Can you solve this 4th grade problem?
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- Опубліковано 19 кві 2024
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If you're a 4th grader submitting one of those "creative" solutions, you'd better hope the teacher is smart enough to recognise it as valid.
Yeah some teachers are like "show your work" even though the paper says nothing like that. I'm not a 4th grader so my initial idea was to shade it like shown at 5:22 because that would be a square and you have shaded half the area. See if you said just yes like some people suggested and the question was worth 2 points the teacher would have given you half credit and said "show your work" on the feedback LoL
"Showing your work" is why most of the potential answers would fail. Drawing that square in arbitrary position is not at all straightforward. The centered diamond, the centered square, or the square in 1 corner can all be done easily with compass and straightedge. The diamond can be done with straightedge only. Anything else is going to be more pain than it's worth.
3:23
Back in the early 70's, I was in EBP / MGM programs. I was in the 3rd and 4th grades doing up to 7th grade level work. Education was beginning to go through its defunding period and my programs were the first to get cut. So, in the 5th grade, doing 5th grade level work, my teacher would give me a failing grade because my work to solve problems were more advanced, not what she taught in the class. I got very bored in school when those programs got cut. BTW in the 4th grade, we were working on dodecahedrons, not squares lol.
What I was hoping was an explanation for a way to construct a square in a corner, using a square root of 2 as the radius of a circle to draw the intersections with the existing lines to draw the shape of the shaded area. The other solutions aren't as simple to construct as the first answer and a square in a corner answer.
Technically, the answer to the question that was asked is "yes".
True, but schools teach you to always "show how you reached your conclusion" so by that overarching rule you'd know that's not enough. Technically, you could answer every math question in your final year correctly, but by only writing down the final numbers and thereby failing anyway
And technically if you don't find how to draw it, answering "no" would also be correct
Once you shade it, the shaded part is no longer a square. So the unshaded part is not also a square, it is the only square. So the answer is "no". lol
@@migssdz7287 I occasionally posed problems where the idea is to check an equality. If a student tries the problem and botches it, he gets partial credit. Or if the problem has a derivative and the student has trouble with derivatives, he also gets partial credit. The way to get zero is simply not to take the derivative or otherwise check the equality, but instead do something fancy that shows himself clueless. (If the question is to check if x=2 satisfies x+2 = 5, all too often, it doesn't occur to the student to add 2+2 and answer "no" based on the result. In this case, a "no" by itself is good.)
That was my first inclination. But then, knowing that the task is possible but realizing that I could never actually accomplish, I changed my mind to "no."
You have to think inside the box with this one!
Eeey that's a good one.
🤓☝️ errmmm a box is 3 dimensional and needs and opening or else it's just a square or cube
nice joke
@@lav-kittyYou know what? Flats you, Uncubes your cube!
Take my like and give me a big hug for that joke
@@KillerKatz12 NOOO NOT MY CUBE
The phrasing of the question is the confusion -- most readers would take the "also" to refer back to the shaded portion (also being a square).
Maybe. But that would be a poor assumption. We humans do that quite often.
I don't think that's the confusion, I think it's the fact that people assume they have to make it symmetrical, while also making it a non-rotated square
I understood it to mean that the unshaded portion should be a square, half the size of the full square. The division into four smaller squares is only there to help me visually gauge the size of 'one half'.
The question did state half which means 50% of that must be shaded no more no less and that each portion must be a square the thing people are getting confused on is the fact that they look at the whole thing and assume that it is a big square which it is not it is for individual squares which means the simple answer is just to shade two squares which means you're left with a square two but still a square it did not say that you cannot have two it did insinuate that they're at least must be one. Such a simple problem it's just people inject information about the problem that isn't present and that isn't needed like it being a big square and that if you shade half you're left with a rectangle which you are not because they are two individual squares.
@@grimmspectrum1547 no, that's not a plausible interpretation. The entire unshaded part has to be "a" square (a as in one).
Sometimes the hard part about math is not the problem itself but rather the lack of details provided in the problem
Honestly yeah like can you shade it so the unshaded part has a hole
Yeah, if they had said half the area of the square it would've been easier
What is happening, is that WE are assuming limitations that were not stated. I did it to myself for about the first 45 seconds of this video ( a little longer because I paused it to look over the Tweet. ) And the "textbook answer" was the easy answer, as it can be done without any of the actual math, and even without a ruler if you are good at straight lines.( I am not... ) And as James said, the way the question was asked, the technically correct answer, is YES. As the question does not state that we are supposed to show or demonstrate the a solution.
And the funny thing is knowing the answer to this question has no purpose later in life for those students
@@janelle9998being able to problem solve, use logical thinking, and project geometric shapes is extremely useful in life. I’m not sure why one would assume the opposite.
My solution was to draw a crappy square, declare the shaded and unshaded areas equal, put out a warning that drawing is not to scale, and call it a day
I passed a calc final exam in my undergrad like this. I just defined something as “a” and skipped some steps.
@@haroldhayes4824 simplifying by taking parts of an equation and declaring it as something is often helpful.
My default was always X, Y, Z, A, B, C as needed. I got so locked into this pattern that I once redefined every variable in a problem like this and my prof left me a note telling me I should break the habit lol
@@VocalMabiMaple lmao
Engineer?
@@VocalMabiMapleI remember problems in college where I ran out of Latin and Greek letters and ended up using some hiragana. I suck at making simplifying assumptions.
6:15
I thought of this instantly, but then thought "no, it can't be that easy."
I'm now apparently smarter than someone with a PHD
And yet I'm failing precalculus
Pov: overthinking the question
Remember the this is 4th grade "lets think this like adults" is your first mistake
The second solution you showed "square in the center" was my first thought.
Same, and then trying to work out exactly where to put the sides of the smaller square made my 4:30am brain error out.
It was my first thought as well
How do you make 1.4142 in geometry? This was my fist question. And I made separate triangle and copied to the squares. And the 1st solution never hit me, regardless I've been so close. I guess my mind is inside so many boxes...
@@YourNickIsTaken it only needs to be root 2 if you each smaller squares are 1x1, which was chosen arbitrarily by the video. We don't have access to the actual paper but if I did I'd've grabbed a ruler.
Yeah theres no way figuring out an irrational number is part of the intented solution @@blakdeth
"Yes. Next question."
It's actually quite easy if you think about it for a moment.
That lady should give up her PhD.
@@shauryaaher1579 I figured it out quickly then saw this video is over 9 minutes long, so I left this comment then left the video.
“No” is also an answer, “No, next question!”
@@martinconnelly1473dang ur smart
I sat for around 10 minutes, thinking without watching the video, and I solved it, but it was a brain teaser
bro its litterally to just shade half of the square to make a rectangele which is also a square
took me around 1 minute by looking at the thumbnail, but then again, I was creative
@@sathvikchillapalli5977ugh. Everything about this comment is incorrect.
Square = rectangle. Not the other way around @@sathvikchillapalli5977
@@sathvikchillapalli5977 it's the otherway around, squares are rectangles but with equal sides
It took me 1 min to solve that and the best thing is I didn't use any hectic math , I knew half the shaded portion of the large square would also be the half shaded portion in the smaller squares and the diagonal of the smaller gave me an unshaded square in middle. That's it
Both "yes, I can" or "no, I can't " would be valid answers
Absolutely! If the question is "Can you?" and you can't, then to say so would be your correct answer :D
@@ruthholbrook Would I? No I would not, but others might..
As a 4th grade teacher, questions like this drive me crazy. I also hated Language Arts questions asking students how the words an author used made them feel, since anything they wrote down was a valid answer.
It’s weird because the question says “Can you shade half of it so the unshaded part is *also* a square?”
It’s just bad question writing like this that trips up people on tests. It makes you think the shaded part also has to be a square.
"no i can't" show proof or your answer is incorrect
Easy. Connect the diagonals to make a square tilted 45 degrees.
My thought was to draw a diagonal of sqrt(2) length and rotate that to form a square of area 2. I like your solution a lot better - going to watch now, I bet that's Presh's technique.
Right? I was wondering why this is 9+ minutes, but I will continue to watch.
@@Gideon_Judges6 Actually, my first thought was to use the standard tool of geometry problem authors. Cut the square straight across. You could say that's a rectangle, but you could also say it's a square - not drawn to scale! 🤪
😅
here I am thinking about b*sqrt(2)=a lol
Even a 4th grade math question feels like a legal document 😂
Here is how you do it: get a pair of calipers and measure the exact length and width of the square. Then you find the volume. Afterwards take the volume and divide it in half and take the square root. Now CAD a square with the dimensions and then 3d print an outline of it(make sure that the outline’s width is expanding outwards and not inwards). Take the outline, put it on any location in the square and shade inside of the outline.
Presto - its now a perfect shading of half of it.
How do you find the volume of a square?
@@KingBobbitoeasy, it's 0 thickness by definition so the volume is 0, so now you just gotta do 0/2 = 0 then do sqrt(0), & your CAD becomes really easy too 😝
Ok we're being jerks, we know they meant area 😄
@@hokayson6518 lol
@@KingBobbito You find the thickness of the paper, and make sure you use a tattoo machine or something to shade extra layers to ensure that it is half.
First time I got an answer right, fast and think: nah it can't be this easy.
Just made my day.
the way school often makes you doubt yourself just cause you found an easy solution
Same
samee
Yeah i was like just fit a square inside a square, how? Half each quadrants and then boom a square inside a square or that's how i did it
Well, it’s still 4th grade. „It can’t be that easy“ fits more to 9th or 10th grade.
The second solution is what came to my mind, along with the thinking of "people probably aren't getting this because they're probably assuming that the shaded area also has to be square somehow".
The first solution with the rotated square is actually so incredibly obvious once you see it that I'm ashamed I didn't think of it instead.
The first solution is the easiest to draw and the easiest to understand. Like you, I came up with the second solution, but it's not as easy to draw to scale, but it's easy to provide the math to explain where the square sits. Once I saw that, I realized that there are an infinite number of solutions that just need the math shown to prove they are correct.
I also did the exact same thing
I did one of the solutions where the square is on one of the four corners of the bigger square. So I also kind of made the obvious solution into a little bit more complicated one for no reason lol.
The second solution (and all but the first solution) requires using the square root of 2, though. So somewhat outside the scope of 4th grade math.
the only solution i thought is to shade an L but i have no idea how thick the L is
I thought of the second solution you gave almost immediately. As a former 4th grade teacher, I would also accept all of the answers you gave because I believe that true inquiry-based, student-centered education is the only way to go. thanks for the video! 😃
I came up with the triangle method immediately. However, to restate what you said in my own words, the original area was 4. So we needed to draw a square with 0.5 of that area, or 2. A square with an area of 2 will always have sides of sqrt(2). So any square with sides sqrt(2) that fits completely inside the original squares qualifies.
It’s weird because the question says “Can you shade half of it so the unshaded part is *also* a square?”
It’s just bad question writing like this that trips up people on tests. It makes you think the shaded part also has to be a square.
th e word "also" implies both are squares
The "square" below is made up of four small "squares" can you shade half so that the unshaded part is also a "square"
The question is right they already talked about the existence of 5 other squares and thats why it says "also"
@@mastergamer-zq8xc bro is coping
@@discussions. coping? about what? understanding basic grammar? or is it you that is coping and whats with the snarky remark if we are talking about this thing sensibly continue to do so or dont continue this conversation as people like that wont learn anything from it anyway
The unshaded part is still a square. it just has another square inside of it. That doesn't make it stop being a square. A square is defined as a rectangle with equal length sides. It doesn't matter if you draw another square INSIDE it. Heck, you can draw a giraffe with a top-hat riding a bicycle inside of it, it's still a square.
The L-shaped shading was the first thing that came to my mind after I studied the diagram and what the question was and was not asking for. I'm reminded of the classic test with "Read all instructions before marking your paper" at the beginning, progressing through increasingly nightmarishly conplex equations you haven't been taught yet and the last instruction is "Disregard all previous instructions, sign your name and hand in the otherwise-blank test."
and from that moment forth, i started all tests at the last question...
i loved that test, i and my friend were the only ones in a class of 30 to just put our name on it 😅
yeah i remember getting one of those, i think it was like 3rd grade for me? never liked them much, i always had the mentality of focusing on what i currently had to do instead of worrying about future questions and stressing myself out. of course it bit me in the ass that time though as i was one of 24 idiots who were all looking for someone who's name started with L who was born in November and had pancakes for breakfast.
That kind of happened to me, but in a more normal way. It was an algebra 1 test, and had normal algebra 1 stuff. It told you to read directions carefully, and one of the questions said at the end to draw a smiley face. Not many people did it. I got a bit of extra credit.
I'm glad that reading "also" isn't part of the instructions
Nice, visually, the second correct one is what I settled on before I started watching lol
yes. draw a line on each of the 4 squares at 45 degree angles. join each line up leaves you with a square (diamond) in the centre.
Shade the whole thing. Look at the back, that was left unshaded. It's exactly half
Thats what I thought
theres no square in the back unless the print ink bleeds through
You are thinking in three dimensions!
That's fine, I agree with your solution. There's a counter surface of a perfect plane with no depth.
I love it but no square there thats double the size of the shading. Wiuld pass you though, thats to good of an answer to fail
There is no front or back in 2D planes though
The tilted square was also my first solution.
Other solutions are more difficult to "construct".
But with compass and ruler, it is possible.
My first was a square in direct center with same orientation as largest square. It's where my mind went first. Nice!
@@MrChrisRP My guess was that as well, but I say "guess" because I don't know exactly where to put the sides of the smaller square. (If you mean the one at 5:22).
I would GUESS the sides go 1/3 of the way from the big square's edges to its center, but that's a total guess. Idk enough geometry for that.
All the other solutions are approximations, because the length of the sides is an irrational number. The first solution is precise.
I started to think that if I wanted an uprigth square, then if one square is 1x1, then the large square's area is 4, then half of it is 2, so the sides of the half is sqrt2, and that is side to diagonal ratio of a square and then the tilted square hit me. You just diagonally cut the corners, and those would make up two squares, so the middle is a half sized square. Maybe this was the aim of the problem. But it did take me five minutes
@frankmerrill2366 Exactly this.
Sure, if the 4th grader actually had the knowledge and the tools to somehow make it geometrically accurate, then it could be valid.
But otherwise, there is just one solution and it's the first one.
(Before watching the video)
I'd calculate the size of a square half the area of the big one, draw it anywhere inside the big square and shade the rest.
(After watching the video)
The "textbook" solution is so clean. Love this kind of problems.
I looked at that for 30 seconds before I figured it out
I played this at 1.25 speed, and it solved my hardest issue with these videos. Bless Presh, sometimes he drags on.
Or maybe you have a small attention span😅
Maybe time to uninstall tiktok
you a gold fish
Hahaha, I'm so intellectually superior, because I watched it at regular speed. I'm *very* smart, you're probably just a TikTok kid 🤓
@@VAVORiAL u built like a gold fish
This is the first time I've gotten the solution on my own, and I feel so happy!
4th grade homework. 💀💀💀
@@trucid2 I have a 3rd grade brain, lmao
This is great really. I made the mistake of thinking that the shaded and the unshaded parts both bath to be squared and could frankly think of nothing at all. I like how you explained it so well!
Draw a diagonal line in every square and shade the outside corner portion. You shadeed half of the squares and you are left with an unshaded diamond in the middle with 4 equal sides
First answer is big brain. I'm not sure I would've gotten it as a 4th grader. My first thought was measure it, calculate the area, halve it, sqrt it, measure that in a corner of the diagram and shade around it.
you probably only think of these other ways because you know more maths now and know there are other ways to do it.
First answer is pretty basic to most fourth graders because they're learning better math concepts nowadays.
The thing is, the "intuitive" solution does require some knowledge to prove it's a square. Still doable by 4th graders I'd say, just not in terms of degrees but by simply saying "this is exactly half of a right angle and this is another half so this is a whole right angle" and "these four squares are the same so these diagonal lines are also the same".
I once solved a similar question that the teacher couldn't solve, dividing a triangle in 4. Luckily I was a Zelda fan already
@@tomdekler9280I really love how the Triforce was able to help you in math!
@@tomdekler9280 I hope that wasn't a math teacher.
I got the answer but was convinced it was wrong because in my mind you have to colour inside the already present lines, because… rules….
exactly!
That’s the trap! LOL
@@ezura4760
No, the trap is starting the question with "Can you..." as as the question is asking about your ability to do whatever. As such, the only correct answers possible are "Yes" and "No".
A common error, reading more limitations into the question than were stated.
@@cigmorfil4101no one's keeping me from answering with "maybe"
5:22 was my initial thought
For the first time ever on this channel, I solved a puzzle in mere seconds and got it right.
"Can you shade half of it so that the shaded part is also a square?"
- "No. I am not a smart man..."
At least you're not trying to showcase how smart you are in the comment section! 😂
Draw a quarter circle connecting the right and bottom edges. Then draw a diagonal line through the square. Then find the intersection and draw lines down and right. Then shade that part of the square. You shaded half of the square and you can easily check that the unshaded part of the square is a smaller square.
Technically you're wrong. Now you know how to do it you can do it. It asked if you can do it, not if you can figure out how to do it on your own.
That is correct!
Short answer:
Yes I can.
Explanation of long answer:
some folding is required.
This is one of those gifted and talented kids’ questions.
nah, you just gotta know the curriculum. this question is most likely testing the properties of a square (all sides are equal, can be split in half diagonally). from there, you just gotta apply a bit of creative thinkin', and boom! you got your answer.
@@wyawarD9677 exactly, it's a solution the curriculum has to come up with a question for but never used during your life
IDK, could be. Only took me a few seconds thinking about it to find a solution, but I was in the gifted program and solve problems (comp programmer) for a living. I would expect most people to have a harder time with it, or not get it at all.
No, because you don't have to do any math to solve it. This video overcomplicates the issue. You don't need to know that the diagonal of a square with side length 1 has length sqrt(2); you only need to know that if you draw a diagonal line though a square, half of the area will be on either side of that line, which is obvious.
To be really accurate, maybe the only solution that can be done by hand and precision, is the first one with the diagonals. The others are okay but you can’t tell if they are the half
My intuition was pretty close to the second solution so I'm glad I was on the right track 😅
My brain said the second solution 😭 the tilted square makes more “sense” but the perfect square in a square was what I immediately thought of
I got the first 2 solutions by the time I read the question. The other solutions you can get by just moving the unshaded square around were interesting. I like that.
Isn’t it great how our brains work? I saw the third solution right away but not the first two.
I loved this because I got the second and third solutions but missed the "intended" solution. That's why I love this channel. I always learn something new!
I did the exact same thing
Same here. Odds are we'd have gotten marked down still because it didn't match the solution in the textbook and we "did math wrong."
Same. I actually immediately thought of the third one.
My first thought was to leave a square in the middle by shading a box around it, and then realized you could essentially place that new box in any orientation or area within the area. I don't understand any of the math formulas that one could use to figure that out, but figured I could divide the small squares into whatever number of smaller squares needed to make visually determining the size easier sort of like real world measurement. 1/2, 1/4, 1/8, 1/16, and so on.
I came up with that second one by myself so im very proud
The "wanted" solution is the only realistic one though, as shading those other ones by hand is very difficult
you don't have to be exactly correct in your drawing, just show that the inner square is 1/2 the area of the outer square. marking the length of each side would probably suffice.
That's what I'm thinking. I appreciate the other solutions and they're correct in some sense, but the question asks whether I can shade half of it, and during the test with limited time and tools the answer is no for all but the first solution, which I can simply use a ruler for
I would agree. The other ones are just free handing and it's hard to tell unless you specify each side is sqrt(2). This is more of a geometry problem at a concept level. Not a numbers kind of math problem.
In fact it is very easy. Cut out the realistic solution and put it onto another 2 by 2 square and shade it with a pencil.
The only correct solution is the one listed in the teachers guide, because they don't understand it either.
You could also shade all of the large square at 50% transparency.
This is an epic response!
@@FirstDarkAngel2001 epic failure
if everything is lightly shaded there is no unshaded area at all that could form a square
"You could also shade all of the large square at 50% transparency" - If you shade all of the large square, even at only 0.00000001% transparency, then you have still shaded 100% of the square, leaving nothing unshaded.
That's still shaded. Any amount of shading is shading. You're trying to hard to be celver and ending up wrong
Great Video! Thank You!
My mind went right to the third solution. I was surprised to see it was valid.
The first solution is the only one you can generate a proof for without direct measurement.
One you have proof for one single solution it is trivial to come up with a proof for all other solutions (as done in this video near the end).
That's not really true as you can't directly measure sqrt(2) as it is non-rational. You can construct it as follows:
1. Draw both diagonals in one of the squares
2. Take a compass and measure from one corner to the intersection of the diagonals
3. Draw a circle on every middle of the outer edges of the big square
4. Connect the intersections with lines parallel to the outer edges.
5. Shade the area outside of the now created square
because presh didnt showed them it doesnt mean you cant draw other solutions with a ruler and compass
No
You can make square root 2 geometrically. So the second is also possible, or any of the corner fitted one. Actually, with copying the distance, you can make all the solutions with just a ruler and a pair of compasses
@@m.a.6478cant you just say that since every sub square is half shaded (since diagonal divides a square in diagonal), their combined total is half the entire shape? Much simpler
5:55 I came up with this instantly but thought it was going to be wrong because math questions never tell you how to do it and they usually have only one correct answer labeling the outside the box solutions as incorrect because Schools don't always allow you to think outside the box and would rather you get the answer they want you to get.
Actually the solution was a bunch of triangles inside of the box 😊
Make a shared area around the edges of the square, it makes a mini square inside
I don't recall doing anything like this in 4th grade, but then I grew up attending a public school. I did come up with the intended solution. I realized I would need the length of the sides to be the square root of 2, but it took me a few seconds to realize I needed to divide the small squares in half by drawing a diagonal through each to form the smaller square inside. That's just the easiest way to get the sides to exactly the correct length. While the other solutions do give a technically valid answer, it's not something that can be duplicated on a written test accurately, so the expected answer is the one that makes the most sense to use.
All the alternate solutions are indeed possible, but the first one is the only one that can be done with a straight adage and pencil.
Edit: I think you're right.
-The second too. Needs a bit more construction, but it's not too hard. I posted how in another main comment.-
The corner solution can be constructed if you allow a compass and straight edge.
Draw a quarter circle centered on a corner, through the center of the large square. For each point where that circle intersects the large square draw a perpendicular line. The smaller square is determined by the original corner we chose, the two intersection points between the quarter circle and the large square, and the intersection of the two perpendiculars. The proof that this is the correct size square is exactly the same as the one presented for the first solution presented here.
But remember, this Is fourth grade math. They're testing If you know how to do something correctly, not your drawing skills. You'd probably pass with some wobbly lines as long as It's clear what you tried to do Is right
@@zaelgreen1670that’s exactly how I did it
No you can bisect the 45 degree diagonal to find a sqrt 2 landmark on the edges.
Anyone else got the answer instantly?
Im a Quilter, so easy!
Yes, after about 3 seconds
Yes, I got it just by looking at the thumbnail, but I went ahead and clicked because I assumed Prakesh would give us more than the obvious. I was not disappointed. Starting at 5:01 is the less obvious stuff and what makes this video worth watching.
Ya just fill In the Diagonals. I am also only 30 seconds in To the vid. I solved it before I clicked the vid
I am 80 years old. Took me about two seconds to figure it out. I just plunked the square right in the middle and the outside was a square. The new math just dumbs down everyone to make everyone at the same level of dumbness.😂
My 6 year old figured it out in 5 seconds... give it up for mag-tiles!
I saw this thumbnail and thought about the puzzle for 5 minutes the other day and couldn’t solve it. Ended up not watching the vid and then saw it again today and almost immediately saw the solution, weird how state of mind and re-reading the question made this so much easier
7:20, since we can move the shaded area anywhere, there are an infinite number of answers.
Yep, that's what I was thinking! Infinite possibilities for the placement of the square
Thank you for sharing this, I've always had doubts about my problem solving skills but this video confirmed that I need to give myself more credit some times. ( I am aware that 4th graders are definitely capable of this but I I got the answer within about a minute or so, which is a lot quicker than I expected)
Im horrifically bad at math and im honestly surprised my solution was correct.
GOT IT!
Shade the squares on diagonals. Shade the outer corners of the larger square.
The answer for the first one is to shade most of the corners so that leaves a white square in the middle while also passing as “half shaded.”
wym "the answer to the first one"? are you literally just repeating what is said in the video?
YES. It takes just a bit of "thinking outside the box(es)".
The solutions are all _inside_ the boxes...
No way i actually got this right, i used the second solution, this actually made me happy because i was failing horribly at some homework a few minutes ago.
Yes. Just have a square within the square with side length v2 (Square root of 2), then shade the rest.
Surely there’s an unspoken “with some accuracy without a ruler, protractor or pair of compasses” in that original question?
This is exactly what I thought. The answer was obvious, but I think I would call my teacher to ask if I am allowed to use the ruler.
It's about the thought process really, so the teacher would probably decide whether to give them hints or just let them tackle it with whatever tools they have. Probably depends on whatever stuff they've been learning too - if they've been playing around with shapes and working stuff by manipulating them (like experimenting with finding the area of a triangle without giving them the formula derived from the basic approach) then this question might fit neatly into that, without anyone even thinking about measuring or drawing circles
At a maths test, you are very likely to have a ruler and a pencil. Nowhere in the question does it say you are not allowed to use these
Yeah there's a bit of ambiguity here, sure you can measure everything and compute the needed size of a square with half the area, and then place it anywhere within the original. You could also compute the radius of a circle that has the correct area etc. The only real answere, given the way the question is phrased, is the rotated 45 degree square.
@@21palica Also, since the square root of 2 is an irrational number you cannot draw a line that is EXACTLY as long as the square root of 2, however you could draw a line that exactly crosses the intersections of the original diagram.
- Can you(...)?
- No, i can't
30 aeconds in and i solved it. Was completely bewildered trying to solve it from the thumbnail.
It’s pretty easy just draw a small square in the middle and shade its surroundings
You have to think outside the box, both figuratively, and literally.
All of these solutions are within the main square, the "box," (as dictated by the question), so not literally
The 4th graders aren't smarter than anyone else, they've just been taught the answer. Question is, do they understand it.
Very presumptuous that no kid could figure this out. Look up marshmallow and spaghetti tower challenge results if you underestimate them.
@@TheMonkeyGrapehell naw I sucked at those xD
It's also not necessarily that they have been taught it, they are also faster at intuitive problem solving than adults. This is why kids can pick up video games faster. Adults are better at logic
If you don't know if they understand it how do you know they're not smarter than anyone else?
Nobody said 4th graders were smarter than everyone else. But the idea that children need to be taught the specific answer to this riddle is ridiculous as well. Children are intuitive learners, they are constantly applying old concepts to new circumstances. Solving this puzzle the intended way plays into their strengths. Grown-ups unlearn some of that creativity and replace it with rule-following, because that is generally more time-efficient. But in this case, it makes you end up with an infinity of purely theoretical solutions of squares that can't even be drawn by hand.
I've never seen this before but I knew what to do as soon as I saw it.
Now I know why my teachers were always saying "if only you went lazy".
With the square in the middle example, you could switch the shaded and non-shaded areas and it would still be correct
I never noticed this before, but you do outros. In this video, I particularly liked your concluded comments. They are quite motivational. Been watching for a year. Keep it coming brother!
I remember solving a logic puzzle like that during counseling in I don't remember what grade.
There comes a point where you realize you're being misdirected.
The solution involved using the pieces to draw the correct shape, but after numerous tries it became clear there weren't enough pieces and negative space had to be used.
I"ll admit that after trying a few I suspected wouldn't work, I settled on the second solution shown.
But the first one is simpler and easier to get precise given the guidelines present.
Realistically questions like this are less about the solution than about the attempt.
I immediately went “oh easy” and thought of the second solution with the square in the middle 😂
I immediately thought of the second solution. Good to know I got it!
You know it's hip to be a square.
Patrick Bateman appears
Tower of Power approves!
I always found that song's lyrical theme questionable.
Catchy tune though.
Yes. Draw diagonal lines that join the midpoints of each edge. Each of these lines will bisect each of the smaller squares diagonally. Then, shade the outer portion, leaving a central unshaded square lying diagonally with exactly half of the volume of the large square.
The second solution is the one I immediately came up with
Got it in a minute, actually watching the vid now to see if I was right
Yes
That was, for me, one of the best of recent weeks. Thank you - it made me look 'outside the box' a bit.
There is realistically only one option for a 4th grader (or any elementary grade) to draw with any accuracy. The diamond solution explained as the first solution in the video is the only practical solution.
As a teacher I would give points for a student who divided up the whole larger square into 16 blocks. Then they colored in all the blocks down one outside edge (4 of 16) and across the bottom (3 more of 16). Then they would have a 3 by 3 square unshaded. They would have to shade in the center block of the 3x3 square. This would give half the area shaded and half the area unshaded in a square.
Using a square root of 2 side to make a square would not be accurately drawn by most adults. There is math theory and then there is math practicality.
If you've got a straightedge and pair of compasses (or even just a straightedge that you can mark distances on and use to measure equal distances), then you can construct a corner square that's half the size of the original pretty easily. That was actually the solution I thought of before watching the video. The real obstacle to a solution like this being accessible to a fourth grader is whether they know the Pythagorean Theorem or not. But actually drawing the half-size square in that way, using ordinary and easily accessible tools (like the folded edge of another piece of paper, for example), is not that difficult.
I feel like drawing accuracy (as far as that even exists) isn't even important here - if they draw the diagonals, no matter how bad it looks you know they got the solution. Anything else could just be the result of a visual estimate rather than working it out mathematically
This is why I wish more kids got their hands on origami during math lessons. It's fun and you can actually fold things very precisely even without a ruler. And the intended solution to this puzzle is what's called a blintz fold, where all the corners get folded to the center. Making a big square into a smaller square. Easy.
@@skoosharama The issue is what are you looking for the student to label the side length as for the new square? Without any labels the diamond shape is clearly half the size due to each smaller square being half shaded. To draw any of the other square shapes there would have to be some labeling of the side length. If there is no label then how would you know that exactly half the area was shaded? If the side length was based off the diagonal of the smaller square, to be transposed somewhere else on the drawing, then the diamond shape should actually be easy to see. It requires no measurement nor understanding of Pythagorus or other complicated calculation. Even if drawn accurately, which could be done with a compass in one of the corners of the larger square, it would be beyond what most 4th graders know. Even then using a compass to measure the smaller square diagonal as a reference should show that using the smaller square halves divided by the diagonal is the answer. While all these other calculations are being done and intricate drawings, the clear and simple answer let’s the student do 3 more problems in the same time. Can it be drawn differently? Yes absolutely. Just not realistically nor without much more understanding than a 4th grade math student would have.
I find it intriguing how people can’t seem to solve problems I started tackling in elementary school.
Today I learned I'm smarter than someone with a PhD. Not every person with a PhD though. Just one so far.
Since the diagonal of the smaller squares is of length root 2. I thought of using a compass to measure out the needed side-length of the square which is half the total area. Placing it in the upper right, you would have a shaded square and a non-shaded L shape which are both half the total area.😊
With a compass you can inscribe a circle inside the big box, draw the diagonals,of the big square, then connect the intersection of the circle and the diagonals.
Pedant here! 🙋♂️ I am not intending to denigrate your correct logic, but you need a pair of compasses to do this. With a compass you could then allign your sides to face North, East, South ans West. Now excuse me whilst I put on my smarty pant.
Funny.. I thought of the 2nd way 1st. When you showed the initial answer I was bummed thinking I was wrong. Whew - thanks for showing the 2nd way.. I feel better, even if it was the harder way
in situations like these, if you get the desired result _(in this case creating a square with an area of 2 within the larger square with the unshaded area)_ you cannot be wrong. Literally by definition you cannot be wrong
same. maing a frame was my first approach
I think most people think of the second solution first. But then they think of how hard it would be to actually execute without a calculator. It took me quite a bit to reset and think of the practical solution.
Same.
Same here, first guess was a square of 1.414 x 1.414 (√2 x √2) sat in the middle, then I thought of the more obvious 45° trick !
It’s easy just shade in half of it in a square shape by shading L 4 times in the edges of the 4 squares
That question is just absolutely diabolical, and even as a 4th grader being taught about that i wouldnt have figured it out. If this was a class about finding creative solutions in your environment, itd be perfect
I would argue solution #1 is by far simplest one, doesn't require any math knowledge, only logic. Without logic you need to walk long way, calculate area, divide, calculate side, make stencil, place it on desired place and shade unmasked area. For that you need math so many of those who opt for other solutions may simply give up.
My solution was a 1x1x1x1 square in the middle ; that is based on logic. I simply envisioned a smaller square in the middle.
* divide
@@jd-zr3vk-- It's just a square with one unit on a side. You don't write 1×1×1×1, because that is redundant.
@@jd-zr3vka square with a side of 1? Isn't it suppose to be a side of square root of 2?
my solution was shade 2 of the small squares diagonally adjacent from each other to leave 2 small squares unshaded HAHAHA technically there is an unshaded square
Cut all the small squares in half at the diagonal with endpoints at their shared border (the point of the inner + sign). Shade the resulting triangles that are located on the outside corners of the big square. The 4 remaining interior triangles now make a square and since we shaded exactly half of all of the small squares, the unshaded portion is also half of the total area.
Haven’t watched yet:
In the top left square: draw a line from bottom left point to top right point, shade the top left triangle.
Repeat this process for ever small square, where the shaded triangle is pointing towards the points on the big square.
I also think there is a way to shade a certain amount of the top part of the top right square, the left side of the bottom left square and the same parts on the top left square, but I don’t know how much to shade in.
Draw four diagonals, one for each of the smaller squares.
In the top-left square, draw your diagonal from the lower-left corner to the upper-right corner.
In the top-right square, draw your diagonal from the upper-left corner to the lower-right corner.
In the bottom-right square, draw your diagonal from the upper-right corner to the lower-left corner.
In the bottom-left square, draw your diagonal from the lower-right corner to the upper-left corner.
Then shade it in until you die. Took me nine seconds.
Figured it out in 5 seconds. Join the intersect of every mid point edges to form another square. Shade the triangles outside. The key was finding an easy square to begin with then shade excess.
Oh, I was disappointed you don't go into building one of the non-rotated square solutions. This is how I started to solve it. It was an interesting journey that involved ending up accidentally writing the quadratic expansion from a geometric pov.
Could you make any of those solutions with just a straight edge, though?
@tomdekler9280 Yes, measure the sides of the smaller squares and use different fractions to shrink them. Then find the area of the smaller square such that it preserves the scale used for the big square. Good luck getting a 4th grader to figure it out though lol
@@grillmaster95 I just pretended the smaller squares weren't even there, since there was no mention that they had to be completely filled in. I didn't do any math aside from shading a 1/4 depth around the interior perimeter of the large square. I guess subconsciously though, I had to do more math to determine the 1/4 depth.
Huh? Can you restate your answer in English, please?
@@grillmaster95
> Just a straight edge
> Measure
Nope.
An alternate solution without any measurement is to use a compass and straight edge. Place the compass center at the center of the squares and draw an inscribed circle where the circle touches the sides of the big square. Then draw the diagonals of the big square then draw a square from the intersections of the circle and the diagonals.
I shaded a margin and left the square in the middle, easy
For me, my own solution are to shade a square in the middle of the square itself.
That's what my first thought on it.
I must have actually learned something by watching Mr Presh because I figured out the diagonal method almost immediately. Six months ago, I simply would have stared woozy eyed. Thanks Mr P. Mike
Very cool. Thank you for sharing your solutions.
I paused at the start, read the instructions, so I would draw a diagonal through each of the four squares (cutting each in half), so shade the outside halves, the unshaded is a perfect square inside (aka a diamond).
Okay so I just fast forwarded, my solution is one of many. I don't get why this is hard?
A diamond.
Split each square diagonally at the corners. Turn the paper a bit and you have your "square".