Can you solve this 4th grade problem?

Рет қаралды 867,252

26 күн бұрын

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Пікірлер: 4 200

@gcewing 20 күн бұрын

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.

@CaytonMyler2008 20 күн бұрын

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

@jursamaj 17 күн бұрын

"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.

@p.y.flegends6800 17 күн бұрын

3:23

@JRcomments 17 күн бұрын

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.

@f.faucon6681 16 күн бұрын

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.

@hypwhoknowsanything3551 22 күн бұрын

Sometimes the hard part about math is not the problem itself but rather the lack of details provided in the problem

@theshadowking3198 21 күн бұрын

Honestly yeah like can you shade it so the unshaded part has a hole

@jorgitoislamico4224 21 күн бұрын

Yeah, if they had said half the area of the square it would've been easier

@javabeanz8549 21 күн бұрын

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.

@janelle9998 21 күн бұрын

And the funny thing is knowing the answer to this question has no purpose later in life for those students

@EffigyofChaos 21 күн бұрын

@@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.

@azazelreficulmefistofelicu7158 15 күн бұрын

First time I got an answer right, fast and think: nah it can't be this easy. Just made my day.

@lav-kitty 5 күн бұрын

the way school often makes you doubt yourself just cause you found an easy solution

@Fish-E-13 4 күн бұрын

Same

@lobitodv 2 күн бұрын

samee

@ice_swallow_come5964 2 күн бұрын

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

@i_can_c_u_2295 2 күн бұрын

Well, it’s still 4th grade. „It can’t be that easy“ fits more to 9th or 10th grade.

@skunkhero 14 күн бұрын

You have to think inside the box with this one!

@StabbyMay0825 5 күн бұрын

Eeey that's a good one.

@lav-kitty 5 күн бұрын

🤓☝️ errmmm a box is 3 dimensional and needs and opening or else it's just a square or cube nice joke

@KillerKatz12 Күн бұрын

@@lav-kittyYou know what? Flats you, Uncubes your cube!

@N1TRO352 Күн бұрын

Take my like and give me a big hug for that joke

@lav-kitty Күн бұрын

@@KillerKatz12 NOOO NOT MY CUBE

@jamesgardner2101 24 күн бұрын

Technically, the answer to the question that was asked is "yes".

@Thornskade 24 күн бұрын

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

@migssdz7287 24 күн бұрын

And technically if you don't find how to draw it, answering "no" would also be correct

@Erik-iu9zt 24 күн бұрын

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

@JohnRandomness105 24 күн бұрын

@@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.)

@Dnallohes 24 күн бұрын

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."

@VocalMabiMaple 24 күн бұрын

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

@haroldhayes4824 22 күн бұрын

I passed a calc final exam in my undergrad like this. I just defined something as “a” and skipped some steps.

@VocalMabiMaple 22 күн бұрын

@@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

@pbsixgun6 22 күн бұрын

@@VocalMabiMaple lmao

@Smokr 22 күн бұрын

Engineer?

@travcollier 22 күн бұрын

@@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.

@okrajoe 7 күн бұрын

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).

@Funslinger0325 6 күн бұрын

Maybe. But that would be a poor assumption. We humans do that quite often.

@lav-kitty 5 күн бұрын

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

@InventorZahran 4 күн бұрын

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'.

@grimmspectrum1547 4 күн бұрын

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.

@francookie9353 3 күн бұрын

@@grimmspectrum1547 no, that's not a plausible interpretation. The entire unshaded part has to be "a" square (a as in one).

@dr.markus-level3researcher 6 күн бұрын

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

@blakdeth 20 күн бұрын

The second solution you showed "square in the center" was my first thought.

@nthgth 19 күн бұрын

Same, and then trying to work out exactly where to put the sides of the smaller square made my 4:30am brain error out.

@lisamdrake5696 16 күн бұрын

It was my first thought as well

@YourNickIsTaken 15 күн бұрын

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...

@blakdeth 15 күн бұрын

@@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.

@nickwhright5848 15 күн бұрын

Yeah theres no way figuring out an irrational number is part of the intented solution @@blakdeth

@jarnevanbec2886 23 күн бұрын

Both "yes, I can" or "no, I can't " would be valid answers

@ruthholbrook 21 күн бұрын

Absolutely! If the question is "Can you?" and you can't, then to say so would be your correct answer :D

@ShorlanTanzo 21 күн бұрын

@@ruthholbrook Would I? No I would not, but others might..

@KyLewin 21 күн бұрын

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.

@discussions. 20 күн бұрын

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.

@mrsquid_ 20 күн бұрын

"no i can't" show proof or your answer is incorrect

@alpha-gy1es 3 күн бұрын

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

@aiyabanana2849 10 күн бұрын

Even a 4th grade math question feels like a legal document 😂

@Veggie13 24 күн бұрын

"Yes. Next question."

@shauryaaher1579 24 күн бұрын

It's actually quite easy if you think about it for a moment.

@tomasdvorak7307 24 күн бұрын

That lady should give up her PhD.

@martinconnelly1473 24 күн бұрын

@@shauryaaher1579 I figured it out quickly then saw this video is over 9 minutes long, so I left this comment then left the video.

@Softcap 24 күн бұрын

“No” is also an answer, “No, next question!”

@sans1331 24 күн бұрын

@@martinconnelly1473dang ur smart

@foxfireinferno197 24 күн бұрын

Easy. Connect the diagonals to make a square tilted 45 degrees.

@johnnyragadoo2414 24 күн бұрын

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.

@Gideon_Judges6 24 күн бұрын

Right? I was wondering why this is 9+ minutes, but I will continue to watch.

@johnnyragadoo2414 24 күн бұрын

@@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! 🤪

@trollm4ny4k72 24 күн бұрын

😅

@sub-harmonik 24 күн бұрын

here I am thinking about b*sqrt(2)=a lol

@Mr.MR2111 13 күн бұрын

I sat for around 10 minutes, thinking without watching the video, and I solved it, but it was a brain teaser

@sathvikchillapalli5977 5 күн бұрын

bro its litterally to just shade half of the square to make a rectangele which is also a square

@lav-kitty 5 күн бұрын

took me around 1 minute by looking at the thumbnail, but then again, I was creative

@BunnySpaceMachine 4 күн бұрын

@@sathvikchillapalli5977ugh. Everything about this comment is incorrect.

@CobaltTS 3 күн бұрын

Square = rectangle. Not the other way around @@sathvikchillapalli5977

@doodleoffice221 2 күн бұрын

@@sathvikchillapalli5977 it's the otherway around, squares are rectangles but with equal sides

@MrRandomer246 15 күн бұрын

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)

@discussions. 20 күн бұрын

@AutisticOctopus 19 күн бұрын

th e word "also" implies both are squares

@mastergamer-zq8xc 12 күн бұрын

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"

@discussions. 12 күн бұрын

@@mastergamer-zq8xc bro is coping

@mastergamer-zq8xc 12 күн бұрын

@@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

@cardigansrule 12 күн бұрын

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.

@bigloudnoise 24 күн бұрын

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.

@timothyball3144 24 күн бұрын

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.

@egekahraman8985 24 күн бұрын

I also did the exact same thing

@alexisalidis9037 24 күн бұрын

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.

@Yora21 24 күн бұрын

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.

@beaconblaster33 24 күн бұрын

the only solution i thought is to shade an L but i have no idea how thick the L is

@the_nikster1 2 күн бұрын

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! 😃

@blacklight683 4 күн бұрын

Pov: overthinking the question Remember the this is 4th grade "lets think this like adults" is your first mistake

@nlpnt 22 күн бұрын

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."

@paradiselost9946 21 күн бұрын

and from that moment forth, i started all tests at the last question...

@Soapy-chan 21 күн бұрын

i loved that test, i and my friend were the only ones in a class of 30 to just put our name on it 😅

@wtgkanp2431 21 күн бұрын

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.

@zelda1420 21 күн бұрын

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.

@Ikaros0153 20 күн бұрын

I'm glad that reading "also" isn't part of the instructions

@dmitryli 24 күн бұрын

Shade the whole thing. Look at the back, that was left unshaded. It's exactly half

@alepale77 24 күн бұрын

Thats what I thought

@RakisahNew 24 күн бұрын

theres no square in the back unless the print ink bleeds through

@DaringDramis 24 күн бұрын

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.

@zydian_ 24 күн бұрын

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

@moo3oo3oo3 24 күн бұрын

There is no front or back in 2D planes though

@leveluck-fg3zs 5 күн бұрын

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.

@KingBobbito 5 күн бұрын

How do you find the volume of a square?

@hokayson6518 4 күн бұрын

@@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 😄

@KingBobbito 4 күн бұрын

@@hokayson6518 lol

@leveluck-fg3zs 3 күн бұрын

@@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.

@TubeTAG 14 күн бұрын

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.

@yourguard4 21 күн бұрын

The tilted square was also my first solution. Other solutions are more difficult to "construct". But with compass and ruler, it is possible.

@MrChrisRP 21 күн бұрын

My first was a square in direct center with same orientation as largest square. It's where my mind went first. Nice!

@nthgth 19 күн бұрын

@@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.

@frankmerrill2366 13 күн бұрын

All the other solutions are approximations, because the length of the sides is an irrational number. The first solution is precise.

@thobetiin8266 9 күн бұрын

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

@hundvd_7 6 күн бұрын

@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.

@TheTransforcer 17 күн бұрын

I played this at 1.25 speed, and it solved my hardest issue with these videos. Bless Presh, sometimes he drags on.

@solomonq2470 4 күн бұрын

Or maybe you have a small attention span😅

@tmangb 3 күн бұрын

Maybe time to uninstall tiktok

@GamerWood888 3 күн бұрын

you a gold fish

@VAVORiAL 3 күн бұрын

Hahaha, I'm so intellectually superior, because I watched it at regular speed. I'm *very* smart, you're probably just a TikTok kid 🤓

@GamerWood888 3 күн бұрын

@@VAVORiAL u built like a gold fish

@stephenhowell7029 4 күн бұрын

Great Video! Thank You!

@sorciere_de_la_foret Күн бұрын

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!

@RealNaine 24 күн бұрын

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.

@excaliber2845 24 күн бұрын

you probably only think of these other ways because you know more maths now and know there are other ways to do it.

@Izzboticus 24 күн бұрын

First answer is pretty basic to most fourth graders because they're learning better math concepts nowadays.

@tomdekler9280 24 күн бұрын

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

@NinjaoftheEnd 23 күн бұрын

@@tomdekler9280I really love how the Triforce was able to help you in math!

@Burtlocker 23 күн бұрын

@@tomdekler9280 I hope that wasn't a math teacher.

@Dash_Gallou 22 күн бұрын

This is the first time I've gotten the solution on my own, and I feel so happy!

@trucid2 14 күн бұрын

4th grade homework. 💀💀💀

@Dash_Gallou 13 күн бұрын

@@trucid2 I have a 3rd grade brain, lmao

@yodude1194 14 күн бұрын

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.

@danielmcelroy4505 7 күн бұрын

My intuition was pretty close to the second solution so I'm glad I was on the right track 😅

@portlyoldman 24 күн бұрын

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….

@sallyshipwreck4315 23 күн бұрын

exactly!

@ezura4760 23 күн бұрын

That’s the trap! LOL

@cigmorfil4101 21 күн бұрын

@@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".

@davedaley9093 13 күн бұрын

A common error, reading more limitations into the question than were stated.

@lav-kitty 5 күн бұрын

@@cigmorfil4101no one's keeping me from answering with "maybe"

@_veikkomies 24 күн бұрын

The "wanted" solution is the only realistic one though, as shading those other ones by hand is very difficult

@tuseroni6085 24 күн бұрын

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.

@Thornskade 24 күн бұрын

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

@2010ngojo 24 күн бұрын

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.

@uwose 24 күн бұрын

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.

@TheAgamemnon911 24 күн бұрын

The only correct solution is the one listed in the teachers guide, because they don't understand it either.

@Be727z 2 күн бұрын

I immediately thought of the second solution. Good to know I got it!

@thebeastoffeasterpark 2 күн бұрын

Nice, visually, the second correct one is what I settled on before I started watching lol

@AlanG512 21 күн бұрын

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.

@anneoreilly4900 16 күн бұрын

Isn’t it great how our brains work? I saw the third solution right away but not the first two.

@zalibecquerel3463 24 күн бұрын

"Can you shade half of it so that the shaded part is also a square?" - "No. I am not a smart man..."

@simplethings1363 24 күн бұрын

At least you're not trying to showcase how smart you are in the comment section! 😂

@Azadnew1 24 күн бұрын

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.

@tonyblake7569 24 күн бұрын

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.

@AlienRelics 24 күн бұрын

That is correct!

@jeremyashford2145 23 күн бұрын

Short answer: Yes I can. Explanation of long answer: some folding is required.

@thymerhemann3230 6 күн бұрын

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

@johnt6806 24 күн бұрын

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!

@A_Productions 22 күн бұрын

I did the exact same thing

@GabeSweetman 22 күн бұрын

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."

@Purriah 21 күн бұрын

Same. I actually immediately thought of the third one.

@TrueNomadSkies 15 күн бұрын

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.

@josephjackson1956 21 күн бұрын

This is one of those gifted and talented kids’ questions.

@wyawarD9677 21 күн бұрын

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.

@DaBlaccGhost 20 күн бұрын

@@wyawarD9677 exactly, it's a solution the curriculum has to come up with a question for but never used during your life

@jasonhurdlow6607 18 күн бұрын

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.

@CasabaHowitzer 16 күн бұрын

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.

@guillermo_yebra 16 күн бұрын

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

@njugunawanyoike146 17 сағат бұрын

For the first time ever on this channel, I solved a puzzle in mere seconds and got it right.

@texastitan6567 7 сағат бұрын

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

@billhill897 24 күн бұрын

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.

@phizc 23 күн бұрын

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.-

@zaelgreen1670 23 күн бұрын

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.

@TrionerExpeliozias 21 күн бұрын

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

@user-cl8tf9rh3u 21 күн бұрын

@@zaelgreen1670that’s exactly how I did it

@kevinnguyen4055 7 күн бұрын

No you can bisect the 45 degree diagonal to find a sqrt 2 landmark on the edges.

@snappybean 24 күн бұрын

The first solution is the only one you can generate a proof for without direct measurement.

@DroppedBass 24 күн бұрын

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).

@m.a.6478 24 күн бұрын

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

@JavierSalcedoC 24 күн бұрын

because presh didnt showed them it doesnt mean you cant draw other solutions with a ruler and compass

@SuperCityscan 24 күн бұрын

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

@navysaw23 24 күн бұрын

@@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

@brianschuetz2614 11 күн бұрын

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.

@austinlewis1212 7 күн бұрын

I thought of each square shaded at an angle like the 2nd example you gave pretty fast, the other examples did cross my mind but they're impractical to quickly draw on a paper accurately.

@MufflesTheGerbil 21 күн бұрын

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.

@theimpostorafungus1213 6 күн бұрын

Actually the solution was a bunch of triangles inside of the box 😊

@brucefulton 23 күн бұрын

You could also shade all of the large square at 50% transparency.

@FirstDarkAngel2001 21 күн бұрын

This is an epic response!

@menfaaanda 21 күн бұрын

@@FirstDarkAngel2001 epic failure

@xenicat 21 күн бұрын

if everything is lightly shaded there is no unshaded area at all that could form a square

@nomore6167 20 күн бұрын

"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.

@NeoHellPoet 20 күн бұрын

That's still shaded. Any amount of shading is shading. You're trying to hard to be celver and ending up wrong

@toyaleejb7714 Күн бұрын

Didn't do it the super smart way you did it, but at least I deduced the diagonal method in less than 3 minutes. Yay!

@OhCrapI_He 3 күн бұрын

Yes. Just have a square within the square with side length v2 (Square root of 2), then shade the rest.

@jimkoss3318 24 күн бұрын

7:20, since we can move the shaded area anywhere, there are an infinite number of answers.

@electrocubic5116 21 күн бұрын

Yep, that's what I was thinking! Infinite possibilities for the placement of the square

@Mr_Boness 23 күн бұрын

Anyone else got the answer instantly?

@karenkwilter3831 22 күн бұрын

Im a Quilter, so easy!

@praisejunkie 22 күн бұрын

Yes, after about 3 seconds

@snoski 22 күн бұрын

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.

@user-mw8sr8ph4w 22 күн бұрын

Ya just fill In the Diagonals. I am also only 30 seconds in To the vid. I solved it before I clicked the vid

@Rileygirl746 22 күн бұрын

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.😂

@herrscherkiller3432 8 күн бұрын

The second one was the one i thought about before watching you solve it.

@5wisher5weet 4 күн бұрын

Figured it out straight away. Shade the 4 squares in hald diagonally to form a unshaded square in the centre

@Pseudo548 17 күн бұрын

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.”

@lav-kitty 5 күн бұрын

wym "the answer to the first one"? are you literally just repeating what is said in the video?

@kinsellaSE7 24 күн бұрын

Surely there’s an unspoken “with some accuracy without a ruler, protractor or pair of compasses” in that original question?

@21palica 23 күн бұрын

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.

@cactustactics 23 күн бұрын

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

@mayanandrobertschraders587 22 күн бұрын

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

@hefy2jefy 22 күн бұрын

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.

@hefy2jefy 22 күн бұрын

@@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.

@outersketcher 2 күн бұрын

My mind went right to the third solution. I was surprised to see it was valid.

@souleternal7 15 күн бұрын

Would the answer be to draw a diagonal line starting top-center to the center-right. Then center-right to center-bottom. Then center-bottom to center-left. Then, shade in the outer parts of the new diagonal square that was formed? That would be half.

@jrkorman 24 күн бұрын

The 4th graders aren't smarter than anyone else, they've just been taught the answer. Question is, do they understand it.

@TheMonkeyGrape 24 күн бұрын

Very presumptuous that no kid could figure this out. Look up marshmallow and spaghetti tower challenge results if you underestimate them.

@MUI_Noam12 24 күн бұрын

@@TheMonkeyGrapehell naw I sucked at those xD

@SabertoothDeathmouse 24 күн бұрын

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

@danielz1666 24 күн бұрын

If you don't know if they understand it how do you know they're not smarter than anyone else?

@haukenot3345 24 күн бұрын

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.

@robertloveless4938 24 күн бұрын

YES. It takes just a bit of "thinking outside the box(es)".

@nthgth 19 күн бұрын

The solutions are all _inside_ the boxes...

@lacamendry1731 4 күн бұрын

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.

@spyrolad 2 күн бұрын

questions like this are exactly how we should teach maths!! questions with logical and creative solutions which aren't just given to you before you even have a go!

@roblowery3188 23 күн бұрын

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!

@Alt-Key_Here 21 күн бұрын

You have to think outside the box, both figuratively, and literally.

@nthgth 19 күн бұрын

All of these solutions are within the main square, the "box," (as dictated by the question), so not literally

@doofs 10 күн бұрын

i actually really like this question, very fun in how you're able to approach it. my solution was just to subdivide the squares in half continuously until i'd have half, longdivision style, zero actual "math" involved lol.

@sathvikchillapalli5977 5 күн бұрын

its a rectangle since a rectangle is also a square

@mattencarnacao5988 4 күн бұрын

This video should be titled “showing how adults overthink compared to kids”

@danieln57 20 күн бұрын

- Can you(...)? - No, i can't

@kamikeserpentail3778 24 күн бұрын

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.

@aaron-justinanderson Күн бұрын

I came up with that second one by myself so im very proud

@nitro5247 6 күн бұрын

What a beautiful video about the fun of math.

@BytebroUK 24 күн бұрын

That was, for me, one of the best of recent weeks. Thank you - it made me look 'outside the box' a bit.

@peppygrowlithe 24 күн бұрын

You know it's hip to be a square.

@mrnukes797 23 күн бұрын

Patrick Bateman appears

@gwiyomikim5988 22 күн бұрын

Tower of Power approves!

@nthgth 19 күн бұрын

I always found that song's lyrical theme questionable. Catchy tune though.

@themexecan Күн бұрын

I looked at that for 30 seconds before I figured it out

@N.Axolotl 2 күн бұрын

Make a shared area around the edges of the square, it makes a mini square inside

@dasc0yne 22 күн бұрын

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.

@richardgratton7557 24 күн бұрын

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.😊

@blaster-zy7xx 23 күн бұрын

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.

@johns9673 22 күн бұрын

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.

@nathanmendoza4046 13 күн бұрын

shade the borders until left with an unshaded center with half the area as the original square

@destinyoneandonly9422 2 күн бұрын

I immediately went “oh easy” and thought of the second solution with the square in the middle 😂

@locheyoutube5252 24 күн бұрын

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.

@skoosharama 24 күн бұрын

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.

@cactustactics 23 күн бұрын

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

@stuchly1 20 күн бұрын

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.

@locheyoutube5252 20 күн бұрын

@@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.

@billydelacey 11 күн бұрын

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.

@katharineg.7686 21 күн бұрын

Very cool. Thank you for sharing your solutions.

@Philip-qq7ql 7 күн бұрын

The square in the middle was the first thing that came to my mind, but i couldnt figure out what the side lenghts would be so i thought for 45 seconds and the tilted square became so obvious

@Stickman_Productions 15 күн бұрын

The four smaller squares got me for a bit. I read the question again and there's no requirement about having to shade full squares.

@mikepolioudakis775 24 күн бұрын

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

@PlasmaFuzer 24 күн бұрын

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.

@ITheNameless Күн бұрын

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".

@graysonrowe9780 2 күн бұрын

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.

@johnmagnotta8401 24 күн бұрын

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

@aguyontheinternet8436 24 күн бұрын

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

@Erlisch1337 24 күн бұрын

same. maing a frame was my first approach

@Held_der_Feuer 24 күн бұрын

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.

@hubertbreidenbach 24 күн бұрын

Same.

@davelordy 24 күн бұрын

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 !

@zoranstankovic2599 24 күн бұрын

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.

@jd-zr3vk 24 күн бұрын

My solution was a 1x1x1x1 square in the middle ; that is based on logic. I simply envisioned a smaller square in the middle.

@robertveith6383 24 күн бұрын

* divide

@robertveith6383 24 күн бұрын

@@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.

@2010ngojo 24 күн бұрын

@@jd-zr3vka square with a side of 1? Isn't it suppose to be a side of square root of 2?

@brownfamily1892 24 күн бұрын

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

@rayneingdown 6 күн бұрын

My first thought was the corner square option, and the center square with a border was my second idea after my mental picture wasn’t matching how I wanted it to. I thought of dividing all the squares into four smaller squares and then shading eight of those to make a square shape out of unshaded spots

@amenahmed672 4 күн бұрын

that 5:47 was the idea that came to me its goo to invoke creative thinking in kids. but i sure do hope the teacher gave the lessons and taught in the proper method that makes that thought possible in the first place

@sharpiemcsharp 24 күн бұрын

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.

@tomdekler9280 24 күн бұрын

Could you make any of those solutions with just a straight edge, though?

@grillmaster95 22 күн бұрын

@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

@MorbidMaximus 22 күн бұрын

@@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.

@cheriem432 21 күн бұрын

Huh? Can you restate your answer in English, please?

@tomdekler9280 21 күн бұрын

@@grillmaster95 > Just a straight edge > Measure Nope.

@blaster-zy7xx 23 күн бұрын

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.

@Rtzoor 15 күн бұрын

answer: yes. solution: ... shade the external diagonal half of each small square such that the unshaded part that remains is a square tilted by 45 degrees, aka a straight rhombus.

@noahnaugler7611 22 күн бұрын

figured it out during your opening spiel, but I reckon that stems from my particular focus on geometry if you designate a shape for the possible solutions, with two axes for the position of the centre of the unshaded square within the larger square, and a third axis for the rotation of the unshaded square, you would end up with an octahedron (or a stretched/squashed one, depending on scaling) with the two vertices along the rotation axis identified. the widest area would correspond to the squares being aligned, and the identified points would be the diagonal square

@sheldoniusRex 24 күн бұрын

Fold the paper to get four lines, making a square centered on the intersection of the four squares. Each outer corner of the square folded to cover the center will put the crease diagonally across the small square adjacent to that corner.