🚀 go-pugleaf

mlady@mindspring.com (Sara) wrote:

>I'm a student teacher in Georgia.  I'm teaching 3rd grade.  I will be
>teaching a two week geometry unit in November and would appreciate any
>ideas or suggestions.  Thanks
>
>Sara
>mlady@mindspring.com
>

I good intro to fractions using geometric shapes begins
with the regular tetrahedron a your basic unit of volume.

Split it into four, then each of the four into six and
you get what are called A modules.

I realize this is hard to visualize.  I've got a pictures
for you at:

http://www.teleport.com/~pdx4d/images/amod.gif
http://www.teleport.com/~pdx4d/summit/modslide.gif

The A mods have a volume of 1/4 x 1/6 = 1/24.  Then there's
the B mod, also of volume 1/24.  

To see the A and B together check out:

http://www.teleport.com/~pdx4d/images/abmod.gif

Together, the A and B assemble into all kinds of familiar 
polyhedra:

Shape        Volume

Tetrahedron      1
Cube             3
Octahedron       4
Dodecahedron     6
Cuboctahedron   20

(see http://www.teleport.com/~pdx4d/images/concent.gif
for a rough idea of how these fit together -- hard to 
show without a classroom model)

Note the simple, whole number volumes, very nice, very
3rd grade.  So you have both fractions (1/4, 1/24) and
relative volumes (which are also fractions e.g. ratio
of Cuboct/cube = 20/3, that kind of thing).

The reason you probably would feel uncomfortable teaching
this material is 

(a) it isn't in the text books -- not at the 3rd grade 
    level, nor anywhere up through grades 12 to 16

and 

(b) the preparation time needed to assemble A and B mods
    from paper cut-outs, plus to develop the other models,
    is pretty great, in the absence of kits or supplies 
    already made up

This is all going to change of course -- tomorrow's teachers 
are going to have a relatively easy time of it -- so if you 
don't have time to bone up on this curriculum now, file it 
away for future reference -- every kid will know the above 
in the 21st Century (and thanks to our homeschooling network 
here in Oregon, many of them are already learning it now).

Kirby


----------------------------------------------------
Kirby Urner  "ALL realities are 'virtual'" -- KU
Email: pdx4d@teleport.com
Web:   http://www.teleport.com/~pdx4d/




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