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Copyright © 2010-3 Joseph Mack
23 Mar 2013, released under GPL-v3.
A video of a lesson on the Platonic solids, given to 3rd graders, about May 2009.
Material/images from this webpage may be used, as long as credit is given to the author, and the url of this webpage is included as a reference.
Table of Contents
Since about 2002, the science teacher at my son's school, Lyn Streck, has let me teach a science class to her 3rd graders. There's four classes in the grade and I give all lessons in one day.
The students cut out and assemble the NOAA Surface of the Earth Icosahedron Globe (http://www.ngdc.noaa.gov/mgg/fliers/04mgg02.html).
The maps are low cost ($0.50 ea), and printed on cardstock making a nice finished globe (I have them on my desk at work and home).
|You can download a pdf of the maps and print them yourself, but you'll need a large format printer, lots of ink and your own cardstock. It's cheaper and more convenient to buy them from NOAA.|
A new version (2008) of the map has press out tabs, which I haven't used (I've been using the ones which need cutting out). With the older version of the maps each student needs
The class is 40mins and can only just be done in the time. The instructions are relatively complicated, and the cutting takes time. Adults need to be on hand to help the kids. Despite my best attempts to give clear directions, some student will wind up cutting off the flanges (tabs) and others turn their scissors around and cut from the inside out, gouging the map (see the video for directions). Following a large mistake, there isn't time to start again, and an adult will have to handle patching the globe. You want every kid to walk out with a functional globe. The last part of the taping (closing the globe) is tricky and usually has to be done by an adult.
Besides building the icosahedral globe, other material covered in the class is
trusses (since the icosahedron is made of triangles).
The tetrahedron, octahedron and icosahedron have triangular faces and are rigid, when you press on them. The cube (hexahedron, with square faces) and the dodecahedron (pentagonal faces) are floppy. Early in the class I ask the kids if they can figure out why some of the Platonic solids are rigid and some floppy. I encourage them try out the models themselves during the class and, if they have an answer, to let me know quietly (so not to let the cat out of the bag to the rest of the class). About half the time, some student figures it out (or already knows, I can't tell which).
The trusses and the earlier versions of the Platonic solids were made from toothpicks and hot glue. These took several sunday afternoons. (Buy your toothpicks all at once; toothpicks bought a year later, at the same store, in the same type of box, were a different length.)
One problem was convincing the students that some of the solids were intrinsically rigid and some were instrinsically floppy. With the glue providing some rigidity at the vertices, the usual answer was that the rigid solids had more glue. While the kids saw the glue providing rigidity, they wouldn't look further to structural elements as the answer. My first approach was to tell them that it wasn't the glue. Quite reasonably kids don't trust adults, who are in charge, make arbitary rules and can make a kid's answer wrong any time they want. It took several years before seeing the futility of this approach. I needed models with demonstrably floppy vertices. This led to the models with rubber tubing vertices. Since I've added these models, students have stopped proposing glue as the agent of rigidity.
By the wonders of digital editing, on combining videos from four different classes, the students give correct answers to all the questions.
Errata. A volunteer at the school kindly edited the videos of the four classes for me in their spare time and I wasn't able to get the following fixed.
There is some duplication of material; the same part of the talk from different classes appears more than once. A virus not mentioned in the talk is HPV.
With only a few minutes at the end for the kids to explore trusses and their globe, an extra 5 mins, if you can find it, can make or break the class. In 2011 I made these changes to the class
At the suggestion of the teacher's assistant, I precut the cardboard sheets (paper cutter/guillotine; a sharp one helps) removing extraneous cardboard and separating the legend and base from the map. This eliminated the first cutting step for the kids.
Several stages of checking are required (cut out, fold along all the black lines) so that the final map folds to a globe. Previously when the first student was ready, I stopped the class and demonstrated the next stage to everyone. However the kids are busy with their efforts and don't have attention for much else and they can't listen.
This is particularly so when the first student reaches the last stage - applying the double sided sticky tape - at which time some students are still back two stages - cutting out. I would have to repeat the taping instructions individually to confused students a few minutes later as they reached the taping stage. Instead, in 2011, as student(s) were ready, I showed them individually how to apply the tape. The tape and the to-be-taped globe were right infront of the students, who could see exactly how I did it. Initially only the first student was ready, then a group of four more students were ready... Using this approach, few students had to return for clarification, reducing the time on this step.
With these changes, after assembling their globes, the students had time to gather around the rubber and drinking straw platonic solids, to figure out why some were rigid. Talking and poking, they collectively figured it out and when I asked for the answer, they all knew it was triangles. Over the previous 10yrs of this class, only a couple of times has a student figured out the answer. I'd concluded that the problem was too difficult for them, when all that was missing was a few minutes poking the platonic solids.
I then had about 5 extra minutes at the end of the class to talk about the trusses and explore oceanic trenches and the location of mountain ranges on their globe. You still have about 1/4 of the class with uncompleted globes, which are handled by the adults, while you're talking.
In 2008 a new version of the map was released. No cutting is required. The map presses out by hand from the cardboard sheet. The tabs fit into precut slots in the cardboard. Like the first version of the map, an adult can make this into a perfect globe in relatively short time. I had plenty of the v1 maps and didn't start using the v2 maps till 2013.
After a little folding of the edges, the map can almost be assembled into a recognisable globe. Unfortunately it springs apart in your hands. I tried a rubber band around a diameter, but the globe collapses. I expect you need 3 not-too-tight rubber bands placed symmetrically to make this work. Thus sticky tape is still required.
With the new globe, the tab in the middle of each flange is required (in the first version, I cut it off). If you use the old method, of double sided sticky tape to seal the flange to the inside of the globe, then each flange requires the positioning of two half sized pieces of double sided sticky tape. The dexterity required is difficult and is OK for an adult with plenty of time, but with 3rd graders under the gun to finish on time, this doesn't work.
Instead, for the initial joins, I used low precision placement of single sided sticky tape on the inside of the globe, covering the tab. I start joining at one end of the unfolded map (as was done for the previous version of the map) interlocking the pair of edges with the tab. The placement of the tape in the inside is quite uncritical - almost anything that holds the globe together will do. You can tape along or across the join of the edges.
At the end you are left with 3 pairs of edges to join, rather than just one. As well the three pairs of edges each have a tab in the middle. If you want no tape showing, you need 6 pieces of double sided sticky tape. Each of these is inserted, after first slightly prying open each of the 6 gaps, to insert a piece of double sided sticky tape on the blade of a small screwdriver. This is OK for adults, but doesn't fly for kids in a class. We just used single sided tape on the outside of all 3 joins.
In the previous version of the map, I had the students cut off the square tabs. Each pair of edges was joined by a single piece of double sided sticky tape. At the last step, an adult handled the final pair of edges. You squeezed the globe (or pried open the final pair of edges) so that the edges opened slightly like a mouth. A piece of double sided sticky tape was inserted into the gap on a not-too-sticky flat object, like a small screwdriver, letter opener, or one blade of a pair of scissors. The tape was pushed hard against the cardboard on the inside of one of the edges, where it would stick, allowing the flat blade to be carefully withdrawn, leaving the double sided tape stuck to the cardboard. You then allow the globe to unpucker, when the two edges meet and stick. A bit of massaging of the join from the outside, with your fingers, forms a reasonable seal.
With the v1 map, to save time, I precut the maps, removing the main extraneous carboard. With the v2 map, popping out the map is simple for an adult, if you've done is a couple of dozen times, but it's new to the kids and they're interested in how it all works. I found the new maps went slower than the old maps, so I pre-popped-out the base and legend, leaving them attached at one or two points, so they didn't separate from the main piece of cardboard. I also pre-popped half of the map (leaving some for the kids, since it's fun.)
The slot is not a 1-D cut. To help get the flange into the slot, the cut is a 3 sided rectangle, so that you can lift a flap to insert the tab. If you then push the tab all the way in, rather than matching up the color edges, then there isn't enough room to close the icosahedron at the end. You have to cut bits of the icosahedron to close it. The resulting icosahedron isn't symmetrical. I couldn't think of a way of telling them to line up the colors exactly.
One of the problems I had was that the kids didn't know how to join the edges. It's obvious to an adult the the flanges and tabs go inside the globe, but it wasn't to the kids. Since I had adult help, it took me a few classes to notice that many of the kids were joining the maps with the tabs facing outwards. For the last class, I had the kids do the base (which has one tab-slot pair) first, rather than last, so I could check that the tabs were folded inwards. Despite my excruciatingle clear explanation, holding the circularised base up to show all the kids, and showing that the tab was inside and putting the tape on the inside, and telling the kids to check with me if they weren't sure what they were doing, almost half the kids had the tabs pointed outwards and taped down so I couldn't easily undo them without tearing. This is no better than random and indicates that my explanation was no better than no explanation at all. I'll have to do something different next year.
Is the new version better? Most of the students don't do a great job of cutting, so the resulting globe from the early version, isn't particularly symmetrical and the colors don't match up well across joins. This problem is gone with the new version. However at the last step in the assembly, there's a lot for the adults to do. The class is finished a few minutes early, which helps. I'd say it was a step sideways but what you've exchanged is different for adults and kids.
Suggestions: The map needs to be tested on kids. (Adults can stand in for kids in the early rounds of testing.) The students have a lot of trouble getting the tab into the slot, particularly when closing the sphere, since the sphere isn't symmetrical and the tab and the slot no longer line up. A pointed, rather than square, tab would help get miss-aligned tabs into the slot. It would be nice to have a sphere that can be assembled without sticky tape. The tabs could be non reversible - e.g. have an "L" shape that catches on the inside of the slot, using the natural spring of the cardboard.
The 240 piece icosahedral jigsaw globe of the earth, seen in the video, comes in 3 versions, with 240, 560 and 960 pieces (search in the internet with "3-D puzzle of the world" or "icosahedral puzzle globe of the earth"). Presumably they're all icosahedrons. An icosahedral globe will have multiples of 20 pieces (4-fold as for my 80 faced toothpick icosahedron as seen in the video, or 3-fold as seen for the 60 subunit capsids of icosahedral viruses).
I have no vested interest in the use of these maps. I like maps and bought a few of these to decorate home and work, several years before I met Lyn. I think everyone should get a chance to build one of these.
|To myself for 2014: I have left everything with Lyn (240 piece zig-saw icosahedron and 80 piece toothpick icosahedron). I have the maps and repair pieces.|
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