Cultivating a Math Rich Learning Space

It's the end of August! This time of year always fills me with hope. Although it's sometimes sad to be leaving the fun and comforts of summer - spending time with my children, sleeping in, enjoying the back yard with my pup - it's exciting to think of the possibilities of another school year. Like a blank canvas waiting to be painted, our classroom evolves and changes over time as the children and I learn and explore together. 

As we head back into the school year many educators are working thoughtfully to create environments that are rich with math possibility. In Reggio Emilia the environment exists as the 'third teacher' inspiring, supporting, and extending children's learning in rich and complex ways. I have been contacted by many educators asking for advice on how to best set up their classroom and routines in order to create as many opportunities for authentic math as possible. This has inspired today's blog post - how to cultivate a math rich learning space for children at the beginning of another school year.

I thought it would be easiest to create this as a 'math check list' with points to read and consider. When I reflect upon my own math pedagogy and practice, these are what I think stand out as mathematically meaningful for the educators, children and families that share our space. Although this check list isn't all inclusive, I thought it might spark some ideas to support and inspire as we enjoy the final weekend of summer and start back in our classroom with open eyes, minds and hearts this week.

1. Make math a part of every space in the classroom and child's school world. In the classroom are there math tools and materials available for use beyond a 'math center or math shelf'? Do children see how math relates to every subject in the space (e.g., how materials are sorted and stored on the toy shelf, how measurement is used when children decide on a size of paper to use for their project)? Can they translate math tools and ideas into other spaces in their immediate school world (e.g., see how math relates to their walks in the hallway or work in the gym)?

2. Ground and build math concepts into known objects for children. When introducing, extending or innovating a math idea is it organic and natural to the child's explorations and world? For example, it is more natural to engage children in an exploration of measurement if they measure things in their immediate world using the stick they are playing with, instead of using a standardized ruler (e.g., "Can you find something the same length as your stick in the yard?", "What is taller than your body?").

3. Use available math moments with children. In our classroom we have a large block of uninterrupted play each day. It's sometimes challenging to manage children, materials and activities during center time. However I try to engage with children as much as possible in the activities, and take on the role of 'play partner' together with them. When I am actively playing I am able to closely observe what they are saying and doing, helping me to identify and extend the rich math learning that is organically occurring (e.g., helping children to recognize why their tower keeps falling, using math terms when they equally share the play dough, introducing math terms as they discuss how many cars are in their parking lot).

4. Become a math role-model for children, families, and colleagues. Even if math isn't your favourite subject, how do you discuss it within your school and classroom? Are you excited by new activities and resources? Do you demonstrate a growth mindset? When mathematical situations arise with children that you aren't sure of, can you use these opportunities to showcase positive thinking and problem-solving? Share your new math learning with others - suggest articles and books you're reading and post these throughout your classroom to enhance documentation displays.

5. Find the math in everything. Many educators plan forward by choosing curriculum and programming expectations and then building activities to fulfill these. Try back-mapping activities from time to time; embrace child-centered, organic experiences and then deconstruct them in order to identify the rich math concepts and curriculum expectations that they utilize. You'll be surprised to find that math happens in almost every experience children have in the classroom.

6. Try looking at life through a mathematical lens. When planning invitations for learning in your classroom, see what math you can sneak in as well. Changing one or two elements of the experience might be enough to engage children in rich math. It reminds me of how I used to sneak veggies into my children's meals - a little can go a long way!

7. Collaborate mathematically with colleagues. Share new ideas and resources informally. It's easy and effective to create math invitations and activities and share these within your school or division. If every educator plans one or two activities and these are shared, children will benefit from many rich and interesting games and activities without the burden of planning and preparation it would take one educator to accomplish the same.

8. Record and celebrate your math moments. Help children, families, and colleagues recognize that math happens everywhere in the classroom by creating a documentation display with photos, anecdotal observations and connections to curriculum. This bulletin board can be built over the course of the school year as artifacts of learning are continually added by staff and students. Keep sticky notes nearby and invite observers to record their own ideas and share them by posting the notes within the documentation.

9. Engage families in joyful math with children outside of school. Consider ways that you can promote and extend math for children after school. Encouraging families to play math games and activities together with their children will not only provide children with additional meaningful math moments, but it may help older family members reconcile their fear or dislike of math. In our classroom we send home 'family math bags' once a week. These are filled with math invitations and materials so that children and their families can play games inspired by our classroom work.

10. Build your collection of math stories, songs and games. Children love to sing, dance and play games. Ask colleagues to share their favourite games and activities, and use these to help with transitions and other 'math moments' throughout the day. Quite often the words in songs can easily be improvised to match something happening in your classroom, and many rich storybooks have mathematical elements and problems embedded within them that can inspire children.

These are just a few of the ways in which I cultivate a rich math space with children. I'd love to hear from you! Share your math ideas in the comments below, and consider following my Facebook page  Joyful Learning in the Early Years for regular math ideas from my classroom!

Exploring Magnitude While Playing with Number Lines

 

Number lines are a great tool for helping young children develop an understanding of magnitude—the idea that numbers have a size and that numbers can be compared to one another.

Children may be able to count to 20, but that doesn't necessarily mean they understand how the numbers relate to each other. They may know that 8 comes after 7, but do they understand that 8 is close to 10? Or that 15 is farther from 10 than 12 is?

A number line can help make these relationships visible.

Start Simple

 

We can begin with a simple number line:

0 — 1 — 2 — 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10

 

Rather than just using it to count, we can ask questions such as:

• “Where would 6 go?”
• “Which number is closer to 5 ... 3 or 8?”
• “What number is between 4 and 6?”
• “Where would you put 9? How do you know?”

These questions encourage children to think about the size and location of numbers, rather than just reciting the number sequence.

Estimate!

 

One of my favourite ways to use a number line is to give children a line with only the endpoints marked.

0 ____________________ 10

Ask:

“Where do you think 5 would go?”

Children have to think about where the middle of the line is.

We can then try:

0 ____________________ 20

“Where would 5 go now?”

This helps children see that the position of a number depends on the numbers at the ends of the line.

 

Use a Floor Number Line

 

A floor number line gives children the opportunity to physically experience number.

“Stand on 4. Move forward 3. Where did you land?”

We can ask children to predict where they will land before they move. This connects counting and movement with the idea that numbers have a position and a distance from one another.

Look for the Thinking

The important part isn't whether children place a number perfectly. We want to hear how they decided where it belongs.

“Why did you put it there?”

“What were you thinking about?”

“How do you know?”

Number lines give children a visual way to see that numbers aren't just a list of words we say when we count. Numbers have size, and numbers have relationships with other numbers.

Helping children develop this sense of magnitude is an important part of building strong number sense in kindergarten.

Multiplicative Thinking in the Early Years

Even though multiplication can be an abstract concept for many, the foundation for it can be nurtured in the early years. Multiplicative thinking for young children involves moving beyond counting when calculating quantity and beginning to think about groups, units, relationships, and patterns between numbers. There are many ways we can help build the foundation of multiplicative thinking early on.

Doubling

Doubling helps children see a number as a unit that can be doubled. For example, children can begin to recognize that 5 and 5 make 10, or that 6 and 6 make 12, without needing to count each object.

We can look for opportunities to use doubling throughout the day. If there are 4 children at one table, we might ask, “How many children would there be if we had another table with the same number of children?” Or, if we have 5 blocks, we could ask, “What would happen if we had another group of 5?”

Doubling also becomes a useful strategy for working with numbers that are close to a double. For example, a child might use 5 + 5 to help figure out 5 + 6. These kinds of connections help children begin to use what they already know to think about new quantities.

Unitizing

Unitizing is an important part of developing multiplicative thinking. It helps children understand that a group of objects can be thought of as one unit that can then be counted or repeated.

For example, instead of seeing 10 counters as 10 individual objects, children might see them as 1 group of 10. They are beginning to think about the structure of the quantity rather than just counting each object.

We can encourage unitizing by having children make equal groups with everyday classroom materials. We might ask:

• “Can you make groups of 3?”
• “How many groups did you make?”
• “How many are in each group?”
• “How many are there altogether?”
• “How did you figure it out?”

The goal is not simply for children to get the answer. We want them to start noticing that the same quantity can be organized and thought about in different ways.

Skip Counting

Skip counting by 2s, 5s, and 10s is an early way of helping children think about units and develop multiplicative thinking.

However, skip counting becomes more meaningful when children understand what they are actually counting. For example, counting 2, 4, 6, 8, 10 can represent counting groups of 2 rather than simply memorizing a sequence of numbers.

If each child gets 2 cubes, we might ask, “How many cubes will we need for 5 children?” Children can make groups of 2 and count them: 2, 4, 6, 8, 10.

This gives a purpose to skip counting and helps children connect the numbers they are saying to the groups they are seeing.

Repeated Addition

 

Repeated addition helps children make a connection between addition and multiplication. When children see 3 groups of 4, they might represent this as:

4 + 4 + 4

This is a useful way for children to begin thinking about equal groups. Multiplicative thinking involves noticing the groups and the relationship between the groups and the quantity in each group.

Educators can encourage this by asking open ended questions including:

• “How many groups do you see?”
• “How many are in each group?”
• “How could you count these?”
• “Could you count them without counting every object?”
• “What do you notice about the groups?”

These questions encourage children to think about the structure of the quantity and look for more efficient ways to determine how many there are.

Arrays

 

Arrays are another great way to help children visualize equal groups. Arranging objects in rows and columns helps children see equal groups and provides a visual representation that can later support their understanding of multiplication.

For example, 12 counters could be arranged in 3 rows of 4 or 4 rows of 3. Children can explore both arrangements and notice that the total stays the same even though the arrangement has changed.

Finding arrays in the world around us is an interesting way to “notice and wonder” about multiplication. We can find arrays in many places:

• windows on a building
• seats arranged in rows
• tiles on a floor
• eggs in a carton
• buttons on clothing
• objects arranged on a shelf

Look for Multiplicative Thinking in Everyday Situations

Multiplicative thinking can be developed through everyday classroom experiences. When children are sharing materials, setting tables, building with blocks, organizing collections, or lining up, there are many opportunities to think about equal groups. Educators can notice these moments of learning and facilitate thinking through responsive questioning. For example:

“There are 4 children at each table. How many children could sit at 3 tables?”

Or:

“We need 2 crayons for each student. How many crayons will we need for 6 students?”

Or:

“Here are 20 counters. Can you organize them into equal groups? How many different ways can you find?”

These questions encourage children to think about how quantities are related, rather than simply finding an answer.

Building the Foundation

Developing multiplicative thinking in young children is about providing experiences that help children see groups, units, and relationships.

When children double, make equal groups, skip count, organize arrays, and look for patterns, they are building ideas that will support their later understanding of multiplication and division. Responsive educators can use their observations of children's actions to help highlight this and invite them into the learning opportunities. 

Turning Children's Art into Holiday Gift Wrap

In our classroom we focus mainly on process-based art. Children are invited to create with open-ended materials. A painting experience that children enjoy involves stamping holiday cookie cutters using festive acrylic paint.

 

When the paintings are dry they are rolled and tied using a sparkly pipe cleaner. A tag is attached inviting families to repurpose the art as holiday gift wrap for a special loved one. A copy of the letter is available for printing here: Gift Wrap Art Letter to Families

 

Doesn't this present look so beautiful with the special wrap? 

Spider Catapults

 

Spiders continue to be a popular topic of exploration in our classroom! To infuse this interest with math and fine motor work we introduced clothespin catapults to the children this week. Wooden catapults are easily made by securing a clothespin to a steady base (like a wooden block) with an elastic. 

They require concentration and perseverance for children to operate. As children become more confident using them they are able to use strategy to aim the catapult in a specific direction or apply pressure to further or reduce the launch power. 

Small plastic spiders (ours were from the local dollar store in the Halloween section) are light and perfect for playing with. We offer 'webs' made from wrapping a shallow basket with yarn. Children are encouraged to fire the spiders into the webs.

    

Once children master launching the spider into the web additional math tools can be offered to enhance the experience. A five or ten frame or hundreds chart are easy tools for children to use when tracking how many spiders they have landed in the webs.   

                   

Additional targets can be provided for children to play with (e.g., alphabet chart, number chart, printable web with points). The possibilities are endless! 

Spider Math

 "Oh look! There's a spider on the school! 

Maybe he's coming to learn too!"

Autumn always brings with it many treasures. Recently my students have been curious about the many creepy crawlies they have been discovering in the yard. Although spiders can be scary for some, they serve a big purpose in our local ecosystem as they eat insects and also are a source of food for others. Exploring them together also helps those who are scared or reluctant learn to see them in a new way. 

I always look for ways to incorporate children's interests into our activities, specifically math. Here five spider math ideas for you to use with your little ones!

1. Which One Doesn't Belong - encourage children to examine and describe these collections of images and articulate which they believe doesn't not belong in the group and their reasoning why.

  

2. See, Think and Wonder - this thinking routine asks children to carefully examine something and clearly describe what they see, articulate their thinking about the object, and express curiosity through wonderings and questions related to the subject. This picture of an intricate web might be an interesting prompt for discussion.

3. Spider Survey - ask children to record their names on a t-chart that indicates whether or not they like spiders. Calculate and interpret the results of the survey with children. Click the image to access the printable.

 

4. Spider Subitizing - use this printable with children to explore different ways of representing a number. Write a number on the spider and ask children to brainstorm and record many different ways of showing the number (e.g., tallies, dots, ten frames, word). Click the image to access the printable.

5. Spider Symmetry - use this printable with children to explore the concept of symmetry. Encourage children to draw the missing half of the spider and web as best as they can. Explore symmetry in photos of real life spiders!Click the image to access the printable.

Summer Professional Development Opportunity!

 I am so excited to be presenting at the summer Play & Possibility Virtual Conference! 

Register here and use code joyfulmath10! 

Code a City!

A favourite small world play activity that the children enjoy is our 'Code a City' challenge. This math invitation requires just a few materials - a city template, blocks, dice, and mini vehicles. The 'Skyscrapers' book is a perfect nonfiction resource to supplement the learning.

Children select a template. They can use one or multiple dice depending on their ability. Roll and add the pips on the dice together. 

Write the corresponding number in a space on the template.

Build a tower with that many blocks.

When your city is complete add mini vehicles for some small world play!

Bringing Math to Life: Sparking Joy and Curiosity through Play

On April 16, 2025 I had the pleasure of presenting my workshop Bringing Math to Life: Sparking Joy and Curiosity through Play for Early Childhood Investigation Webinars! With over 3000 registrants it was my largest audience to date! I absolutely love inviting educators into my kindergarten classroom and sharing the rich math learning that children experience through play and inquiry! Connecting with others drives my practice and inspires me greatly! A big thank you to all who attended! A copy of the presentation slides are available and can be found at this link.

The presentation was recorded and is available for viewing if you are interested in revisiting the information I shared, or did not have a chance to view it live. You can access it here:

STEAM in the Garden - Constructing Insect Houses using Natural Loose Parts

"Look deep into nature and then you will understand everything better."

Albert Einstein

The children were gathered around a large landscaping rock, working together to arrange twigs and flowers they had picked from the ground nearby.

"I think that this side should be the living room and the bedroom can be over here," Jack gestured as he spoke. "The living room will be next to the bedroom and the ladybug can crawl across by using this little bridge."

"So what are these little sticks here for?" Mary pointed to a little row of twigs placed next to each other.

"Oh, those are going to be the bed." Olive answered.

"But that's way too big to be a ladybug's bed," Mary responded.

"Oh," Olive pondered. "I didn't think about that.

 

"That's okay," Mary smiled. "We'll just find more than one ladybug and then the bed will be the perfect size for them to share." 

Spring was in the air and the children were excited to discover that many little creatures were venturing out into the warm sun. Ladybugs, rolly pollies, and ants were abundant and this sparked the children's imaginations. Eager to 'help' the insects the children set to work building little houses for them. They searched the yard to gather materials they felt would be best suited to this task. 

 

Each day the children would return to the mini houses and continue their work, focused on creating the most aesthetic and functional space for whatever creature they had found that day.  

   There are four steps to the design process for young children. When I reflect upon the children's garden engineering of the habitats I observed these steps in action:

Identifying a Problem - the children felt the insects needed a home
Imagining and Planning - children brainstormed that natural loose parts could be used to design and construct a habitat and engaged in conversations about what this might look like
Creating - children spent time over many days creating different homes for different living creatures
Improving - children revisited their creations each day and revised their plans when necessary after they noticed new things about the insects or had engaged in conversations with peers

  

What might seem like a playful activity outdoors has the potential for much rich learning using an engineering mindset. When children create habitats outdoors they are participating in rich math exploration in action including:

 

-discussing, designing, and refining a plan

-classifying and sorting materials by common characteristics

-considering proportion as they build for specific insects

-using spatial reasoning and design as they manipulate materials

-thinking about measurement as they incorporate area and perimeter into their 'house' or discuss the attributes of materials (e.g., the heaviness of rocks, the length of sticks)

-counting materials gathered and used in the design process

-naming colours and shapes that emerge in their work

-using positional language to describe their creations

-thinking about balance and stability as they assemble materials 

-incorporating patterns or symmetry as they create aesthetic structures

 

It's amazing to notice and name the rich math learning that emerges in children's self-directed play outdoors. Taking photos and videos of the work, engaging in discussions with kids about their play, and reflecting upon the experiences can help educators make this rich learning visible to others! Sometimes nature is the most effective math teacher of all!