“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!

“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!

“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! 

“Go around the tree, through the tunnel, over the rocks, under the parachute and onto the swing. Then throw a beanbag through the hula hoop and run and touch the fence. The first person to do that WINS!”

I listen as five-year-old Juan walks his eager friend through the steps of the obstacle course he has just created.

When people think about early math skills, they often think about numbers—including number recognition and counting. But spatial reasoning is another important aspect of early math learning.

Juan has kicked off our morning of math learning with a burst of spatial vocabulary!

Words like around, through, over, under, above, below, between and beside describe where things or people are in space.

Obstacle courses are a great way for children to learn, hear and use spatial language while developing their spatial skills. Obstacle courses also teach sequencing, memory and following directions. Best of all, kids LOVE them!

When designing your own obstacle course, consider the elements that will make it both fun and challenging. Try out these options:

• Something to jump over or into such as rope, pool noodles, chalk lines or hoops. I often use chalk to draw shapes such as circles, squares, rectangles or triangles just to sneak some more math into our day. As children start to identify shapes, they are building the foundation for geometry.
• Something to climb over. When we’re indoors, we use pillows. When we’re outside, we climb over the picnic table or up the slide. The slide is a feature in many of our obstacle courses.
• Something to weave around and between. We often use cones or buckets, recycled two-liter plastic bottles filled with water or natural landmarks such as trees, bushes and gardens.
• Something to crawl through or under such as tunnels, parachutes or boxes.
• Something that requires a bit of balance or care when navigating such as a curved rope, river rocks or tree stumps.
• Something to run to, such as a fence, a tree or a door.

When older children are here after school, we often use a stopwatch to time how long it takes to complete the course. This exposes our children to data analysis and record keeping.

Some students may want to use their drawing skills to create a map of the obstacle course. Keep clipboards and pencils nearby because this activity catches on quickly!

You can add more math learning opportunities by counting the hoops or cones as children go through or around each one.

You can measure the distance between cones or stones—or simply use spatial language to describe the distance, using words such as closer together or farther apart.

Obstacle courses are also great for developing gross-motor skills. Include activities such as crawling, jumping, skipping and hopping. If your outdoor area has natural slopes and uneven terrain, these areas are perfect for fostering the development of early gross-motor skills.  

We all see the need for self-regulation in young children. Occupational therapists often use movement to support physical and mental regulation and increase a child’s attention span, focus and alertness. That’s reason enough to create a math curriculum that involves an obstacle course!

An obstacle course may look like play, but it’s chock full of learning opportunities. When we take the time to explain how activities like these can support early childhood learning and development, parents and administrators begin to develop a deeper understanding of our early childhood curriculum. 

Ready to take a deeper dive into spatial learning? Check out the Early Math Counts lesson plan Over, Under, Through. After you engage in the activity, click on the Connect With Families button on the left side of the page and customize the letter to send home to the families of the children in your classroom.

Be sure to let us know how your obstacle course turned out and share helpful tips in our Comments section. Have fun!

“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 >

Materials:

• Quartette board print-out QUARTETTE BOARD
• 8 markers in two different colors ex. 4 red and 4 blue

Directions:

• Give each player their 4 markers in whatever color they choose
• Take your 4 markers of the same color and place them on the board so the colors alternate on the top and bottom rows
• Take turns moving your markers vertically or horizontally into any square that is adjacent and empty
• The first player to get four in a row wins!
• You must always move one of your markers on your turn, markers cannot be moved diagonally, and you cannot “jump” over someone else’s marker

As you are playing this game, it’s a great opportunity to work on logic with your child and have conversations about directions. Some things you could say are, “My marker needs to go up one space for me to get two next to each other, how many spaces does your marker need to move?” “Are you going to move yours right or left now?” “I have three markers next to one another, how many do you have?”

Materials:

• Construction paper in four different primary colors
• Index cards or small sheet of paper
• Small ziploc bag
• Dot stickers
• Dry erase marker

Directions:

• Take the construction paper and cut out four large circles from four different colors of paper that are large enough that your child can easily stand on the circle. I recommend using one sheet of paper for each circle you create.
• After you have your circles, take an index card or sheet of paper, and use the dot stickers to create your map.
• Your map will be a in a 4×4 pattern, keep in mind that every row needs to have the same color dot stickers.
• Make sure your dot stickers are the same color as the construction paper you are using.
• After you have made your map, lay your paper circles out on the floor in the same pattern as your map.
• It’s best to secure the circles on the floor with tape so they don’t move around too much while you are playing the game.

• Now take your map and put it into a ziploc bag.
• Take your dry erase marker and draw a path on the ziplock bag so it shows up on the map.

When first playing this game, keep it simple and draw an easy path with two different turns of direction in it, and then get more complicated as your child becomes more confident. You can draw arrows marking the start and end of the path to make it easier for your child to follow along.

As you encourage your child to follow the directions on the card and stand on the matching dots, ask them to anticipate where they need to go next. “Which way do we turn here? Right or left?” or “Are you going to take a step forward or back? How many steps are left before we get to the end? Let’s look at our card for directions!”

Sometimes, the animals, people, or objects are actually sewn to the house.  I imagine this is so the pieces don’t get lost.  I would cut them right off, so that children can really explore all of the possibilities that this manipulative has to offer.

Remember to use spatial language when playing with these toys.  Ask about putting the animals “inside” or “on top” of the house.  Look up the signs for these words so you can encourage those as well.  Encourage all sorts of language by labeling the objects and situating them near or around the house.

These can be piled up, lined up, knocked over, and thrown about.  They are created so that providers and parents can label them and encourage language, especially mathematical language.  Using words like “blocks” and “squares” encourages spatial thinking language.  Using color words encourages categorizing.  Using words like “more” and “less” and “1, 2, and 3” encourages number and quantity.  These blocks are a great infant manipulative.