Spiral Science & Math Manipulative

Fibonacci numbers are practically unheard of outside of math circles, and yet the math, science, and even art concepts that tie into them are many. Spiral Science & Math Manipulative is an elegant and inexpensive way to extensively explore these relationships.

Ds#1 and I have been trying out the many acitivities available at the web site. Middle school or above students with a good understanding of fractions, decimals, and percentages will get the most out of this neat kit, though upper elementary kids can use it for simpler activities. Ds#1 does not have that much math under his belt, but enjoyed the activity on hand bone ratios nonetheless. He was able to figure out the pattern of the Fibonacci sequence after a bit of thought--and that made it all the more wonderful for him.

The 13x21 cm kit consists of 7 magnetic sheets that have numbers and a spiral-forming curve on one side and examples of spirals in nature on the other, a magnetic sheet to work on, and a thick vinyl pouch to keep it in. The Teacher's Guide is included, containing six lessons, and the web site has another 8 activities all aligned to national standards (if you keep track of them.) You can also buy class packs for your co-op, but these are significantly more expensive.

Some of the vocabulary and concepts you will explore with this kit include logarithmic (Archimedes) spiral, tessellations, ratio, proportion, golden mean, interval scale, X and Y axis, controls and variables, histogram, average, and more. With a cost of less than $15, this kit certainly offers a lot of science and math exploration for the dollar.

More About the Golden Ratio: Zomes

The folks at Zometool have created a very sophisticated "toy" using Φ. Vaguely reminiscent of Tinker Toys, it is far more elegant and mathematically designed.

Basically, it consists of struts and nodes. In a basic set, the struts are blue rectangles (representing 2,) yellow triangles (representing 3), and red pentagons (representing 5.) 2, 3, and 5 are part of the Fibonacci sequence.

Each strut comes in 3 sizes--small, medium, and long--and guess what the ratio is among them? That's right, Φ. You can easily build golden rectangles with them like those overlaying the chameleon's tail in the previous post.

The struts connect to the nodes. These are white with carefully placed rectangular, triangular, and pentagonal holes such that structures can be built that demonstrate mathematical and geometric principles. That is what you see in the Zome logo.

They also have green line struts, which are advanced pentagon struts that have angled ends, that can build additional geometric structures. Here's the strut catalogue:

Fibonacci numbers and the golden ratio are abundant in nature. In fact, I noticed the ratio while admiring a dragonfly. I went to work and eventually built one out of Zomes.

I actually needed a few extra small struts--these, too, maintain the golden ratio in relation to the other struts. I didn't have enough struts to make the second wing.

The website and kits have a wide range of geometric models, from simple Platonic solids to a complex taurus (doughnut) and even a large DNA model. You can download a set of challenge cards, or lesson plans for grades 1 through 12.

This makes a great math and science manipulative especially if your kids like to build like my boys do. Their imaginations are their guides!