Math Monday::Gumdrops & Toothpicks

Tis the season for Christmas candy! To take advantage of all the gumdrop packages on the grocery shelves, the Creative Math Club went ahead and organized a gumdrops & toothpicks day. Each kid had two packages of gumdrops and a container of toothpicks to use, and we started our meeting by making 2D shapes with them–officially called regular polygons because the equal sized toothpicks make them automatically equilateral (all sides have same length) and equiangular (all sides have equal in measure).

gumshape8

I made a spreadsheet with 20 spaces for regular polygons, starting with a triangle. It also had spaces to fill in how many edges and vertices it had, as well as space for what the angles measured. Edges are the sides, denoted by how many toothpicks are used…vertices are where two sides meet up, denoted by how many gumdrops are used. Once the kids modeled a 2D shape, they measured the angles with a protractor and then they filled in the spreadsheet information.

gumshape7

The wikipedia article on regular polygons has the names for the polygons up through 20 sides, and then the names for even bigger polygons like the megagon.

I found it really fascinating to watch how the angular shapes changed the more toothpicks we used. A triangle opened up into a square, which opened up into hexagons and octagons. By the time we got to the 20 sided icosagon, it more closely resembled a circle. Those were used as necklaces and embellished into peace signs.

gumpeace

Once we were done investigating 2D polygons, we moved on to 3D polyhedron shapes. But! Not just ANY polyhedron shapes, we focused on the five platonic solids. I also made a spreadsheet for this, with spaces for the polyhedron name, how many edges, how many vertices, and how many faces it had. And then we went to town building, from simple to more complex. I used a hands on resource page, here, as a rough lesson plan.

Tetrahedron:
gumtria

Cube:
gumshape4
Octahedron:
gumshape2

Dodecahedron:
(which apparently I forgot to take a picture of)

Icosahedron:
gumshap

we talked about how Plato associated each of them with one of the four elements, and also how they were the shaped dice used for games like D&D (any kid who’s a gamer will enjoy this association a lot!)–those dice are actually called polyhedral dice that we use for most if not all of our math games!

gumdie2</a

Being creative math, I’m not promising that everyone filled in their spreadsheet 100%, or that there wasn’t a fair amount of creating other shapes going on. But I am promising that we all had a good time discovering shapes (2 and 3D) and characteristics using gumdrops & toothpicks!

gumdrop math

*********
If your kid really gets into hands on building with gumdrops, I highly recommend the Zometool, which is based on this kind of constructing, and it takes it into different interests like chemistry (making chemical reactions), biology (making viruses), etc. It’s a big hit over here.

Links to resources I used to prepare for this that I’ve bookmarked on delicious is here.

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9 Responses

  1. Math has never tasted so good! Drool.

  2. crazy genius!!!! once again! love it!

  3. AAGH! I wish i didn’t get sick! that looks so awesome!

    • we missed you, Tynan! Bring some games this week for math club, and I’ll have some gumdrops and toothpicks you can play around with!

  4. Target here I come for gumdrops and toothpicks!

  5. i’ve seen this idea before a bazillion years ago – but not so cool with the mathy shapes. ;) we’ll have to pick up some gumdrops. my engineer brained boy would LOVE THIS!

    • lol! mathy shapes rule! and yes, make it so much cooler. I’ve also seen this where you engineer something to hold as many books (or other heavy objects) as you can. The possibilities are endless!!!

  6. We tried it at home yesterday and it was a big hit. So much so that my son announced that he was ready to move to Colorado and join the math club. Oh, if it were only that easy. Anyhoo, so, last night I told him that I was presenting him with another challenge. I wanted him to observe his figures for a relationship between the sides. I was trying to be sneaky and let him figure out the equilateral measurements, which you pointed out. This is where his 2e side came out. He pointed out that while, yes, technically the toothpicks are the same size and the gumdrops were pretty much the same size and that we could assume that all the figures would have the same size as a result but… that would depend on how much you pushed the toothpick into the gumdrop. If you shoved it all the way into the gumdrops, that side would be shorter than if you just barely pushed it into the gumdrops. When, I acknowledged his point, he beamed. Just one more reason to marvel at these kids!

  7. [...] which I’m not yet 100% sold on, despite the great support from Tiffany and how much I loved her hands-on math class last Thursday¬†(seriously, head over there and check out the cool stuff we [...]

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