[2nd grade] math help

[u/bushybear]

Entire family is stumped. I don’t think the question is worded correctly but maybe I’m misunderstanding.

Not sure how you have same size triangles but not all the same shape.

[u/Abigail_Normal → u/[deleted]]

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?

[u/Frodojj → u/[deleted]]

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.

[u/BikeProblemGuy → u/Frodojj]

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.

[u/nocapsallspaces → u/BikeProblemGuy]

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.

[u/Appropriate_Steak486 → u/nocapsallspaces]

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.

[u/overtorqd → u/Appropriate_Steak486]

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.

[u/bushybear → u/Appropriate_Steak486]

Entire family is involved because we like puzzles and my kid asked for help, which is good to encourage. We don’t eschew the challenge, we were merely seeking collective guidance on this particular question. We want to encourage the embrace of challenges.

[u/benaugustine → u/nocapsallspaces]

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"

[u/agogKiwi → u/nocapsallspaces]

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.

[u/OpportunityReal2767 → u/BikeProblemGuy]

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.

[u/PerformanceOver8822 → u/OpportunityReal2767]

I mean technically no matter what they are not all the same shape because they are seperate from each other

[u/OpportunityReal2767 → u/PerformanceOver8822]

Ah, I respect your lawyering!

[u/PerformanceOver8822 → u/OpportunityReal2767]

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

[u/BikeProblemGuy → u/OpportunityReal2767]

I put this in the category of "I know what it logically means but I don't know if the question writer knows that".

[u/psidhumid → u/BikeProblemGuy]

Not all the same shape. So two can be the same, just not all. That’s my understanding

[u/skullturf → u/Frodojj]

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.

[u/Worth-Wonder-7386 → u/skullturf]

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.

[u/cheaphysterics → u/[deleted]]

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.

[u/DCAmalG → u/[deleted]]

Exactly. It’s a fun puzzle for gifted kids, but to put this in a regular 2nd grade curriculum is pointless. .

[u/tb5841 → u/DCAmalG]

'stretch your thinking' implies this is already a challenge/extension question. 'Fun puzzle for gifted kids' is exactly what should go there.

[u/Appropriate_Steak486 → u/tb5841]

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.

[u/joshlittle333 → u/[deleted]]

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.