), then solving it in that system according to its rules, then interpreting the formal answer into a real life answer. Exactly the second part seems to be the only one the curriculum is interested in, when it is entirely useless without the others.
My brain went to '30 + 1/8P = 3/4P' and solved from there.
same, right? Nerds unite.
True, I just did 3/4P - 1/8P = 30 or 5/8P and did it easily
Mine too
@@DeathmetalChadsince when did you have to be a nerd to answer an easy math question
@@forgmanguy Since society accepted "normal people = hate math"
1/8 + 1/4 = 3/8, 1-3/8 = 5/8, so 30 pages is 5/8 [of the book]. From there, I just divided 30 by 5 to get 1/8 of the book and multiplied by 8. Took a minute to solve
That was my exact thought process
Not everyone is as smart as you.
You would get 48 pages. If 30 is 5/8 of the book, then 1/8 of the book is 6. I added 30 and 6, and then 12 to get 48. I know I was in the AGP program in 5th grade, but I don't think a regular 5th grader would be able to do this. It took me about a minute to do this as a HS Sophmore. Whatever the kids are learning today is rather unnecessarily complicated.
YES! At 66yo that's exactly how I did it, and I'm pretty sure we were solving similar problems in that way when I was 10yo. As another commentator has said, people are making primary school maths look far more complicated than it needs to be.
You didn't give the answer, zero marks.
Parents thought they escaped homework once they became adults. But like a horror movie, it follows them all through their lives.
And all because they didn’t understand 1 + 1 = 3.
@@stuartmcconnachie all because they didn't memorise the tables of 7
Thats why grandparents only visit during vacations.
I keep losing hope everytime I see questions like this that adults can't solve
_Some_ adults.
Well, many (if not most) adults don't regularly deal with math that's more difficult than basic addition and subtraction. And no one would encounter something as strangely worded as this problem in their daily lives.
I mean, it's a trivial problem to solve, but probably not so much for that age group. I quickly did it in my head to arrive at 48 pages.
I did make the unstated assumption that he started reading the book on Monday.
At my age, I did it the "old way".
Same here. It hardly took me 2 minutes to calculate while sitting on my toilet seat. I was suprised and opened the video link simply to check what is so challenging about it.
@@shubhamdwivedi1432 Yep, did the same.
@@shubhamdwivedi1432 -- I don't give a *crap* that you did it sitting on your toilet seat.
1:04 if it's not stated, then it didn't happen. Just focus only on the given information.
The question is badly worded. It should say that Klein began reading the book on Monday. If someone told you they read two chapters of a book yesterday, you can't assume they started reading it yesterday & those were the first two.
@@DavidZ4-gg3dmNo, it doesn't need to say that.
Have you forgotten the context? This is a question for 10 year olds. We should therefore presume it is not meant to be a trick question requiring an outside-the-box assumption that some information could be missing. We should presume that all necessary and sufficient information is given to us. It would be irrational to presume otherwise, given the context.
Being able to apply this sort of pedantry is a useful skill when it's appropriate. But being unable to recognise when it isn't appropriate shows a weakness in someone's logical reasoning ability.
@@DavidZ4-gg3dm the wording says he read it ON Monday, not by Monday, so there's nothing vague about the question
@@gavindeane3670just the anti-sociality and autism of these times that people can't humor a problem in a kids' math textbook despite the ambiguity (moreso as it's unsolvable otherwise.) Though I imagine many became like this from all the times they tried to meet someone or some thing halfway, only to be bitten in the -
many people's model for all interactions and whether they assume good faith is squabbles on sm
@@gavindeane3670 Exactly my thoughts. I think it's because there are often "solve this riddle" items on the internet. These are also fun, but we get used to reading between the lines, and looking for hidden meaning in words, and other items of sneakiness. A maths problem given to 10yo kids isn't going to have this, at least not intentionally.
1:22 This is not a creative writing assignment where you get to add your own ideas to the prompt or a detective mystery where you're trying find the missing clues. This is a math problem and you work with the premise given to you.
I solved it by setting up an algebraic equation or as you described it "The Old Way"
No, Presh is saying the issue is like being asked to find the numeric value of x + 1, without being given any info about x, key words being *the* and *numeric* .
Incorrect. The premise given to you requires an additional unstated assumption that the 30 pages read on Monday were the FIRST pages read.
It's a very reasonable and natural assumption to make (especially for a 5th grader who probably won't have had their basic assumption that "questions I am given will contain all the information needed to get an answer" challenged yet) but for the sake of completeness and pure logic this point is worth making on a channel like this.
Exactly. These sort of things always attract a bunch of commenters who are really impressed with their own ability to apply maximal pedantry, despite having no ability whatsoever to know when that is and isn't appropriate.
@@theomegajuice8660Completeness???
If Presh's goal was completeness, he failed.
Of course, which is what the video shows, but the language in the question should be more precise and state “read the first 30 pages on Monday” so it’s clearer that’s when he started
"No school like the old school".
Seriously why do people always have to be surprised by simple concepts???? Math literacy is in the gutter it seems
For me its like this: concepts like square roots, prime numbers, fractions and long division I literally do not understand. But when it comes to googology I DO understand it. I guess it depends on what you are most interested in. Also, me doing algebra is like godzilla in his most powerful form vs a coughing baby.
the main reason i belive is when mixed units are presented (as in us) wich adds an extra layer of complexity
1/5 inch + 1/8 feet + 1/35 yard = ??
ofc the solution is to convert everything to a common factor
1 yard = 3 feet = 36 inch ->
1/5 + 12/8 + 36/35 inch ->
1/5 + ( (12*35) / (8 * 35) ) + ( (36 * 8) / (35 *8) ->
1/5 + 420/280 + 288/280 ->
280/1400 + 2100/1400 + 1440/1400 ->
(280+2100+1440)/1400 ->
3820/1400 = 382/140 = 191/70 = 2 + 51/70 inch OR 2 + 5/7 + 1/70 inch
This is the primary reason US students struggle so much ..
and even scientists actually has to work with this nightmare of a system called imperial-/customary-/freedom- units
curiosa: 19028/7000 is aproximately equal to e
Eh, I learned the "old way", which is Algebra I for me, in 9th grade in... 1973? And there a lot of people in my class (the college prep course) who had lots of trouble with word problems. These were considered the hardest part of the class, at least to them. So I wouldn't be quite so quick to say that this demonstrates anything (though I think there is a strong likelihood that math and science skills are lessening).
@@Patrik6920what do you mean, struggle? fractions are easy to work with, certainly far more so than decimals. i always convert to fractions when doing mental math.
No it’s because it’s worded in a very wrong way
Thank you for solving it the old way.
I must have missed the abacus
I read a bunch of books in this way until it came out right. Took several weeks, but I trust my results.
I did it the "old way" in my head, by working out 8/5 of 30 - simple!
Exactly.
You forgot to divide by the age of the captain...
But who is the bus driver?
30 pages + 1/4 of the book + 1/8 of the book = whole book
30 pages + 3/8 of the book = whole book
30 pages = whole book - 3/8 of the book
30 pages = 5/8 of the book
So if N is the number of pages then:
30 = N * (5/8) , divide both sides by 5/8 to get N by itself.
30 / (5/8) = N, dividing by a fraction is the same as multiplying by its reciprocal, so:
30 x (8/5) = N, so:
240 / 5 = N, so:
48 = N. There are 48 pages in the book.
Double checking against the problem, 1/8 of 48 is 6, and 1/4 of 48 is 12. 30 + 6 + 12 = 48. Everything checks out.
That's way more math than I did to solve...
1/4 + 1/8 = 3/8
8/8 - 3/8 = 5/8 = 30
30 ÷ 5 = 6
6 x 3 = 18
30 + 18 = 48
@@invisalats841 well done!
@@invisalats841That’s pretty much how I did it.
30 pages = 5/8th, so I did 1/8th of a book = 30/5 = 6 pages. Then I did 6x8 = 48 pages.
@@PlasteredDragon thanks my 1 semester of high school seems to still be useful lol
I got 48 in my head.
p=number of pages in the book
p=30+(1/8)p+(1/4)p
p=30+(1/8)p+(2/8)p
p=30+(3/8)p
p-(3/8)p=30
p(1-3/8)=30
p(5/8)=30
p=(30/5)*8
p=(6)*8
p=48
Yikes, overly complicated (or should I say simplified?)
I just saw 30 + 1/8 = 3/4 = 6/8, therefore 30/5 = # of pages in 1/8 (which is 6), then 6 * 8 = 48.
Guess I'll finish watching to see Presh's derivation.
I also had this thought process.
everyone did, i dont know why presh keeps giving such easy problems
I'm 53, and some days I am smarter than others. Today, they're 5th graders.
Because of the way the problem is presented, with "Klein" reading a certain amount per day, my mind immediately latched onto the _rate_ of reading and I tried figure that out, which was completely pointless and impossible. After a few seconds, I realized that the reading rate and the days he read on weren't even relevant and solved the problem easily, but I can imagine someone being lead down the wrong path and getting very confused. It's kind of a weird problem and strangely presented in my opinion. It feels like an overcomplicated mess for such a simple idea, which maybe leads one to dismissing the obvious and simple answer because it seems _too_ simple to be worth asking about in such a complicated way.
so he read 1/8 on Tuesday and 1/4 was left for him to read on Wednesday
so Tuesday + Wednesday combined is 1/4 + 1/8 = 2/8 + 1/8 = 3/8.
so the rest (what he read on Monday) is the rest of the full thing, meaning 8/8 - 3/8 = 5/8
5/8 = 30, so 1/8 = 30/5 = 6.
so the full book is 8/8 = 1/8 * 8 = 6 * 8 = 48 pages.
This is the kind of problem my 69yo autistic brain can solve almost instantly. I don’t know why that is, but it works for me. I had the answer to this problem before you finished reading the question. I’m glad you’re good at explaining math problems, it saves me from trying and failing to explain it to my friends and family! 😎❤️
It's impossible to answer because in a Klein book you flip the last page and go back to the beginning with the text turned upside down.
This comment deserves more likes! 🙂
That does not change the number of physical pages, just the number you read.
I worked it out in my head in 30 seconds
No, you didn't lol
@@mrowlsss don't see why not, it took me a lot less than that, mental arithmetic like this comes easy.
@@mrowlsss
It's pretty simple
what are you gaining by asserting this lol
is it public recognition?? I'm unsure but curious
@@mrowlsssIt's not hard, 1x - 1/8x - 1/4x = 5/8x, which was 30 pages. x = 48.
I was so lucky when I first started learning arithmetic back in the early 50s because I felt like this was a class where I got to play puzzles. It was fun. It was cool to be able to figure out these things. I never once had this fear and dread of mathematics. And I never once fell into that. When are we gonna need this after school mentality because I found myself using it in thewoodshop, and the projects I did as a graphic designer, and even sometimes in music. It was fun!
Me being 10th grade and having solved it mentally the "old" way questioning if kids actually use rectangles to solve that now:
I think the rectangles are just to illustrate the process.
I solved it the first way but I didn't actually sit down and draw rectangles.
The "old" way is usually called algebra. Don't they teach it in schools any more for some reason?
@@Chris-hf2sl10 year olds aren't learning the sort of algebra that he showed in the second solution in the video.
I hate to be the old fogey, but… While visual intuition is useful on its own right, algebra is the master tool that opens the world. Kids don’t need to learn how to get-by on a grade school test with toy problems; they need to learn how to harness algebra for future complex problem solving in school and life. That’s how you train people to become engineers and scientists. And if you are not going to need algebra in your adult life these approaches are just as useless to you as algebra would be anyway.
@@gavindeane3670 Well, that may be the case, but I don't think that the first method with the green boxes was any simpler.
Stumped me for a few seconds until I re-read it and saw the word 'remaining'. Then it was easy. Assuming, of course, he didn't read any pages before Monday.
You also need to assume that he read all the pages in order. And that the book is only full of readable pages. And that he didn't read any page twice. And that he's not in Congress giving a Tarot reading to a Congressional page.
@@Dominic_Muller Or skip any pages, though I suppose "remaining" handles that just fine.
I don't understand. This is not a hard question. The real question is who reads 62.5% of a book before setting it down.
He got distracted or bored 😅
They had him in the first half
I guess that depends on how mind numbingly boring it is. Maybe that's his best effort. I have been there.
His Mum called him for dinner, or it was light out.
Me? Except I wouldn't put it down till finished 😅
There has to be a level of trust between the people making the test and those taking the test. While being unsolvable if you assume the test maker was purposely leaving out key details, this is bad business. This is why I do not like trickery of any kind on a test unless, they tell the students ahead of time they will be purposely ask misleading questions. The rest of the world outside of school will provide plenty enough opportunities to learn of the dishonesty of others.
Exactly. Amongst people who know *how* to apply maximal pedantry, not all of them know *when* to apply it.
@@gavindeane3670 Something something something, Knowledge is the ability to be pedantic, Wisdom is understanding *when* to be pedantic?
That is not a good reason not to set a rigorous question. I solved this in about 10 seconds as I knew to make assumptions. I am pretty sure my ten year old self would have crossed it out as unsolvable. I was a precocious brat and often knew more about maths and science than my teachers who tended to be arts graduates. One tried to ridicule me when I said not all infinities were the same size - I had read a book* which covered such stuff at a basic level. * more accurately it was probably an article by Isaac Asimov "varieties of the Infinite" in an SF magazine my older brother had. Amazing what you can remember from nearly 60 years ago when you turn your mind to it!
@@matthewryan9323Yes, I think that's a very good way to put it.
I think what happens is that people have seen occasions when someone pointed out a genuine, problematic flaw in a logic or mathematics question, been impressed by what they saw, and concluded that that's the only way a clever person should ever respond to these things.
People who try and show how clever they think they are by pointing out all the holes they can find, are often actually showing how clever they aren't.
@@Llanchlo To me it is not about any specific question but more about the long-term benefits of students trusting the system. Many people get caught up in the here and now and ignore the accumulated distrust these kinds of questions build in many students over time. Clever tests don't teach students, clever teachers teaching the right way teaches students.
I did it the old way.
I find it amusing that one of the first answers is always “it’s unsolvable” and an assumption that something is left out.
‘I’m not wrong, it’s the problem that sucks.’
1:14 NO Presh, the question AS STATED IS SOLVABLE. Adding UNSTATED "details" to the problem makes it "unsolvable" and is intellectually DISHONEST! You should KNOW BETTER!
Exactly.
There are times when a maximal approach to pedantry, to identify unwritten assumptions, is appropriate. Solving a homework question for 10 year olds is not one of those times.
And just for completeness, if you wanted to actually TEACH something useful, you COULD solve the equation for "starting 1 day earlier than stated". Then solve for "two days earlier", and so on until you discovered a pattern. THEN you would have a function to calculate the pages based on when Klein stated reading. But I guess that's just too much work for you.
@@ThorsHammer1
He added that assumption because the problem can't in any way be solved without making that assumption in which case there would be nothing more to say about it, and he later specifically said that it's reasonable to assume that the question meant for you to make that assumption given that it's a question for 10 year olds and was probably not intended to be some kind of trick question.
There is no formula for how many days earlier he started, you need to know how many pages he already read, not how many days he started earlier. And it would be completely and utterly trivial if you had that information, you'd just replace 30 with (30+previously read pages) and perform the exact same steps as he did, so there's really not much point mentioning it (the days of the week never had any relevance, the only thing that matters is that you know that all of the numbers added together will equal the total number of pages in the book, which requires him to make the assumption he did).
@@asdfqwerty14587It's a bit weird to just pick out one of the assumptions though.
0:18 I think 48 after thinking for a bit
Since 30+1/8=3/4 I first swapped to decimals and used .75-.125=.625 to find 30/.625 gives you 48
You kinda cheated by making the inital green rectangle representing 30 pages aready the right size. To be honest you have to start at the end.
The possible _What If's_ have to be ignored, if the exam question doesn't give all relevant info then it can't be done properly (like about what day starting).
For a 5th grade assignment, I agree. But if you got this question in a job interview they are probably looking for why it cannot be solved.
This demonstrates how phrasing can affect maths problems stated in a textual format.
I agree that, if you take it as stated, where it doesn't *explicitly* state that Klein started the book on the Monday that he read the 30 pages, it is unsolvable. If you assume that it's not meant to be a trick question and that we have all of the information we need and it's implied that Klein did indeed start on Monday, it's just a matter of choosing the right method to plug the numbers into.
There will of course be those who will still try to "outsmart" the question, whether because they legitimately feel that it should be interpreted in the unsolvable way due to the lack of explicit details, they enjoy exploring different interpretations of these sort of things and exploring more deeply, or just have a weird need to "prove" how smart they are to randoms on the internet.
It's usually the last one.
You must NEVER assume that it isn't a trick question, because usually they are. Not in this case, I admit. But these questions usually do not only give the needed information (which you would have in a non-textual math problem, in this case: solve 5/8x=30 for x), but a plethora of misleading "clues" to derail the normal student. This is done to trick and outsmart those who know the maths but may lose time to eliminate all the junk information. I find this ethically reprehensible, but that's how maths education works in many places.
Don't be daft. It's a homework question for 10 year olds. It would be completely irrational to assume it's a trick question.
Edit: I’m just gonna use a philosophical razor and say he started reading the book on monday, as there used to be no other information provided that would state otherwise. the creator of the problem could have assumed that it was clear that he started Monday without explicitly stating it.
First find the fraction of the book the first 30 pages were. I will use p and b as units for pages and books respectively.
30p + 1/8b + 1/4b = 1b
30p + 3/8b = 1 b
30p = 5/8b
so 30 pages is 5/8ths of a book. to find out how many pages is 1 whole book, multiply each side by 8/5ths to get 48p = 1 book. Checking the math, 1/8 of the book would be 6 pages, and 1/4 of the book would be 12 pages. 30+6+12 = 48
I am so happy I was finally able to figure out one of your problems during the pause.
Since 1/4th book is read on Wednesday
So remaining 3/4 th book read on monday + Tuesday
3/4 of x = 30 + 1/8 of x
x=48
It's like they're lawyers during cross-examination trying to poke holes in a witness' testimony.
It's solvable in the head in mere seconds. Simple, straightforward fractional arithmetic. What the heck are they talking about?
Despite having never learned the "new" way, that is basicly what my brain defaulted to when i did it in my head.
same, and easily got the answer in less than half a minute.
Me too. It's a quick bit of mental arithmetic. Reaching for an algebraic equation and manipulating it to a solution seems like massive overkill.
It takes a minute to solve lol
More like about 10 seconds.
@@beauthestdanemore like 1/1000th of a sec
I had this in a slightly different way. I basically saw a 1/4 and 1/8, saw that that was 3/8 because quarters and eights are fairly intuitive common denominators, and just solved for what would make 5/8x=30. Which is basically the old way with mental shortcuts that could resemble common core if put on paper.
It's the new way without actually drawing the diagrams.
This one was an easier to solve. Did variation of equation, but by multiply everything with 8 beforehand, so the numbers wouls be whole instead of 3/8 fraction.
Easy 😒
You can do this one in your head if you can add simple fractions and factor small numbers. Here's how: Tuesday and Wednesday combined are three eights of the total book. That means that the 30 pages read on Monday were five eights of the total book. To see what one eighth of the total book is, therefore, divide 30 by 5. That means that 6 pages is one eighth of the total book, so EIGHT eighths of the total book would be 6 times 8. That comes out to 48 pages for the entire book.
Word problems are all about setting it up as simply as it can be expressed. This is easier when the word problems deal with real-world situations involving whole numbers like this one. Usually in these types of word problems the factors stand out quite visibly, and the fractions have simple common denominators. Perfect for head math.
Problem reads very straight forward, so no need to complicate
30 + 1/8book + 2/8book = book
30 = book - 1/8book - 2/8book
30 = 5/8book
book = 30*8/5
book = 48
You don't need blocks or squares.
That IS the blocks and squares solution. It's just that you already know how to do it so you don't need the thought process illustrated step by step to show you how it works.
Did it the "old way" in my head in 5 seconds. Thanks for the mini-challenge.
Its baffling that the adults could not solve it. It’s basic algebra
It took about 1 second to see what needed to be done. Then about 30 seconds to write it down. I probably could have just done it in my head. But if I had tried it the "common core" way, it would have taken a lot longer.
It isn't even algebra. If you don't throw X in there, it can be solved with basic third grade math skills (at least, the skills we were taught back in the 1970s-80s). back then, first grade math was addition and subtraction, second was multiplication and division, third was fractions and decimals. Mind you, we also didn't have preschool or head start when I was a kid and kindergarten was half a day. With as much school as kids get these days, a first grader SHOULD have the skills to solve this, second at worst. And yet this was given to a fifth grader.
@@ValosiTiamata But it IS algebra. You may not be throwing an explicit "x" in there, but 30 + 1/8*(book) + 1/4*(book) = book is basically the same thing with "book" being the unknown.
To echo the sentiments of others here before finishing the video: the combined reading of Wednesday and Friday is 3/8. Ergo, Monday's reading of 30pp must equal 5/8 of the book, making 1/8 of the book equal to 6 pp. 6*8=48. QED.
From a pedagogical point of view, problems assigned in elementary school math classes should have a numerical solution within the understanding of the students. Thus assigning a problem for which the answer is "not enough information" is not worthwhile, and we are justified in making the assumption that Klein started the book on Monday. Any parent who recognized the error in the statement of the problem should also be wise enough to see that answering the question as "unanswerable" would defeat the purpose of the question, identify and make the missing assumption and help the child arrive at the numerical solution the problem setter expected.
Exactly. A depressing number of people don't seem to know how to judge what level of pedantry is appropriate.
@@gavindeane3670 The question may be originally for a 5th grader but the audience for this video are people enthusiastic about logic and problem solving. It's not a homework channel just about helping kids get the answer the teacher is looking for.
This level of pedantry very much IS appropriate to give a complete answer to this audience. Assumptions about what the intended/ correct answer should be can massively trip you up in other more complex problems this channel frequently deals with.
Or that the first assumption is that the problem is solvable.
@@theomegajuice8660I don't know about you, but I am not impressed at all by people who only know how to apply pedantry and have no idea when to apply it. It's juvenile.
@@gavindeane3670 How do you agree with a nit-picking comment that uses the term "pedagogical" and think you're somehow the down to earth working-class hero in this scenario?
If Klein had read a pages before Monday, then the equation would be:
a + 30 + 1/8 * x + 1/4 * x = x,
which gives:
x = 8/5 * a + 48
So if a=0 (as assumed in the solution), the book would have 48 pages. If a=20, for example, then x=80.
Saying that problem is unsolvable if the value of some constant is unknown, doesn't sound very mathematical.
4/3 of Americans have no idea how fractions work. The rare 6/5 of them do, though.
Yeah. That's why the 1/3 pounder from McDonalds failed.
The 1/4 and 1/8 immediately stood out to me, so my first step was Tue = 1/8 and Wed = 2/8. Add the two together for 3/8, so Monday must be 5/8. Monday was 30 pages, so (30/5)*8 to get the total number of pages = 48.
This question baffles adults. This is why we have President Trump.
When i saw it was a 6 minute video i had to see the crazy alternate long way solution, but it never came
I solved this in my head in under 30 seconds.
No, no you didn't lol
@@mrowlsss Mockers don't make.
No wonder people have problems with this question. Who's ever seen a book that thin?!
I know you're joking, but plenty of books for elementary school aged children (especially early grades when they're in the "starting to read for real" stage) would be that thin.
Who sees how thick a book is these days? I bet people count how many screens now.
It took me about 10 seconds without a calculator. Truly challenging this problem.
I don't think 5th graders (in the US) would be using algebra. The first line of reasoning seems more aligned with the normal curriculum (even in the "old" days). But, as usual, there are multiple valid lines of reasoning. 👍
I don't get the ideas behind common core but maybe I am stuck in my "old" ways. I just hope all these young people who are learning common core grow up to be able to have the flexible reasoning to solve all the engineering and science problems they will face.
Common core is basically trying to teach math on an abacus (highly effective) without giving the child an abacus. It also relies heavily upon the exact grammar of a problem without allowing for basic mathematical principles such as 5x3 = 3x5 (commutative property), so the child has to learn ADDITIONAL terminology to explain how they went from 5x3 to 3x5 as an additional step in the problem to avoid their solution being marked wrong.
In other words, someone saw what China was doing and decided to copy it without investing in an abacus for every student, then decided to do their best to remove the math aspect (because "math is racist") and turn them into grammatical problems that you have to solve by making an illustration representing an abacus and explaining in detail each step of using that abacus. It's substituting art class and grammar class for math class and expecting better results as someone teaching just simple math.
My approach was sort of a hybrid. I didn't try to set up an equation, but I also didn't try to match up blocks.
1/8 + 1/4 = 3/8
So Klein read 30 pages on Monday, and the remaining 3/8 on Tuesday and Wednesday. So...
30 pages = 5/8
6 pages = 1/8
And 6 × 8 = 48
Just step by step deduction and hardly any "math".
@@briant7265That IS the matching up blocks method.
It's just that you already know how to do it, so you don't need someone to draw diagrams to illustrate how the thought process works.
@@briant7265That's exactly the solution he illustrates with rectangles and blocks in the video.
Obviously those of us who already know how to think of it like that do not need a bunch of diagrams to illustrate the thought process.
(30/x)+(1/8)+(1/4)=1 [Multiply by 8x] 240+x+2x=8x [Subtract 3x] 240=5x [Divide by 5] x=48 Figured 30 over the total pages plus the two fractional portions of the book had to equal 1 book.
Another quibble is to ask whether he read any pages twice over.
It taken longer to read the question than to workout the answer.
This is one of those that makes me wonder how these people passed school. I'm one of the worst exampled of a student and I did this instantly in my head, it's like 3rd or 4th grade math.
48, took about 10 seconds to work out and 5 more to double check.
Took 5 seconds to write down the equation, and bam. 48. Took 10 seconds to solve fully.
30+x/8+x/4=x
240+3x=8x
x=240/5
48 pages
The book must've been hella boring by the end for the kid to take 2 days to read 18 pages when he could read 30 on one day
1/4 of book was read on Wednesday that means 30+1/8 = 75% of the remaining book. 1/8 is 12.5% and since the total is 75% it implies:
75%-12.5%
62.5%
Which means 30 pages are 62.5% of the total pages. So we can find total like this:
62.5%(x) = 30
For me, the "old way" was introduced later. For my 5th grade level, we would have taken 1/4 to be 2/8, and used 30=5/8 as a basis for converting the others in a table. While we would have variables at the time, it wouldn't be until year 6 that we'd do complex equations like that, and probably year 7 or 8 when we'd bring it all together for solving problems this way.
Solving the problem in my head in seconds, I used the first method without the boxes. If I had written it down, I would have used the second method.
As an Asian, i can confirm this is too easy for 5th grade
I was a little baffled at first since I first read it as Klein reading an eighth of a page on Tuesday and a fourth of a page on Wednesday.
It's been a long time since I've been in school so I haven't done stuff like this in a long time. Still, from the comments, I knew I was on the right track when I figured out 3/8 for Tuesday+Wednesday, so 30 pages is 5/8 of the book. I admit I stumbled next, but I'd like to think that's more from not doing this sort of thing in a long time then anything. Once I read the comments and got my brain to co-operate, just divide 30 by 5/8 to get the number of pages in the book.
To be fair, Presh, you learned to solve this type of problem algebraically (variables and equations) when you were in middle school (for me, it was “junior high”). This problem, as you say, was given to a 10yo. I taught 4th/5th graders math for many years; I introduced them to algebraic thinking/solving via the “Singapore Math” bar model strategy on display here. I regularly teach/tutor middle (even high) schoolers to understand algebra through pictures and models when the variables and equations don’t make any sense to them. I can’t tell you how many students wonder why, for example, they don’t understand functions yet can’t begin to tell you what a particular function might look like if/when graphed (some don’t even know such a possibility exists) let alone whether/how it relates to real life
That's something middle school level, but parents not understanding it is crazy
Thanks for the challenge. I nailed it in less than a minute using the second method, which is way faster than the first.
You gave 2 ways. There is a 3rd that is similar to both combined. 1 = 30/x+1/4+1/8 where x is the total number of pages and the number 1 stands for one whole book. So, 30/x is the fraction of pages read on Monday, then add Tuesday & Wednesday to it.
Word problems can be extremely tricky, especially for those out of practice, because you need to be able to pick all the relevant info, then figure out how it all fits together. For example, if the problem were
30 + x / 8 = (3 / 4) * x
Or
30 + x / 8 + x / 4 = x
I bet most parents who remember even a little algebra would know to solve for x and may know you need to isolate x. However, trying to pick the info for these equations from a word problem is a skill of its own that is entirely different from solving algebra equations.
"The Old Way"
Not to 10 year olds you don't. I've taught 10 year olds. They do not know algebra.
I was stuck for about a minute because I forgot to think of "the book" as the unknown variable.
But then after that point, it was essentially just the equation 30 + x/8 + x/4 = x.
I originally thought that the question said that he read a quarter of what remained on Wednesday, and that’s a very different question 😅.
I was falling asleep waiting for you to get through the problem the first time. No kid would have the patience to turn a simple math problem into art school like that. And then you said "kids today" and I realised you were doing common core instead of proper math. Mind you, your algebraic answer was still a bit long-form, but at least I could wrap my head around it.
Using basic math, I solved the problem completely in my head in about 20-30 seconds: 1/4 and 1/8 are basic fractions, so common denominator makes it 1/8 + 2/8 = 3/8. So 30=5/8. 30/5 is 6, 6x8=48
Common core makes this problem feel like something out of early calculus when I had learned everything I needed to solve this problem in third grade and my three year old will probably be able to solve this problem in about two more years because he's learning proper math. I feel so bad for Gen Alpha, knowing they're going to leave school with next to zero education because of stuff like this.
Another question of overthinking it that would make it difficult to solve, how do we know the 1/8ths of the book didn't include any rereading? The question doesn't say he read "the next 1/8th of the book"
That's why you shouldn't overthink it.
We don’t know whether there was any overlap between Monday and Tuesday’s pages. If he’s anything like me, he probably had to turn back a couple of pages to refresh his memory!
I can understand a ten-year-old having to dig deep for this but adults baffled by it, really? It's a simple mental arithmetic problem.
If 1/8 + 1/4 (3/8) is the remainder of the book after Monday then 30 is 5/8 of the book, so 1/8 is 6 and 8/8 is 48!
Oh my sweet child. You underestimate the lack of basic mathematical and even logic knowledge in our current society.
So as I read it 30 pages are 5/8 of the book because the rest of the book he reads over two days is 1/8 and 1/4 of the book to finish it. So the first 30 pages he read must have been 5/8 of the book. So you multiply 30 x 8 and divide it by 5 to get a book with 48 pages. So he read 30 , then an 8th (so six more pages) taking him to 36 and then a quarter of the book, 12/48 to get to the full 48 page read.
At 2:28 on, you could improve the graphics, by colouring the segments in the order they were read. Don't colour the first 1/8 segment green, colour the 5th one! It's still 1/8th, but it's in the right time position. Similarly, don't colour the first 1/4 segment green, colour the last one. It's the last 1/4 of the book that was read on Wednesday.
_ _ _ _ _
_
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I went with the equation x-30-x/8-x/4=0 because on Wednesday there are 0 pages left, and we start with x pages. This quickly resolves to the same path as the second solve.
The question as stated needs two assumptions: a) the reading starts on Monday, and b) no pages have to be re-read.
In most cases, the hardest part of a math problem is figuring out the wording.
If the remaining 1/4 completes it, it means that 30+1/8=3/4 of the book. Pages= 30+1/8+1/4 which is equal to 30+3/8 so 30 is the remaining 5/8. So to find the pages we can do 30•8/5=48
My method of solving this was to look at the question and yell 48. It's sad that there is at least one person in the world who is not able to solve these kind of equations in mere seconds.
Similar to the old way, I just converted Monday's reading to a fraction: 30/x. Then added the other two fractions to it and set the sum equal to 1 for the whole book. Solve for x.
Been a long time since I've done a fraction problem. Once i remembered least common denominator it became easy.
Basic fraction problem.
30 pages are 5/8th of the book.
So the book is 48 pages.
What got me was I thought it meant 1/8 of the remaining pages after the initial 30 was read 😢
After watching this video I understood why this question might have stumped many people. It might be due to the fact they were just overthinking by focusing on the part of the missing "starting point" which in a maths question for 10 years olds or for that matter any school grade will be like an inherent assumption.
The issue with the first method is that you don't build abstract intuition by doing it this way, most of the time learning the algorithm first and then deconstructing it helps you learn it better. The black box method basically. Don't understand something? Think of it like a black box. Once you know how to use the black box, disassemble it, you will find smaller black boxes inside, and you will have an intuition on how the larger one works, repeat process until you understand the whole thing. The new method is kinda backwards.
What??? The second method in the video goes to the concurred lengths of constructing, manipulating, and solving an algebraic equation. That's massive overkill compared to the first method, which simply and clearly visualises the problem.
The first method is how I solved it. Intuitively. With a few seconds of mental arithmetic.
This is a damning indictment of the public education system.
You know, to be fair I learned it the "old way" too... but I'm pretty sure this was in Algebra I which was 9th grade. So if this is really 5th grade, that's actually fairly advanced for that age. I still think the old way is more general since algebra is pretty fundamental, but I think it works for 5th grade math.
I can’t believe my 50 year old brain thought to setup an equation for x and solve it to get the right answer.
My 70 year old brain did the same thing. Why is new math more complicated?