MMT SMU Blog: Geometry in Nature

Geometry in Nature

As the weather gets warmer, I notice many of my students walk a little slower to my classroom. Not because they’re being lazy, but because the weather outside is simply more enjoyable. “Mr. T! It feels so nice out here! Can we please have class outside? Please!?” says one of my 7^th grade students as she walks to my portable classroom. Lately, my usual response of “Sorry, kiddo, not today. Maybe after the STAAR.” has made me feel a little guilty for not figuring out a way to actually teach outside my classroom. Every time a student asks me to teach outside, the first thing that comes to mind is how much I loved being outside as a kid. I loved going to the fields and exploring the different types plants, color patterns, and shapes.

Last year, I decided to take my kids outside the classroom, for one day, to collect the measurements of my portable for a project they needed to create on SketchUp. That was the only time I taught anything outside the classroom. Since then, even though the idea has always been there, I haven’t really made an effort to create another project that would take my students outside the four walls of my classroom.

One of the ideas I had in mind for outside the classroom activities was to connect mathematics to nature. However, I knew very little about those connections. After reading some articles on geometry in nature, and visiting the Dallas Arboretum (for the first time!), I realized that I can come up with some ideas to teach mathematics in a different environment. The articles were very informative on both animals and plants, but I was more interested in the plants, particularly in the Fibonacci sequence. I did not know much about it until I read the articles, and during my visit to the arboretum, I was able to see how it is found in nature.

There is a particular part of the arboretum, in the children’s garden area where the kaleidoscope is located, where you can find mathematical concepts such as patterns, shapes, and structures. Inside this place, you can also find the Fibonacci sequence in many different plants and designs. As you walk around, you will also find fractal geometry in plants and other types of nature. There is also an area of geometric plastic plants that can be used to design a geometric garden. And in another area, I found tangrams and tessellations stations. Although the part of the garden dedicated specifically for math was small, compared to the entire arboretum, the math was very well presented.

As much as I would love to take my students to this place, it would be very difficult, logistically speaking. However, I know there are parks and green areas very close to our school that I can use as a setting to replicate some of the things found in the garden at the Dallas Arboretum. One activity I could do would be to find the grass areas in our school that do not have any flowers or designs, and create geometric designs that could be proposed to the principal as a way to “beautify” our school with mathematical themes. This activity would involve concepts like regular shapes, composite figures, symmetry, similarity, congruency, transformations, dilations, and of course area.

Another activity I could create would be to find all the trees that can be cut into geometric shapes (if none are found, then this would work as a proposal project similar to the first activity). The students would have to come up with geometric designs for each tree found considering their individual measurements. In this activity, the students would create models of the tree designs using wooden stick and Styrofoam, using the scaled versions of the real measurements. Concepts such as measurements conversion, scaling, 3-dimensional figures, similarity, congruency, and volume would be deeply involved in this activity.

Although, not everything can be connected to nature in every way, we can always get a little creative when we connect geometry concepts to the real world our students see every day. Activities like the ones mentioned, not only would allow the students to learn outside the classroom, but would also give them a better understanding of geometric concepts and how they can be used in the world around them. These types of activities require good understanding of geometric properties, which would challenge the students to use everything they know about the geometry they are using or learn about what they don’t know. Experiences like these, are the ones that kids remember the most, mainly because they take place in a setting so different than the traditional classroom learning environment.

Here are some additional photos of geometry found in the garden's floor.