“LOOK!” Ellie summons us with such joy that there’s no doubt she has spotted something wonderful.

Our eyes follow the four-year-old as she dashes to a very large, very hollow tree. A tree that is still alive and thriving—with an opening over four feet tall just inviting a group of children and their teacher to peek inside.

“Who lives in there?” asks Clare as she summons up the courage to move closer.

Can we go inside the tree?” asks Veronica, although the question is a rhetorical one because the three-year-old has no intention of venturing inside.

“Is the tree hollow all the way up to the top?” Alex asks in wonder as he approaches the tree and glances upward to assess the tree’s height.

“I think a whole family of squirrels might live in there . . . or bats!” Harper’s pronouncement prompts her peers to quickly back away from the tree.

It’s so quiet and still as everyone contemplates the hollow tree that I’m not sure if the children are even breathing. All eyes are locked on Ellie, our resident risk-taker.

Emboldened by the children’s curiosity, Ellie inches her way closer to the tree’s interior. She is cautious but curious, brave yet apprehensive as she simultaneously challenges herself and calculates the risk at hand. 

Research tells us that children won’t take risks if they think they can’t succeed. But I know Ellie. She is an amazing observer and a visual learner who tends to rely on her senses when approaching an unfamiliar situation.

Today is no different. I watch as Ellie inspects the size, strength and thickness of the trunk. She inspects the ground outside of the tree cavity for animal droppings. She pokes her head into the hole and peers up, down, left and right before stepping inside. Ellie thrives on moments like these and trusts herself to evaluate the situation.

I trust Ellie as much as she trusts herself. These moments of risk-taking and assessment help a child develop cognitive, social-emotional, and self-regulatory skills—traits that make Ellie a natural leader.

Suddenly, Ellie pops back out of the hole in the tree, looks around and beams at the rest of us. “It’s so cool!” she exclaims. “You have to come in!”

One by one, slowly but surely, the children all make their way into this amazing gift from Mother Nature. Children grow in their ability to appraise risk by observing other children at play.

When children observe their friends taking risks and succeeding, they become more confident about taking risks themselves. This confidence carries over to the classroom and prepares them to try something new, possibly fail, and try again.

This hollow tree trunk has evoked wonder and curiosity in the entire gang, sparking a STEM investigation that helps lay the foundation for later math, science, and engineering concepts.

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.

Today, 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. An understanding of spatial relationships helps children talk about where things are located. I hear them use words such as in, out, down, over, under and next to, vocabulary that helps lay the foundation for geometry. 

When children use words such as wide, heavy and light, they are using descriptors for measurement. We begin to get a better sense of measurement as we visually estimate the height of the tree, the height of the entrance hole, and the number of friends who might be able to fit inside the tree. 

When children are guessing, predicting and classifying their ideas, they are engaging in early algebra, the scientific method, and basic engineering design. This morning of play is strengthening their understanding of these concepts as they use the vocabulary words repeatedly throughout their investigation.

Hands-on learning 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 structures during block play, art projects and clay play.

These are opportunities that are rich in learning, creativity and friendship. Whether they are on the playground or in the classroom, children must take risks that enable them to develop new skills and explore their ideas in a safe and supportive environment.  

Look for opportunities that can build your student’s risk-taking skills. Like our exploration of the hollow tree, these learning adventures will not only build their confidence and self-esteem but lay the foundation for academic success!

“Saaliha, come with me to the light table,” Evelyn whispers. “I have to show you something!”

Hand in hand, the two preschoolers quietly make their way over to our light table. This darkened corner of our classroom never fails to mesmerize the children with its soft glow and luminous colors.

As the days grow shorter and darker—and the hectic holiday season approaches—it’s the perfect time to engage children in calming investigative play with light and color.

Before we gather around the light table, I dim the lights in the classroom and put on some soft music to create a soothing and tranquil setting for the children, who are often overscheduled, tired and anxious during these busy December days.

“Look!” says Evelyn. “I took a play silk from our dress-up bin and put it on the light table!”

Evelyn moves over to make room for Saaliha at the light table and the two friends immerse themselves in STEAM collaboration, problem-solving and investigation. The girls are completely absorbed in their play—and the learning is enhanced by the presence of a friend and collaborator.

“That’s cool!” says Saaliha. “It makes everything look a little different, but you can still see all of the different colors!”  

The light table allows for open-ended play, where children can experiment and create without strict guidelines. This type of play fosters the development of creativity and problem-solving skills as the children follow their curiosity, devise their own experiments and draw their own conclusions. This child-led play also fosters an investigative mindset, which can lead to hours of exploration and discovery.

“Try this!” Evelyn suggests as she shows Saaliha how to duck under the silk to compare the views. 

The girls experiment with different color combinations and share their theories and discoveries. The light table always seems to spark curiosity and encourages children to ask questions and seek answers.

As more children join the investigative play, they expand their knowledge base by collecting data and adding probability to their investigative skills.

This is a shared space that encourages collaborative investigations. Collaboration fosters communication skills, teamwork and the ability to share ideas with peers.

Children work together to create patterns, build structures and explore different materials—a process that helps foster the development verbal and social skills.

The hands-on nature of these activities promotes a deeper understanding of mathematical principles through play.

Children can investigate fundamental mathematical concepts such as counting, sorting, patterns and shapes on the light table. 

These long play periods extend the learning as the group explores spatial relationships, patterns and sequencing, laying a foundation for more advanced mathematical thinking.

Play at the light table is naturally enjoyable for young children. The combination of vibrant colors, interactive materials and the freedom to explore creates a positive and joyful learning experience that can contribute to a lifelong love of learning. 

Light tables allow children to learn at their own pace, which makes the play developmentally appropriate for every early learner. The children build on their own knowledge and share their observations with others.

When children are making observations and discoveries, they are forming and testing hypotheses. These self-directed learning experiences empower them to continue to explore and investigate beyond the classroom.

So turn on that light table and watch the magic of play and discovery brighten the day! 

“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!

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It’s another 90-degree morning, and we’re going deep into water play to keep our budding mathematicians as cool and happy as possible on this humid, sultry day.

I glance over just in time to catch three-year-old Tahin playing with one of the small watering cans. It’s obvious that no one has mentored him on the fine art of submerging his watering can to fill it up with water. I observe him closely as he problem-solves.

First, he reaches for a small yellow cup, fills it up with water and tries to pour it into the small opening of his watering can. Most of the water runs down the side of the watering can, but he keeps trying, oblivious to his surroundings as he repeats the process over and over with the same disappointing results.

But this little guy is resilient. He doesn’t get frustrated or angry, he doesn’t give up and he doesn’t ask for help. He persists!

Tahin, like most children, can spend countless hours playing with water, pouring it back and forth, watching it spill over the edge of the cup, splashing gently and pouring some more.

My love of water play has been well documented on this blog, and it’s one of our favorite summer learning adventures.

Math might not be the first thing you think of when you think about water play, but water presents many opportunities to explore one of the main areas of mathematics, which is measurement!

If you’ve been using your water table as a “sensory table” filled with something other than water during the winter months, now is a great time to move it outdoors for some long periods of math play.

Children are naturally drawn to water and this naturally occurring (read “free”) element fosters curiosity, imagination, investigation and experimentation. What more could one ask of a learning tool?

I watch as Tahin abandons his first idea and tries a different approach, using the yellow cup to fill a larger yellow bowl, which he then uses to pour the water into his watering can.

When Tahin empties the smaller yellow cup into the larger yellow bowl, he also begins to learn which container holds more and which container holds less.

He also has the opportunity to use the cup as a unit of measurement and see how many cups it takes to fill the larger bowl.

Tahin carefully lifts the larger bowl, moves it close to his plastic watering can and tips it to pour the water into the can. The bowl’s wider rim and the greater volume of water are a winning combination.

Tahin’s second method proves to be successful, and the watering can is soon filled to the brim. This is persistence and problem-solving at its finest!

Water play is always developmentally appropriate, regardless of a child’s physical condition, age, language, gender or culture.

When children are engaged in water play, they tend to lose themselves in the activity and can spend long periods of time experimenting and playing. This encourages children to focus.

Any activity that requires sustained focus will increase a child’s attention span, sharpen problem-solving skills and enable the child to solve more complex problems later in life.

Open-ended water play also presents opportunities for children to use both sides of the brain as they problem-solve.

Children can explore and problem-solve in any manner that they choose, which forces them to be creative as they try out new ideas.

This is an example of executive functioning at work! Executive function skills help us make a plan and troubleshoot when the plan is underway.

Eve (pictured below) is developing and practicing her executive function skills through play!

We like to stimulate the imaginations of our early learners by changing our water-play tools frequently.

Here are just a few of the tools that we add to the mix on different days:

• Throw some ice cubes into the water and give the children slotted spoons to fish them out.
• Scatter sponges around the water play area. This often leads to activities such as washing the bikes or the plastic animals that we keep in the sand play area.
• Styrofoam meat trays and toy boats can be used to transport those plastic animals in water as well.
• Funnels, soup ladies and turkey basters are also big hits.
• Condiment squeeze bottles are great for building grip strength and strengthening the muscles of little hands.

Whenever children play with water, they are exploring mathematical concepts such as volume, capacity, size and shape.

There are many good reasons to bring water play into your outdoor play space. It’s a fun, refreshing pastime that will chase away the children’s lethargy on muggy summer afternoons—and it’s chock full of learning and skill-building opportunities.

What better way to knock out those early learning standards when the temperature and humidity soar?

“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! 

A pair of four-year-olds in my classroom are happily playing “dice wars,” a simple but fast-paced game. To play, each child rolls a die and the player who rolls the highest number wins. No one is keeping score today—and nobody seems to care who wins each round. 

I watch as Juan shakes the die between his palms, rolls it, counts each pip (dot) on the side that’s facing up and announces, “1, 2, 3!” I rolled a three!”

“My turn!” exclaims Maria as she shakes the die between her hands and rolls it. “SIX! I win! Six is more than three!” Maria doesn’t need to count the pips. She recognizes the pattern immediately and her number sense tells her the value of the pips on the die.

Rolling a die is fun in its own right, but these friends are working on the math skill known as subitizing. When children begin to recognize the pattern on the die and associate it with the number of pips (dots) without counting each pip, that is subitizing!

Children develop subitizing skills in much the same way that they learn to read sight words.

In a previous Early Math Counts blog post, Jen Asimow, M.Ed, explained it this way: “Remember when you learned about ‘sight words’ and how children learn them? According to one school of thought, children memorize sight words by taking a mental snapshot of the entire word. By using context clues, they learn the word as a ‘whole’ rather than as a series of letters. Consider how children learn the words EXIT or STOP.  Both of these words appear in the same way—on signs above doors or on red octagonal street signs—and nearly always in the same colors and typefaces. All of these clues help children form a mental picture of these two words, and they often learn the pictures before they learn the individual letters that make up the words.”

Maria and Juan are playing with a die, so they are only working with numbers ranging from one to six. As they play successive rounds of the game, they are beginning to recognize the patterns on the die without counting the individual pips.

With every roll of the die, Juan’s pattern-recognition skills are growing stronger. Before long, he can recognize the total number of pips on each throw without counting.

According to child development experts, the ability to subitize quantities up to and including four by the age of five represents a significant developmental milestone. 

Subitizing is a fundamental math skill, and dice games are a good way to help foster the development of this skill.

“Hey! Do you want to play that block-building dice game?” asks Pierre as he grabs a die from the jar and joins the group. 

Roll and Build is another dice game that we’ve played in our classroom for years. One child rolls a die and the other children add that number of blocks to their towers. Children learn to recognize four dots on a die, which helps them understand the cardinal value (how many four represents), which they can then link to the symbol (4) and the word (four).

Games like this provide repeated opportunities to interpret the dot images. As children figure out how many pieces to collect or add or how many spaces to move on a game board, they develop their number sense and other early math skills such as counting, number identification, the correlation between numbers and the items being counted and concepts such as greater than or less than.

Keep a jar full of dice within easy reach to give the children plenty of opportunities to practice and make up their own games.

Begin by subitizing quantities of 1, 2 and 3. In a math workshop that I attended, the trainer had blacked out the pips representing 4, 5 and 6 for the younger children.

If a child is having difficulty subitizing, reduce the quantity of dots. 

Dice games help young children develop math and social-emotional skills in a fun and engaging way.  So grab some dice and introduce your gang to subitizing fun! 

Check out our Early Math Counts lessons page for dice game ideas. Be sure to click on the Connect With Families button in the left-hand column of each lesson to download a Parent Letter that you can customize to share the day’s learning activity with parents and other family members.

We also use songs to work on vocabulary, memory and repetition. This week, the children asked if they could sing the song “Head, Shoulders, Knees and Toes” over and over again.

It’s fun to watch children of different ages and abilities participate in this activity. The beauty of this song is that everybody loves it. Everyone feels successful and happy, regardless of their developmental level, their physical coordination or their ability to anticipate and execute the moves.

When children sing songs like “The Wheels on the Bus,” the music and movement stimulate so many areas of the brain that learning is enhanced by as much as 90 percent. Physical movement also enhances memory and recall.

When I see students singing and laughing their way through “Heads, Shoulders, Knees and Toes” or “Teddy Bear, Teddy Bear,” I know that they are developing physical skills such as balance, spatial awareness and hand-eye coordination, as well as social skills such as cooperation and taking turns.

Children also learn how to think, explore, work things through and develop their language and self-expression skills as they sing and dance or play an instrument.

Have you ever heard a child make up all of the words to a song as they sing it? That’s brain development in progress!

Using songs in your daily routines can help you meet the math standards for early childhood education. Keep it light, easy and age-appropriate! Sing loud, sing often and sing off-key! The children don’t care. That won’t be what they remember. They will remember the words to the song, which will lay a strong foundation for their future math learning.

We use songs to work on vocabulary, memory and repetition. This week, the children have begged to sing the song “Head, Shoulders, Knees and Toes” over and over again.

It’s fun to watch the different levels of coordination, anticipation and expectations as children of different ages and abilities participate in this activity. The beauty of this song is that everybody loves it. Everyone feels successful and happy, regardless of their developmental level.

When children sing songs like “The Wheels on the Bus,” the music and movement stimulate so many areas of the brain that learning is enhanced by as much as 90 percent! Physical actions and exercise also enhance memory and recall.

When I see students singing and laughing their way through “Heads, Shoulders, Knees and Toes” or “Teddy Bear, Teddy Bear,” I know that they are developing physical skills like balance, spatial awareness and hand-eye coordination.

Social skills like cooperation and taking turns, as well as the shared experience of learning how to dance and play with friends is simple and fun.

Children also learn how to think, explore, work things through and develop their language and self-expression skills as they sing and dance or play an instrument.

Have you ever heard a child make up all of the words to a song as they sing it? That’s brain development in progress!

Using songs in your daily routines can help you meet the math standards for early childhood education. Keep it light, easy and age-appropriate! Sing loud, sing often and sing off-key!

The children don’t care. That won’t be what they remember. They will remember the words to the song, which will lay a strong foundation for their future math learning.

“One, two, three, flip!” 

“I win!” shouts Matif.

Remember playing War as a child? It’s simple and fun and it teaches young children how to win and lose without a lot of drama.

I love playing cards with young children because that little deck helps foster the development of early math and social-emotional skills in a big way.

When I play War with very young children, I often pull out the face cards and any card higher than a six. Depending on the ages and developmental levels of my students, I may even pull out the aces because it’s too difficult for young children to associate the letter “A” with the number “1.”

Start by dealing the cards evenly between all of the players, stacking the cards face down in front of each child. 

No peeking allowed!  On the count of three, each player will flip the top card over into the center of the table, face up.

“One, two, three, flip!”

A chorus of young voices chants in rhythm as our game continues.

“I have a five,” shouts Mable. “That’s bigger than your two, so I win!” 

Compare the cards played. The highest card wins the hand. The winner takes all of the cards played in the round and adds them to a new stack of “won” cards. 

One, two, three, flip!”

“Ah, you both have a six! War!”

When there’s a tie between the two highest players, you have a “duel.”

To play a duel, the two players each place three cards in the middle of the table, face down. Then they each lay down another card (the fifth card for this round). This card should be facing up. The highest card wins, and the winner takes all of the cards from this round and adds them to a new stack.

“One, two, three, flip!”

I watch as a four and a three get turned over by the players in the duel.

“Ah, you won all those cards!” says the child with the losing hand. “Lucky you!” 

When children are playing cards, this is a great time to observe their number sense. Can they identify the numbers by name? Can they determine which number is higher? Can they follow the rules?  When the cards match, can they count out the three additional cards that they will need for a duel?  

Play until your main stack is gone and then count up how many cards the players have in their stacks of “won” cards. The player with the most cards wins. Once the children have mastered the cards through the number six, I will add the sevens and eights back into the deck. Later, I will add in the nines and the tens.

Many children will be able to play a full game of War by the time they reach kindergarten—face cards included. Keeping it simple in the beginning is a great way to assess your students’ number recognition skills and value development.

As children play this deceptively simple game, they are developing their number-recognition skills and beginning to grasp concepts such as number value, greater than and less than.

They are also learning important life skills such as how to follow rules, take turns and take their turns quickly without making the other players wait too long. That’s a lot of learning for a game that fits in your pocket! 

We also want to teach children how to win and lose graciously. I love playing War because it’s a game of chance and everyone has an equal chance of winning. Because each round has a winner, we are practicing the win/lose concept over and over again in rapid succession. There isn’t time for the winners to jump up and do a victory dance or the losers to break down and get weepy. The same child will not win every round, which gives every child many opportunities to practice good sportsmanship.

There’s a reason that children have enjoyed playing War for generations. It’s fast and fun and a bit addictive. So grab a deck or two, play a few rounds with your early learners and call it your math curriculum for the week. You’ll be teaching invaluable life lessons along with those early math skills!

Do you have collectors in your midst? Those young children who can turn a five-minute walk into a 15-minute treasure hunt? The children who fill their pockets with treasures and then load up your pockets with the overflow?  I love these kids. They can wreak havoc with our daily schedules, but they help us slow down, take a breath, smile and find beauty in unexpected places. They also make me smile when I remind myself that these impromptu, child-led collecting and sorting expeditions are worth their weight in gold as we work with young children to build a strong foundation for later math learning.

We collect lots of natural loose parts like acorns and buckeyes, feathers and rocks. But we also collect colored gems, bottle caps, keys and other odd items. This, my friends, is the rock-solid, hands-on play that lays the foundation for number sense.

At all ages, children classify intuitively to make sense of a world that seems largely out of their control. By the time infants are two weeks old, they can distinguish between objects that they suck on and those they do not. By the age of two, toddlers form sets of similar objects. In preschool, children begin to sort objects into categories according to a given attribute.

If it attracts their attention and they touch it, that’s the moment the child-led learning begins! So grab a bag, a basket or a bucket, take a walk and see what sparks the imagination of the children in your life. A good pocket comes in handy on these expeditions!

Along the way, observe the collecting habits of your budding mathematicians. What captures their attention? What treasures do they deem worthy of pocketing? Does one of the younger treasure hunters in your group need guidance or mentoring?

During your expeditions—and other daily outings—keep your eyes out for heart rocks. It’s a great opportunity to build some early math skills, whether you’re waiting for a table to open up at a restaurant or killing time before an appointment. Hidden in those landscape rocks, there is sure to be a heart rock!

Children will naturally begin to sort their collected treasures into piles or “sets.” Separating will come very naturally as children sort acorns into one pile and bottle caps into another. They may group by colors, shape, texture or weight. They may also organize their objects in a line by size or other attributes.

As they sort the objects that they collect, children are building their analytical thinking skills, which are the lifeblood of mathematics. This is a great opportunity to introduce vocabulary words such as more and less.  Young children have an inborn sense of more and less. They always know if someone has more than they do!  Children can learn number sense simply by playing with their collections!

If the grouping of sets leads to counting, this is another great opportunity for young children to build foundational math skills. Regardless of how high a preschooler can rote count, a child’s sense of what those numbers actually mean develops gradually. We call this “understanding number sense,” and it requires relating numbers to actual quantities.

There are three core counting principles:

Counting Sequence 
There is an ordered sequence of number names. Counting involves using the same sequence each time, starting with one. By using counting songs and moving each object as you give it a “name,” you can help children learn the counting sequence.

One-to-One Correspondence
One number from the counting sequence is assigned to each object in a collection. Instruct the children to put each object into a container or slide it across the table as it is counted.

Cardinality
The last number assigned to an object when counting a collection indicates the total quantity of objects in the collection. Ask: “How many?” If the children don’t know the answer to this question, count the objects together and note the last number that you counted as you push the objects all together into a group.

By turning counting into an enjoyable, hands-on activity, you are also introducing the children to mathematical concepts such as place value and addition.

Remember to take it slow and make it fun. Children develop at different rates and have different learning styles. They will master early math concepts in their own time and in their own way.

So let the children set the pace. Enjoy the cooler fall temperatures as you embark on your collecting expeditions—and see what collections land in your pockets!

Looking for some great activities to introduce sorting and counting to your early learners? Look no further than the Early Math Counts lessons page.

Here are a few of my favorites to help you get started:

• Cereal Sorting
• Laundry Sorting
• One Fish, Red Fish