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>> Susan Osterhaus: OK.
Well, we are going to look at an even different way to fold nets
into polyhedrons and, specifically, platonic solids.
And we had worked on putting a couple together,
this octahedron using Braille paper
and our tetrahedron using swell paper,
and we scotch taped them together, and that we saw
that I wasn't the most artistic person
in putting these together, but I did it.
And what I want to show you what these look like from things
that you, from 3D models that you can purchase
at your math store online or wherever.
This is a tetrahedron in yellow plastic,
and here's that octahedron.
And so sometimes it's a good idea to go ahead
and show your students what the final product is supposed
to look like, but sometimes it's also fun
to just let them explore.
So maybe after they explore, you can say, well, this is,
do you think that your figure looks like this particular one.
So, again, this is the tetrahedron,
and this was your octahedron.
Let's start back with this tetrahedron.
I want to show you a different way yet to do this,
and this is the way I prefer because of my klutziness.
Has nothing to do with vision as far as I'm concerned,
and these are some manipulatives from Geo Metro.
It is a company in Canada,
and their website is www dot geo metro dot net.
How clever is that?
OK. So what happens is, you will recall, I'm not sure
if it was laid out, if I, I think our net was laid
out like this before, and we had it
on either swell paper or Braille paper.
But now we've got these four triangles,
and they're just stuck together
because Geo Metro manipulatives are made, outlined in Velcro,
and that's why they are sticking together for me,
and look what happens.
Totally easy for someone as klutzy as I am,
and you now have your tetrahedron.
OK. And then what I often say to the students is, OK,
now your net looked one way.
Can you make that net look a different way?
And, for instance, here is another way.
Remember, when we started, it didn't look like that.
This was over.
We had this over here, and, again, just to remind you,
we folded it up, and it was a tetrahedron.
But if I had given it to you this way,
it would have also folded up to be a tetrahedron.
So anyway that's a fun little activity to see
if they can come up, make the net just a little bit different
and still come up with a tetrahedron.
Now if you think it's always going to come
up to be a tetrahedron, think again.
OK. Let me move this around like this, OK.
So we have a different net.
Now, if you try, you kind of get something different.
You get a square pyramid that's not closed on the bottom.
So that's not a tetrahedron.
So that does not work as a net, or, oops.
Oh, there's another one that would work.
OK. But bottom line what we're saying is the net has
to look a certain way, or it's not going to fold up to be,
in this case, the solid that you wanted, which was a tetrahedron.
OK. So that is using four different triangles,
and sometimes I just give them to the students like this,
and they have to form the net.
Right now, I'm going to go ahead and put these four to rest.