Symmetry in Nature

posted by Lindsay Maldonado

Despite being an urban metropolis, Chicago is surprisingly a great city for nature lovers. We are lucky enough to have access to some incredible natural spaces, both inside and outdoors. Two of my go-to nature spots in the winter are the Peggy Notebaert Nature Museum and the Garfield Park Conservatory. It’s been a mild winter, but when the temperatures start to dip, we all seek the refuge of somewhere warm and humid – and, these two ‘museums’ are the place to go for nature. And, nature just happens to be full of opportunities to talk about math!

One of the smaller museums in Chicago, the Nature Museum brings together a living collection of animals with a collection of animals that were once alive. Its most notable exhibit, the Judy Istock Butterfly Haven, immerses you in a tropical paradise surrounded by nearly 1,000 butterflies (and some moths too). A true haven for Chicagoans in the winter, this exhibit offers the perfect opportunity to observe math in nature. Specifically, butterflies give us the chance to explore symmetry. Exploring symmetry helps young children recognize patterns and hone their observation skills. There are many ways an object can be symmetrical. The simplest form of symmetry is bilateral or mirror symmetry – and, butterflies are a perfect example of mirror symmetry. Take a look at the butterfly pictures below. Can you see the symmetry? What makes them symmetrical?

Buckeye butterfly

longwing butterfly

atlas mothMirror symmetry is seen when one half of an object (or insect in this case) is the mirror image of the other half. If we held a mirror at the line of symmetry we would see the same image reflected on the mirror (it is not recommended to hold a mirror to a butterfly, unless of course, you have a butterfly that was once alive).

mirror symmtery

In the case of butterflies, the line of symmetry runs along the body of the butterfly. It runs directly between the butterfly’s antenna, lengthwise along its head, thorax, and abdomen (in case, you want to add some science content too).

longwing butterfly line of symmterySymmetry in nature is fairly easy to find. Leaves are another great example of mirror symmetry.

FernsThis picture of the fern room at the Garfield Park Conservatory provides unlimited opportunities to observe mirror symmetry. Let’s not forget about the other kinds of symmetry that exist though! It’s hard to pick my favorite place at the conservatory but my family really loves the desert house. And, what do you know? The desert house is a great place to explore a different kind of symmetry: radial symmetry! Objects that have radial symmetry can be equally divided like a pie. Do you see the radial symmetry in the pictures below?


succulent radial









You can continue to explore symmetry in the classroom with these activities.

Thanks for exploring museums with me this month! There are so many more museums in Chicago that we couldn’t have possibly visited them all for these posts, but with all of these museums there are even more opportunities to apply the big ideas of mathematics. With a deeper, more focused look you can find math anywhere. Next time you visit a museum, look around and ask yourself, what big ideas of mathematics can I find here? Now that you’re thinking in this way, I bet you’ll find math ideas with ease and you won’t be able to un-see them.



Researcher for a day: What kinds of animals live in the Amazon?

posted by Lindsay Maldonado

By day, I’m a researcher at Shedd Aquarium. I study people though, not animals – but, at Shedd, there are also a lot of people who do study animals. Some of these people are conservation research scientists or aquarists, who use math, and science, to help them learn more about the animals in their care, or animals in the wild. No matter who, or what, your subjects are, collecting data helps researchers collect information (i.e., data) that can provide answers to important research questions. For example, I might want to know how many visitors learned something about how they can help animals after their visit; or a conservation researcher might want to know how many seahorses live in a certain area of the world. So, to get us started, let’s pretend we are research scientists. We have our clipboard loaded up with our data collection sheet, some pencils, and our observation eyes. Now we’re ready to start collecting data!

penguin survey

Data analysis is one of the big ideas of early mathematics and can serve as a foundation for introducing other big ideas like sets, number sense, and counting — and, what better place to apply these ideas than at the aquarium with real living animals.

We have some important research questions to answer, so let’s get back into scientist mode. Today we want to know how many different animals live in the River Channel – and, we’re going to answer this question by observing animals (i.e., gathering data) and documenting what we see (i.e., organizing and describing data). These are all important steps to data analysis! If we want to know what animals live in the River Channel, we first need to make some observations. What do you see? A variety of animals live in the River Channel. How many animals do you see? Can you count them? I see 8 animals.

how many animals

Like the Amazon River, this habitat shows the diversity of animals that live in the river. What kind of animals do you see? I see turtles, stingrays, and fish.

kinds of animalsWe can sort the animals in the River Channel in a number of ways. First, we can sort by the attribute: type of animal. There are fish, turtles, and stingrays. Let’s put these animals on our graph. Representing data, in this way, is an important part of data analysis and allows us to interpret the data we collected.

blank graph

Let’s revisit our research question. We want to know how many types of animals live in the Amazon River. Through observation, we saw that fish, turtles, and stingrays live in the Amazon River so there are three types of animals in the River Channel. But how many of each live there? Let’s use our graph to help us organize our data. How many fish do you see? How many turtles? How many stingrays?

animals on graph

In what other ways can you sort these animals? You can use any number of attributes to sort the animals in this picture. We used the attribute of type (turtles, stingrays, and fish) but you could also sort these animals by size or shape. Observing animals at an aquarium is full of math possibilities. You can use data collection and data representation as the foundation for exploring the big ideas of early math. Keep exploring data analysis in the classroom. Try more data activities here.

Museums and Math: The Perfect Pair

posted by Lindsay Maldonado

The shedd aquariumMuseums are likely the most common setting for informal learning. Unlike formal learning (i.e., traditional classroom learning), informal learning is voluntary, unstructured, and learner-led. These settings provide a variety of learning experiences for a diverse group of learners. Museums offer opportunities to be hands-on with objects and even live animals. Museum visitors can observe objects and animals, engage with exhibits, participate in programs, and listen to chats and presentations. Museums afford visitors with flexibility and choice, offering a more customizable learning experience. This is particularly important when you consider the variability of learning styles within one classroom or one family. The ability to create an experience that suits the needs of many makes museums an ideal learning setting.

But you might be asking, museums and math? You might be thinking; how do I teach children math at a museum? There are science museums, art museums, natural history museums – but, there are no math museums. Well, there is one museum in New York that is dedicated to math but in general, math museums are hard to come by so it’s a good thing that math is all around us — all the time, no matter the setting.

Growing up in Chicago I remember visiting Shedd Aquarium often as a child. I would stand in front of the habitats, gazing up to observe small fish, big fish, colorful fish, dull fish, and everything in between. I was in awe of the diversity; it was kind of like reading Dr. Seuss, “One fish Two fish Red fish Blue fish.” There were so many fish, but there were also fish of every color, size, and shape. At the time I wasn’t thinking about math, but as I reflect back on that experience I know that math really was all around me. This experience is not unique; I see thousands of children visiting Shedd every year. As they gaze into the same habitats I did many years earlier, I can see the sense of wonder and awe in their faces. Knowing what I know now, though, I think about taking that moment of wonder and creating a math moment too. I think about using that awe and excitement as a springboard to a conversation about how many fish, how are the fish different, or how are the fish the same. These teachable moments are all around you when you visit a museum.

As we explore museums and math together in the posts to follow, let’s first consider the big ideas of early mathematics: sets, number sense, counting, number operations, pattern, measurement, data analysis, spatial relationships, and shape. These nine ideas laid out by Erikson Institute’s Early Math Collaborative provide the foundation for exploring mathematical concepts in and out museums. We’ll touch on many of these ideas as we explore some of my favorite museum exhibits. So for a moment, let’s focus our exploration on math in museums. Let’s reflect on the ways in which these big ideas exist in museums. Come join me on a mathematical adventure!