If a sponge and a brick have the same density, which has the greater volume?

If their densities are the same then their volumes must be the same (for the same mass), which is correct if you don't make any assumptions about bricks or sponges. If one has a different volume then they must have different masses also, which defeats the point of the question. (Which is heavier a tonne of bricks or a tonne of sponges?)

Another thing was that she marked off for me writing ---> = reaction, and some other kid in the class wrote ---> = yields, and she said the correct answer was chemical reaction. I'd say I'm right here, I know the other kid is 100% right. She basically marks off if it isn't her strict definition from the notes.

---> is an arrow. It doesn't mean anything out of context. If you have been given notes on what ---> means then that is the correct answer, whatever the teacher wrote in the notes. So I think you are wrong on this one, this time, sorry.

As for density, the only way for the sponge and brick to have the same density is for both their masses and volumes to be different.

Not technically correct. They could both have the same mass and volume. They should both have the same ratio of mass to volume, i.e. density LOL

We know that their masses aren't equal,

No we don't, do we?

You must then rationalize to say that the sponge must have the greater volume in this case because it is porous

It is a little ambiguous if you need to make such assumptions.

Assuming that's the exact wording of the question, there is not enough data to answer.

Perhaps she meant "if they weight the same" - but it is not given in the question, so it is not part of the question.

I agree with Borek.

I mean, the sponge could literally be much larger than the brick and have a greater mass and weigh more than the brick.

This wouldn't change the density part of the question though.

I answered they have the same volume and got it wrong.

So what is the teachers answer then?

In my experience most college professors tend to think of their students (especially lower level students) as a distraction from their real job.

Well one undergraduate student with one 5 minutes question may seem to be not much hassle, but what about the other 200/400/600 students? Lets say you had 300 first year students and each one only wanted , say 3 minutes of your time, that is 15 hours of contact!! Not to mention other students, staff, research, eating sleeping, life LOL, cut your teachers some slack!!