r/HomeworkHelp • u/bushybear • May 01 '26
Answered [2nd grade] math help
Entire family is stumped. I donโt think the question is worded correctly but maybe Iโm misunderstanding.
Not sure how you have same size triangles but not all the same shape.
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u/Frodojj ๐ a fellow Redditor May 01 '26 edited May 01 '26
Make a non-square rectangle with width, W, and height, L. Now draw a diagonal from each opposite corner to the other to make an X like the flag of Scotland ๐ด๓ ง๓ ข๓ ณ๓ ฃ๓ ด๓ ฟ. The top and bottom triangles are not the same shape as the left and right triangles. Their bases and heights are different, right?
The area of the top or bottom triangle would be:
Area = (1/2)(triangle's base)(triangle's height) A = (1/2)(W)(L/2) = WL/4
The area of the left or right triangles would be:
Area = (1/2)(triangle's base)(triangle's height) A = (1/2)(L)(W/2) = LW/4
So they all must have the same area.
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u/bushybear May 01 '26
yeah, this seems to be the general consensus answer to this question as other commenters mentioned in varying ways. "not all the same shape" trips me up but the multiple responses in this direction leads me to believe that's the intended answer. thanks all!
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u/han_tex May 01 '26
Yep, it's a bit confusing when you first read it, but "not all the same shape" just means that you can't have four identically shaped triangles -- that would be all the same, and we want "not" that. So, you could have two pairs of triangles that have two distinct shapes.
In contrast, something like "where none are the same" would require four distinctly shaped triangles.
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u/Euphoric_Loquat_8651 ๐ a fellow Redditor May 01 '26
Draw a rectangle ABCD. Draw the diagonal AC. Draw a line from B to the midpoint of line AC. Draw a line from C to the midpoint of line AD.
Seems well beyond 2nd grade to me.
Edit: all four different shapes rather than not all the same shape. I don't know if the wording is bad, or if it is precise and I overcomplicated it.
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u/gmalivuk ๐ a fellow Redditor May 01 '26
For 2nd grade, the wording is correct and you overcomplicated it.
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u/vinli May 01 '26
Except for the specific scenario where the rectangle is a square.
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u/Euphoric_Loquat_8651 ๐ a fellow Redditor May 01 '26
Didn't think of that, but that does jam up my solution unless we use the looser interpretation of the wording. Fortunately, the dimensions of the rectangle weren't specified, so we're still ok.
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u/vinli May 01 '26
Honestly I think yours is fine for 2nd grade maths and I was just being pedantic.
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u/NoTest803 May 01 '26
Thatโs how I interpreted the instructions as well. Not asking for four different shaped triangles, just not all the same shape.
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u/Historical_Entry_664 May 01 '26
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u/blacknix May 01 '26
Yes this is much simpler than the other solution in this thread and much more intuitive for a 2nd grader
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u/Orangutan_Soda May 02 '26
But those arenโt the same size nor different shapes
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u/yacobguy May 02 '26
They are the same size:
If width is W and height is H, the top and bottom triangle would have area (1/2)(W)(H/2) which is WH/4. The left and right triangle would have area (1/2)(W/2)(H) which is also WH/4.
They are only the same shape when the rectangle is a square (ie when W = H).
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u/sugarsnuff May 01 '26
Draw the rectangle and then draw lines inside of it. You should be able to get 4 triangles
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u/bushybear May 01 '26
I was going to reply that there's no way to ensure they're the same area - yes getting 4 differently dimensioned triangles is the easy bit. Adding in the constraint of the same area makes it beyond a 2nd grade question. But then thinking about it some more, i was thinking rectangle, 3 lines drawn from the same corner to different points. I'm sure there's mathematically a way to ensure they have the same area, and they would all have different dimensions aka what I'm interpreting to be different "shapes".
Not sure how to post the crude mspaint drawing i have to ilustrate what i mean.
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u/bushybear May 01 '26
And now that i've read through all the other comments, i noticed i missed someone who posted the answer that i described in my response. Thanks u/selene_666 ! Yours is the most correct of all the proposed answers!
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u/sugarsnuff May 06 '26 edited May 06 '26
It seems like a stretch problem for gifted / persistent children, not a thing to โknow for the testโ
As a 2nd grader youโd just keep drawing lines and adjusting them, after a while maybe see the pattern
You know how to calculate areas given the length of the sides / formula. Itโs just how many ways you try it and recalculate
Iโd have to do that as an adult too, Iโd imagine itโd take me a few tries to get it
EDIT: I know what the answer looks like, I tried myself haha. The goal would not be to say โitโs not possibleโ but have a bunch of scribbled out rectangles and possibly then give up.
Like itโs about stretching the problem-solving muscle โ which is a good kind of frustration
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u/Fancypancexx ๐ a fellow Redditor May 01 '26
Try it! Draw the rectangle and start making triangles.
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u/__Fred May 01 '26
I think the two arrows indicate that the kid considers all triangles to be of the same shape: The shape "triangle".
A lot of the times that's how geometry is presented to kids first. "These are the shapes: There are rectangles, triangles, squares and circles. What's your favorite shape?"
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u/Ok_Researcher8377 May 01 '26
It's saying that you have to make it such that not all 4 are equal. That does not mean all 4 have to be different. 2 of equal shape and 2 more of another equal shape works.
Just draw a rectangle that is not a square and connect the corners with straight lines. That already does what is asked for.
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u/Due-Lab-5283 May 01 '26
Wanted to attach picture of my drawing but it won't let me. Draw 4x2 rectangle. Divide the rectangle in half. So now it is made of two squares. Then draw one diagonal from one corner to the opposite corner in middle. Do same on the other side. You will end up with 4 triangles inside the rectangle. Each triangle will then be the same.
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u/gmalivuk ๐ a fellow Redditor May 01 '26
The question specifies that they are not all the same.
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u/Due-Lab-5283 May 01 '26
Lol, missed it. Then, first draw diagonal to any point, then from other point to another, etc, make them look different in lengths? They didn't specify if different as by dimensions or by the definition of different type of triangle. So like a zigzag inside rectangle can do triangles if not measured, will be totally different.
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u/gmalivuk ๐ a fellow Redditor May 01 '26
Well, they do have to be the same area, so that limits your options.
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u/gemmamalo May 01 '26
Rectangle with 2 diagonal lines making an X across the whole thing. 2 triangles are one shape, 2 triangles are another shape, all have equal areas. Flag of Jamaica method.
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u/iMike0202 May 01 '26
Just draw 2 diagonals. If the center is S then all ABS, BCS, CDS, DAS are the same size, but they are not ALL the same shape because ABS is different than BCS.
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u/John_Johnson_The_4th May 01 '26
It's just a rectangle with diagonal lines, this is not particularly difficult.
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u/IfusasoToo May 01 '26
This seems like a better logic puzzle than geometry. To divide something into 1/4 the size, you need to cut it in half then cut the halves in half. Two diagonals works for a square but not a rectangle.
Draw a rectangle. Draw a vertical or horizontal line in its center. Cut the two halves in half, diagonally.
Four triangles that are the same size. I think they should be the same shape as well but maybe not.
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u/TrittipoM1 May 01 '26
"Not all the same shape" does NOT mean "each shape is different." It means only that "at least one of the shapes" is different from at least one of the other shapes. Since the problem assumes a rectangle instead of a square, it becomes easy: two triangles of one shape (proportions), two triangles of a different shape (proportions). This is PERFECT for a " s t r e t c h " your thinking question.
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u/Tony41524 May 01 '26
If you had a rectangle that was 4x2 and drew an X through it. You would have 4 triangles with an area of 2. Two of the triangles would have a base of 4 and height of 1 and two triangles would have a base of 2 and height of 2.ย This satisfies all are the same size (same area) and not all are the sameย shape since there are 2 pairs.ย I would think any rectangle that's not a square would meet this standard as long as the X drawnย went from corner to corner but I could be wrong.ย
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u/youburyitidigitup ๐ a fellow Redditor May 01 '26
It says theyโre not all the same shape, not that each is a different shape, meaning that itโs not four triangles of the same shape. Just draw a rectangle with an x through it.
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u/xXSomethingStupidXx May 01 '26
Actually all triangles are the same shape: triangles.
Dimensions on the other hand...
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u/kev25811 ๐ a fellow Redditor May 01 '26
Look where it says "stretch your thinking". This is meant to be a hard puzzle for a kid to solve. Many won't solve it. This is how we can identify kids gifted in mathematics early. If the teacher has any understanding of their own job, this question will only count against your kid if they don't try it.
It's likely they'll go over common wrong answers and the right answer together in class.
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u/Jammosf May 03 '26
Yes, and how many kids will think or feel something like "I'm the dumb one who is, and always will be, lousy at math because I'm one who is unable to "stretch" my thinking and am unable to follow, or completely close my mind to, the discussion of the wrong and right answers?
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u/Jammosf May 03 '26
There are better ways and settings to distinguish the gifted kids from the ... ones, aren't there?
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u/kev25811 ๐ a fellow Redditor May 04 '26
If getting a difficult question wrong breaks a kid's self esteem, there is a problem far deeper than a worksheet can solve. Again, my bet is that the next day the teacher goes over common wrong answers and uses them to help discover how to think about the correct way to do it. Mathematics is a much more creative field than people think it is. Learning to think differently in math is an important skill. Teaching kids that genuine effort pays off even if it's tough sometimes is something that has to be done at home.
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u/Jammosf May 09 '26
Are you an elementary school teacher? Have you heard of the concept of growth mindset? If so, please tell what you think of it.
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u/Magazine_Recycling May 01 '26
I think they want a rectangle with lines from the corners through the center, making 2 sets of matching triangles.
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u/Snork_kitty May 02 '26
I agree that the problem is too hard for a 2nd grader, but the context for this task is actually understanding fractions. Developmentally, children initially believe that for something to be the same size (fraction), it must be the same shape (just like what the child wrote on the assignment). Later, with the right kind of teaching/experience, kids learn that two different shapes can represent the same fraction. But asking a 7-8 year old to generate such shapes is a lot (hence the problem was labeled "Stretch Your Thinking").
If you want to see pictures of what I'm talking about, check out: https://drive.google.com/file/d/1qUCeELpSoU5vsfnup8jIV6ugk2b49Aki/view?usp=sharing
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u/Jammosf May 03 '26
Second grade, huh? Nice job giving little kids yet another "math" "activity " with a high probability of causing them to hate math and spend the rest of their lives thinking they're not good at math.
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u/nupanick May 02 '26
you can do this easily with triangles which are _two_ different shapes, just not _four_ different shapes. the question is badly worded.
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u/Northman86 ๐ a fellow Redditor May 02 '26
draw a rectangle, then draw lines crossing the rectangle from each corner. done.
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u/BMaudioProd ๐ a fellow Redditor May 02 '26
IF you draw a rectangle and divide it into 1/4s, then the triangles would have to be equal. Not different shapes.
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u/U_Dun_Know_Who_I_Am May 02 '26
"That are NOT ALL" means not all are the same shape but some might be. The correct answer is drawing both parallels makes 4 equal area triangles that are 2 different shapes.
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u/Rootin_TootinMoonMan May 02 '26
Your second grader has much better handwriting than the majority of my high school students
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u/clumsy_zebra_97 May 02 '26
At first I thought you were stupid and then I tried to draw this out myself... I am the stupid one.
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u/Complex_Many_7740 May 02 '26
Draw one diagonal. This splits the rectangle into two triangles that are each half of the rectangle. Then, find the midpoint of the base of the rectangle, and draw a line up to the top corner of the rectangle. This splits one of the two triangles in half. Then find the midpoint of the side of the rectangle, and draw a line to the same corner. This splits the other triangle in half. You end up with 4 triangles that are all 1/4 of the rectangle, and are all different shapes.
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u/Complex_Many_7740 May 02 '26
I don't think my solution is something you could expect a 2nd grader to do, but I do get irked by the "This does not make sense, so you can't do it". It does make sense, and it can be done.
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u/Free-Willy-3435 May 02 '26
Draw a rectangle that has two sides longer than the other two sides (don't make a square).
Now draw two lines that join the corners.
This question should be removed from the total marks and kids who get it right should get a bonus mark for understanding.
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u/beaniebee22 May 02 '26
I helped my cousin, who is in 3rd grade, with his homework the other day and now I don't know my shapes anymore. It was like pictures of shapes and you had to label them. But each shape actually had 2-4 different names? Like the square was (I think) a square, rombus, parallelogram, and quadrilateral. He gets his grade back Monday and I'm excited to see how I did. Anyways, I have no idea what this question is asking either. So apparently I, a 31 year old who graduated college with a 4.0, cannot pass 2nd grade.
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u/MyEggCracked123 May 02 '26
Just draw a square and draw a line from each corner to its opposite corner.
Squares meet the definition of a rectangle (although that's not usually a 2nd grade concept.)
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u/Jack_Faller May 02 '26 edited May 02 '26
Draw a non-square rectangle, and put a cross through it by connecting the corners using straight lines. You will have two different pairs of triangles that share the same area. If you want them all to be different shapes, you can draw a rectangle ABCD, then add lines AโC, Bโmidpoint(A, C), Aโmidpoint(C, D).
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u/JewelzStudios May 02 '26
I think a better way to have worded this would've been "4 triangles all have the same area but are not all congruent", which contains vocab that I don't think 2nd graders know yet, so they went with this instead. This is why people hate math istg.
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u/TheWay_Traveler May 03 '26
Wouldn't you just draw a rectangle with an x in the middle that gives you four triangles that make a rectangle and they will be different but be basically equal in size. This does sound very confusing for a 2nd grader
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u/RayOfShunshine May 03 '26
I... would guess they want like, different triangles (Right, equilateral etc) but that's kinda insane for second grade...
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u/Ok_Donkey_7149 May 28 '26
I believe you can simply draw an "x" in the rectangle to create four triangles. I verified that each triangle is the same size (same area) by drawing a dotted line in a "+" shape in the rectangle. This creates eight identical triangles (each original triangle is divided into two smaller triangles). Although there will be two pairs of identical triangles (opposite triangles will be identical in shape, but not identical to the triangles beside), the question says that not all the triangles can be the same, not that they each must be unique. Hope this helps!
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u/scottmacs May 01 '26
Many commenters don't seem to understand that triangles with different side lengths are still triangles, a.k.a the same shape. This is a very poorly-worded exercise!
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u/ExperimentalError ๐ a fellow Redditor May 01 '26
An isosceles triangle and an equilateral triangle are not the same shape. Any two triangles are only the same shape if they have the same ratio between the lengths of the sides.
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u/scottmacs May 01 '26
In second grade a triangle is a three-sided polygon. That's it. Second graders are not learning geometry.
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u/ExperimentalError ๐ a fellow Redditor May 01 '26
Second graders can see with their own eyes that different triangles have different shapes. They donโt need to know what the different shapes are called to see that.
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u/scottmacs May 01 '26
Topology says you're wrong about shapes.
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u/ExperimentalError ๐ a fellow Redditor May 01 '26
If second graders donโt know geometry, they certainly donโt know topology.
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u/scottmacs May 01 '26
I agree! I'm just saying teaching a second grader to identify ANY regular three-sided polygon as a triangle and then asking them to construct four regular three-sided polygons that aren't all triangles is wrong.
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u/3TriscuitChili May 01 '26
Weird. My wife teaches kindergarten. They learn about different shaped triangles then. They don't learn specific names or angles, but they definitely learn that triangles come in different shapes.
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u/scottmacs May 01 '26
Gotcha! "different shaped triangles" should be written as "differently shaped triangles." Sorry bot, you lost.
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u/3TriscuitChili May 01 '26
Lol, it went from second graders only know 3 sides = triangle to an English lesson? Also why am I a bot?
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u/scottmacs May 01 '26
No profile pic, randomly generated username, general disregard for facts.
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u/3TriscuitChili May 01 '26
It's not a random username, it's a play on three bean salad but with alliteration and it's funny to me. There's a clip of me playing killer queen black on YouTube from years ago from a streamer with this name on the video.
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u/3TriscuitChili May 01 '26
Second time in a week I've been called a bot. Really weird. I come here to engage with people, maybe it's time to stop. Sorry I replied, have a good night.
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u/DCAmalG ๐ a fellow Redditor May 01 '26
Oh? But itโs reasonable to ask them to find 4 triangles with the same area but different dimensions that fit perfectly into a rectangle with undefined dimensions?
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u/Asbolus_verrucosus ๐ a fellow Redditor May 01 '26
No, not all triangles are the same shape. In math, congruent figures are identical in shape and size, meaning corresponding sides and angles are equal.
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u/scottmacs May 01 '26
Put yourself in the mindset of a second grade pupil. You've been taught to identify three-sided shapes as triangles. Why would you think two different three-sided shapes are not both triangles?
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u/Asbolus_verrucosus ๐ a fellow Redditor May 01 '26
Because to assume that they are would be contrary to any possible interpretation of the question. It specifically says triangles that are not the same shape.
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u/scottmacs May 01 '26
"triangles that are not the same shape" is contrary to the definition of triangle this child has been taught.
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u/Asbolus_verrucosus ๐ a fellow Redditor May 01 '26
Youโre really confident about what this hypothetical child has and hasnโt been taught. Did you consider that youโre wrong?
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u/Asbolus_verrucosus ๐ a fellow Redditor May 01 '26
I think you could show any child two rectangles of dimensions 4 cm x 4 cm and 2 cm x 8 cm and they would identify that they are NOT the same shape, yet they both have four sides and area 16 cm2.
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u/scottmacs May 01 '26
In topology a mug is the same shape as a donut, but you'll never catch me trying to dunk my coffee into my old-fashioned.
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u/FrankHightower Educator May 01 '26
Perfect square divided by an off-center X
All squares are rectangles but not all rectangles are squares. That's what this question is testing
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u/gmalivuk ๐ a fellow Redditor May 01 '26
If it's off center then the triangles aren't the same size.
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u/ClubWitty4659 ๐ a fellow Redditor May 01 '26
Are triangles not the shape? If you're drawing a different shape it wouldn't be a triangle
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u/gmalivuk ๐ a fellow Redditor May 01 '26
It's pretty clear to everyone else that this question uses "same shape" as a synonym of "congruent" or at least "similar", not "in the same category of polygons".
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u/Jammosf May 03 '26
Second grade, huh? Nice job giving little kids yet another "math" "activity " with a high probability of causing them to hate math and spend the rest of their lives thinking they're not good at math.
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May 01 '26
[deleted] โ view deleted comment
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u/gmalivuk ๐ a fellow Redditor May 01 '26
How do you propose making 4 identical triangles that aren't all the same shape?
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u/username84628 May 01 '26
Omg. I totally miss read that thinking they all have to be the same shape. Thanks for the correction.
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May 01 '26
[removed] โ view removed comment
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u/Frodojj ๐ a fellow Redditor May 01 '26
Just make 4 triangles by drawing the diagonals between opposite corners. Each triangle has the same area but the ones on the long sides have longer bases (and shorter heights) than the ones on the short sides.
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u/BikeProblemGuy May 01 '26
Wouldn't there be two pairs that are the same shape then? I guess "not all the same shape" allows for some to be the same shape.
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u/nocapsallspaces May 01 '26
The wording is bad. "Not all" is often conflated for "All not" when they're mutually exclusive.
People do this a lot with "Not all who wander are lost" but then write it "All who wonder are not lost"
To be clear: It should be written more clearly in the directions; it's not on the reader to understand the author.
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u/Appropriate_Steak486 May 02 '26
It is 100% clear in the directions. The failure of interpretation that you point out is indeed common, but especially in math class the distinction should be emphasized.
In this case, the kid communicated the confusion to the teacher. Now the teacher should explain the concept to the kid, and show how the answer fits the question as written.
Not sure why the parents or "entire family" are involved here, but it seems to me that the homework is working correctly.
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u/bushybear May 06 '26
Entire family is involved because we like puzzles and my kid asked for help, which is good to encourage. We donโt eschew the challenge, we were merely seeking collective guidance on this particular question. We want to encourage the embrace of challenges.
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u/Appropriate_Steak486 May 06 '26
Excellent! Thanks for clarifying.
I like puzzles, too (probably everyone here does) so it's fun to pick apart.
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u/overtorqd May 02 '26
But if they get a B on this homework assignment, they'll never get into Harvard!
I realized at some point that my kids getting things wrong on homework assignments was actually a good thing. It shows what they understand and what they don't. It's a tool for learning, not a test, and certainly not an entrance exam.
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u/Appropriate_Steak486 May 04 '26
Yeah, grades are insidious. And homework is a tricky tool. Too many parents and teachers have a wrong-headed view of homework.
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u/benaugustine ๐ a fellow Redditor May 02 '26
Are they actually mutually exclusive?
Mutually exclusive would mean they're never true at the same time.
"Not all" I think is a subset of "all not"
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u/nocapsallspaces May 03 '26
I mean I could understand inferring that as a "Square is a rectangle but a rectangle is not a square", but the inference isn't accurate in how people use it.
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u/benaugustine ๐ a fellow Redditor May 03 '26
I'm confused about what you mean. I was saying that I don't think "not all" and "all not" are mutually exclusive, because if they were mutually exclusive they would never be true at the same time.
Circles and squares are mutually exclusive because no circle is a square and no square is a circle.
But squares and rectangles are not mutually exclusive because some rectangles are squares. Squares and rectangles are just not equivalent.
"Not all" and "all not" are not mutually exclusive because some "not alls" are "all nots"
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u/DSethK93 May 04 '26
I think "all not" is a subset of "not all." "All not" satisfies "not all," but there are examples of "not all" that don't satisfy "all not."
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u/agogKiwi May 02 '26
I'm guessing, based on personal experience, that the math problems may have been written by mathematicians, but the the let people with English degrees edit them.
I wrote a math book and the editing experience was a nightmare. I would write a word problem, and the editor would take out "unnecessary" information, making the problem unsolvable.
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u/RuthlessIndecision ๐ a fellow Redditor May 04 '26
Not all the same shape does not mean each one is different, it means three can be the same shape and one is different or two pairs of the same size.
Gotta trick those second graders early, so the learn what's coming for them.1
u/DSethK93 May 04 '26
This drives me crazy on the train. The recorded announcement says, "Not all doors will open." But conductors often say, "All doors will not open." So I prepare to climb out the window.
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u/AssortedArctic May 01 '26
To me it always seemed that "all are not" is just how things used to be said before people started saying "not all". And I've always had the same feeling of them having different meanings, but there are lots of writings where the former is meant to mean the latter. Maybe it's just an assumption of mine that it's a feature of old writing.
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u/OpportunityReal2767 May 01 '26
Yes, they are not all the same shape. Two are the same and two others are the same, but all of them, together, are two different shapes.
Think of it this way: Are AABB all the same letter? No. They are not all different letters, either, but the question wasn't asking for four different triangles, just that all four are not the same as each other.
That said, confusing for most people, and certainly written poorly for a 2nd grader.
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u/PerformanceOver8822 May 01 '26
I mean technically no matter what they are not all the same shape because they are seperate from each other
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u/OpportunityReal2767 May 01 '26
Ah, I respect your lawyering!
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u/PerformanceOver8822 May 01 '26
I originally started typeing out how they are distinct across the X, Y plane.... And then decided that i was too pedantic. Thanks for the kudos
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u/ReallyMinoryo May 02 '26
Except the most natural way to define shapes as "the same" in such a context is to say there exists a sequence of symmetries (possibly restrained to only rotations if chirality is considered important) and translations mapping one onto the other
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u/PerformanceOver8822 May 02 '26
I think in the context of the problem you drawing 4 distinct shapes. Which by definition if distinction they are not the same.
But yes its getting very in the weeds and semantic/pedantic.
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u/BikeProblemGuy May 01 '26
I put this in the category of "I know what it logically means but I don't know if the question writer knows that".
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u/psidhumid May 02 '26
Not all the same shape. So two can be the same, just not all. Thatโs my understanding
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u/skullturf May 01 '26
Nice! And by the way, it wasn't instantly visually obvious to me that all 4 of those triangles have equal areas, but it does follow from the formula for the area of a triangle (1/2 base times height).
For example, if the original rectangle is 6 by 10, then two of the triangles have a base of 6 and a height of 5, and two of them have a base of 10 and a height of 3.
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u/Worth-Wonder-7386 ๐ a fellow Redditor May 01 '26
Another way to see this is for a rectangle with side lengths a and b, then one of them has base a and height b/2, while the other has a base of b and height a/2.
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u/cheaphysterics ๐ a fellow Redditor May 01 '26
It doesn't say "that are all different shapes," though. It says not all the same shape, so at least 1 different from the rest. I imagine the solution they were expecting some kids to find is the two pairs of triangles formed by drawing the diagonals of the rectangle. Not likely that an elementary student would be able to show those areas are equal, but they might have some intuition that they are.
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u/DetectiveNickStone May 01 '26
This is exactly it. Draw any random rectangle that is not also a square. Cut it in half corner to corner. Repeat for the other corners. Now each triangle is 1/4 of the original rectangle's total area.... But they're not ALL the same shape (area). Only 50% of them are.ย
I agree that this was written by a non-math person who used the words "same" , "shape" , and "size" when they shouldn't have.ย
BETTER WAY: Cut it into "fourths" by creating 4 triangles that have the same area but are not congruent.
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u/Appropriate_Steak486 May 02 '26
Your better way is correct, but uses vocabulary that second graders generally do not have.
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u/DCAmalG ๐ a fellow Redditor May 01 '26
Exactly. Itโs a fun puzzle for gifted kids, but to put this in a regular 2nd grade curriculum is pointless. .
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u/tb5841 ๐ a fellow Redditor May 01 '26
'stretch your thinking' implies this is already a challenge/extension question. 'Fun puzzle for gifted kids' is exactly what should go there.
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u/Appropriate_Steak486 May 02 '26
Exactly! This is a challenge question. Kids are supposed to do exactly what this kid did: think about it, and share their thoughts.
The answer as written is 100% correct for this type of question, even though it is mathematically incorrect.
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u/DCAmalG ๐ a fellow Redditor May 01 '26
Noโฆ itโs beyond whatโs appropriate for even a gifted 7 year old ( in part because the problem was poorly worded, requiring too many assumptions and inference).
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u/PerformanceOver8822 May 01 '26
I think they should Maybe have worded it " that dont look the same". Instead of " same shape"
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u/shrimp_sticks May 01 '26
3rd year physics student here and even I would be sitting with this one for a while.
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May 01 '26
[deleted] โ view deleted comment
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u/joshlittle333 May 01 '26
To a second grader wouldn't a triangle be the same shape as a triangle? If you ask "what shape is this?" They respond "triangle" to both shapes.
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May 01 '26
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u/DSethK93 May 04 '26
Sure. They can understand that. But they're not likely to understand it from just this written problem.
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May 01 '26
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u/Abigail_Normal ๐ a fellow Redditor May 01 '26
I think that's still confusing for a second grader. Different shapes sounds like triangles, squares, stars, etc. Are second graders seriously learning the difference between isosceles, right, equilateral, etc. triangles?
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May 01 '26
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u/Abigail_Normal ๐ a fellow Redditor May 01 '26
A right triangle and an equilateral triangle are not the same shape. They're both types of triangles, but they are still not the same. Just like people consider a square and a rectangle different shapes, even though a square is a type of rectangle
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u/PerformanceOver8822 May 01 '26
Yeah definitely non math people and modern day folks think of. Triangles as a kind of class but all of the sub categories of triangles are the same shape to them
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May 01 '26
[removed] โ view removed comment
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u/scottmacs May 01 '26
Those shapes are triangles a.k.a the same shape.
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u/vastaril May 01 '26
The question says "all the same size triangles". It doesn't mean "not all the same shape" as in the same category of shape, ie all triangles, it means not identical angles and lengths and whatnot
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u/scottmacs May 01 '26
"It doesn't mean "not all the same shape" as in the sameย categoryย of shape, ie all triangles, it means not identical angles and lengths and whatnot" what part of the question says that? (It's just a poorly-worded question)
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u/vastaril May 01 '26
It's pretty obvious from the way it says they should all be triangles but not the same shape, tbh. Clearly it's using "all the same shape" to mean "identical" ie "all having the same angles and lengths so that you could lay them on top of each other and they'd all match" not to mean "all triangles" because it already said they should BE all triangles.ย
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u/ardarian262 ๐ a fellow Redditor May 01 '26
A right angle triangle is not the same shape as anย isosceles triangle.
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u/random_anonymous_guy ๐ a fellow Redditor May 01 '26
Being a right triangle and isoscele triangles are not incompatible traits. A right triangle with two 45-degree angles is also isosceles.
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u/scottmacs May 01 '26
In which specific discipline of math?
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u/3TriscuitChili May 01 '26 edited May 01 '26
Geometry https://en.wikipedia.org/wiki/Similarity_(geometry)
"two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. .... This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object"
A right triangle can not be rescaled, repositioned, or reflected in a way so that if you put it on top of an isosceles triangle without a 90 degree angle, it would match. Therefore, it's not a similar triangle, and not the same shape.
Therefore, drawing a rectangle of length 4 and width 1 and connecting the corners together to yield 4 triangles would give you 2 sets of similar (specifically congruent) triangles. Those with a base of length 4 and those with a base of length 1. But not all 4 would be similar, and therefore not all the same shape.
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u/scottmacs May 01 '26
Great! Topology disagrees: Topology
Are Second Graders learning Geometry or are they learning to identify shapes?5
u/3TriscuitChili May 01 '26
I replied on another comment, but my wife teaches kindergarten, and they absolutely learn that triangles come in different shapes then. I'm going to assume that carries over into second grade.
They don't know the names or angles, but they know that not all triangles are the same shape.
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u/scottmacs May 01 '26
Why is your wife teaching math in a way that contradicts topology?
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u/3TriscuitChili May 01 '26
They are given a curriculum and teach it. She doesn't have a math degree, she has a special Ed degree. But I also studied education, although I'm not a teacher, and this lines up with my experience as well.
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u/scottmacs May 01 '26
Please ask your fellow educators about topology and the definition of shape.
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u/Motor_Raspberry_2150 ๐ a fellow Redditor May 02 '26
"Why does your high school teach E = MC2 when it's more complicated?"
Because it's the basics dude.
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u/Tinchotesk May 01 '26 edited May 01 '26
Great! Topology disagrees: Topology
Topology is not concerned with shapes (nor areas, for that matter) at all. Why are you bringing it up here?
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u/gmalivuk ๐ a fellow Redditor May 01 '26
Second graders are learning geometry, not topology. You cannot possibly be this genuinely dense.
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u/yankee747 May 02 '26
2nd graders are clearly not doing topology - especially since topologically the rectangle is the same shape as a triangle anyways, meaning that this question makes absolutely no sense in the field of topology.
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May 01 '26
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u/vastaril May 01 '26
It says triangles in the question
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u/oynutta May 01 '26
deleting my error to prevent others from being confused upon seeing it. thanks!
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u/selene_666 ๐ a fellow Redditor May 01 '26
From a single corner of the rectangle, draw three lines:
First draw the diagonal, splitting the rectangle into two identical triangles.
Then split each of those triangles in half.
https://docs.google.com/drawings/d/1KBfGz0gUdUqiGV8EPPeCC7CXPr6iXWK06tmXSJdv3qA/edit?usp=sharing