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Video: The Platonic Solids and Assembling the NOAA Icosahedral Map of the Earth

Joseph Mack

jmack (at) wm7d (dot) net
AustinTek home page

25 Mar 2016, released under GPL-v3.

Abstract

A video of a lesson on the Platonic solids, given to 3rd graders, 29 Apr 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

1. The Platonic Solids, Assembling an Icosahedral Globe of the Earth
2. The Video
3. Speeding up the class
4. 2008: new version of the map (v2)
5. miscellaneous
6. Detailed class notes
6.1. Goal
6.2. Introduce Platonic Solids
6.3. Introduce them to Viruses
6.4. Globe
6.5. Trusses
6.6. Smoother Spheres
6.7. Question Time
6.8. Materials
6.9. Setup, day before

1. The Platonic Solids, Assembling an Icosahedral Globe of the Earth

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).

Note
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 of the map (released in 2008, here called v2 globe) has press out tabs. In the video I'm using the old version, v1, which needs cutting out. I didn't start using v2 till 2013, when my stock of v1 maps ran out. With the v1 globe each student needs

  • a map
  • scissors
  • a table with a square edge
  • double sided sticky tape

The class is 40mins and can only just be done in the time. The instructions for assembling the globe 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 cut off the flanges (tabs), while 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

  • the Platonic Solids (http://en.wikipedia.org/wiki/Platonic_solid).
  • viruses (since some have icosahedral capsids)
  • trusses (since the icosahedron is made of triangles).

    The tetrahedron, octahedron and icosahedron have triangular faces and are rigid (when you try to deform the sides). 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. For the first 10 years, I encouraged 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). As I discovered accidentally in 2011 (see below), the problem was that I wasn't giving the kids enough time to play with the models.

    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 I saw the futility of expecting them to believe me. I needed models with demonstrably floppy vertices. This led to the models with rubber tubing vertices in the video. Since I've added these models, students have stopped proposing glue as the agent of rigidity.

    The kids, when inspecting the platonic solids, were breaking the relatively fragile toothpick and glue models. In 2015, after displaying the toothpick and glue models in the front row, I moved them behind the more resilent rubber tubing and drinking straw models, and let the kids play with the more resilient models.

    With about 30 models arrayed on various tables, one student asked in amazement if I'd made all of them. I said "yes, and it was great fun".

  • using the colours on the globe as a guide, locate and discuss high (mountains) and low places (oceanic trenches) on earth. This reinforces mountain building and plate tectonics, which they've had in class.

2. The Video

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.

  • a screen shows bacteria causing plague; they cause plaque.
  • The coloured scale showing elevation is a legend, not a ledger.

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.

3. Speeding up the class

(There is not enough time in class to refer to these notes; you have to know the material off by heart.) 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.

  • I had held off putting out the maps until the kids were ready to start building the globes. I had expected the kids would be distracted by the map and not pay attention to my explanation of the platonic solids. However stopping the class to hand out the maps adds time to the class. In 2015 I put out the maps before the class, and first thing acquainted the kids with the maps by having them put their name on some blue spot (ocean) with marker pen. This seemed to give them time to satisfy their curiosity about the maps and they were happy to pay attention to my discussion about the platonic solids.

  • First I have them make the stand. This requires them to put the tab in from the outside, align the colours, so that the white is just not showing. I tell them to show me their stand before putting the tape on. In 2015, in the first class, despite holding up a sample and showing them how to put the tab in from the outside, half of them got it wrong (==random), which means that none of them were listening. Next class I emphasised that they had to show me that they'd got it right before taping otherwise the next part of the globe would not work. By the last class of the day, I'd emphasised it enough that they'd all showed showed me the correct insertion before taping.

  • I found that none of the kids knew how to tear off a piece of tape. This must have been the first time they've ever used a tape dispenser. They pulled the tape down straight, rather than tearing from one corner. This required enormous force for success. I wasn't prepared for this and didn't know how to handle it. The next year, in the preparation part, I showed them how to tear off tape.

  • I told the kids to only tear off a piece of tape long enough to just cover the tab (1cm). Instead they tore off a piece about 4cm long. I let this go.

  • Several stages of checking are required (cut out, fold along all the black lines) so that the final map folds to a globe. At time time I did the video, as soon as the first student was ready, I stopped the whole class and demonstrated the next stage to everyone. However the kids are busy with their efforts and quite reasonably 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. This didn't work.

    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 few minutes later, a group of four more students were ready... Although this method required me to be in a constant frenzy, repeatedly explaining the next step to whichever student was in front of me, 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 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; these are handled by the adults, while you're talking.

In 2016 following a disasterous first class, when the kids barely completed the globes, and we didn't get to talk about trusses, I made the following changes.

  • Pre-popped out the maps, stand and legend, and discarded the rest of the cardboard. When the kids arrive in class, they see only the popped out pieces of cardboard.
  • The kids need 12 pieces of tape, if they get it right. The kids don't know how to use a tape dispenser. For the last 15yrs or so, I've been letting the kids pick up the tape dispenser and tear off the tape each time they needed tape. This requires them to put the globe down and pick up the dispenser and then when they have the tape, pick up the globe again. Despite my instructions to only pull off a piece of tape as long as their thumb, the kids routinely pull off long pieces of tape. I expect they don't have the dexterity to pull off a short piece of tape. In 2016, one of the assistants (Miss Connie), suggested that 15 short pieces of tape be pre-dispensed and attached to the edge of the table, with enough tape hanging over the edge for the kids to pick up the tape. What goes wrong is that the kids in idle time, push the freehanging end of the tape down onto the table, or else brush up against the tape, pushing it onto the table. We evetually put the tape on the side of the table where the kids would not brush up against it and at the beginning of the class, asked the kids not to push the tape down - the ends are there so they can life the tape off easily.
  • As the globe is closed up, it is harder for the kids to put their smaller fingers into the globe to put the tape on top of the tab. Previously I've had the adults help with this. This time I said that if they couldn't reach inside, to put the tape on the outside. In the time allowed for the class, the last three joins, which close up the globe, have to be done by an adult, for almost all the kids. One or two kids in the day (of 74 kids) managed to put tape inside for the 2 rows of 5 tabs, and close up the last three tabs with tape on the outside, without any help from adults.

4. 2008: new version of the map (v2)

In 2008 a new version of the map (here called v2) was released. (I had plenty of the v1 maps and didn't start using the v2 maps till 2013). With the v2 map, 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 v1 map, an adult can make the v2 into a perfect globe in relatively short time. With the v2 map (like the v1 map) the kids, particularly under the gun of time, need adult help.

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 v2 globe, the tab in the middle of each flange is required (for v1, I cut it off). If you use the v1 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 OK for an adult with plenty of time, but is beyond 3rd graders, under the gun to finish on time.

For the v2 globe:

  • Have the kids pre-cut off about 15 1cm long pieces of tape and touch them to the table (so they can be easily lifted off later). It's too hard to flip between taping the map and cutting off tape from the dispenser.
  • The adults need boxcutters to lift off misplaced tape.
  • There are two types of joins: the initial joins along the top and bottom (2 x 5 tabs) and the three final joins to close the globe.
  • Initial joins:

    There are two rows of tabs to tape down; top and bottom. Pick one row and then start taping from one end to the other interlocking the pair of edges with the tab Do not start taping in the middle; it's hard to get your hand in to insert the tape.

    Insert the tab (from the outside), carefully line up the colours on the maps, so the white cardboard underneath just disappears. Alignment of the edges (using the colours on the outside) is critical, or you can't close the globe. (You won't find this out till the end. If the globe doesn't close well, an adult has to cut pieces out of the globe.) Once the edges are aligned, put a piece of tape lightly on the tab (inside of the globe). Check that the map join is placed correctly. If you want to change it, an adult can lift the tape off the inside of the globe with a boxcutter, and the kid can do it again. If the alignement looks right, press the tape hard between your fingers.

    As you work along the top/bottom, you'll find that accessing the inside of the globe needs longer fingers or more dexterity than the kids may have.

    While the alignement of the colours at the edges of the join is critical, the placement of the tape in the inside is not; almost anything that holds the globe together will do. You can tape along or across the join of the edges.

    Once you've done the top, invert the globe and start on the bottom, taping from the end.

  • Final joins

    At the end you are left with 3 pairs of edges to join As well the three pairs of edges each have a tab in the middle. For almost everyone in the class, an adult will have to join these edges. We just used single sided tape on the outside of all 3 joins. It doesn't look great, but the kids get the class done in time.

    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 time limited class.

In the v1 globe, 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, once you've done is a couple of dozen times, but it's new to the kids and naturally they're interested in how everything works. I found the v2 maps went slower than the v1 maps. For the first year, 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 to pop out, since it's fun.) For 2014, the class was 5 mins shorter (now 35mins) and I had to pop everything out before the class, just giving them the relevant pieces of cardboard, and throwing away the trim.

About half the joins have to be done with adult help or the class won't finish in time. It helps to have a couple of adults on hand.

In the v2 map, the slots are 1-D cuts rather than a real slot. You can't get the tabs in easily, unless you expand/open the slot a little bit with scissors or a screwdriver. One of the problems was aligning and joining the edges. The kids should push the tab in till the colours match. If you push the tab all the way in, rather than stopping just a bit short, i.e. when the colours match up at the edges, then at the end, there isn't enough room to close the icosahedron and you'll have to cut bits of the icosahedron to close it. The resulting icosahedron isn't symmetrical. With all the instructions being foisted on them, the kids had a hard time adding colour matching to their tasks. In 2014 I found that telling the kids to leave the thinnest white line between the adjoining colours worked.

It's obvious to an adult that the flanges and tabs go inside the globe, but it wasn't to the kids. 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 in the set of four classes for the day, 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 and the colours matched. Despite my excruciatingly clear explanation, holding the finished circularised base up to show 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. The success rate for my explanation is no better than random and indicates that my explanation was no better than no explanation at all. For 2014, I had them do the base first and made sure they had the tabs facing inward before letting them put the sticky tape on the inside.

Is the v2 map better? Most of the students don't do a great job of cutting, so the resulting v1 globe isn't particularly symmetrical and the colors don't match up well across joins. The cutting problems are gone v2, but the colour matching at the edges is still a problem. At the last step in the assembly of v2, there's a lot for the adults to do. Even so, the class is finished a few minutes earlier, which helps. I'd say it was a step sideways, but what you've exchanged is different for adults and kids. Some things are easier and some things are harder. The cutting is gone, making that easier for the kids, but closing the globe is impossible for kids and has to be done by adults. (Note: For 2013 we had the kids close the globe by putting single sided sticky tape on the outside, rather than the adult method of double sided sticky tape between the flanges and the inside of the globe. Many of them do this on their own, without waiting to be told how to close the globe.)

Suggestions: As part of the design phase, 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, when their sphere isn't symmetrical and the tab and the slot no longer line up. A pointed triangular tab, rather than a 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.

5. miscellaneous

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.

6. Detailed class notes

There is a large spread in skills in any class. Usually there will be one kid for whom the whole process is obvious, and who won't need any direction, while there will be another kid who has no idea what's going on and has to be walked through the whole process and then thrown over the finish line. There must be at least a log difference between the top and the bottom kid in each class. I had not expected this, but now after being a soccer coach and referee for 10yrs, teaching several different classes at the school, and teaching astronomy to boy scout troops, I find the same spread no matter what you're teaching. Presumably professional educators know about this spread, but I didn't. Previously all my teaching had been at university level where the difference between the top and the bottom kids wasn't so marked.

I remember in one of these 3rd grade science classes, when I was showing the kids how an eclipse occurs, having one of the whizzes from my soccer team, looking at me with exasperation - he had no idea what was going on. So as the kids move between environments, the kid on top and the kid on the bottom changes every 40 minutes.

6.1. Goal

Goal is to make the NOAA globe, starting from a flat sheet of carboard (hold both up). Everyone will go home with a completed globe.

6.2. Introduce Platonic Solids

  • show and name the 5 platonic solids
  • explain regular solid nomenclature: edges, faces (modern)/heads (ancient), vertices
  • ask for examples of words with names starting with the prefixes tetra, hexa, octa, penta (photo of the Pentagon on the board), (in the dodecahedron, the face is a what?). Note for oct (octave, octopus, octane, Octavia, october). Is october the 8th month? (Most cultures around the world start the new year at the spring equinox. The Romans also started their new year in the spring, but for political reasons decided to shift the new year back by two months, but didn't bother to renumber the months. The politicians in the US aren't any different, with the result that the US is the only major country in the world not using the metric system.) Octavia (a highly respected woman in Rome, one of the first Roman women to have coins minted in her image), Octavian
  • Named after Plato. Plato lived where? (Athens). Student of Socrates, teacher of Aristotle. Founder of the Academy in Athens, the first institution of higher learning in the Western world. The Academy was named after Academus, the previous owner of the land on which the school was built. Plato is one of the most important founding figures in Western Philosophy.
  • show that some are rigid and some are floppy. show still true even for models made of straws and rubber tubing. explain rigid==stiff.
  • demonstrate polyhedral dice. First demonstrate the normal 6 sided dice as a way of generating random numbers from 1 to 6. Then ask them for the shape of a dice that will generate a number from 1 to 4. This will take a few seconds, but insist on the correct name (tetrahedron). Then roll the tetrahedral dice on the table. Then ask for 8,12 and 20 - they will pick it up pretty fast and call out the names as you roll the dice on the table.

6.3. Introduce them to Viruses

  • If nature wants a sphere it has two choices. icosahedron makes a rigid near sphere. the dodecahedron is a sphere too but it's not rigid.
  • show T4 picture, hold up toothpick icosahedron. Head holds the DNA, which is injected into the host cell, thus turning the host cell into a virus producing factory.
  • virus is simple - it's self assembling
  • why do we care about viruses? flu, cold, polio (FDR, vaccinations, Salk - in 2015 I noticed how angry I was that the US govt did not think it was any of its business to fund Salk's polio vaccine - it was someone else's job to develope the cure for polio), rabies, chicken pox/shingles, smallpox, rubella/german measles, mumps, ebola, HIV (AIDS), hepatitis, herpes (cold sores), scarlet fever, HPV, rota and noro viruses cause diarrhea. Mosquitoes carry yellow fever and dengue fever West nile and zika (from mosquitoes). Measles was so common in ancient Egypt that it was thought to be a normal stage of human development Social history of viruses (http://en.wikipedia.org/wiki/Social_history_of_viruses). Pneumonia comes in both viral and bacteria versions.
  • do viruses only target humans? (all living forms, plants, animals even bacteria have viruses)
  • non-viral infections: (only in case any kids ask about them) the plague (black death, killed 1/4 the world's population in the 1300s) (Yersinia pestis), cholera (Vibrio cholera), diphtheria (Corynebacterium diphtheriae), Lyme disease (via deer ticks, Borrelia genus), tuberculosis/consumption (Mycobacterium tuberculosis), typhoid (Salmonella enterica) comes from drinking water that has been contaminated by poor sanitation, The different disease Typhus comes from Rickettsia bacteria carried by lice on rats. Rocky mountain spotted fever (via ticks, Rickettsia rickettsii),

You kids probably haven't heard of many of these viruses. That's because you don't have to worry about these diseases now. Vaccinations, modern medicine and public health measures have handled most of the problems. When I was growing up, every kid was off for a week from school, sick and home in bed, with some viral disease every semester. Vaccinations have made a huge difference to the health and lifestyle of children. You get your shots before you start school or daycare and you go about your daily life without worrying about when you'll next be sick.

Anyone know the most significant advance in modern medicine in the last 100yrs, as far as preventing disease, saving lives and increasing our lifespan? (washing your hands and having safe drinking water - it turns out the best safety measures are also the cheapest.)

6.4. Globe

The video shows cutting out the v1 globe. The v2 globe, which I'm using now, instead pops out and is done a little differently. With the v1 globe, once the kid's folds were checked out, the kids could tape the globe up in one go, only requiring adults to close the globe. Here with v2, I'm doing it more stepwise till I know what the kids can do.

  • You will all take home a globe today.
  • the globe starts with a flat sheet of cardboard. you will fold it up and hold it together with sticky tape.
  • Before you do anything, put your name on the globe (the middle of the Pacific Ocean is good.)
  • start with the stand. make sure all kids fold tab/flange inside (not poking out). then tape on the inside with single sided sticky tape.
  • fold globe along black lines on the edge of the table. fold at 60, NOT 90, you're making a sphere, not a cube. do all black lines and flanges. have adults check before taping. Some kid always manages to fold the cardboard over 180 and press it down hard with a ruler.
  • Before they start taping, tell them NOT TO CLOSE UP THE GLOBE. Many of them do this as the first step. They usually make a cylinder out of it, rather than a sphere. Even if they make a sphere, they won't be able to get their hands into it when they attempt to join the sides.
  • starting at one end, do ONE taping (single sided tape, on inside), showing kids how to line up the colours. Have adults check that the colours are lined up and a thin white line of uncoloured cardboard is showing before allowing the kids to tape on the inside, or else globe will not close up at the end.
  • tape (single sided) along that side. when reach the end, don't try to close. Then start on the other side.
  • When get to the end of the 2nd side, ask an adult to close it with double sided sticky tape.

As I was watching the kids I noticed their lack of dexterity compared to adults. The other thing I hadn't noticed previously is that their fingers are shorter than adults. An adult's fingers are long enough that a dexterous adult can put a piece of sticky tape on the back of a tab in one move. A kid just can't do this.

6.5. Trusses

When 1/2 to 3/4 of the kids have taped up their globes, move on to the next section. Have adults finish the globes of the last kids (the slow kids are not going to finish in the time of the class). If not, you won't finish the class and the kids who have finished, with nothing to do, will go crazy.

  • 1-D truss - crane jibs, highway signs and bridges
  • 2-D truss - roof in large store
  • 3-D truss - box kite

Tell the kids who have finished their globes, to look at the rubber and drinking straws platonic solids to figure out why some are rigid and some are floppy. They can also roll the polyhedral dice.

In one of my earlier sessions, I had them all try to figure it out together; once the first kid figured it out, they all knew and they could check the answer on the spot. However that way only one kid gets to figure it out. That didn't work.

The next year, when they had an answer, I had them not tell each other and instead asked them to sit down. After a few kids had sat down, I asked the class for answers. To my dismay, I found that only some of them had the correct answer. The kids who were wrong, and now back in their seats, couldn't check the right answer. This didn't work either.

Being stumped, I asked Lyn (the professional educator). The way you do it is

  • let the kids come up and try to figure it out all together, but to keep quiet if they think they know.
  • when they have an answer, come check with me, but tell me quietly enough that the other kids don't hear their answer.
  • if they're right they sit down, or play with the polyhedral dice, but keep quiet about their answer.
  • if they're wrong, try again. Most kids are wrong (but are convinced they're right) and need multiple attempts.
  • when about half the class is up at the table (i.e. half the kids have finished their globes), get everyone to sit down. Ask the kids who had the right answer to identify themselves by raising their hands, then to call out all together, the single word that is the correct answer.

Only about half the kids got up to the table; the rest were working on their globes. In 2014 I had four classes of 18-19 kids, in which 1,0,2 and then 3 kids found the right answer (i.e. a total of 6 kids out of 74, only half of who made it to the table).

I didn't pay much attention to the wrong answers. Once I realised that the kid hadn't got it, rather than listening to a long winded wrong answer, I just said to try again. One kid was talking about squares and triangles, so I asked which ones were rigid and which were floppy and then they got it. All the other kids who got it just said "triangles" and that was that. Some kids didn't know what "rigid" meant. Afterwards, recalling the wrong answers, it was clear that the kids had no idea about falsifiability. They said it was due to the structure (well, what is it about the structure?), that the rubber in some of the models was more bendy...

Falsifiability is a modern (20th century) concept, and was only arrived at after several centuries of thought. I've had a lifetime of reading examples of falsifiability and the consequences of mistakes. You can't expect kids to rediscover falsifiability on demand, in a matter of seconds, at a table. I was told about the requirement for triangles in rigid structures long before I started thinking about why structures stood up, so I'm asking the kids to do something I hadn't done at their age.

Perhaps I should ask them "if you think you have the answer, before you come to me, check that your answer is true for all the rigid structures and false for all the floppy structures" .

6.6. Smoother Spheres

I have an 80 piece and a 240 piece icosahedron (in the video). These show how you can make smoother spheres, still using triangles. The piece in the video was shot between classes. I've never had time to show them to the kids.

6.7. Question Time

The class is sequenced to follow the section on plate tectonics and mountain building. The questions are designed to reinforce this material. Only obvious (high and low) places on earth shown on the globes, are discussed in the class e.g. Greenland, Antarctica, Himalays, Andes, Colorado Plateau, Hawaiian Is, deepest part of the ocean (it's not in the middle, it's at the edge) - Marianna's trench (deeper than Mt Everest is high), Atacama trench to the west of the Andes (26kfeet deep).

Posters on the wall

  • (cloudless) view of the earth from space, showing the white of Greenland and the Himalayan Plateau.
  • The Himalayas from the ground.
  • floor of the Pacific showing Hawaiian Is, Mariannas trench, and the Atacama trench to west of South America. Also shows the Andes.
  • Map of the Alps. There is also a photo of the Matterhorn, showing the glacial carved faces that make the horn. The circular arc of the Alps shows the collision of Italy with Europe. I have never had time to talk about this.

Questions

  • Easy questions to get the kids used to looking at their globes: What are high spots (Antarctica, Himalayan Plateau, Colorado Plateau, Greenland). Is Greenland green? What famous person connected to plate tectonics is buried in Greenland? (Remember, if you're the only person in the world who thinks something, and everyone else tells you you're wrong, it doesn't mean you're wrong.)
  • What caused the Himalayas, Andes, Hawaiian Is? (Except for volcanoes, all mountains on earth are caused by compression of the earth's crust.)
  • Where is the deepest part of the ocean (it's on the edges, although till not so long ago everyone thought the deepest part was the middle, just like it is for a lake). Why are the deepest parts of the ocean on the edges?
  • USA has 169 active volcanoes. (http://www.businessinsider.com/americas-most-dangerous-volcanoes-2014-9) Although it's not obvious on the map, the active volcanoes in continental USA are on the west coast. WA; Mt Ranier, Baker, St. Helens. OR; Mt Hood. CA; Mt Lassen, Shasta. AK; about a dozen have erupted in the last century, none of whom have names you know. HI; Kilauea

6.8. Materials

At home:

  • I have the maps and repair pieces.
  • In one of the boxes (with me, Lyn?) there is the original DVD of the class.

With Lyn, at school in the icosahedron class kit:

  • 240 piece jig-saw icosahedron and 80 piece icosahedron (toothpick and hot glue).
  • Trusses: 1-D, 2-D, 3-D (two copies) octet trusses, Bailey's bridge (toothpick and hot glue).
  • assembled NOAA cardboard globe
  • platonic solids: 5 of them (toothpick and hot glue, a few extra toothpicks in ziplock bag)
  • toothpick and glue icosahedron, with one face (triangle) outlined with masking tape.
  • platonic solids: 5 of them (rubber tubing and drinking straw) disassembled in ziplock bags. two section octet truss (rubber tubing and drinking straw). spare octahedron from Lynn (purple rubber tubing and longer drinking straws).
  • 7 piece polyhedral dice set normally used for games. 5 of these dice are the Platonic Solids.
  • posters: Eno River bridge (truss), 1-D trusses holding solar panels on ISS, Pentagon, Matterhorn, Plato, Salk, T4 electron micrograph (T4 has icosahedral head), diagram of platonic solids with differently coloured faces.
  • maps: Antarctica (including TransAntarctic mountains from the collision of east and west Antarctica), Alps - shows the collision of Italy with Europe producing the arc of the Alps. Tsunami sources.
  • poster of Pacific Ocean floor and surrounding countries showing Andes, Hawaiian Is, Atacama trench to west of the Andes, Mariannas trench.
  • mercator projection image of cloudless earth from space, showing ice covered Greenland and the dry Tibetan Plateau with the white line of the Himalayas visible along the southern edge.
  • posters of Mt Everest and close by mountains. strip showing the length of the Himalayas from Nepal.
  • signs placed in front of models: Bailey's Bridge, Hartford Center Space Frame Diagram (2-D octet truss), 1-D Octet Truss: example crane jib, ISS spars holding solar panels; 2-D Octet Truss: example Home Depot or Airport Roof; 3-D Octet Truss: example Box Kite.
  • signs placed in front of platonic solids: Tetrahedron, Hexahedron, Octahedron, Dodecahedron, Icosahedron (duplicate sets).
  • wikipedia article on Plato: (in case the kids ask me about him, they never have.)
  • printouts on articles about icosahedral viruses used to write the class.

With Lyn at school, materials not specific to this class, that have to be located:

  • kid safe scissors, single sided sticky tape marker pen (for enscribing your name on the globe and stand).

6.9. Setup, day before

Note
2014: this took about 5hrs. 2015: after getting organised last year, this took 2hrs. Nothing was broken.
  • assemble rubber tubing and drinking straw platonic solids.
  • put out platonic solids on table in front of class (including polyhedral dice).
  • put trusses on back table
  • put up posters/pictures
  • v1: for each pair of kids, a single tray containing: sticky tape (two single sided and a single double sided reel), two kid grade pairs of scissors, marker pen.

    v2: marker pen and single sided sticky tape.

  • partly pop out the maps (including the stand) (leave stand holding at only one point so the kids can start get onto it quickly, but leave half of the map points attached). On the day, finish popping out the maps in the break before each class.
  • have single sided razor blade handy to undo tape on missassembled globes.
  • Write my name on the board. (2015: Demitra has made a sign for this.)
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