Head, Shoulders, Knees and Toes

posted by Debbie Lee

So far I have written about patterns that involved objects you can pick up and manipulate. Those are usually what we think of first when we think of patterns. Patterns, however, are so much more than that!

The old children’s song “Head, Shoulders, Knees, and Toes” is a pattern. You and the children can make up patterns using various forms of movement. Hop, twist, hands on shoulders; hop, twist, hands on shoulders is an ABC pattern of movements. If you want to keep the children seated on the floor or chairs, you can use less grand movements. Touch ears, pound on chest, flap arms is also an ABC pattern. The various movements are limited only by the various body parts that can be used and your and the children’s imaginations of what can be done with them.


HEAD PHOTO                                SHOULDER PHOTO







Remember with all forms of patterns it is best to start with the simpler forms. Do ABAB patterns first; then progress to ABB, AAB, and ABC. If your children are starting to catch on, think about longer patterns such as ABBC or ABCD.

It helps when you are doing the patterns to describe them aloud and not just do the movement itself. This helps those who learn best through what they hear. You are reaching those who are more auditory learners and with this form of pattern you are also engaging young children who are kinesthetic learners and find it difficult to sit quietly.

Patterns do not always have to be a special time set aside just for math skills. If the children in your care are having troubles sitting still to listen to a book or do another sedimentary activity, take a quick break to do a movement pattern. Stand up, jump, clap, twist, jump, clap, twist for a minute or two and the children will find it easier to sit and you will have provided a quick “lesson” on patterns.

As with the other forms of patterns, don’t forget to have the children first copy your pattern. Once confident, have them extend the pattern. Do tap head, touch chin, hug self, tap head, touch chin…..what comes next? What comes after that? Have the children extend the pattern through at least two repeats so that they can show that they are truly understanding what the pattern is.


CHIN PHOTO                                        HUG PHOTO





Lastly, don’t forget to have the children create their own patterns. Have a child suggest a pattern, name it first by its movements and then by its type (ABAB, etc.). Then have the other children (and you!) copy it. Give each child a chance to create a pattern of movements to share with the others. You can also use this as an educational “filler” – for lack of a better word. When you have a few minutes to fill, have the children take turns creating patterns that the others can do. This makes these short periods of time between activities more than just ways to bridge activities but also gives these moments educational value.

As in past weeks, I encourage you to share in the comments section how you have been using movements to make patterns with the children you serve. Everyone has great ideas – share them!

The Attributes of Patterns

posted by Debbie Lee

Last week I wrote about patterns and using everyday household items to make them. Did you think of some items around your house you could use? I also wrote about simple ABAB patterns in a row formed by having two different elements (fork/spoon or red/green) that alternate. There are other ways to make patterns with everyday items though!

Elements of patterns are distinguished by an attribute. That can be WHAT an item is such as a spoon or a fork. It can also be by color, such as red or green. Those are easy visual ways to distinguish one element of a pattern from another. Don’t stop there! Again, start to think “outside the box.” Think positions!

You can use all of one type of item and make it into two elements just by altering the position. A soup can that is sitting upright, and then one sitting upside down, and then again one upright, and one upside (and so on) is also an ABAB pattern. What about a row of knives, one straight up-and-down and one diagonal, one straight up-and-down, one diagonal? That’s an ABAB pattern too. You can even have one knife straight up-and-down and two knives “crossed”, one knife up-and-down, two knives “crossed.” The possibilities are endless!










Don’t stop there! A row of cups sitting upside down with a small pebble sitting on top of every other one – that’s another ABAB pattern.   In other words, two items can be combined to make one of the elements and the second element can be just one of those items by itself.




Once you start to think of positional patterns, the sky is the limit! Almost anything you can use to make a “regular” type of pattern can also be used in a pattern that includes positioning.

Now that you know lots of ways to make patterns – ABAB, AAB, ABB, ABC, etc. – where do you go? Besides the different types of patterns we’ve talked about, there are different pattern skills. The easiest is copying a pattern. To do this, a child is shown a pattern and copies it, laying the same items under the presented items.



Once confident doing that, a child can move onto extending patterns. In this scenario, a child is presented a pattern and is asked what comes next, then places that item in the row, then is asked what comes next, etc. until at least two repeats of the pattern are completed.

PATTERN EXTENDING PHOTOThe last skill comes after much practice with patterns in their various forms. For this skill, a child is asked to create from scratch a pattern following one of the pattern types.



Once the children you work with begin to become confident with patterns, continue to challenge them with new and different types. Then let them create patterns that you or other children in the group have to try to extend. As they use their imagination to create new patterns, their understanding of the concept of patterning grows and grows!

Let us know what you have done with patterns this week by sharing in the comments section.


Patterns – An Introduction

posted by Debbie Lee

From birth, the human brain is wired to recognize patterns. It is how infants are able to figure out the world around them. Because of this, young children can recognize patterns from an early age. We get excited when a child says “foots” even though, in English, that is incorrect. It tells us that the child has internalized the pattern concept that plurals have an “s” on the end. What they cannot do automatically is match the vocabulary of patterns to the concepts. Just the word pattern is something that must be shared by a more advanced peer or an adult. Children are not born knowing the words particular to their language (English, Cantonese, Urdu, etc.) The labeling of patterns as ABAB, ABB, AAB, ABC, etc. also need to help of a more advanced helper.

That is where the adults in a child’s life (and, yes, the more advanced peers also) can help a young child to identify, extend, and create patterns. There are all types of patterns in this world and it is important that children be helped to recognize them in all their different forms. This is so important because, besides being an important math concept, patterns are also a science concept. Scientists make discoveries when they notice patterns in what they are studying.

Probably the easiest and simplest way to start with patterns is to use real objects. Pattern blocks are great for this (see photo below) but they are not present in most homes so that means looking for something else. Here the possibilities are endless!! Look into the kitchen drawers. Use forks and spoons to make a pattern. Coins – pennies, nickels, dimes, and quarters – can also be used. Have a piece of paper and some crayons? Cut or tear the paper into strips. Color each strip a different color. Then cut the strips into squares. Use the various colored squares to make patterns. Have books and DVD cases? Those can be used to make patterns. It is not necessary to spend a lot of money to make patterns. It just requires a little “thinking outside the box.” If you have ideas for everyday household items to use, share them in the comments section.






What are some of the different types of patterns? The simplest patterns are ABAB patterns. This would be fork, spoon, fork, spoon, etc. It could also be red, green, red, green, etc. An ABAB pattern has two elements that are placed alternately in a row. Because at all times we should be modeling important literacy skills, teach patterns that appear in a row as going from left to right, as the English language is written and read in that direction. You can progress to ABB or AAB or even ABC (three elements) as the child with whom you are working becomes comfortable with ABAB patterns.

I am challenging you this week to find various items in your house that can be used for making patterns. Then share your findings with the rest of this math learning community by telling us what you found in the comment section. I’m excited to read what

Blocks and Building

posted by Diann Gano

rainbow blocks     I am block crazy. I love blocks, particularly wooden blocks. Block play is so important in the early years to help children understand important concepts in measurement, spatial reasoning, comparison, estimation, symmetry, and balance. It fosters creativity and reasoning skills. Our home runneth over with blocks and we very often take these blocks outdoors. With all the emphasis on STEM and STEAM these days, block building is our passion, which fits in just wonderfully. You can’t teach creativity. It is learned through play; through trial and error and gifts of time to make their works of mastery grow.

Unit blocks used to be the standard in kindergarten classes across the nation. Teachers aren’t given the time or opportunities to allow children to explore with these very much anymore. It is vital that our children have time to play with these wonderful blocks. They are pricey, but definitely will be passed down for generations. We actually have a small set our family used fifty years ago, included in our block area.

large blocks

We have unit blocks in all sizes. There are tabletop versions and large hollow unit blocks. The hollow blocks also come in a smaller preschool size. We like to use those inside and the full-size hollow blocks outdoors. We also have Kapla blocks, Magnatiles, tree blocks, Legos, Duplos, Tegu, Korxx, the list goes on and on. We love them all.

My obsession with blocks may be partially responsible for the amount of building that happens daily, almost hourly around here. Block building is full of math learning possibilities. We have blocks in every room of our home, but we build indoors and outdoors with things other than blocks. When children learn to create with blocks, they take those skills and re-create that building in larger and smaller scales with supplies that are made available. Yes, loose parts!

Before I share with you our outdoor building set up, I want to share a bit about two of the blocks I mentioned above. The Korxx blocks are literally made from cork. They come from Germany and we have left them outdoors. That was the primary reason I bought them in the first place. However, the minute my “not so loving all these blocks” husband laid eyes on them he was sold. Why? They don’t crash and knick our hardwood floors. J True. So if that has been an obstacle for you and blocks, try these blocks. They stack great, they are quiet and are pretty close to unit blocks!

I also mentioned Tegu blocks. For those of you who haven’t been introduced to these, they are magnetic. The secret is the magnets are built inside these wooden blocks, so there is never a fear of choking or swallowing with young children. Genius, right? They also challenge our kids to figure out the polarity of the magnets, which is a true critical thinking skill, which we love! Tegu blocks are made by a socially responsible company that treats it’s workers, the land, and the people kindly. You can learn more about these beautiful and addictive blocks here.


outdoor blocks basket of blocks







On days when the yard is too muddy, the sun and humidity are stifling, or we have all just hit the wall and need a calming day, I set the stage. I usually do this on our deck, but depending where the sun or shade or wind is, other parts of our outdoor play space work also. You need a flat space to build on. The deck, sidewalk, any flat area will work. A sheet of plywood covered by a blanket or rug will suffice.


When setting the stage for block play, I usually start with the unit blocks, but we have acquired a large number of wooden blocks of different shapes and sizes that create for some wonder hours of play.

One of the reasons that I love blocks so much is that although it is often a group activity, it is very individualized.

children with outdoor blocksThere are six children playing blocks, they are all getting along just great because they are sharing space. They aren’t sharing blocks or ideas. It is very personal play above. It’s not always like that. It was on this given day. It’s the beauty of block play.building wiht blocks outdoor blocks play block structure babies with blocks balancing on blocks









It is always developmentally appropriate because the child creates at the level they are at. It’s very personal and very perfect! It is gender neutral. I also love to watch the mentoring and scaffolding that happens when children watch what their friends are building and how it was built. Block building follows the natural flow of children’s curiosity and concentration. They can try something over and over again until they are satisfied with their creation. When opportunities for math occur in such enriched environment and children are given the time to create, and think, they will develop the skills needed to be successful in the future.Our block area is also an ideal setting for loose parts to be added in. People are often added to the block area in the form of fairies, guys or Playmobile characters to name of few. We like people that don’t have a screen character associated with them because it allows for more imagination and creativity without repeating a scene we saw on television yesterday.

Our block area is also an ideal setting for loose parts to be added in. People are often added to the block area in the form of fairies, guys or Playmobile characters to name of few. We like people that don’t have a screen character associated with them because it allows for more imagination and creativity without repeating a scene we saw on television yesterday.

people sorted

Our farm and zoo animals are added, along with rocks, sticks and other natural materials.

block vehicle


If you have the great fortune to own a set of hollow blocks, taking them outdoors will change the amount of time they are played with and how they are played with. Often these blocks get lost in a closet because they are big, loud and heavy. These have all the outdoor big block cartelements needed for some great outdoor building. We first built a box to store them in and added them to a pushcart. This worked well for a while, but it was still a bit difficult to get in and out of the garage to play with.






bin of blocksoutdoor container






outdoor platform

We are constantly building something. It may be in the sandbox, or in the rain garden. It may be hideout or a hut. All that building is math. It’s problem-solving and logical thinking. It’s estimating and measuring. It’s creative and risk-taking. We need to take risks to try new ideas in our math equations. It’s all so very, very good.


small rocks with child in pinkrocks as blocks

The Five Senses of Math

posted by Diann Gano

We spend a lot of time outdoors. Playing. That play involves math in such natural ways that it is easy to overlook how often math comes into our lives. Research has found that early math proficiency is a better predictor of future academic success, high school graduation and college attendance than any other childhood skill. (National Governors’ Association, Unlocking Young Children’s Potential: Governors’ Role in Strengthening Early Mathematics Learning

So, here at Under the Ginkgo Tree, we encourage that investigation and provide materials that support children’s development of math concepts. Outdoors, the process for mastering the fundamentals of math is truly enhanced in a holistic and inviting environment. Come see how we create these opportunities using all five senses for all types of learners.

SIGHTexamining a tree trunk

Regardless of the season, we often spend time seeing how tall or small our friends are using resources that are available to us. Sometimes we use tape measures, but often we have other ideas.

Adding magnifying glasses, kaleidoscopes, and binoculars will slow your children down. They will look closer, longer, and think harder. Remember, we are giving them lots of time to investigate and explore and enjoy their childhood. Add these to your play space!

measuring with apples





mesauring with carrots








magnifying glass







Right! Three! Did you count? No, you subitized! We love to subitize. Subitzing is seeing a small amount of objects and knowing the number without counting. Playing with dice, you roll a six and without counting the 6 pips, you know it is six. We often play this game with fingers. We place both hands behind our back and then bring forward one hand with a few fingers showing. As they get better at this, we make it faster, or change the finger arrangement, or add both hands. We also work with subitizing outdoors with any given object. Kids love this game and I encourage you to play it often. Restaurants, long car rides, or waiting rooms are all great places to subitize! If you have fingers, and a bored child, subitize!


cutting vegetables cutting vegetables 1 snacks

Well, this one is almost too easy. If you put six cookies in front of three children and tell them to figure it out…they will. F A I R is a favorite math word that we hear around here. Everyone has to have EQUAL amounts of everything! Every meal we serve has some sort of math discussion available.

I invited the four-year-olds to help set up lunch. When they asked if they could cut the cucumbers, we discovered lots of investigation on size, direction, more, less, and equal.

When it came time to put out the fruits and vegetables, they created sets and counted out tomatoes, cut sandwiches in half. We had a math buzz going on!

Cooking is a great opportunity to bring in math vocabulary and concepts. When cooking with children, we always try to have enough bowls, utensils and, of course eggs, for each child to make their own portion. Think about it, if you watch your friend whip up her award-winning recipe, it’s just not the same as doing it side by side with your own version. This also offers great opportunities for mentoring and scaffolding with their peers on tricks for measuring and cracking eggs. It may not seem like math, but it is. If your body and brain don’t have the energy to deal with the egg mess on any given day, we have been known to cheat with the infants and cracked the egg into the measuring cup. That counts as an egg turn for anyone not old enough to roll her eyes at the thought of it. (Usually your four- year old.)snacks

SMELLsmell dandelion holding an iris

Those little noses often lead us to food. We routinely have

discussions about how many raisins or chocolate chips are in our cookies. We also like to smell in gardens and parks. Did you know that there is a math pattern in nature called Fibonacci? Some refer to Fibonacci as nature’s number system. From the pattern of florets on a flower to the bracts of a pine cone or the leaf arrangements in plants, the same number pattern appears over and over. The basic pattern is 1,1, 2, 3, 5, 8, 13, 21, 34… The next number is found by adding up the two numbers before it. It forms a spiral. This is a bit complex for most of the young learners in our program, but we talk about it and the spirals that we see in pineapples, and pinecones and flowers.

bunch of flowers

We often count the number of petals on our flowers. Last summer we planted perennials to our play space and included a number of flowers that include this Fibonacci pattern. Cala lilies have one pedal; euphorbia have two; triilium and some iris have 3 petals; buttercups and columbine have 5; bloodroot have 8, black-eyed Susan’s have 13; shasta daisies have 21 whereas other daisies can be found with 34, 55 or even 89 petals. Isn’t that crazy fun?

spring flowers


baby at fence baby ringing the bellSOUND

We live a block from a college campus and the bell tower. So every hour on the hour we have some counting sound opportunity in our own backyard. Music is an easy way to add math to your outdoor play space.

We have bells placed throughout our play area. We often have obstacle courses that include ringing a bell or drumming on a drum. Music is a big part of our lives. Singing songs, counting rhymes and fingerplays combine music and math. Really is there any better place for those loud drums, bells, tambourines and maracas? What were we thinking? These are outdoor toys!




bells on deck
baby with tamborine children with musical instruments




TOUCHacorns child holding an acorn

When you give children real materials to touch and smell and feel, the learning is deeper and more authentic. There is a major difference between touching real apples and moving them from basket to basket, than counting apples on a worksheet. Looking at stripes and circles on a page is not the same as touching and understanding that each rock has stripes or circle textures or has six shades of green. It makes sense to them. They control it. They aren’t rushed to move on to the next box on the worksheet. Give them real materials.

We talk about blocks and rocks often in our program. Those two things create an unbelievable amount of building. Building is math. We spend hours and hours building things that we may not ever even play in or with. We have spent days making forts. Sometimes, we don’t ever actually play IN them. We just build them. We build zoos, and fairy homes and squirrel traps. It is the building that is the fun, the creativity, and the play. Give your children time to touch, and think and process, and arrange and rearrange. It’s all good.stack of rocks

We also play games where one child plays a rhythm and the other needs to repeat it. There’s very often pattern play going on with this. For many children that rhythm and counting go hand in hand. When we follow singing commands to go in or out, or up and down, around and through, those build spatial awareness and reasoning skills that are important skills for geometry. Everyone is happy when we have music in our lives. Make your own or fire up Pandora!

Have fun this week noticing how often math is in your child’s life. It will make you smile and give you peace to know that you are doing just fine as a parent and an educator. Keep creating math environments and playing with your kids. It’s all quite simple. Put the worksheets away. It will come when their brain development is ready and it is relevant to them. Until then, just watch, listen and smell the learning coming their way!





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.



Pattern walk at the Field Museum

posted by Lindsay Maldonado

Today I visited the Field Museum of Natural History. Another one of my favorite Chicago museums. The Field Museum houses thousands of artifacts from dinosaur bones to pottery and clothing from ancient civilizations. Again you may be thinking, math? Isn’t this a natural history museum? With thousands of artifacts on display, math is easy to find. Just a quick walk through the halls brings you upon any number of dioramas with countless animals of all shapes and sizes.

It’s easy to count animals (Big Idea: Counting) or classify animals (Big Idea: Sets) by their varying attributes like size or color – but when you start to delve deeper into the exhibit halls you’ll come across other kinds of artifacts. There are cases upon cases of decorative clothing and art from cultures near and far. In my recent visit I happened upon the Hall of Native North Americans exhibit.

Native North American exhibit

At first you’ll be enamored by the craftsmanship. You’ll wonder how long it must have taken to create something so beautiful and intricate. You’ll wonder why Native North Americans wore such adornments but then you’ll notice something else; you’ll notice the shapes and patterns woven together or threaded with beads that make up each artifact. There are circles, squares, rectangles, diamonds, and triangles intricately designed to create simple and complex patterns. We see color patterns too.

Patterns exist in the world, as we see here, and also in mathematics. Through patterns, we find sequences bound by a rule (e.g., a chess board is made up of black and white squares, with a predictable black-white, black-white or AB, AB pattern) that brings predictability and allows us to generalize. Hence, we can predict, with a good amount of certainty, what comes next. Let’s look at a couple of these objects. What patterns can you find?


beaded ornaments

beaded bagThe beaded bag has blue and orange flowers arranged in a simple ABAB pattern. Each row alternates orange flower, blue flower, orange flower, blue flower, etc. It’s easy to predict what comes next. We see a similar ABAB pattern in the beaded ornaments (i.e., yellow blue, yellow blue). One big idea of patterns is just this; the same pattern can come in different forms.

We also see more complex patterns when you look more closely at shapes. Can you see the pattern?


decorative artPatterns are found in many places and children are particularly attuned to patterns. As we observed, patterns offer a sense of predictability, which children desire (e.g., we create routines for children to add order and predictability to their lives). When children understand the rule of a pattern they are able to extend that thinking to other situations.

Keep talking about patterns in the classroom! You can search for more activities about patterns 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!

Using Children’s Literature to Reinforce Classification

posted by Dr. Jeanne White

When older children and adults perform chores such as doing laundry or putting away dishes, they may not even realize they are making decisions about how to classify objects into categories—washing the white clothes together and putting the plates together on a shelf.  Young children can begin to see how objects can be sorted into categories with the help of several children’s literature books.

Young children naturally sort objects by color.  Have a variety of books available that introduce colors and show objects of a particular color so children can make associations with the object and the color.  A fun book that can be used to explore colors is The Color Box (Dodds, 1992), in which a monkey named Alexander crawls into a box to discover a world where everything is black, then another where everything is white, then yellow, and so on until he ends up back in his world where there are objects of every different color.  Then provide groups of objects that can only be sorted by color such as Unifix cubes or square tiles.  Once children have sorted these objects by color, they can count the number of cubes or tiles in each group and compare them—which group has the most?  Are there more red cubes or more orange cubes? Then make several types of objects available for children to sort by color such as beads, tiles, cubes and blocks.unifix cubes scatteredunifix cubes and other shapes

After children have had several experiences sorting objects by color, they can begin to explore other attributes.  In the book, The Button Box (Reid, 1990), a boy visits his grandma and finds a box with hundreds of buttons inside.  He sorts them into categories such as buttons covered with cloth, sparkly buttons, metal buttons and buttons from uniforms.  He also lines them up based on size and color.  At the end of the story, the boy and his grandma close their eyes and each choose a button from the box.  Then they look at them and talk about all of the ways the two buttons are alike and the ways they are different.  Follow up the story with a game similar to the one in the story, by comparing two buttons or other toys that have similar attributes such as two dolls or two cars.

Another book that can be used for classification of objects is How Many Snails? A Counting Book (Giganti, 1988).  On each page there are illustrations of one type of object but they vary by size, color or design.  On the first page there are eight clouds for children to count.  Then there are more questions to answer, “How many clouds were big and fluffy?  How many clouds were big and fluffy and gray?”  Children can use their toys to count, sort and answer questions such as, “How many frogs?  How many frogs are yellow?  How many frogs are yellow with a green stripe?”  Incorporate science by introducing various types of insects and asking children to tell you how they can sort them—by putting all of the insects that are the same color together or by putting the insects with wings in a group. four frogs

When children sort and classify objects into groups, they are building a foundation for graphing and data collection.  grasshoppersThey can create unique ways of sorting objects into groups and once they know how to put objects into categories, they can help with all of those chores!