“Do you know about our Magic Tree?” four-year-old Rowan asks Alex. She pauses dramatically before passing on the secret of the beloved old tree that has long been a source of delight and inquiry for the children in our early learning program.

“Watch, Alex!” she instructs. “I will push this stick into the tree, way up here, and say ‘Hocus Pocus.’ Then I can pull the stick out of the tree way down here at the bottom!”

Alex is the perfect audience for Rowan’s magic trick. I watch as the rest of the gang joins in the fun to demonstrate the tree’s “magical” abilities, much to Alex’s amazement.

“See?  I put the stick in this circle hole. It’s a hollow tree! There isn’t any tree inside, it’s just a hole!” explains Rowan. “And then you can pull it out down here at the bottom of the tree!”

“The tree is hollow?” Alex repeats in wonder, moving closer to the tree to peer into the hole.

“Yep, it is!” exclaims Owen, who has just joined the gaggle of STEM explorers gathered around the tree. “So you can just push your stick in and say the magic words and pull it out down here!”

Our Magic Tree has evoked wonder and curiosity in the entire gang, sparking a STEM investigation that helps lay the foundation for later math, science and engineering learning. Nature has provided the ultimate learning tool and transformed a moment of outdoor play into an exploration of the concepts of spatial relationships and geometry.

As the children explore the Magic Tree, each moment of learning comes naturally and at each child’s developmental level. When the older children share the secrets of the tree with younger learners, relationship building and trust building add to the magic of the moment.

An understanding of spatial relationships helps children talk about where things are located. Physical, hands-on play like this helps build a child’s mathematical vocabulary in a natural way that is easily understood. When a child can push a stick through a cylinder shape, the concept behind the word through is easier to grasp.

So we allow the children to investigate by pushing sticks down the circle hole, through the hollow part of the tree and out again through the bottom of the trunk. This exploration of spatial relationships—which leads to an understanding of where objects are in relationship to something else—is an essential building block for later math learning.

Children need to learn the language of math to think through and solve their math challenges and then communicate their thought processes to others.

When children play and experiment with sticks and hollow trees with their friends, they learn how to problem-solve and put their thoughts into words. This strengthens their understanding of early math concepts as they use math vocabulary words repeatedly throughout their play.

Geometric shapes are a kindergarten common core standard. When children actually play with (and within) these shapes as they explore the inside of the hollow tree, the learning becomes deeper, more intentional and more relevant.

“I think it’s stuck!” yells one child.

“Wait! How many sticks are in there?” asks another.

We begin to get a better sense of measurement as we visually estimate the length of a stick that will fit into the hollow tree and come out the other side.

Opportunities like these are rich in learning, creativity and teamwork as we share theories and develop hypotheses about stick sizes and shapes, as well as angles of insertion, that will result in the “magical reappearance” of the stick at the bottom of the tree.

Problem-solving play helps children develop foundational skills that will be used in math learning in the years to come. Our gang of STEM explorers is busy making predictions, gathering data, studying cause and effect and organizing their information to try something new. We are knocking out those Illinois Early Learning Standards by the minute!

“Can we make the stick go UP the tree?” wonders Linnea.

“I’ll try!” Rowan chimes in.

Hands-on learning also enables children to take their understanding to a deeper level, so that they can analyze the information that they have collected and then apply this knowledge when they create their own experiences.

The children’s enthusiasm for experimenting with the Magic Tree is contagious. When we let children learn through play, movement and trial and error, we lay the groundwork for the kind of deep learning that builds new neural connections. These are the moments that inspire our early learners to investigate the possibilities.

When we introduce children to the vocabulary of math, we are building a foundation for future math success. This early math website has a fabulous glossary of math vocabulary words.

Introduce these vocabulary words into moments of investigative play and you’ll not only see but “hear” the connections being formed in the brains of your budding mathematicians.

If you don’t have a magic tree nearby, a large box can create the same kind of magic. Cut two holes at different heights on opposite sides of the box and bring in yardsticks or other long objects. This can also be done on a smaller, individual scale with oatmeal boxes and rulers or pipe cleaners.

The possibilities are endless, so let the STEM magic begin!

Looking for more ways to explore math concepts such as measurement and length? Check out our Links and Length lesson plan and parent letter here >

Each spring, we eagerly anticipate the arrival of the growing season—from the greening carpet of grass to the buds bursting into blossom on the trees. We especially delight in the dandelions that can turn any grassy area into a STEM wonderland!

Dandelions introduce so many math adventures into our early childhood program. The neighborhood park is our favorite destination for a day of dandelion STEM adventures.

Our spring dandelion days create hours and hours of exploration, investigation, observation and just plain fun!  Mother Nature is serving up math opportunities everywhere we turn!

When we find ourselves in these nature-based outdoor classrooms, the learning is always developmentally appropriate and child-centered.

On the day that this photo (above) was taken, the flowers were too tall to spend much time on patterns or subitizing or blowing seed heads in the wind. We kept finding longer and longer stems, some with flowers and some with wispy white seed heads.

The giggles were contagious as the children continued to find taller and taller dandelions. It was a day that was unplanned, so the measuring tapes were back at school, but it didn’t matter!  This was a great moment for estimating, predicting and comparing attributes side by side.

“My grammy says the tallest dandelion you can find equals how many inches you will grow before your birthday!” said one STEM explorer.

Oh boy… GAME ON!  Giggles and screams of discovery floated down the hillside as our dandelion math morning took on a life of its own.

“If you grow that much, you will be a GIANT!” predicted one preschooler as Violet studied a dandelion stem that must have been at least two feet long.

“Violet! You keep finding longer and longer stems!” exclaimed another. “Wow, look at the one behind you!  Add that to your collection! Are the tallest ones up there?”

When you are yards away from your friends AND on a hill, it’s hard to determine who has found the tallest dandelion until you walk over to compare sizes and see which dandelion has the longest stem.

Measurement is one of the earliest mathematical concepts that children learn.

Comparing the sizes of objects, determining which stem is the longest, comparing which child is the tallest and identifying that a friend is high up on the hill are all examples of the ways that young learners begin to understand the concept of measurement.

By building on this rudimentary understanding, we can help lay the foundation of logic, reasoning, comprehension and critical-thinking skills that will lead to later math success.

“Did they all grow from the same seed family?” mused one dandelion hunter.

“Maybe we blew on a tall dandelion the last time we were here and the seeds got planted in the ground and grew this tall,” postulated another.

Whoa, now those are some interesting ideas! But, before we could discuss their theories, the children had moved on to yet another area of investigation.

“Hey guys! You need to pick the flower at the very, very bottom of the stem to keep your stem super long,” instructed one of the older children.

This concept was way beyond the comprehension of some of our younger friends, despite the efforts of the other children to teach them.

Ah, the beauty of multi-age groups. The beauty of allowing learning to take place as the brain and physical development allows. The beauty of friendships and childhood on a sunny spring day, when all of the stars (or, in this case, dandelions!) align and the learning comes so naturally.

I knew that we were using our math vocabulary when I heard the words, “height, tall, taller, tallest, short, shorter, shortest, long, longer, longest, more and less.”  These simple but important words proved that the children were reaping the benefits of this springtime STEM lesson without the support of lesson plans or a word wall.

Exposure to experiences such as our Spring Dandelion Day STEM Adventure enables early learners to begin to interpret the mathematical qualities in real-world settings.

By observing, measuring, comparing and analyzing objects in their environment, they are also learning more about the world that they live in.

Our springtime “field study“ offered an invaluable opportunity for young learners to practice early math skills while guiding their own mastery of important math concepts.

The experience was an empowering one for every one of our STEM explorers, inspiring the children to build on their nascent knowledge by seeking out new ideas and experiences.

Carve out time and opportunities for your early learners to acquire, practice, rehearse and build upon the skills that will carry them through their academic life. Your math curriculum and early learning standards are outside—just waiting for you!

Click here for a lesson plan on Flower Fun and measurement for your class!

Two-year-old Elizabeth screams with delight, “I made a ball, I made a ball!”

Ah, it’s another magical moment with clay. Making shapes, discussing length, adding loose parts or subtracting pieces of clay to share with a friend. There is a whole lot of math in that ball of clay! Clay allows children to build in three dimensions, unlike coloring and painting. Children get to experience their first lessons in geometry as they begin to grasp concepts such as form, shape and perspective. When we talk about building that strong foundation for math success, we can add clay to our list of building materials. This month, I would like to help you set up a math-rich environment with clay or playdough—and I promise not to let it get too messy!

Containing the clay

When I returned from a study tour in Reggio Emilia, Italy, I tried to recreate the clay-rich environment that I encountered in the schools there. It did not work for me. Their resources and set-ups were far different from mine. As a one-teacher classroom, I needed something that was simple, easy and not too messy. Yet I saw the many benefits of clay, so I set out to create a design that would work for me. We use our clay indoors and outdoors, but there is one basic rule that I live by: All clay stays at the table. A hard lesson for our traveling two-year-olds, but they love clay so much that they always return to the table.

My favorite clays

We all draw our lines in the sand. That invisible line that says, “This item is more than I care to deal with.” For many early childhood educators, that item is playdough. If you hate playdough, give clay a try. If you use playdough already, you may want to add clay to your classroom. After we started using clay, we rarely went back to playdough. I’ve discovered two versions of clay that I really, really love. If money were no object, I would spend my days playing with Jovi Plastilina, a non-toxic, non-hardening modeling clay that is excellent for young artists with small hands. When I’m on a budget, which is always the case, I purchase a classroom pack of Crayola modeling clay, which contains 24 packs of clay in 12 colors. It never dries out and it’s easy to mold, even for my youngest learners.

My favorite trays

Trays give us a sense of order and add to the beauty and calmness of clay time. I love keeping our clay and loose parts in trays or low baskets. Chip-and-dip trays work very well. I like trays that are divided into sections. Small compartments invite children to touch and explore new materials with their clay.

Themed clay trays

We have nature-based trays, beach-themed trays and people-building trays, to name just a few. Trays will make your clay activities so much easier. When my students were robot crazy, I created a tray full of robot-inspiring parts such as googly eyes, straws, pipe cleaners, bottle caps, corks, gems and other oddities. This simple tray gave rise to an abundance of math language skills, including words like on, in, under, beside, above and below. Predictions about how tall a robot could be before its head became too heavy for its body. This is math! Don’t worry about actual number recognition or addition facts. This is our deep math foundation that is strengthened through play. 

The possibilities are endless!

Clay and playdough offer many rich opportunities for mathematical reasoning and thinking. By creating a math-rich environment with clay and loose parts, you will fill your room with limitless opportunities for children to construct, invent and think divergently. Children will be introduced to measurement, spatial awareness, similarities, problem-solving and sorting and classifying every minute that they are working with clay. It’s a math extravaganza, all in one little ball of clay!

The units are color-coded which provides additional visual cues for children. If you look carefully at the above photo, you can see that the units of 1 are white and the units of 2 are red, units 3 are green and so on.  When using them with children, you can refer to the lengths by their unit number as well as their color.

Unlike Unifix cubes, traditional Cuisenaire ® Rods do not attach to one another (although there are sets that do attach).  This provides a different set of possibilities for children as their uses may be less obvious and may require a bit more ingenuity.

A few weeks ago, I wrote about the “trading game” that is played with the family bear counters. Well, a more developed “trading game” can be played with the rods since each of the rods has a specific value.  White is worth 1 and red is worth 2 and green is worth 3.  In order to get a green rod, children must trade 3 whites, or 1 white and 1 red.  Give this a try and tell us what you think.

Children’s hands are also a great tool for measuring.  Since each child’s hands vary in size, it is important to use the mathematical language “nonstandard unit of measure” so they all know that their answers will be different depending on the size of their hands.

What can their hands measure?  They can use their hands to measure length, by placing one hand down and then the other right next it, and continuing until they have spanned the length (or width) of whatever they are measuring.  This also works well if the children trace their hands and cut them out, so the cut-outs can be used as the measurement tool.

Hands are also a great tool to measure quantity.  Using the questions, “How many” or “How much” children can explore quantity in meaningful ways.  “How many Unifix cubes can you hold with one hand?” or “How much sand can you carry with one hand?” are realistic activities that can be explored with several children.  They will discover that bigger hands hold more and smaller hands hold less.  However, they will also find out that it takes fewer larger hands to measure a length and more littler hands to measure the same length.  Be prepared for how confusing this might be for them.

Try using hands as manipulatives and let us know  how it goes.

There are few manipulatives out there that are as interesting and beautiful as a wooden set of Cuisenaire® Rods.  Developed 75 years ago by Belgian teacher Georges Cuisenaire these “rods” come in beautiful colors in varying lengths.

Using Cuisenaire® Rods to compare length is as simple as putting shorter rods next to longer rods and seeing how your children observe those differences.  Although these manipulatives were designed for a very specific purpose (units of 1, 2, 3, etc.) I think  it is far more likely that children will explore the rods by laying them out, standing them up, and comparing them.

Most young children will be able to identify which rods are shorter and which are longer, especially when they are laid out next to each other.  It is far more difficult for children to compare several rods of differing lengths simultaneously.  Putting many of them in order from shortest to longest is really challenging because it asks children to think about 2 things at the same time; which rod is shorter than these – but longer than the others?

If you look carefully at the above photo, you can see that the units of 1 are white and the units of 2 are red, 3 are green and so on.  They provide a visual representation of number units, up to 10, or for today’s purposes shortest to longest.

Links are one of those really versatile manipulatives that children will play with throughout their young lives.  As infants, they will use them as chew toys as well as to connect their other toys to something.  Later, children will connect them to make chains that are “long” or “longest” or to go across the room.

They can also be used to show numerical differences over distance. For example, stretching a 10-link chain next to a 5-link chain shows that it is twice as long.  You can also explain that the 5 link chain is half as short.

Links provide children with a nonstandard unit of measure. Here is a great lesson plan that uses links as way to measure common household areas.

Click here to see a video of a child using large connecting links in a whole other way.

When I was growing up my parents measured my sisters and I against the door jamb of the kitchen.  You could see our upward progress with names and dates.  I remember thinking that leaving that evidence of our growth was so sad when we moved out of my childhood home.  My husband and I have done exactly the same thing with our kids.  When I look at it now, I can’t believe that they were ever so small.

You can measure your kids on the wall (covered with a piece of paper) and make marks to show each child’s height.  You might place each child’s picture next to her/his mark so they can see themselves.  This now means that the children can compare the heights of the children in their group.

Here is a link to a lesson plan that involves length measurement using a nonstandard unit of measure.

The measurement of circumference is hard.  It is hard to imagine how big something is in general and it is really hard to imagine how big around something is. Children may be able to tell you that one apple is bigger than another, but it is really difficult for them to see more than one aspect of a problem at the same time.  They are also fooled by appearances, so if you hold up one big apple that is rather skinny and another apple that is short and fat, the child cannot see both of those aspects at once.  S/he will therefore choose the most obvious attribute to base her decision on which one is bigger.  The child may choose the fat apple because it is fatter, or the tall apple because it is taller, but the child cannot tell you which one is actually bigger based on measurement.

In order to measure the circumference of apples, you will need several different sized apples and string.

Give each child an apple to measure and then give them each a length of string that will easily go around the middle of the apple.  Have the child hold one end of the string up against the apple and then pull the string around the apple until it meets at the other side.  Go around and help each child cut the string where it meets.

Once they each have their strings, you can lay them on the table top and compare the lengths of string, explaining that the length of the string is the “circumference” of the apple.  They can observe their apples and their strings to come up with their own conclusions about how the measurement worked.  Be sure to tell them that the longer strings represent a bigger circumference.  Make sure you use all of this great math vocabulary to continue exposing children to it.