- They're not there very long (usually less than an hour).
- Each student may or may not be interested in math and science.
- They usually have NO experience with engineering to build on.
And I have a good time, too. That's important, because doing this stuff better be fun; we certainly don't get any credit for doing it.
I've done this about five times now, and I've developed a comfortable rhythm that seems to work. It's not restricted to middle schoolers. I did it with my introduction to engineering students, requiring them to compute the balance points. I think you could do this with a statics class, too, requiring students to do calculations and make predictions. And I think you could do it as a team-building exercise with adults or older students. If you extend this or apply it in different situations, I'd really like to hear about it.
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Step 1: Materials
Shapes cut from foam core. You need at least one for each participant, but you might want to have 10%-20% more, so that participants feel they have a choice. For the aesthetic I enjoy, and to make them easily ahead of time, I cut geometric shapes with straight edges from black and white foam core. Other choices may have color on only one side, with white or black foam on the inside. If you have more time with the students, you might want to let them make their own shapes from whatever materials you provide. You don't even need to stay with two-dimensional shapes, but you do want to stay lightweight. Heavy items may be balanced, but they won't float or move in light breezes, and your horizontal members will need to be stronger. The shapes should have their largest dimension between 50% and 80% of the length of your short dowel sticks. Check the relationship of the thickness of the shapes and the small binder clips; the clips should hold the shapes securing without making big dents.
Short (12" - 14") dowel sticks. These should be fairly small, say 1/4" in diameter. You need one of these for every 2-3 participants. Check the relationship of the dowel sticks and the small binder clips; the clips should grasp the sticks securely without slipping.
Longer (30" - 36") dowel sticks. These could be slightly thicker than the short ones, but mine are the same diameter. I enjoy the light look of the longer, light sticks, but the long ones sometimes bend a bit if they are loaded near the ends. You need one of these for every 6-8 participants. Check the relationship of the dowel sticks and the small binder clips; the clips should grasp the sticks securely without slipping.
Long (8'-10') conduit. I used 1/2" pvc, but 3/8" emt seems like it would work. The metal might look better, but it's heavier, harder to hang, and more slippery. The PVC droops a little, but I think it's safer. You need one of these for 20-25 participants.
LOTS of binder clips that can securely hold your foam core and your dowels. Test your clips with the dowels to make sure they fit securely, large enough to fit but tight enough so they don't slip easily. You will need at least 4 times the number of shapes you plan to hang (which is also the number of participants).
SOME monster binder clips that are large enough to grasp your conduit. This is kinda tricky. They've gotta be big enough to fit but not loose enough that they slide on the conduit. The giant ones I used fit perfectly on the 1/2" PVC. You'll have to figure out exactly how many you'll use; you can fit 4-5 sets easily on one conduit, depending on the length of your long dowels.
Piles of paperclips.Lots and lots and lots of them.
index cards, if you want to include the "notebook" step.
A room with lots of vertical space. My lab has open metal rafters from which we could hang these creations.
Rope and pulleys and appropriate hardware to rig the conduit in your room so that they can be lowered to be loaded, and then lifted to be admired and displayed. You can manage with looping the line over a rafter, but if you're going to do this repeatedly, think about a quasi-permanent rigging. Pulleys are expensive, but the smooth motion really helps in lifting the creations up for admiration, and for adjusting them if the space is used for other activities while the displays are up. After the first two times I did this activity, I was confident enough that we'd do it again that we mounted three of them in a lab. Six pulleys, 150' of line, cleats and miscellaneous mounting hardware cost about $60.
Spending a couple of hours on ladders figuring out where to put the pulleys and the cleats was a bit of a pain, but having it all set up felt great when 50 middle school visitors arrived with their teachers and parents.
computer and projector if you want to include the Calder mini-lecture
Step 2: Welcome and Introductions
When the students arrive, I group them around tables so that each person has some work space, and so they are in groups of 6-8. Put coats and lunches and backpacks out of the way. I introduce myself and my helpers, and say something about their town or their team or recognize where they're coming from in some way.
I ask if they've ever been in engineering class. Probably not. But they have had art classes. Then I talk a bit about how engineers and artists do very similar things: we work with stuff, and we make things that have never existed before. We often work in groups to do large projects. We try things, see what works and what doesn't, and we make adjustments. We keep notebooks and records of what we do. We sketch and experiment. Usually there are lots of "right" answers to any problem we're working on, and we spend a lot of our time designing. And all that is what we're going to do together in this activity.
If you want to include the note-making part of this activity, have each student put his or her name on a card, along with the date, just like engineers and artists do.
Step 3: Balance Your Shape So That One Edge Is Horizontal
The first challenge: choose one of the shapes, and hang it so that one edge, either the top or the bottom, is horizontal (confirm that everyone knows what horizontal means). Hang your shape from a chain of 2-3 paperclips, connecting the shape and the chain with a small binder clip. You can test how horizontal a bottom edge is by lowering it to the table top. You can test how horizontal a top edge is by comparing it to the edge of the table.
In this challenge, everyone is active, and everyone is learning basic skills and patterns that are needed and repeated throughout the activity.
If it's not balanced so that one edge is horizontal, you need to move the clip on the shape, right? In what direction? Try one, and see if that change makes the situation better. If it does, cool. Keep adjusting, maybe making smaller changes. If it makes things worse, change back in the other direction.
Can you see why it changes that way?
Get everyone so that they are dangling shapes with horizontal edges. Look around and admire and adjust.
notebook step (optional-requires index cards)
Put your name on the lined side of an index card, and then sketch your solution to the challenge on the unlined side. Both engineers and artists sketch, and they keep records of what they do, especially if they did a lot of experimentation to figure it out.
Step 4: Balance Your Shape So That Another Edge Is Horizontal.
So, now that you've got it dangling with a nice horizontal edge, choose another edge and make it horizontal, either at the top or the bottom.
And sketch that solution.
If someone near you is having trouble, see if you can help without touching their shape.
See how the same challenge has different solutions, even with the exact same shape?
See how many different solutions we have as a group?
Step 5: Pairing Up Shapes
Now each pair has a new challenge: balance your two shapes on this new dowel so that the new dowel can hang horizontally from a chain of clips and so the two shapes do not interfere or touch as they move. This means getting more clips, and making another chain.
- you don't need to change anything about your shape and how it's connected to its chain.
- you can adjust where you place the two original shapes OR where you hang the dowel.
- you might need to shorten or lengthen the chains between the shapes and the dowel to keep the shapes from touching each other as they move.
See how may different ways there are to do this?
Step 6: A Calder Interlude (optional)
If you want to share some images and information about Calder, or anything else in this activity, this is a good spot for a break. The students should carefully put their balanced shapes down on the table and assemble around the projector for some pictures.
The slide show I use is built around this long quote from Calder:
" On Making Mobiles
I used to begin with fairly complete drawings, but now I start by cutting out a lot of shapes .... Some I keep because they're pleasing or dynamic. Some are bits I just happen to find.
Then I arrange them, like paper collage, on a table, and "paint" them -- that is, arrange them, with wires between the pieces if it's to be a mobile, for the overall pattern. Finally I cut some more of them with my shears, calculating for balance this time.
I begin at the small ends, then balance in progression until I think I've found the point of support. This is crucial, as there is only one such point and it must be right if the object is to hang or pivot freely.
I usually test out this point with strings to make sure before bending the wires. The size and angle of the shapes and how to use them is a matter of taste and what you have in mind.
To most people who look at a mobile, it's no more than a series of flat objects that move. To a few, though, it may be poetry."
- Alexander Calder
Step 7: Combining Pairs Into Small Mobiles
When the students return to their work spaces, give each group of 4 or 6 a single longer dowel. Challenge the group to balance two or three pairs of shapes on that dowel so that the dowel is horizontal and so that the shapes don't touch each other. This might mean lengthening or shortening the chains of paper clips, but it should not require changing the balance points of each pair very much.
At this point, we have have some pretty impressive mobiles, and we spend some time admiring them and noticing how much variety there is. But these are just the starting point ...
Step 8: Making It Magnificent
Now it's time to lower the conduit from the rafters, challenging the entire group to combine all the mobiles made so far into one really big one. It's also time to bring out the monster binder clips, which are nearly as impressive to the middle schoolers as the idea of making mobiles as big as Calder's.
The goal of this step is to place all the mobiles on the one conduit so that it remains horizontal and there are no collisions. The group may have some ideas about how to arrange the mobiles, and how to do the assembly process. Let those ideas bubble out, and proceed gently. It takes some care to make all the adjustments, and some kids are more interested in this than others.
Once the biggest mobile is constructed, raise it a bit so it can be properly admired. Take some time at this step, and ask each person to think of a single word that describes some portion of the work you've all just completed. Go slowly around the room, and ask each person to share their word. Allow duplications.
Step 9: An Academic Extension
I've used this with college students as well as with middle schoolers.
In an intro to engineering class, this is a real but fun example of torque and a simple statics example.
I require them to actually compute the balance point for the two shapes on a stick and predict it before actually trying to balance them.
Then they have to comment on what differences they find, and how they responded to any problems they encountered.
Here is one student's lab report on that experience.
Notice that this requires the addition of a scale, and perhaps some calculators (phones will do) to the supply list.