explain Calculus to a 6th grader

Never understood calculus. One college professor told me; “your brain is nor wired to do calculus”. At 75 I now know that professor had very limited teaching skills (or just a putsch). Thanx for the lesson. Don’t stop learning. 1.5K Madman6505 Madman6505 1 month ago (edited) I hated calculus in college until I took physics. Calculus on its own is like doing puzzles for the purpose of getting the right answers. But when you learn apply it to things in the real world (and more specifically, to things that actually matter to you in the real world), it becomes magical. 135 Anthony de Jong Anthony de Jong 5 months ago In the integral case, the one point that is missing is that, in the integral notation, while the "S" shape stands for "Sum," the f(x) represents the height and the dx represents the width. In other words, the notation includes the well known "base times height" formula for the area of a rectangle except reversed. Similarly, in the differential case, the differential notation includes the equation for a slope with the f(x) representing the rise and the dx representing the run. Thus the terms of the calculus notations must represent the physical term you are looking to solve for. I was most of the way through an engineering degree before that subtlety dawned on me. I got a C in the first semester of electromagnetics without this understanding, and, in the gap between semesters, this notion occurred to me, and I went back and aced the second semester of e-mag. 431 NucularLuc NucularLuc 5 months ago I tutored Calculus at university for almost 4 years, most of my students struggled more with the algebra than the concepts of Calulus. 185 weetabixharry weetabixharry 1 month ago My understanding is that calculus is taught at a very young age in south Asia and east Asia (where more than half the world's population lives). So it would be interesting to see how they teach it. I thought I was a math superstar in high school (in England), but was instantly humbled when I went to university (in London), where almost my whole class were foreign students (predominantly from China). 18 Dave Witter Dave Witter 4 months ago I took college physics without calculus, because I barely got thru trigonometry. I am drawn and enjoy engineering. I believe math gets fuzzy at the higher levels because instructors can't relate the subject to the average student. I would like to see the instructor ask an interesting question with a real world example and work backwards, using mathematics to find the solution. 97 Poop Eater Poop Eater 5 months ago As someone still in the womb, this video helped me immensely on what calculus is really about! 862 The Masked Man The Masked Man 1 month ago You also could've explained in simple terms how the derivative and integral are related to each other. This video kind of gives the impression that differentiation and integration are two useful but separate things, when they are actually inverse operations. The derivative (the rate of change) and the integral (the area under the curve) could've both been explained using the speed of the car and the distance someone travels between, say, home (A) and the nearest gas station (B). The derivative is the rate of change (miles per hour) at any point in time between A and B. And when you add up all those tiny little changes you get the total distance you traveled between home and the gas station (the integral). Both operations are fundamentally related to each other. Another thing that may be confusing about calculus for an elementary school student is the idea that the answer to a differential equation is not a single number (like x = 3), but an actual equation. We want to find the equation that gives us the rate of change for every point along a curve, and thus we are dealing with the problem of continuous change here. It's very different than finding the slope of a straight line in algebra (which is an average), and far more useful in terms of "real world" calculations. 82 Justicewillprevail110 Justicewillprevail110 1 month ago I’m watching this at 46 years of age because I can’t remember any of this from when I was young and I need to freshen up my math so I can help my 12 years old daughter when she asks me for help in math. You’ve made it so simple and clear. Thank you so much . 56 Jimmy Lee Hook & The Long Island Sound ® Jimmy Lee Hook & The Long Island Sound ® 1 month ago I love your explanation, and appreciate you taking the time to do it. One point worth noting: At 11:50, you hand-waived the concept of “dx” in the integral. that was a key concept that you passed off as mere notation. But it is not mere notation. In order to get the area of a rectangle, you must take the length times the width. The length of your infinitely small rectangle at any point on the graph is f(x). The infinitely small width is “dx.” They must be multiplied together in order to calculate the area. You might consider explaining this, in order to tie your entire concept together in a nice neat package. Regardless, thank you for such an interesting post, and well done. - Jimmy Lee Hook 37 Raymond Jackson Raymond Jackson 1 month ago (edited) As an inner-city kid in the sixties, I didn't learn anything about geometry. The Detroit Public Schools were a complete waste of time, even detrimental and dangerous, much as they are now. They steered us to 'business math", which, is being basic math, with bigger numbers, got boring REAL QUICK. I didn't learn deeper math, geometry, equations, formulas until I was in college, and had to take them to stay in school. So the courses were like remedial and not nearly the fun and joy math can and should be. They scared us from math, very early. Watching this guy, I can only imagine the head start a kid learning this in the 6th grade, over a kid who didn't learn it at all. I don't think it's changed at all. Suburban kids are getting smarter and smarter, while city kids are getting dumber and dumber. The "woke" crowd talk about disparity and in equality. Well it starts here, education. With education, comes critical thinking. With critical thinking, comes problem solving. That's simply gone in inner-city culture. 54 Patrick Donovan Patrick Donovan 5 months ago This is a good explanation. My HS calculus teacher talked about how way back in the day before radar, troopers used those car counting cables and a stopwatch to determine who was speeding. But people would go over the first cable, then slow down before the next one, defeating the purpose. So they moved the cables closer. Calculus is moving the cables infinitely closer. 23 Horizon3165 Horizon3165 5 months ago A good way to keep brain active and stimulate is to review "math." I am 69 years old and enjoy all of your math lessons. I remember quite a few of them and skip to the next lesson. Thank you. 234 DNTME DNTME 3 weeks ago Differential calculus wasn't too difficult. There seemed to be a certain logic to it. But integral calculus perplexed me to no end. It seemed to jump all over the place from one example to the next. I kept trying to find THE "pattern" in it all. Eventually it dawned on me that there was no single pattern. It was all a game of finding the appropriate function equation from a list of them which best fit your need. It was a form of pattern matching. My tutor never pointed that out to me (home schooled). 12 Old Scribe Old Scribe 2 months ago Replied to Chuck McGlynn: He is so right. Some teachers just don't know what they are talking about. This teacher is outstanding. He is the sort of engaging, patient voice we really need in education. He makes you feel that you can actually do this stuff. Then he guides you gently step by step to understanding. To anyone reading this, don't listen to ANY teacher or professor who tells you you can't do something. That is a limitation of the teacher - they can't communicate it to you. They can't give you hooks to hang the next bit of information on. I was told by a Medical Professor that I was too old to do Medicine at 25. I went on to get 10 degrees from Undergraduate to Post Graduate to Masters to Doctoral level. I duxed the course several times. My final PhD won the University prize for Doctoral level research. So did that Professor eat crow? Damn right. Just don't listen to nay-sayers. They are a black hole to many students and kill many careers because of their position, title, power and influence - and their own limitations. 20 Kjdjrh Kjdjrh 1 month ago Studied Calulus at Drexel University eons ago. My favourite problem was: Using calculus…find the diameter and height of a metal can to hold a quart of oil using the ‘least’ amount of metal in the manufacturing process. Naturally…the answer Is the standard can we see on the shelf of an auto parts store- but if you had to manufacture 50 million cans..the application of calulus is fiscally vital. 😄 3 Luke Simons Luke Simons 1 month ago (edited) First: Thank you for the video and for shining a light on the simplicity of calculus. I think there is way too little emphasis in elementary school on the spatial and temporal concepts behind this part of math. Second: It would be great to see a precursor video talking about space and time with none of the notation. Like watching a time-lapse of fruit growing with David Attenborough pondering the ways to measure it. Third: My only critique is that it seems strange to begin with integration. The reason for the "squiggle" is sort of skipped or swept aside as trivial. Like "we do this because I asked for the area and that is what you are going to give me". It seems like you started with the "hack" to approximate a solution to a problem I didn't know I had. Instantaneous Rate of Change and its representation with a tangent line is the keystone of calculus. No problems, no solutions or approximations. Just what is it, where does it happen, and how do we talk about it. My suggestion would be to plot something like rainfall per year, talk about the differences per year and plot those separately. Then do it per month, and then per week. This gives an easy illustration of 6 graphs with 3rd grade understanding. No speed, no acceleration , just counting and plotting bar charts. The best part about this method is that it draws the attention to plotting things that are yet to happen as well as how exponentials work without number or notation. 6 Mike Griffin Mike Griffin 4 months ago Excellent video. As a freshman in college had to take advanced calculus for pre med without ever taking pre calc or calc in high school. Never understood what was going on. Failed. Left pre med. Had to get my doctorate in another field. Wish I had you as a teacher. Might have made it in pre med. 75 year old. 21 CapAnson12345 CapAnson12345 5 months ago I think if I had been presented Calculus in the right way I could have easily handled it in 6th grade. Possibly 5th. By the time I started senior year in high school too many distractions and I just didn't care. Eventually I got it down in college.. but it could have been absorbed much earlier by my younger sponge-like brain rather than my older, calcified one. 19 BOB A BOB A 4 months ago I do the actual calculus on those simple geometric shapes first to demonstrate it works before moving onto the more complex curves. Also need to demonstrate the "so what" by using a velocity graph and transforming it into an acceleration curve. Not that what you're saying is wrong, its very very good in terms of the mechanics but I've found you need to connect something they fully understand to the method and provide a real world reason for understanding it. Same goes for other areas of math and science. 16 Night Fox Night Fox 5 months ago (edited) Be careful saying "Infinitely small". dx is finitely small, its just getting smaller and smaller until your result is accurate enough that it doesn't matter. This can create some misconceptions about limits that lead to paradoxes and may confuse people. 98 Citizen Brain Citizen Brain 4 months ago (edited) I was first introduced to the concept of the Derivative, then Integration and methods of Integration was the 2nd Semester. After that we got into 3D vector fields, partial derivatives, and differential equations. Calculus will utilize some of that mundane Algebra and Trigonometry they taught you in high school that seemed so useless back then, and makes you go "Aha! That's why they taught us that stuff!" 19 Joseph Mann Joseph Mann 1 month ago Great job. I’m forever trying to explain the beauty and usefulness of calculus to folks who didn’t take calculus. Lol, I’m stuck saying “it gives you intuition about the universe you never realized before.” This was a great. Have you (or someone who works as your tutors) ever worked with visually impaired students? My son is a blind sixth grader, so we’re always hopeful and looking. Thanks again. -jom 5 Ron Jetko Ron Jetko 3 months ago great presentation - at 70, I decided to refresh my math skills starting with math and trig and proceeding to Calculus. I was always good with derivatives - integrals not so much, yet :) 27 J Hemphill J Hemphill 1 month ago For me, the value of calculus was demonstrated as thus: "We have been given the formula for the area of a circle. It is πr². It seems to hold true for every case we've encountered so far. However mathematics is not about faith in received wisdom. It must be possible to derive any formula, for ourselves, from the very fundamentals. Accordingly, here-in we shall derive the formula and prove it true. Behold!" 16 BVale BVale 2 weeks ago When I was taking calculus, one day the professor's own 12-year-old son asked me what calculus was about. I was surprised that he didn't know-- or maybe he was just pretending not to know. I asked him if he knew about drawing graphs of simple equations like Y=2X. Yes, he could do that. Then I said that these graphs are straight lines, but other formulas produce curved lines, and calculus helps us deal with those situations. Blind leading the blind... I didn't know much calculus myself yet, but it looks as though I was on the right track and he got a sense of it. 3 Ordinary Man Ordinary Man 1 month ago For derivatives, my calculus class explained it as the slope of a line tangent to the function graph (intersects it at one point). They started out with finding the slope of a secant line, which intersects at two points on the graph, and moved them closer together until the distance between them was 0. The result of that process is the derivative. I thought you were going to explain it in that way. I think the related rates problems involving instantaneous velocity that you described are an application of the derivative rather than an explanation of the concept. 4 V M V M 2 months ago (edited) I think letting children know the value of calculus so they can look toward learning more exciting concepts is valuable! I wish someone had told us how to use math and why it was useful. Helping students apply what they are learning is the secret to getting them interested in learning. Why would a child be interested in learning area of a squiggly? Find that answer or create the need to know and this is a great lesson. 11 Jordi H Jordi H 4 months ago It was going great until 14:00 or so when he leaves the first graph without explaining the relationship between f (x) and the area in the graph. 3 sparky dog sparky sparky dog sparky 1 month ago Thank you so much for taking the time to create this video! I'm 70+ and failed more math courses than I passed, but have always wanted to have at least a basic understanding of some of the basic mathematical concepts. 1 Thomas McCarley Thomas McCarley 1 month ago I only had one quarter of calculus and like most of my fellow students, we were terrified. On the first day, the prof knew this and offered this soothing bit. You shouldn't fear Calculus, every year thousands of students successfully complete a Calculus course, then paused a long time. However, he continued , every year tens of thousands fail to complete it. 21 Twidget Twidget 4 months ago (edited) When I was in fourth grade we were studying how to figure areas. A teacher posed the question how would find the area under this curve. She explained that you could break it up into smaller and smaller rectangles to approximate it's exact area. That was just a seed planted in my brain to the understanding integral calculus years later. No cool notation just a question. I do admire Fermi's(?) solution to graph it on paper, cut it out and weigh it. Brilliant! 56 Darion G Darion G 2 months ago Thanks for doing this. I've always been afraid of calculus but this shows me i've never had a teacher able to teach me until your video. Thanks again! *Subscribed 12 Moe pow Moe pow 3 weeks ago In my specialized classes I had to start at the very foundation of math, past the assumptions. If your proficient at math this might bore you, but it might help if you have children struggling in math. Symbols in math take the place of something you don't know & and known or learned symbols, such as dots, grouping, or sometimes that's even absent... 3x=9 + 3. The 3 by the X means to multiply, but your teacher has to to tell you that first or you have to read it in a book. Formulas are like instructions that tell you what to do, 3x=9+3, tells you there is a missing number and after learning the instructions of this formula you then solve to learn what X is. Learn the Symbols and you at least know what the formula is telling you. Vocabulary is a huge part of math. You must learn the words and their meaning in context. I always reminded my students that some words have multiple meanings. Example, derivative. Look it up it has meaning in math and art. This seems fundamental, but assumptions is where a lot of teachers lose their students. Don't assume your learner knows the basics. I run into this all the time with my cell, many steps in using a cell are assumed. If you have no clue what a drop down arrow is, you have no idea you can even do anything with it! Find out what your students don't know and go from there. Obviously you have to adjust in an advanced class, but....you never know. 2 Ronald Dery Ronald Dery 1 month ago Hello. I just found your channel and enjoyed this lesson. It’s been 32 years since my college level calculus classes. I was just wondering what software you are using as a virtual blackboard in the video. Thanks and keep up the great work. The world needs more teachers of your calibre! Mateus Menezes Mateus Menezes 5 months ago Incredible job! This is the true value of education, teaching something everyone says its 'difficult', on a very easy way! 6 Hamid Ata Hamid Ata 2 months ago You brought such a complex topic to a very simple and easy concept. You have explained it in a very good and simple way so everyone can understand it easily. Thanks a lot for your beautiful explanation. 1 Shadowoftheoldones Shadowoftheoldones 5 months ago Area is geometry, geometry is generally covered in 10th grade. I used to teach physics to 11th graders using geometric logic like yours as a stand in for the calculus, and it was beyond most of them. 12 Jeffrey Zaiser Jeffrey Zaiser 6 months ago This is how an analog signal is sampled and converted into a digital signal. You should approach it from that perspective since AD and DA conversion processes are part of our digital existence. Kids would get that quick 29 Andrew Watkins Andrew Watkins 4 months ago I’m an Engineer now, but I wish I’d had you as a teacher in High School. 8 Ceo founder Ceo founder 4 months ago Even though I am a grown adult; this educational video upload is a gift! The way the narrator/educator explained the basic fundamental/principle of calculus is so excellent! Thank you so much. I live to learn. 24 Russel Redner Russel Redner 3 months ago Hey, John, love your program here. It is really great and I am refreshing my Math Skills at 76....I was a teacher for over 20 years and taught Lakota children primarily on a Indian reservation called Pine Ridge...located in South Dakota. I experimented with teaching Calcuus to younger students...in the primary grades....because they do do this is China and Russia for a long time now. Children at the younger ages have more fantasy than concregteness which is what holds back people. Children can grasp concepts of higher mathematics faster and better and by the time they reach the old age of a 6th grader have incorporated these concepts. Lakotas have a mathematical mythology even thinking and seeing themselves and the world they live in as geometrical....their art also reinforces this thinking and worldview. Just thought I`d share this story with....love your program.... John D John D 2 months ago It's really effective to make a connection for the student between a real-world example and the "squiggly thing" graph. I've had success explaining, on a similar graph, that we can use calculus to model the travel of a car. I explain that the X axis is time going forward, and that Y at any time is the speed of the car at that moment. The slope at any instant corresponds to the acceleration or deceleration, and the area under the curve is miles traveled. This really turns on a lot of light bulbs. Then they can answer questions like deflection points (they moved from the gas to the brake) and crossing the X axis (they are going backwards now) etc. This helps them get a very intuitive understanding of what the graph MEANS. 3 rlevoi rlevoi 4 months ago I appreciate this, but when teachers state something or in this case write a formula and then add on “don’t worry about that right now” or “it doesn’t matter” then you lose the student. If it didn’t matter it wouldn’t be a part of the formula. 7 Mike R Mike R 5 months ago In the lat 60s, while in high school, I was doing very well in math until I took trigonometry. I got nervous and dropped it. Because, I couldn't visualize it in the physical world. Later, in my analog electronics classes, I was using more difficult formulars with ease. We used slide rules in those days. I don't think my trig instructor ever explained that I was just calculating the elements of triangles. Perhaps she wasn't qualified. If She had taught more like you, I believe I would have breezed through it on into calculus with no problem. 8 eli zhu eli zhu 1 month ago woah ~ This is nice i dont really consider myself the brightest person specially when it comes to math, number and sciences and stuff, but the way u just explained it was very much comprehensible! I am actually looking forward to learning about it soon! 2 Colin MacKenzie Colin MacKenzie 1 month ago My first calculus teacher walked in the first day, "Calculus is easy; the fear is unwarranted. You do it every time you gauge the oncoming car and ask yourself...do I have enough time to accelerate out and into my lane before that car hits me? In a split second you determine how fast he is going, and how fast you can accelerate and you know. Calculus is simply rates of change." He gave a few more examples but I lost my fear after day one. Awesome teacher. I wouldn't start a 6yo with integrating area under a curve...there are numerous every day examples to draw from that are more natural. 9 Russell Copeland Genius student solved this in 1 minute - insanely hard geometry problem 1,678,511 viewsMar 8, 2018 35K DISLIKE SHARE DOWNLOAD THANKS CLIP SAVE MindYourDecisions 2.68M subscribers Thanks to Bill from New York for this suggestion! Bill emailed me a problem asked in China to identify talented students. A few very talented students did solve it in less than one minute! I was not able to solve the problem at all. The question involves finding the area of a red triangle in a parallelogram, for a diagram you can see in the video. Even though I didn't solve it, I really enjoyed learning the solution. My blog post for this video: https://wp.me/p6aMk-5r6 If you like my videos, you can support me at Patreon: https://www.patreon.com/mindyourdecis... Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: https://mindyourdecisions.com/blog/ Twitter: https://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Y... Google+: https://plus.google.com/1083366085665... Pinterest: https://www.pinterest.com/preshtalwal... 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RAJANGAMER RAJANGAMER 4 years ago I always thought I was smart and really good at math and logic problems Until I started watching this channel 8.5K AWildKITsune AWildKITsune 1 year ago Math questions like these are usually super easy when you know the trick. It doesnt make you smarter than someone else to know a trick that they do not. The students who understood the trick could do so without trouble in less than a minute, everyone else takes time to discover the trick for themselves. 1.2K Jiacheng Xue Jiacheng Xue 1 year ago Your channel remind me the days I studied math in China. And I really appreciate the teachers always show us how to solve questions with flexibility and creativity. Moreover, we are not born to be good at math, but most of us have been taking tons of practice questions ever since the elementary school. Everything comes with a cost I guess. If you want to do better in something, you have to keep practice on it. 185 MusicalBasics MusicalBasics 2 years ago OH WOW SO EASY HAHAHAHA I TOTALLY KNEW IT (aka spending 5 hours trying to figure it out, giving up, waiting a year and a half until finding this video) 596 Kanrio Kanrio 2 years ago got this in about five minutes. you don't need to know any special theorems you just need good geometric intuition 195 2DarkHorizon 2DarkHorizon 1 year ago I solved it thinking differently. The parallelogram can be thought of as 6 identical separate triangles. Area of 1 of these triangles is 0.5x + 36 + 4 Area of 2 of these triangles is x + 72 + 8 Area of 3 of these triangles is 1.5x + 108 + 12 There area of 3 of these triangles equals half of the total area of the parallelogram. Therefore 1.5x + 108 + 12 = y + 79 + x + 10. y = 0.5x + 31. y is the area adjacent north to unknown (?) The area of y + ? equals the area of 1 of the separate triangles of the parallelogram. Therefore y + ? = 0.5x + 36 + 4 We already calculated y previously and we substitute it in. 0.5x + 31 + ? = 0.5x + 36 + 4 31 + ? = 40 ? = 9 5 James Smith James Smith 4 years ago The thing about these "less than a minute" problems is that it all comes down to how quickly you see how to solve the problem. I'd bet that the kids who solved this problem in under a minute had been working with geometry of shapes and were very familiar with this sort of problem. 2.3K Rockford Tech Rockford Tech 1 year ago This is one of the most beautiful solutions on this channel. No trig, no calculus - just the very basics. 16 Thijs Beentjes Thijs Beentjes 1 year ago Never realized the 2 triangles thingy, once you explained that and I saw the problem again I instantly saw the solution too 59 Ben V Ben V 10 months ago After I figured it out, and looked at your solution,I concluded a simpler answer, but basically the same reasoning: The two triangles at the base od AB touching the line DC = half the area of the parallelogram and also = the the area of the one triangle at the base of AB. The 2 white areas ( you call them a & b , I named them Y & Z ) are common to both and will just cancel out in the equation anyway, so I ignored them and end up with X + 80 = 89. X=9 2 T Est T Est 3 years ago (edited) More than 20 years ago these things came easy for me. I even used triangles to solve physics math problems that I didn’t necessarily know how to solve otherwise, for as I was lazy and didn’t always attend classes. Probably would have done it in my head back then, now I definitely would have needed pen and paper and put some real effort into it. Mathematics is like a muscle when used a lot it’s strong, not using it it will become sloppy. This is my view of why young kids can solve these problems quickly, they have a talent and that tallent is put to work. Geometry was always my strongest field. 3 Sarah Sarah 10 months ago I figured it out, but slowly, by writing down the area of the parallelogram in terms of h1 and h2, substituting h2*AD with h1*DC, and solving multiple equations until I was left with x. Seeing that two triangles that use the whole base (and height) of the parallelogram have the same area as one is a genius idea. 1 pusheen pusheen 4 years ago I was born yesterday and I solved it in half a Planck time. Took me that long cuz I was working on Riemann zeta function and building a quantum computer at the same time. 2.7K Zoe Porphyrogenita Zoe Porphyrogenita 2 years ago (edited) This is a very recognisable pattern. Once you know how to do it with one set of numbers, it's easy to see how to apply it to any comparable alternating pattern inscribed in a parallelogram. Chances are, the children who solved this were drilled in the method. The quick, accurate ones were just average at arithmetic. 1 Daborshy Daborshy 3 years ago I watched the video up until he explained the 2 triangle thing, and then I got it in about a minute. I have to believe that the students who were given this quiz are taught these kinds of rules. That would be too incredible if they were able to figure out the approach and follow it through to a solution in under a minute. 1 Lenocis Lenocis 1 year ago I remember this question in an International exam and I'm pretty sure I got it right, when the results came back I was in the top 1% worldwide and I also know with certainty that I am not Chinese (I am Australian) 6 Blobfish111 Blobfish111 1 year ago Wow, I've tried to solve this many times and only now figured it out. In the end I solved it pretty much the same way as in this video. It took me probably an hour altogether but I made it. :) 2 Todd Farkman Todd Farkman 2 years ago I came back to this a few days after watching it. It still took me 5 minutes to do the math. But a lot of these problems are simple to someone just learning the concepts. If you were just practicing triangles in a parallelogram, this problem is really simple. lennidary s lennidary s 2 years ago I am a chinese person, and now I am thinking am I really Chinese? 4.7K Kishan Shukla Kishan Shukla 2 years ago Knew the concept but never thought it can be used this way. Thanks @MindYourDecisions 4 Alexander Horter Alexander Horter 2 years ago The red triangle looks a little bit bigger than the triangle with an 8. I guessed 9. 1.9K Joe 54 Joe 54 2 years ago Hi Presh. I love your videos. I know you can’t do it all but sometimes I like to fiddle around on the computer and play with problems like this. The only problem is all the things online make it really difficult to make shapes. What do you use for your videos that I could use to solve things without having to write it out? Rowdy Prostate Rowdy Prostate 4 months ago i’m usually pretty good at these, i’d be embarrassed to say how long some of them take me, but i usually come to answer after a long pause. this one completely stumped me though, i was trying to find the side lengths from D to the top right corner of the triangle we were looking for the area of and the parallel side length from B to the bottom corner of the area 8 triangle. I knew i couldn’t find any side lengths from the given area triangles as they weren’t drawn to scale and didn’t have 90 degree angles but i thought by reflecting the area 10 triangle to the left of the line from B to the bottom corner of the area 8 triangle that i was getting somewhere. one of my longest pauses to date and none of the work i was doing was getting me anywhere, i could have had a year to work on this and i don’t think i’d have arrived at an answer. the 2 triangle within a parallelogram where the 2 of the sides make up the length/width of the parallelogram and they share a height/length being equal to half the parallelogram area part is crazy to me. after it was explained it seems so simple, but it’s far from intuitive as i’ve never seen something similar used in other problems. seems crazy that children can spot a way to set up equal equations from this to cancel like unknowns and solve. 1 Derek Maeshiro Derek Maeshiro 2 years ago This really wasn’t that hard. You just need to know that specific theorem 570 japeking1 japeking1 2 years ago Thanks for this.... it took me about the 10 minutes, so I can't match the kids but I'm fading in my 70's and have done nothing like this for 55 years.....so you have made me very happy and even reinvigorated my dull existence. 2 Sai Phaneesh K.H. Sai Phaneesh K.H. 1 year ago Wow it was an awesome problem I knew that area of the triangle with one of its sides same as the base or width of a parallelogram and the other vertex rests on the opposite side has half the area of the parallelogram. But I didn't knew that the sums of area of 2 triangle will be same too. Nice learning... 2 John-Paul Mathieu John-Paul Mathieu 4 years ago This is a great problem, and if you are thinking there is no way many American students would be able to solve this, as a middle school math teacher I can tell you why many students can't. In my math class I never give a formula and instead show what's happening and then the students derive the equation. This way when they forget to do something, I ask them questions related to what is actually happening. For example, we recently finished up our geometry section and I was talking to the other math teachers. They were like, "I don't know why my students can't remember simple things like radius is half the diameter or when doing area of a triangle, you divide by 2 after doing base times height. These equations are so easy!" Then I ask if they showed where the equation comes from and they said, "Yeah, it's base times height divided by two".... So basically, they just gave the equation and that was it. In my classes, I first show what it means to find the area of a rectangle and then go on to show how a triangle is literally half of a rectangle. I then show different triangles and show how no matter what, it's always half. Then, when they forget to divide by two I ask how many triangles are in a rectangle and they immediately say, "Oh crap, there's two, I was supposed to divide by two!" Once the students have the meaning, they can actually make sense of what's happening and they drastically improve. Anyway, why am I bringing this up? Well, I asked why they don't show the meaning behind the math and I got replied with, "Students don't care about the meaning, they just want to know how to do it so they can pass." This was coming from math teachers that have been teaching for 8+ years (I'm a first year teacher). With this sentiment, it's no wonder many students here in the US would have almost no chance of figuring out a problem like this. 580 Garry Cotton Garry Cotton 2 years ago (edited) 9 Took me a lot longer than 1 minute though! Many dead-ends were reached along the way. In my opinion, problems like this really help push home three important things to remember when doing math puzzles and people usually give up before doing this: 1. Diagram everything. Visualize whatever you can. We're visual creatures and when we can see something it becomes much more understandable. 2. Get everything relevant down in symbols. All the relevant relationships, everything. What's relevant? Start with things that overlap or have something in common. For example, in this question, two of the triangles for which we know their partial area have the same "missing" piece. Get that relationship down on paper. At first it looks like there are just too many unknowns and it becomes overwhelming but things almost always start to cancel out once you start to work through them on paper. 3. Keep the faith. Going back to being overwhelmed by unknowns, sometimes you can't envisage how things will become manageable but if you just keep going through the steps it'll happen. 1 X Jungbluth X Jungbluth 1 year ago Oh my, I made it in two minutes because I remembered about the triangles within a paralleogram rule!! Very nice one, it is simple but still fun!!!! 1 Fierzo Fierzo 1 year ago Took me about two minutes, basically you have to be able to observe and find the two equivalent half parallelograms and it's pretty easy from then on. I definitely remember doing these kinds of problems in fifth and sixth grade when I was in China about a decade ago. I was really good at these being the maths kid of the class lmao. 1 Cyber Geek Cyber Geek 3 years ago Your videos are awesome and very intellectual. Keep up the hard work 2 Aurora Aurora 1 year ago (edited) OMG, I guessed it correctly! Now, some may say that that was just a combination of lucky guessing and good approximation skills—even though the drawing isn't even drawn to scale—I'm gonna say that it was my subconscious that pulled up and helped me solve it. Edit: after watching the video, the problem is mindnumbingly easy. 1 James Sarungbam James Sarungbam 3 years ago A 5th grader in China is solving under a minute.... But in US grown adult are still arguing that the earth is FLAT.... RIP America.... lol 6K DT DT 2 years ago (edited) First, I transfer the parallelogram to a rectangle because you can arrange the points inside to preserve all the areas Then calculate the area of 2 big triangles, 1 containing 72 and 8, and the other containing 79 and 10 with the edge AD. Then calculate the triangle next to the red and yellow ( contain the edge AD). THen you will see the same answer (maybe it will take 1 min ) 1 rwold rwold 3 years ago This is pretty easy but it requires you to know that property of parallelograms --- the fact that you can "slide" the end point of the triangle and still wind up with half the area of the parallelogram. I never learned that, as far as i can remember. I can imagine a world where that is taught to students, and they would inherently know how to do a problem like this. But we never learned to think about that. 2 Jón Snöw Jón Snöw 7 months ago 🙏Thanks a Lot Guruji for Everything you've done for Us🙏 ❤️Love You 3000❤️ IonKatt IonKatt 2 years ago (edited) I solved it in 10 seconds by guessing 9 based on observation and extreme luck lmao 9 Adam Gillespie Adam Gillespie 1 year ago "the diagram is not to scale" oh damn I was really going to take out my ruler 87 S Ross S Ross 2 years ago I am Chinese but usually these questions are just for fun. 1.9K Russell Copeland 2 months ago i like hearing this. When