Current Events > I gave my math students an online test last week. Due date is tonight.

(+) Yeah! (+)

AssultTank posted...

Right? <_< (I may have made a mistake somewhere, but...)

The way I understand it, you need to do something like this

https://www.varsitytutors.com/intermediate_geometry-help/how-to-find-the-diagonal-of-a-prism# :~:text=To%20find%20the%20diagonal%20distance,%3D%20width%2C%20and%20%3D%20length.

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AssultTank posted...

So I believe you just need Pythagorean theorem to get the length of the cut, sqrt(35^2+54^2), then simply add that to 35+54, and then just (35*54)/2 for the area of the cross section and multiply that by 35 if you want total volume...
Which would be
Perimeter; 153 inches
Area of the cross section; 945in^2
Volume of each piece; 33,075in^3
Right? <_< (I may have made a mistake somewhere, but...)

Not sure I understand the English here but the way I read it is that the cross section will be rectangular with one side being 35 and the other being the length of the cut. If you wanna mess around you could always just define two vectors that span the cross section and their cross product will describe the surface area.

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so how many did it

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Teachers that put due dates in a Sunday night are dumb.

Friday night or something idk. Those kids will just procrastinate on it all weekend.

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gna647 posted...

Teachers that put due dates in a Sunday night are dumb.

Friday night or something idk. Those kids will just procrastinate on it all weekend.

Due date on a Friday night is an actual crime against humanity.

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you know what, i changed my mind. that question is too ambiguous. what exactly do you mean by diagonally lengthwise? i assumed the cross section would be a rectangle, but i think a triangle is also possible. should definitely label the vertices and tell the kids specifically which cross section they're looking to find.

edit: i changed my mind again, lol. i think 'its diagonal" means specifically opposing vertices. so it would definitely be the rectangle cross section. scar is almost right, but it's not 35, it's the third leg of the 35 35 x right triangle by 54

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Epilogue:

I had a handful of students who had legitimate technical issues. The home screen of the website was not properly loading and it turns out the site had an update that required you to clear your cookies if you left the tab open (which these kids had done). Obviously neither myself nor the kids would have known to do this, so I couldn't fault them.

I had a talk with the students today and gave them the class period to work on the test. I gave a serious "No really, it's due tonight so don't screw around right now" talk, and now I think all but 4 have it done now.

As for that one problem with the marble, the perimeter is 207in and the area is 2673in^2 after rounding to the nearest whole number.

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ZMythos posted...

Epilogue:

I had a handful of students who had legitimate technical issues. The home screen of the website was not properly loading and it turns out the site had an update that required you to clear your cookies if you left the tab open (which these kids had done). Obviously neither myself nor the kids would have known to do this, so I couldn't fault them.

Yeah at this point and time, you either allow lots of flexibility with students completing online assignments or revert back to a 'paper and pencil' model where students just submit a picture/pdf of their work.

I had a talk with the students today and gave them the class period to work on the test. I gave a serious "No really, it's due tonight so don't screw around right now" talk, and now I think all but 4 have it done now.

Don't make it due at night, make it due at the end of the period. That way you're ensuring they do the work during the time you're requesting and not procrastinating. Also, these kids are probably staring at their screen all day, so you're allowing them time in the afternoon to (hopefully) detach themselves from technology.

As for that one problem with the marble, the perimeter is 207in and the area is 2673in^2 after rounding to the nearest whole number.

That question is poorly worded but I got different results as well. I'm getting 199 for the perimeter (35*2+(sqrt(35^2+54^2))*2) and 2252 for the area (35*sqrt(35^2+54^2)).

Also from a child psychology perspective, you should totally not 1) put due dates at midnight and 2) put due dates on the weekend.

Hopefully the other students bullied those 5 nerds who took the test before 11 PM the night it is due.

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pistachio12 posted...

Yeah at this point and time, you either allow lots of flexibility with students completing online assignments or revert back to a 'paper and pencil' model where students just submit a picture/pdf of their work.

With kids going in and out of quarantine still for COVID, I'm gonna ere on the side of flexible. The hard part is when you get one or two students who take advantage of that flexibility.

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RchHomieQuanChi posted...

Sounds about right

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pistachio12 posted...

That question is poorly worded but I got different results as well. I'm getting 199 for the perimeter (35*2+(sqrt(35^2+54^2))*2) and 2252 for the area (35*sqrt(35^2+54^2)).

Also, I can see where you're coming from in this claim. Students have seen this problem before and know that we're cutting lengthwise using the diagonal of the 35x35 square side.

Thus the cross-section will be a rectangle with a length of 54 and a width of 35sqrt(2).

So the area is 54*35sqrt(2) = 2672.86 (rounded up to 2673) square inches

and the perimeter is 2*54 + 2*35sqrt(2) = 206.99 (rounded up to 207) inches

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LordFarquad1312 posted...

Not really, it's just a cilindre and half a sphere. You could solve it using integrals over a solid of revolution, but why complicate things?

To be fair my first thought was to integrate it lmao, and I was like god damn these kids are doing shit I learned in sophomore year of college

Didn't even think about just using the formulas for volume and area

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Gwynevere posted...

To be fair my first thought was to integrate it lmao, and I was like god damn these kids are doing shit I learned in sophomore year of college

While we're certainly not going to be learning integration, it is exposure to the concept of rotational solids. We talked about how a lathe, a pottery wheel, and glass blowing all are examples rotational solids. We also did an activity where we made different paper shapes (starting with basic ones and working up to complicated ones) and taped them to a pencil to rotate like an axis.

I really like this kind of geometry because it extends your previous knowledge of both 2D and 3D shapes, while also bridging the gap between them. There are many ways of making a 3D object from a 2D framework. Nets and rotational solids are just two of those examples.

We also talked a lot about how scaling an object in 3D affects its surface area and volume. Great stuff. Deeper than just slapping numbers into formulas 30 times on a worksheet.

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ZMythos posted...

Also, I can see where you're coming from in this claim. Students have seen this problem before and know that we're cutting lengthwise using the diagonal of the 35x35 square side.

I see now and with the cut on the diagonal lengthwise, I understand it now.

ZMythos posted...

With kids going in and out of quarantine still for COVID, I'm gonna ere on the side of flexible. The hard part is when you get one or two students who take advantage of that flexibility.

For sure. But always remember to set your expectations for the majority and not the minority.

ZMythos posted...

While we're certainly not going to be learning integration, it is exposure to the concept of rotational solids. We talked about how a lathe, a pottery wheel, and glass blowing all are examples rotational solids. We also did an activity where we made different paper shapes (starting with basic ones and working up to complicated ones) and taped them to a pencil to rotate like an axis.

I really like this kind of geometry because it extends your previous knowledge of both 2D and 3D shapes, while also bridging the gap between them. There are many ways of making a 3D object from a 2D framework. Nets and rotational solids are just two of those examples.

We also talked a lot about how scaling an object in 3D affects its surface area and volume. Great stuff. Deeper than just slapping numbers into formulas 30 times on a worksheet.

Damn man that's pretty cool, I feel like I would have really benefited from a math class like that in HS. It really was just pages of plug and chug when I went through it.

Kind of a miracle I had any interest in pursuing it after HS and made it to partial diff eq haha

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I'm curious if the wording on that question, "cut it lengthwise", is sufficient? Like, now that you explained I understand how to cut it, but is the way I thought not considered lengthwise? Is it "along the diagonal" instead or something?

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