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

Order in the Classroom

by Alison Balis Hirsch




  1. the arrangement or disposition of people or things in relation to each other according to a particular sequence, pattern, or method
  2. an authoritative command, direction or instruction


  1. to put into a methodical, systematic arrangement
  2. to bring about order

One of the first learning experiences I recall as a student teacher in a Boston Public School pre-k was on the subject of classroom design and organization. Our room was especially small and we shared it with 16 three and four-year olds. “Order” was not only a math concept we wanted to explore with the children, but also a necessity in terms of keeping the materials organized for both children and teachers working together in that space on a daily basis.

The head teacher had begun the school year by sorting, according to habitat, all of the plastic animals used for imaginative play: oceans, jungle, forest, etc. Taped to the open bin in which they were stored (on shelves at the child’s height) was a photo of a few of those animals together with the written word of its habitat. Categorizing helped the children identify where both to find the items s/he was seeking and also return the items at clean-up. This is a system I have used not only in my classrooms, but also to an extent in my home. Using uniform, clear boxes with lids (so they can be stacked if needed) for the storage of ALL playthings and classroom supplies is ideal. This way, everyone can see what is inside. On the container you can adhere the laminated photograph. Alternatively, I’ve used wide packing tape over the entire width and length of the photo, which works beautifully.

BlocksThe blocks area was another place in need of an organization system so the many various shapes (½ unit, unit, double unit, quad unit, pillar, ½ circle, ¼ circle, pillar, roman arch, triangle, arch, circle curve, crossing, y-switch, elliptical curve) could be quickly found and put away with relative ease. We cut out from colored contact paper a template of each shape and adhered them on the area of the shelves where children would stack the matching blocks.

Having a system in place for children’s personal belongings also helps everyone keep track of items. Individual and personalized hooks and/or cubbies where children hang their backpacks and jackets on a daily basis is preferred so that children can come to expect where to find their items from home. We alphabetized the names along the row of hooks, and below each name was a different color swatch. The color swatch (used from hardware store paint swatches) helped children who were not yet identifying their names, or first letter of their name, to recognize their hook.

Sorting classroom items by attribute (markers/pencils/crayons; red/orange/yellow; cars/trains/trucks) is an early math concept which is relevant to a child’s world. Identifying and naming shapes increases match vocabulary. To take it a little further, managing to identify attributes of objects, and then placing them where they belong, empowers kids to help maintain and respect their environment, keeps items organized for the community and is visually calming.


What Games Do You Have in Your Math Center?

I can’t help but look through each classroom I visit to see what kinds of materials make up each center.  Sometimes it feels like snooping as I try to ascertain whether or not the math center is also the science center or if there is a math center at all.  In some rooms, there are shelves near a table and there are materials on those shelves that may or not be math materials.  If I can’t tell, then there is a problem.

Math Centers should be rich with a variety of engaging, open-ended materials that children can explore on their own, with their friends or in groups.  They should be specifically presented and used for math investigation (even though they may clearly use them for other explorations as well.)

I really like to see a wide variety of developmentally appropriate games in the math center as well.  Ideally, a good math center will have:

Checkers and Chess

Bingo (all varieties)

Dominos (with pictures and pips)


Chutes and Ladders ( a.k.a Snakes and Ladders)


Snail’s Pace

Hi Ho Cherry-O

Connect 4

Shut the Box

Chinese Checkers

Guess Who?


This list is far from complete, but it is a good start.  Many of these games are too sophisticated for younger children, but they will find ways to play with them, if allowed.  They will develop into them with experience, over time.  Remember, three-year olds need an older peer or adult to support them as they begin to develop interests in games with rules; so offer to play with them.  Encourage them to count the dice, move their pieces themselves, and match their cards, etc.  This is how they develop the skills necessary to play unassisted with their classmates.

What other games can we add to our list?

A Great Estimation Activity

FullSizeRender-11I had the great good fortune to observe a very interesting Estimation Activity the other day at a local child care center.  Before the observation took place, my student and I discussed how estimation can be a pretty engaging activity for young children because it feels like a game – a guessing game. We talked about the counting skills of the children in her group and she felt very confident that they all had a pretty secure sense of number, at least up to 10, and were all able to count reliably.

We discussed ways of creating the jars so the children’s number and counting skills would be challenged appropriately; enough to be stimulating but not too much to be frustrating. My student decided to stick with small items that fit easily into empty baby food jars and chose items that at first glance, seemed easy enough to count.

The children came over to the table at their leisure during free choice and my student explained the game to them.  She defined estimation and explained what they should do.  Each child estimated how many of each item were in each jar.  They then wrote the numbers on small pieces of paper and stuck them to a graph next to their names and under the items.


What I found fascinating was how the careful choice of the items created a challenging math exercise for the children.  The pom pons were large and nearly filled the jar but because two of them were red they looked almost like one, making it hard to see where one began and the other ended.  Many children counted the five pom pons as four as they were “tricked” by the red ones.

The beads were straightforward; seven beads in seven colors, easily discernible and easy to count, as evidenced by the chart above.  The marbles were harder as they rolled around the jar a lot and it was hard for the children to know which marbles they had counted and which ones needed counting.  The really challenging jar was filled with Cheerios.  First, there were 8 Cheerios in the jar, which was the biggest number they had to count to.  Second, all of the Cheerios looked the same, so it was nearly impossible for the children to know if they had counted each one once, or if they had recounted some.

These small challenges are important to consider when setting up an activity.  For children with a secure sense of number and solid counting skills, the jars did not allow the children to point to each individual item or to line them up or to separate them for counting.  Many children still use these strategies to ensure they are counting correctly and following the counting rules.  One-to-one correspondence provides a framework for counting so that children know that each separate item has a one number attached to it, no more and no less.  One bead = one and the next bead = two, and so on.  The Order Irrelevant Rule  says that as long as each item is only counted once, it doesn’t matter what order the items are counted in.  This activity challenged both of these rules which is what made it really engaging and interesting both for the teacher, the children, and the observer (me)!

Big Jenga


Do you have a Jenga set in your classroom?  If not, you should.  Jenga is a set of  small wooden blocks designed to be set up in a tower formation.  Players take turns removing one block at a time and placing it on the top of the tower until the tower becomes so unsteady that it falls over.  The box says, “6 yrs. +” but I think preschoolers could find a millions and one ways to play with a Jenga set.

Because of their size, small hands can use these as a tabletop manipulative.  Their open-ended design allows for creative play.  I found a set on Amazon for $8.99 but I imagine you can find these at garage sales and the like for a lot less.  Well-built wooden manipulatives can cost a fortune, so these are a really good option for a tabletop block set.  They also come in a few other sizes, so you can really create a “set” of tabletop blocks for your classroom.

The game of Jenga requires well-developed hand-eye coordination, balance, spatial awareness, fine muscle control, and enough social/emotional development to take turns.  These are just a few of the reasons that Jenga is a good choice for children as they are all working on these skills.  If you want to introduce the game and its rules, start your tower small.  Instead of stacking the whole set, create only 5 or 6 rows.  This makes the tower less heavy, and therefore easier to take the blocks out, and when it falls over it is not such a big deal.  It also takes a long time to stack the entire set, which with young children might mean 5 minutes of set-up for 30 seconds of play.IMG_0253

When I was on vacation recently, there was a GIANT Jenga game going on.  It was made out of big wooden blocks, much like the large wooden blocks in many preschool classrooms.  This got me thinking that you could create a Jenga-like game on the rug and have children take turns taking a block out from the bottom and placing it on top.  It doesn’t have to be in a tower; in fact, it would probably be better if it weren’t.  This would be a great way to introduce the game and its rules to the children and could be an interesting circle time game.

Give it a try and let us know how it goes.

Weighing with a Bucket Balance

Balances and scales are rich with opportunities for children to consider weight and size.  The Bucket Balance, pictured below is made for the classroom and it encourages children to weigh objects “relatively” to a standard weight or “relatively” to another object.  Through trial and error, they can see if an object is lighter or heavier than another object and then adjust the balance until they make it the same.

Remember, young children may be fooled by appearances, so they may think that something that is “bigger” may weigh more, while that might not be true at all.

Learning Resources says of the Bucket Balance that it is “Perfect for exploring basic measurement concepts.” Children can measure, explore volume and compare solids and liquids.

Bucket Balance


This coming Thursday, I am going to write about a gross motor game that uses the bucket balance.  I think you are going to like it.


The World is a Puzzle and the Child is Just Trying to Figure it Out


Sometimes I dread meetings.  Honestly, I dread most meetings but this past week I attended the annual Board Meeting for the Chicago Children’s Museum (since I am on the Advisory Board of the Tinkering Lab and we were invited to the BIG meeting) and it was exceptionally fun and entertaining.

Once the voting was over and introductions had concluded, a puzzle maker by the name of Sandor Weisz took over the meeting, broke us into groups and together we worked out an interactive and engaging puzzle.  His business, The Mystery League, is all about creating puzzle hunts for groups of people (meetings, parties, etc.).  We worked in teams, hunted for clues, uncovered the hidden meanings and solved the puzzle.

When Jennifer Farrington, the President and CEO of the museum introduced the activity, she reminded us that young children unravel the mysteries of the world much like we approach puzzles.  They examine the pieces and consider how they fit.  They twist and turn them until they make sense. The pieces are complicated and seemingly disconnected yet they try and err and try again. This is the beginning of the lifelong process of assembling understandings and making meaning of their lives, the people around them, and the world they live in.

I love this analogy.  It is accurate and uncomplicated.

PS. In each area of the museum, staff members were there to answer questions and to ask provocative questions in order to scaffold our understandings.  Brilliant.


A Visit to the Museum of Math and an Idea for an Activity

Last month, I visited my son in New York City for his fall break from school.  The only thing on our agenda was to visit the Museum of Math.  You may remember that I wrote about this museum when it first opened after I saw a segment about it on a news program.  I was very excited to see it in person, enjoy the exhibits, take some pictures, and then share it all with you.

Most of the exhibits are very sophisticated and designed for a mature audience.  However, the entire place was thoughtfully planned with people of all ages in mind. Most, if not all, of the exhibits have a hands-on component that even very young children can enjoy.  IMG_0089


Here, you can see that there are oddly shaped solids that when rolled across the table follow or create a path. The goal of the activity is to determine which shape matches the path is creates.  Both my son and I thought it looked easy but once we began trying, we found that it was much harder than we thought.  Trying to get the shapes to roll on their path was very tricky.

The Activity

I think a version of this would be quite easy to create and could be a really interesting activity for young children. Using the lid of a large box, draw a thick straight line down the inside of the lid  then a curvy line down the middle.  On the far side, draw a more complicated path from one end to the other.  Using a simple ball, encourage children to move the ball down the 3 paths.  This can be done alone or as a cooperative activity between 2 children as they hold onto the box lid and move the balls along the lines.

Give it a try and let us know how it turns out.

Activities to Support Subtizing

Young children develop subtizing skills much like they learn to read sight words.  The ability to take a mental snapshot of letters or objects and know what the number or word is comes because of opportunity, exposure and reinforcement.  Eventually young children learn to recognize the number of small groups of objects simply by sight (we call this subitizing).  Using common patterns of object placement, such as the ways pips appear on the side of a die, children recognize a group of 2 or 3 dots and eventually, without counting, they know how many there are without counting the pips themselves.

Just like frequent opportunities to read sight words support the development of the skill, so too, do frequent opportunities to subtitize number. In addition to having several kinds of dice and dominoes in the classroom, other materials with small numbers of objects should be available so children can practice. Begin with groupings of 1 to 5 as these will provide the foundation for subitizing larger groups using part/whole understandings as well as composing and decomposing number.

This memory game has small groups of objects with matching numeral cards.  Start with 1-5 and put the rest away for later.

memory game


Even though I don’t like flash cards for young children for any reason I think that these cards could be used in interesting ways.number_flash_cards