Setting the Stage for Outdoor Math Experiences

posted by Diann Gano

rocks and shellsAs I look around me I see busy, happy children. Avery, Linnea and Anderson are busy seeing how high they can stack their rocks. Maya and Noa are near the sandbox creating a tea party for fairies, while Rowan and Parker are creating homes and meals for the squirrels over in the rain garden. It is calm. Everyone is happy and learning. We call this a play buzz.

When I stop and take a closer look, I recognize that not only is everyone happily playing, they are all working on math. M A T H! Did you know that nearly half of all children’s play involves math? (Seo and Ginsburg, 2004). The latest research also shows that early math skills are a better predictor of academic success than early reading skills! So here at the Gingko Tree, we are creating even more opportunities to introduce math concepts and problem-solving through play. As a family childcare with a Nature Explore Certified Outdoor Classroom, we spend a great majority of our time outdoors.

The environment IS our curriculum. When we add natural elements to their areas of play, it leads to playing in math-rich environments while creating and problem-solving in very deep and complex ways. As more and more classrooms and families are returning to the outdoors, simply giving our children the gift of time will lead them to mathematical play. It comes very easily to them without worksheets or number cards or dreaded memorization that may not be developmentally correct for where their brain development is at this time. As spring arrives, take this opportunity to create math-rich environments in your own backyard or play space. The only thing you can do wrong is not to do it! Bringing math into your outdoor or indoor environment is easy and even better it’s often free! In outdoor classrooms or family backyards, educators and parents are learning the beauty of loose parts in children’s learning and play experiences.

Architect Simon Nicholson, first proposed loose parts back in the 1970’s. Nicholson believed that we are all creative and that loose parts in our environment increase and empower that freedom to create. Loose parts are materials that can be moved, carried, combined, redesigned, lined up and taken apart and put back together in multiple ways. They are materials with no specific set of directions that can be used alone or combined with other materials. (Kabel, 2010)

We like to think of loose parts as shells, rocks, sticks, acorns, feathers, pinecones, flowers, flower petals, material, water, sand, dirt, moss, leaves, bark, rocks, pebbles, pine needles, seeds and else whatever may be native to your region. We also use blocks, people, animals and other manipulatives. Loose parts can range from dramatic play props to play cars, pots, pans, and pouring devices. If your environment doesn’t already contain those things, bring it in. If you have those, take them out! We rarely take walks without bringing home all kinds of the loose parts or “treasures” listed above. Use what you have. If it’s little, and your child hoards them in containers just to carry around and create “things” with; your child is playing with loose parts! Take advantage of what you have around you. Those are your tools for setting up a math rich environment. Let’s get started!

Storage is an important part of loose parts because it gives a sense of order and allows children access and knowing where those materials are. Indoors, I try to keep our natural loose parts materials in wood bowls, sturdy baskets, or other natural containers that look nice and add calmness to my environment. Outdoors we have used galvanized buckets, plant containers, crates, or any container source that we have nearby. Use your imagination. I can tell you from practice, the happier the container makes you, the more relaxed you will be with loose parts. Also, be aware that buckets and baskets may get dumped from what you are “storing” to become a piece of their loose parts puzzle. That’s a struggle for me. Usually, it means I need more containers for them to carry around or create with. The beauty of loose parts is that they can be moved, and so the child has power to create new adventures every day. Storage and carrying pieces are an important piece of the puzzle.

buckets of shells

I recycled our spring planting containers. These worked out well, and were free! Win, win! We have these next to our sandbox. They are full of rocks, shells, bark, and birch branches today. We change our materials often. By “locking” these in under the fence, it kept them permanently placed without getting dumped.

buckets of rocks and shells

We have galvanized buckets in a wire window box. You can find galvanized buckets at IKEA, Farm Stores, and Amazon.

As more and more of your outdoors space becomes filled with natural materials and less plastic and branded play toys, you will see your child’s play change. It will become deeper, more focused and more creative. Trust me. It’s amazing.

Now we can bring in the materials! Do you have rocks nearby? Take a walk. You will find some. We have found some very pretty river rocks at the Dollar Tree. If you take a vacation, the rocks in different regions are often different colors, shapes, and textures. Add those to your collection. We love rocks and they often come home in pockets and backpacks.

rocks and feet

stack of rocks

We play with rocks a lot. They line them up; they stack them up. They sort them by color, size, and texture. All of that is early math. They use them for food and phones and building. They rarely throw them. Honest. Call them your math rocks. There are throwing rocks and math rocks, and we only have math rocks.

Find some shells. Goodwill, Salvation Army, and garage sales have been our gold mines for shells. Any found on your own are even better because there is a story and memory behind it.

picking shells

Bring in small tree branch slices, driftwood, bark or small twigs. We’ve used all of them. Pinecones, acorns, buckeyes will all add new discoveries and wonder to your math center. Children are full of math vocabulary, more or less, bigger or smaller, fair or equal. Loose parts will add this vocabulary into your child’s world on a daily basis.bucket of wood slices pile of wood slices



squirrel trap

It’s a squirrel trap. You already knew that, didn’t you? It’s also logical thinking, creative problem solving, measuring length and size, comparing and estimation. Whew! That’s a lot of math in a squirrel trap built by a group of kids under the age of 5. This is where that gift of long, uninterrupted time is so important. Fifteen-minute recesses are not enough. Give them time.

If you want to learn more or see great examples of loose parts, I highly recommend looking at Dr. Carla Gull’s Facebook page, Loose Parts Play. She has great ideas on there, and contributors from around the world!

We love, love our mancala boards. mancalaWe use them with shells, stones, seeds, and pretty glitter marbled stones. You could use egg cartons or ice-cube trays, also. These are perfect for one to one correlation for teaching numeration. You won’t need to mention that of course. They will play with them where they are developmentally at that moment. It will all come. You are setting the stage to make it come so very easily, through play.

geoboardsWe also use our geoboards a lot. Besides all the geometric shape experiences they create, this also works the small muscle development and fine motor skills they will need when it is time to start writing. It may not look like math to them, but we know better!

This is a “family” of leaves. It started innocently enough with a Daddy leaf and the play took off from there. Children are exposed to math vocabulary anytime size or comparison is involved. All these experiences are building blocks for early math development.

When four-year-old Gabe, discovered that the oak leaf was torn like the number three, it set off a flurry of creating numbers. We captured it on clear contact paper to admire and share with parents.


Math is all around us. Creating a math environment into your children’s play assures your child of future academic success. Including loose parts into your play area will create a learning environment that your child will be drawn to effortlessly. They will be learning. If you thought you needed worksheets or flashcards or screen time to prepare your child for school, I hope you will give this a try. You will be excited about the learning your child is experiencing. You will see it. They won’t. They will think they are playing. Which is just what we want our children to be doing. If you build it, they will learn. It will be fun for both of you! Go play!leaves in size order numbers

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.



Symmetry and Snowflakes

Do you remember the day you were told that each and every snowflake in the entire world is unique and that no two snowflakes are alike?  The idea of infinite possibilities still rattles my brain.  How can each of the billions and billions of snowflakes be unique?

Spatial awareness or concepts about space and shape, are pretty interesting to young children.  Snowflakes are one way to explore shape in an engaging and meaningful way, especially if you live in a part of the world that is filled with the cold, white stuff a good part of the year.  Also, as children begin working on their cutting-with-scissors skills, creating snowflakes is great way to practice.  Some kinds of paper are harder to cut than others but the easiest paper to cut is also the most likely to tear.  I like simple copy paper for snowflakes as it is sturdy enough to withstand some three-year old torture, but light enough to cut easily with children’s scissors.

Begin by folding the paper in half and then in half again.  018The difficulty in cutting increases with the number of folds, so fold the paper to meet each child’s individual developmental needs.  One fold reveals the least interesting patterns and more folds reveals more complicated designs.  Ask the children about the shapes they have created.  Show them that they can fold the paper back up and continue cutting, if they so choose.  The snowflakes will just become more interesting.

020 021






If you want them to look more like snowflakes, and you think the children may enjoy it, you can begin with circular paper.  Again, fold at will, but the thicker the folded paper is, the more difficult it is to cut. 023 024





If you are working with older children, snowflakes are also a great place to discuss symmetry.  They provide concrete examples of “mirror images” that are easily (maybe not easily) seen. Notice how unique and distinct each of the children’s snowflakes are. No two are alike and that is what makes them special.

Snowflakes and Symmetry

There is something fascinating about snowflakes.  I still don’t really believe that each one is different from all others.  Really?  All of the billions and billions of snowflakes out there and no two are the same?

Even the youngest children can make snowflakes out of white paper and a pair of scissors.  It is a great way for them to work on their fine motor skills and they can be fairly successful at making approximations of snowflakes.

Take thin white paper and fold it in half.  Fold it in half again.  Then let the children have at it.  You can show them how to make small cuts in the paper or larger cut-outs.  When the paper unfolds, the paper looks like a snowflake.

When the children unfold their snowflakes, you can help them identify the different shapes they have cut out.  You can also show them that there may be “symmetry” in their snowflakes.  Each side is a mirror image of the other.  This is a great “math” word that you can introduce when making your snowflakes.

Spring Cleaning

I don’t know about you, but I am already thinking about the end of winter!  I love breaking out my winter boots in December but by mid-January, I am desperate to pack them away again.

This got me thinking about Spring Cleaning and the opportunity for children to help us sort and pack, as well as clean and organize. Young children have not decided that chores are a drudgery and should be avoided at all costs.  In fact, if presented in the right way, many young children will enjoy these activities as much as an other, as long as they are free to play within them.

Noah could sweep a room all day.  If we gave that boy a broom, a mop, a Swiffer, or a Dustbuster, he could keep himself busy for hours.  Larry and I would sit back and watch him clean.  It was like having our very own Roomba.   Unfortunately, that stage didn’t last as long as I would have liked.  I think that if we had participated with him rather than simply watching him, he would not have realized so quickly that we were using him as unpaid child labor.  Oh well.  He has made up for it in his teenage years by rarely lifting a finger to clean anything.

Spring cleaning means sorting through gloves and mittens, hats and scarves, boots and woolen socks.  Finding pairs is a great game for children.  Have them match up the items that look alike (by color or type) and then find the pairs within the groups.  It is more effective if you ask them to look for one attribute at a time since young children have trouble/cannot think about 2 aspects of a problem simultaneously.  First, have them separate the gloves from the mittens and then find the pairs.  Separate the white socks from the colored socks, and then find the pairs.  You can show the children that shoes, boots, mittens, and gloves are mirror images and even though they look almost the same, they are  not exactly the same.  This will give you an opportunity to talk about symmetry and how the human body is symmetrical, so the clothes that fit them must be as well.  Encourage the children to put a left glove on their right hand to see if it works, or the right shoe on the left foot.  This will reinforce the concept that they are the same but different because they will feel the difference.

This is what was left over at my house at the end of last winter.  Where did all of the matches go?  Another great unsolved mystery!