## Thursday, January 19, 2012

### Project Spiky Door

Ever since Riley and I had this exchange, I've been dissatisfied with my classroom's plain door that is not covered in spikes. Well, like, lo:

This took three days of class time (129 minutes) for a non-honors Geometry class of almost all tenth graders. Many students also needed some additional time outside of class. The goal was for students to get hands-on grokking for the meanings of height, slant height, surface area, and volume. They designed the net of a pyramid and labeled dimensions, calculated the total surface area and volume of their design, and constructed and decorated the model.

I offered a bonus for a base that was not a square. I also suggested making a cone instead, but none of them chose to make a cone, so next time I should make the cone worth a bonus as well. I specified a target range for the area of the base, and a target range for the volume, mostly so that the door would look cool.

Here is the project description and scoring sheet.

In order to make grading less ultimately-annoying, since they were given lots of flexibility in choosing measurements, I programmed my TI to do calculations for me (link goes to TI-Nspire .tns file.) The vast majority made a square pyramid, and just about every student first decided on the length of a base edge and the slant height, and went from there, so the program takes these measurements as inputs, and returns all the other values they were supposed to calculate. This way, if their numbers match my numbers, I can just move on, and only have to spend more time inspecting their work if there is a discrepancy.

Here is an example of what a student turned in. Since they had to organize their work, I had to say things like "Label EVERYTHING! Make it REALLY EASY for me to grade! I am VERY LAZY and I DON'T CARE if you get a good grade!" That sounds awful but it's funny only because they know neither of those things are true. It would be easier to grade these if you gave them like a template where they had to fill in stuff, but I think there's a ton of value in them deciding how to present their work sometimes. This is hard for me to explain, but when they are in filling-in-blanks mode it's different from figuring-stuff-out mode.

This was pretty fun and a nice break from the usual. I believe the goal of reliably distinguishing both slant height from height, and volume from surface area was achieved. And my door is looking pretty badass. I'd do this again.

Shoulders this project stands on:
Mimi
Riley

pshircliff said...

i gave mine 12 nets like these and they are coloring, measuring, folding, and calculating SA & V..2 days so far...no one is done yet

Dan Anderson said...

"It would be easier to grade these if you gave them like a template where they had to fill in stuff, but I think there's a ton of value in them deciding how to present their work sometimes. This is hard for me to explain, but when they are in filling-in-blanks mode it's different from figuring-stuff-out mode."
DEAD ON. I'm a huge believer in the *students* figuring out what to present, and how to do so. In grad school speak, this detail bumps the student up several notches on the Bloom's taxonomy pyramid (do you see what I did there?).

Mimi said...

Beautiful!

NancyTrent said...

I do something similar to this but make a cylinder instead with radius is month born in cm...September is 9cm and height is day of Month born in cm... I then generated a spreadsheet with both surface area and volume to make it easier to grade. . Gave extra credit for cone that matched height with same base.
We also extended project by comparing dimensions that were doubled like Feb 4th to April 4th and then to April 8th. To their surface area and volume.

Kate Nowak said...

Those are some cool variations Nancy. Thanks.

ClassProf said...

Kate, great post.
I'm with Dan - you are so right that students learn more when they have to figure out the details of the solution for themselves.
Your students no doubt are proud of their creations and how they contribute to your "badass door".
Great stuff.

Bowman Dickson said...

love it! i think i'm teaching geo next year, so i'm going to be coming back to the f(t) archives to do some major thievery. thanks for sharing

Kate Nowak said...

Thievery is a teaching core competency! That's why it's here. Consider it a payment on all your calculus lessons.

Mr. Patrick said...

Kate - this is a project right up my alley.

I would suggest one more thing - getting access to Google Sketch-Up as a tool for the design. Sketch-Up might make it an "easy way out" - but it will get you a kid going for the gold. About six clicks and bam! design more a 3 - 99 and higher sided polygon.

No idea about the cone though.

--Mr. Patrick

Fawn Nguyen said...

I've done these but never thought to stick them on the door like this -- how cool is your door! How are they sticking, by the way? We're in southern CA, meaning our classrooms doors face the elements. Thanks for another great post, Kate!

Kate Nowak said...

Maybe you could stick them to a bulletin board. Or the ceiling? I just stuck them on with a few curls of scotch tape. Looked cool while it lasted. :)

TRT said...

@NancyTrent
Good idea! Have you ever proved with birthday produces the cone with the largest volume or surface area?

Emily Hughes said...

Hi, LOVE the idea!
I'm in the middle of collating a bunch of rich tasks for maths classes, which will be free to all via pdf and iBooks when it's done: http://ilovemathsgames.wordpress.com/2012/03/11/rich-tasks-or-being-less-helpful-4/
Would you mind if I used the general idea (and picture) from this blog in it?
Not sure where else I'll find such an awesomely spiky picture... ;)

MathBruin said...

Tried your project! Found it online Thanks!

PS I made it a group project and each group had to have 4 different bases for their pyramids. Took us two days.