3-D Printing in My Classroom -- Project #1

Background

Our story begins one day two years ago when I wandered by our tech office and noticed that there were a couple of 3-D printers sitting on a table.  They had been donated to the school, but it wasn't clear how we were going to use them.  "Hmmmm," I thought.

I knew that I could find a use for them in my classroom, but I wanted it to support and extend what I was doing, rather than simply be a cool thing I was using -- there needed to be mathematical substance.  After some investigation, I decided that the right tool was Mathematica.  If the goal was to design 3D objects to print, it would make sense to use one of the CAD programs that would allow students to simply draw lines and circles by clicking and dragging.  Mathematica demanded that they have equations for every line and curve they use.

The school was kind enough to purchase me a copy of Mathematica so I could figure out how to use it.  So I spent the summer of 2016 playing with the program and the printer.  At first I spent a lot of time with calculus ideas, in particular printing solids of known cross-section. Much of my time was spent making a 3-D "Match the Solid" activity for AP Calculus.  The result was cool and different, but I'm not sure it was worth the time that it took.  Unless you factor in the fun I had -- then it was totally worth it.

The next step was to do something with students.  I decided that my Algebra 2 - Honors class was a fine set of guinea pigs.  For some reason, I've always been intrigued by magnets, especially those little powerful ones that can hold up a hammer and such.  I purchased a bunch of small ones, and the project that I had my class do was to make a refrigerator magnet based on an original 3-D design.  (It's a school assignment that was built to go on the refrigerator!  How meta.)

Some of the magnet projects

I only had the one copy of Mathematica, so I showed my class how the coding worked, and had them write the code in a word processor and then e-mail it to me.  There was a little awkwardness to this, but it did require them to really focus on their equations and with Desmos as a tool, it didn't hinder them too much.  It also removed the technical "missed comma" type of error from their experience.  The downside, of course, is that my experience was all about missed commas and such.  Still, it worked out well.  Some students sat at my computer to tinker with their equations, and all were able to produce something they were proud of.  Some designs were relatively simple, using mostly lines; others were more complicated, involving circles that changed radius depending on the z-coordinate (see the Christmas tree).  It was a good review of lines, absolute value functions, circles and parabolas.  The students were proud of their work, and had something tangible to take from it.

Our chess set in action.

A cat.  Notice the trig tail.

Later in the year I decided to do a second trial run with my AP Calculus class.  In that awkward period after the exam and before graduation (about 3 weeks at our school), I had my students download a 10-day trial of Mathematica.  When I explained what we were going to do, one of the students suggested that we make a chess set.  The students divided up the pieces, and went to work.  You can see the rendered pieces in the columns on the sides of this blog.  The printed pieces live in the lobby of our schoolhouse.

I had the good fortune of sitting in on one of Professor David Bachmann's classes at Pitzer College last March.  He was using Mathematica to have students explore parametric equations, and introduced me to a book that any math/foodie should have -- Pasta By Design.  I showed this to my class this year, and one student said that he is glad to live in a world where a book like this exists.


After doing these projects last year, I wanted my Algebra 2 students to have access to Mathematica.  Research and some negotiation with Wolfram landed on a price of about $2000 per year for enough licenses for my students.  Ouch.  I'm fortunate to work at a school with the resources to support these kinds of things, and my proposal to our business manager was approved.

Project #1

I decided to start simple.  We typically do a review of graphing lines at the start of the year, so I integrated that unit with an introduction to Mathematica.

We began on Desmos, and students were asked to draw a square using a set of inequalities.  Then we moved into Mathematica, where I showed them how to use the function we'll be using most:  RegionPlot3D.  Student plotted the same equations from the Desmos square into Mathematica, and saw that it created a square-based box that went from one end of their window to the other.  In order to make a cube, we needed to add restrictions to the z-axis.  I showed them how to make a second object using the "or" command (|| in Mathematica), and then they were on their own to complete five challenge objects that I'd created (an approach I saw Professor Bachman use.) 

It was then that I knew I was onto something good.  I started to hear things that I love to hear in the classroom:
"Aaaargh!" followed by "I got it!!"
An involuntary "Yesssss!!"
"I did it! I did it!" 
Student to another student:  "Help me!"
And so on.

I loved the instant non-judgemental feedback that technology can offer -- "Why is my object not there?"  (Experienced teacher guess:  "You have one of your inequalities going in the wrong direction.")  Some students were more frustrated that I would have liked, but they all found a way out of the woods and were ultimately successful, even if they didn't get through all five objects.  Their homework assignment was to make an object with only boxes. 

A few days later, as the last question on a quiz on equations of lines, I asked them to determine what the following equations would produce if graphed in three dimensions:

y < x + 5, y < -x + 5, y < z + 5, y < -z + 5, y > 0.

About half of them figured it out, and others were close.  After the quiz, I gave them an information sheet on the Great Pyramid of Giza and challenged them to render it in 3D.  A few students were able to complete the pyramid (more shouts of "I did it!"), but there wasn't time in the period for everyone to get there.  We did talk about it at the start of the next class, but we needed to move on to other (non 3-D) things.

Now it was time for project #1:   Make an object using lines.
Your object should:
1)  Use only linear equations
2)  Use equations in all three directions (x, y and z), beyond just adding "thickness" or "length"
3)  Have at least two parts connected by an "or" (||) in your code.
4)  Have comments in the code, including indications of what each part of the code describes.  (*comment*)
 I also gave them a grading rubric for the project.

Creative projects always create a dilemma for me.  There are always some students that will create something remarkable, but this can be a mixed blessing for the group.  Seeing someone else's excellent work can inspire or discourage, and it's sometimes a fine line between the two.  So I tried to keep expectations reasonable when I spoke about the project, knowing that my goal was to get each student to push themselves to do something great, and that the results might vary from student to student.

The x-wing code.

I gave them two weeks to do the project, which was plenty of time.  About four days after I gave the assignment, I received my first submission:  an X-wing fighter.  It looked awesome, used close to 70 equations (all lines), utilized the NOT function that I'd mentioned briefly in class, and demonstrated real passion and persistence on the part of the student.  As pleased and excited as I was, I chose not to print the X-wing until the other projects were finished, so as to limit the intimidation factor.

As students continued to work and completed their projects, I heard more of those things you love to hear:
"I made this!"
"I'm really proud of this!"
"I could have done even more."

The printed results looked great, and the students were excited to be able to hold their creations and to see what everyone else had done.

A sampling:

A man.

A chair.

A ping-pong table.

An "N".

A star.

A house.

The porch on the back of the house.

Initials.

 

Conclusion and Future Adjustments

Simply:  This is good stuff.  Students were challenged by the task and lived up to the challenge.  The task was open-ended enough that it had room for a chair and an x-wing fighter.  It was a good review of the graphing of lines.  There was also some friendly and quiet competitiveness that had some students realizing that they could have done more.  I hope this will carry over into the next project.

Some future adjustments:

1) My initial challenge objects need to be more interesting.

2)  I want to make sure every student gets through the pyramid rendering -- in retrospect, it would have been valuable practice.  I had also planned to follow up with having students render the Washington Monument from the dimensions of the monument.  This would have been useful too.

3)  Next time, I will emphasize and have students practice the NOT command.  (This allowed for the windows in the building, for example.)  This will add to the creativity and also add some good logical challenges to the process.

4)  Next time, I will require at least one set of perpendicular lines that are not horizontal-vertical.  This would be good practice for that skill.  I thought of this when the student who made the desk told me that he was thinking of putting a notebook at a diagonal on the top of the desk, but he ran out of time.

5)  I wonder if there's value in narrowing the assignment somewhat.  Since many students did furniture, one student suggested that we make a class IKEA-type catalog.  Another student suggested a hanging mobile with all the objects.  I had initially considered creating a small village, which would allow for buildings, vehicles, etc.

Next Projects

As we move into quadratics and other conics, the possibility for even more interesting designs increases.  A few possibilities:

1)  Refrigerator magnets.

2)  Make a game piece that you can use during our unit on probability.  (I also think I'd like to create a culture where people carry their own game pieces with them.  For example, you're at a friend's house and you're going to play Monopoly.  "Do you want to be the hat?" she asks.  "Don't worry, I've got it covered," you replay as you pull out your own personally designed token.  I'm sorry I didn't think of this when my children were little.  I would have raised them differently.)

3)  Design an animal head and/or body.  Print them separately, and then we can mix-and-match among the class (with carefully placed magnets in the neck area.)  Cool.

4)  It occurred to me that we could learn how to (for example) change the radius of a circle depending on the z-coordinate using sliders in Desmos.  Extending that, can you do the same with an equilateral triangle?  What about a star?


The Bottom Line
So far, so good.  The students are engaged, they feel like they are doing something new, unusual, challenging and accessible.  My job is to keep it that way.

If you've read this far, thanks!  Please offer any suggestions you've got.