“I’ll carry the biggest container,” volunteers four-year-old Matthew as the younger children fall in behind him.

Picking strawberries during the first week of summer break is an annual tradition in our early childhood program. What better way to learn about counting, measuring and estimating than to get out in the fresh air and sunshine and enjoy hands-on activities that engage all of the senses—from seeing and hearing to touching, tasting and smelling?

I am fairly certain that we are eating as many strawberries as we pick! But that makes this math-packed adventure even better because children learn best through their senses.

The friendly folks at our local U-pick farm assign us a numbered row to pick from, which gives us yet another way to factor math into our strawberry-picking adventure: number recognition!

“We are in Row 66 today,” I call out to the children as they march behind me, wearing their strawberry boxes as hats.

As we walk past each row, Matthew begins to count, “1 . . . 2 . . . 3 . . .”

“I can do it!” blurts out three-year-old Owen. He races to the front of the line, positions himself at Matthew’s side, and picks up where his older friend left off:  “4 . . .  5 . . . 6 . . .”

Matthew gently takes over the counting when Owen reaches the limits of his number knowledge at the 13th row. But as Matthew counts out the double-digit numbers, I can hear Owen echoing him, which is a great way for Owen and his younger peers to practice their counting skills. 

“Row 66!” Owen stops abruptly and swivels his head from left to right as he surveys the row dotted with bright red strawberries just waiting to be picked. “There must be millions,” he observes in awe.

Maybe not millions, but this is a great opportunity to introduce concepts such as quantity and estimating. In fact, one of the best places to strengthen math skills is in the garden.

“Kindergarten” is a German word that literally means “children’s garden,” which covers Froebel’s concept of “a place for children,” as well as his beliefs regarding childhood growth, development and learning (Elkind, 2015).

Teaching math in a garden comes naturally as children count, sort, find patterns, and organize by size, color or other attributes.

“Look at how big this strawberry is!” Owen exclaims excitedly. “I bet it’s the biggest one we find all day!”

What starts out as a competition to find the largest strawberry is soon replaced by relaxed camaraderie as the children bite into the sun-warmed fruit and the juice stains their lips, chins and fingers bright red.

“Close your eyes and open your hands,” Asa tells Harper as she plops a strawberry into each of Harper’s outstretched palms. “Now tell me which strawberry weighs more.”

Harper obliges. “Definitely this one!” he answers, holding up his left palm and opening his eyes. “But that’s weird because the heavier strawberry is smaller . . .” 

“I know! I thought that was weird, too!” Asa replies.

Hands-on activities with everyday objects help children learn about measurement. Moments like these also offer real-world opportunities for them to discuss math concepts such as size, weight and capacity.

Children need to talk about mathematical concepts and share their theories with one another and their teachers.

“I wonder which basket will weigh more?” I ask Joseph. “Your basket with eight big strawberries or Vera’s basket with 14 little strawberries?”

“Vera’s! She has 14!” shouts Joseph. We decide to weigh them after we’re done picking to see if his guess is correct.  

“I found a double strawberry; I bet it weighs the most!” announces Gabriel with a mischievous grin.

“That’s not FAIR!” the gang whines in unison.

Gabriel laughs. “It’s really cool. I’m taking this one home to show my mom and dad, so please don’t eat it!”

We finish filling our baskets and make our way to the checkout to see how many pounds we’ve picked this year. The sun is getting warmer and our legs are getting weaker. It’s time to rehydrate with some cold water and refuel with a protein-packed lunch.

We’ve picked 13.2 pounds of strawberries! The eight big strawberries in Joseph’s basket did weigh more than the 14 small strawberries in Vera’s basket—but only by two ounces.

No one seems to care. The sun and the heat have sapped us of the energy and enthusiasm we need to discuss size and weight at greater length, but there will be other chances when we return to the classroom.

Although some of these concepts may be a bit too advanced for some of the younger learners in the group, we have planted the seeds for future academic success during a day of fun in the strawberry fields.

Later, back in the classroom, we set up a farmer’s market and invite the parents to purchase baskets of strawberries from their children, who serve as cashiers.

In the days ahead, there will be lots of strawberry snacks, jam-making and strawberry smoothies—along with more opportunities to learn and share early math concepts. 

Sink your teeth into some juicy math this summer. Whether you make it to your local farm, the farmer’s market in your community, or simply introduce fruits and vegetables into your early learning program, there’s plenty of math packed into that yummy summer produce!

“Oh, I like your mosaic, Avery!” says Claire, who has wandered over to look at the mosaic that Avery has just created with sidewalk chalk and tape. “Yours only had triangles. We did squares and triangles and those long skinny squares.”

“Oh, you mean rectangles! I want to see it!” Avery exclaims. He jumps up to compare their creations.

Our days have been full of busy children drawing shapes and creating colorful chalk mosaics on the sidewalk. This activity offers many opportunities to work on shape recognition while extending the learning to the outdoor classroom.

Start by creating a shape on the sidewalk or a flat surface with masking tape. Divide the inside area into smaller shapes. If this is your first attempt at introducing chalk mosaics to your students, I would suggest beginning with a few small areas that measure about two feet by three feet, with smaller shapes inside.

Why start out small? The children can see results faster—and smaller is better for our youngest students, who haven’t yet developed the hand and wrist strength to color in larger shapes. On a more practical note, I’ve discovered that smaller shapes are better when the children are using smaller pieces of chalk.

You can always go bigger as the children get the hang of chalk mosaics. If you have an endless supply of wasabi tape, this easy-to-tear tape enables them to create their own shapes inside the larger shape. 

Leaving a basket of chalk nearby will invite the children to start coloring in the shapes. Once the children have completed the mosaic, simply remove the tape and admire the masterpiece! 

As your students learn to identify shapes, they can use spatial orientation vocabulary to describe the relative positions of the shapes. Preschoolers should understand and be able to use positional words such as above, below, beside, in front of, behind, next to, between, on, over, under and inside.

Shapes are the foundation of geometry. Geometry involves shape, size, position, direction and movement.

In early education, geometric skills include identifying and comparing shapes, differentiating between shapes and creating shapes.

Children need hands-on investigation to understand more than just naming or classifying shapes. Our chalk mosaics introduce children to simple shapes—as well as more advanced concepts such as symmetry, angles and fractions.

“My chalk is shrinking really fast!” giggles Rowan.

Oh, how I love shrinking chalk! Yes, we are definitely collecting data, making observations and noticing cause and effect.

But there’s more happening here than meets the eye. We know that the transition to smaller writing utensils helps promote the development of better gripping skills. As the children continue to draw and their pieces of sidewalk chalk get shorter and smaller, they are effectively transitioning to smaller writing tools and increasing their grip strength.

We try not to rush writing in our young learners. But when it happens spontaneously, we try to promote the use of smaller pieces of chalk, crayons or pencils to help them develop age-appropriate gripping skills.

These are all bonuses for kindergarten readiness—above and beyond the early math learning standards. This is the foundation that we talk about when we play our way into academic life. These small steps will enable our children to succeed when it’s time to sit at a desk. 

I have a few insights into the hidden benefits of chalk play—insights that can be shared with parents who may question the value of outdoor play and its role in advancing their children’s kindergarten readiness. Kindergarten, sadly,  involves a lot of sitting time. Children need strength throughout their bodies—including strong core muscles to sit all day. When children get down on their hands and knees and support their upper-body weight with their arms and hands, this strengthens their core muscles, as well as their shoulder muscles, which are so important for fine motor dexterity.

There’s a lot of math built into our chalk play. Follow the lead of your students, connect the curriculum to the play and you’ll meet your learning standards every day!

Looking for more ways to play with shapes? Extend the learning with these Early Math Counts shape lesson plans!

“When we drive to school in the morning, the sunflowers are facing one way and when we drive home after school they are facing the other way. That’s because they always want to see where I am going!” brags Melania to the other children on the bus.

“That’s not true,” grumbles Roberta, who is clearly not a sunny morning person.

“Yes, it really is true! Melania insists. “Ask my dad!”

I planned this morning field trip to a local sunflower farm to set the stage for some hands-on STEM learning. But it’s going to be a long Thursday if the kids are already arguing about the science behind the sunflowers we are about to see.

Hoping to lighten the mood on the bus and soothe the “hangry” Roberta, I reach into my bag and pull out some Sun Butter Energy Bars.

“Actually, what Melania is saying is partly true,” I explain as I hand out the energy bars. “As a sunflower grows, it turns its face to follow the sun from sunrise to sunset. So the sunflowers do face in one direction when Melania sees them in the morning and another direction when she sees them in the afternoon.”

By the time we arrive at the sunflower farm, the energy bars have worked their magic. Roberta’s morning grumpiness has dissipated, everyone seems perkier, and the group is staring at the giant flowers in amazement.

“Look at how tall they are!” gasps Lauren. “They are even taller than the grownups!”

“Can I touch one?” asks Lauren. She reaches up and touches the center of the sunflower. “It’s bumpy,” she observes. “Wait, inside the middle, are those all little tiny sunflowers? Look! There are a million little tiny flowers inside the big flower head!”

Maybe not a million, but this is a great opportunity to introduce concepts such as quantity and estimating. In fact, one of the best places to strengthen math skills is in the garden!

Whether you bring flowers into your classroom, plant a school garden or take a field trip to a sunflower farm or a pumpkin patch, you can extend the learning by creating hands-on opportunities for children to practice their early math skills. When children observe, measure, compare and analyze their surroundings, it helps them make sense of their world.

“Look how big this one is!” says Jason, staring up at an enormous sunflower in awe. 

I pull out a measuring tape so that we can measure how tall it is. We discuss how to measure an object. This leads to a conversation about concepts such as diameter and circumference.  Of course, these concepts are too advanced for this group, but I like to “plant the seeds” for later vocabulary development.

As we wander through the sunflower farm, I prompt the children with conversation starters such as:

“I wonder how many seeds they planted.” 

“I wonder how tall the sunflowers get.”

My goal? To inspire the children to find the math hidden in this field of sunflowers and start asking questions of their own.

“I wonder how many times people get stung by all those bees hanging around the sunflowers?” muses Roberta.

“There are a lot of bees!” responds Melania, ever the Pollyanna to Roberta’s pessimist. “But they aren’t bothering us. They are so busy eating nectar that they don’t even know we are here.”

“Look, this one has four bees on it!” observes Jason. “Look, Roberta! Let’s see if we can find more!” 

When children are learning to count, they love counting anything, even bees! By teaching math in the garden, you can show children how we use math in our daily lives.

Soon the children are comparing the sunflowers in the field, using math vocabulary words such as big, bigger and biggest, small, smaller and smallest, and tallest and widest.

When you return to the classroom, you can build on this lesson by encouraging the children to arrange flowers, fruits or vegetables in order from smallest to biggest or biggest to smallest.

Our morning at the farm has inspired a morning of math-filled conversations. From the shapes that make up the sunflower, to counting bees to measuring stalks, math concepts come to life when we take the time to look for math in our everyday encounters.

Ready to find more math in the garden? Check out these Early Math Counts lesson plans: The Tiny Seed and Flower Fun.

“I-am-a-robot!  I-can-do-anything!” squeaks Terrell in his best four-year-old robot voice.

“Oh, I like that you used that octagon for your robot’s head,” says Michaela. “I am going to try that!” 

We are deep into robot construction this month and robots are popping up all over our play spaces. We are constructing robots from clay. We have block robots. We have MagnaTile robots and button robots. What a great opportunity to work on shapes and spatial reasoning! 

When children play with shapes, they are building rudimentary skills that lay the foundation for later math learning, as well as reading and writing. Shape recognition and identification can help children understand signs and symbols. Children begin to notice shapes before they have the language to name those shapes. In the toddler and preschool years, children learn to name their first shapes: circles, squares, triangles and rectangles.

Shapes are the foundation of geometry. Children need hands-on investigation to understand more than just naming or classifying shapes. Our robot play acquaints children with simple shapes—as well as more advanced concepts such as symmetry, angles and fractions—as they engage in activities such as measuring, counting or investigating 2D and 3D shapes.

Geometry involves shape, size, position, direction and movement. In early education, geometric skills include identifying and comparing shapes, differentiating between shapes and creating shapes.

During our robot-building bonanza, the children are combining shapes in their constructive play. I watch as they learn that they can combine two squares to make a rectangle. They begin to see what happens when they turn a shape upside down. It is still the same shape even if it looks different. 

Research suggests that preschoolers’ early mathematics learning—including spatial-thinking skills—is related to later success in both reading and math. When children hear us use spatial terms to describe the size, shape and location of objects—and then adopt those words themselves—they perform better in activities requiring spatial skills.

Playing with blocks and puzzles and using spatial words such as above, below, across, on top of, inside and outside enables children to talk about where things are located. This strengthens their understanding of these concepts as they use the vocabulary words repeatedly throughout their play.

Geometric shapes are a kindergarten common core standard, and when children actually play with shapes, the learning becomes deeper, more intentional and more relevant. When children manipulate 3D shapes during hands-on play, they build a deeper understanding of these shapes.

Research has also shown that young children’s spatial skills—rather than their numerical abilities—predict their overall mathematics achievement. The key skill is visualizing what the shapes will look like when they are combined or rotated (Young et al., 2018). A focus on shapes and spaces may provide a more accessible route to math for some children, rather than focusing on numbers alone.

Spatial reasoning develops when children learn how to recognize relationships between 2D shapes and 3D shapes. How is a circle like a ball? How is a square like a box? As children discover that they can rotate, flip and rearrange shapes in different ways to change their possible shape and direction, they become increasingly aware of 2D shapes.

There is a lot of math built into our robot play. Follow the lead of your students, connect the curriculum to the play and you’ll meet your learning standards every day! 

Looking for more ways to play with shapes? Extend the learning with these Early Math Counts shape lesson plans! 

Today is one of those magical winter mornings when snow blankets the ground and clings to the trees around our center.  The sun is shining and the world looks so sparkly and irresistible that we head outside in spite of the freezing temperatures.

“Hey! Who has the smiling boot?” Jacoby calls out to the group. He scans the play space, which looks like a snowy white canvas dotted with boot prints.

“Do you have the smiling boot?” he asks Maria.  

Maria looks confused as she glances down at her boots. “No, my boots are pink.” 

“No, no…on the bottom!” Jacob points to her boots. “Does your boot have a smiling face on the bottom?” 

Even I am confused by Jacoby’s question—until he points to the clue in the snow. 

“Look!” he declares. “Somebody has a smiley face on the bottom of their boot.”

Ah-hah! Indeed, we do have a smiley face boot print staring up at us from the snow-covered ground. Well, this will warm us all up!  Let the STEM investigation begin!

After a fresh snowfall, it’s so much fun to find and follow animal tracks. But we’ve never really paid attention to the patterns on the soles of our boots until now.

One by one, Maria and Jacoby begin to check the bottom of each friend’s boot. This simple moment of exploring patterns leads us to measurement, reasoning and comparing attributes.

Young children instinctively seem to notice attributes. It may be the shape, size, color, length or some other characteristics of an object, such as today’s smiling boot face.

Children develop their understanding of matching and patterns through experience. Because it’s difficult to consider a lot of attributes at once, children often begin creating sets by finding exact matches.

When children create pairs of boots or find an exact match to the smiling boot face, they are creating sets of items that are exactly alike. Maria and Jacoby are using rudimentary math, science and engineering skills as they observe and ask questions—all while solving the smiling boot print mystery!

Suddenly, everyone is stomping their boots and comparing and analyzing the shapes and patterns that their boots are leaving in the snow.

“I have zigzags!” announces Liam.

Sure enough, as we all run over to look at Liam’s boot print in the snow, we see row after row of zigzags.

“They look like mountains!” laughs Rokia. “That’s so cool!”

 “I have rectangles!” announces Rachel. “If I turn around, it looks like a house with a roof. Look!  See, at the bottom of my boot print?”  

Our focus is now very intentional and the mood has shifted from playful curiosity to deep observation and concentration. 

This is what child-led learning looks like. For those of you who believe that “child-led learning” can only lead to chaos, I urge you to put on your winter wear, head outside and see how effective and wondrous it can truly be.

“I have diamonds!” shouts Julio, “Oh and triangles at the top and bottom. Wow! Look at my boot print, it has really cool patterns.”

We are working on spatial reasoning, direction and positional vocabulary. This is the deep learning that takes place when children have ample time to explore and investigate.

Every day, children learn something new.  Every day, they deepen their understanding of STEM principles and share their insights and theories with their fellow STEM explorers.

Time is the key to deep learning!

“I have snakes!”  Josie shouts.

“Snakes?” 

Everyone comes running to see the newly discovered boot-print pattern. And, yes indeed, Josie’s boot print really does look like snakes.

But Isaac sees it differently. “I think it looks like waves,” he counters. “You know, like when you throw a rock in the river and it makes those lines?”

Then five-year-old Maya reorients the group to the smiley-face boot prints that started the morning’s STEM investigation.

“Where did that smiley face boot come from?” she asks, putting an end to the snake-shape and wave-shape discussion.

“I don’t know!” retorts a frustrated Jacoby. “That’s what I am trying to figure out!” 

“No, I mean, where did the smiley face boot print start?” Maya clarifies, assuming the role of lead investigator. “Where did you find it? Did you follow it, like we followed the cat paw prints last winter?” 

Jacoby pauses and I can see the wheels turning as he considers Maya’s questions. This is a lightbulb moment when the children suddenly recall a forgotten game from winters past. We have plenty of wandering cats in our neighborhood. For years, we have engaged in follow-the-cat-print expeditions on snowy days, following the tracks and trying to figure out the exact route that the cat took and why. Today has ushered in a new season of snow—and now we are rediscovering the game all over again.

Five-year-old Maya has had a few more years of brain development and a few more years of winter play, so she has retained more memories of those snowy-day games than the younger children who started the smiling boot print investigation.

Suddenly we are tracking movement, direction and the changes in how the boot print is left. We don’t have paper and pencils to collect data outside today, but our friends are forming hypotheses and making deductions as they piece the clues together and abandon the ideas that don’t pan out.

Maya continues as the lead investigator. “Look at the size of this boot track. It’s much bigger than our boots. See? I think it’s an adult boot print. Look how far it is between the foot prints. It takes me three steps to their two steps.”

“Maybe it’s the mail carrier,” suggests Lois.  “She brought a package to the door yesterday.”

“It can’t be the mail carrier,” reasons Maya. “She doesn’t walk on this side of the center.”

“It must be a parent!” shouts Jacoby. “Who has a parent with a smiling boot?”

The question is met with dead silence. No one knows the answer.

Suddenly, Maya turns to me and asks, “Do you have a smiling boot? You are an adult.”

Much to my disappointment and the chagrin of my young friends, I am not the owner of the smiling boot. We are getting cold and our investigation has hit a dead end. We decide to go indoors and warm up with some hot cocoa and banana muffins.

At pickup time, the children check the boots of every parent for a smiling face, but no one has the matching boot. Many weeks later, we discover that the smiling boot belongs to a grandparent of one of the children at our center. By then the thrill of the hunt is over. But the learning has not been lost. A great morning of STEM investigation is tucked away safely in the developing brains of our early math explorers.

Ready to start your own Snowy Day STEM Investigation? Check out Show Me Your Shoe, an Early Math Counts lesson plan that can be adapted for your own boot-matching investigation!

Our spring dandelion days create hours and hours of exploration, inquisition and just plain observation!  There was plenty of math happening everywhere we turned.  One day we collected dandelions just to see how many we could collect.  The five year olds collected more than one hundred, while the two year olds were happy with six.  That is developmentally appropriate math right there!  When we find ourselves in these nature-based outdoor classrooms, the learning is always developmentally appropriate and always child centered.  It is the beauty of learning in a place that gives us everything we need. “When you look at a field of dandelions, you can either see a hundred weeds, or a hundred wishes.”
We had plenty of math vocabulary going as we searched for the longest and shortest dandelions.  We looked at the circumference of the flower, and made flower bracelets out of them.

We discussed the number of pedals.  We found the pattern of petals and I introduced them to the term “Fibonacci”, a number pattern that we often find in nature.  On this day, the flowers were too tall to spend much time on patterns.  We kept finding longer and longer stems, some with flowers, some with wispy white seed heads!  We discovered that we could divide the stems in half! Wait! We could even split them into four sections! Would it be possible to blow through a stem? Would it make a whistling sound? Would it taste bitter?  The investigation and process of discovery with dandelions was fast and furious, yet lasted for hours. This was math at their level, on their timetable.  Why would we rush this?I watched as some very young children could subitize better than their older friends.  Subitizing is the ability to “see” a small number of objects and know how many are there without counting.  When we roll a dice, we don’t need to count the pips, we know the number when we see it! Some children seem to grasp this concept with ease while others need to work with it a bit more.  We subitize a lot in our program, and being the math geek that I am, it just fascinates me to watch the difference in learning styles as this concept becomes effortless!

Giggles and screams of discovery were filling the hillside as our dandelion math morning took on a life of it’s own.  They began to classify, grouping according to length or size of the flower head.  I watched as a game developed of who could find the tallest one.  When you are yards away from your friend AND on a hill, it is hard to distinguish until you pick it and compare sizes! Then the realization comes that you need to pick at the very, very bottom of the stem!  This was a concept that was way beyond the comprehension of some of our younger friends, as hard as their peers tried to teach them.

Ah, the beauty of multi-age groups.  The beauty of allowing learning to enter as the brain and physical development allow.  The beauty of friendships and childhood on a sunny spring day, when all the stars align and the learning comes so naturally.

As we bring in the month of November, you may be able to find pumpkins at closeout special prices- I mean CHEAP.  Once Halloween is over, people are generally finished buying pumpkins, which makes them the perfect early childhood item for exploration.

Many of the ideas about apples we explored during September can be revisited with pumpkins.  Click here and here and here for those ideas. Instead of making apple sauce, you can make pumpkin butter, but everything else fits.

Since pumpkins are so much bigger than apples, children may be really excited to get their very own pumpkin to explore.  It  might be really fun to pull out the bathroom scale and show the children how to weigh their pumpkins.  You can then graph their weights and put them in order from lightest to heaviest.  The most interesting part of this experiment is that you may find that the biggest pumpkin (the one that LOOKS the biggest) does not weigh the most.  This will create a great discussion with the children.

This book tells the story of a pumpkin so big that the witch who grew it cannot lift it so she asks all of her friends to help her.