Sunday, September 25, 2022

Algebra in Kindergarten? Absolutely!

 "Pure mathematics is, in its way, the poetry of logical ideas."

Albert Einstein

When you think about algebra you might have memories of sitting in a high school math class, searching for unknown values in linear and quadratic equations. Those long ago math courses may seem far removed from today's kindergarten classrooms but did you know that it is essential for educators to promote algebraic reasoning in early childhood education?

I devoured the most recent issue of Young Children (Volume 77, Number 3), especially the article Promoting Algebraic Reasoning in the Early Years by Lindsey Perry. 

In her work Perry advocates for algebra in early math programs that explore two main ideas: composition and decomposition of numbers and properties of operations. According to Perry (2022) algebraic reasoning "involves seeing and describing patterns and relationships between quantities that may be unknown...which builds upon students' understanding of patterns and relationships with known quantities and values" (pg. 17). Perry posits that if children can observe and describe number relationships they can begin to symbolically represent relationships between numbers. 

Composition and Decomposition of Numbers

When children compose they understand that a number can be put together using its parts (e.g., 5 plus 5 equals 10). Decomposition is the opposite where a number can be broken apart in different ways (e.g., 10 can be broken into 8 and 2 or 7 and 3). When children compose and decompose numbers they understand how to manipulate numbers in different ways, which helps them become flexible when solving calculations. For example mentally adding 68 + 22 can become easier when children realize that the ones values total 10 and then add this to the tens value (10 + 60 + 20). Adding 68 plus 22 is the same as adding 10 plus 60 plus 20 but the second strategy may be easier to mentally calculate for many people.

Properties of Operations

Properties of operations encourage children to work flexibly with numbers in order to recognize and manipulate their relationships. This helps them simply calculations in order to more efficiently and accurately solve them. For example the order of addends (numbers added together) does not matter in order to arrive at a sum. 

a + b = b + a 

6 + 4 = 4 + a therefore a must be 6.

The commutative property applies to addition and multiplication. The order of numbers can be switched and it does not change the answer of the operation.

2 + 7 = 9 and 7 + 2 = 9

4 x 5 = 20 and 5 x 4 = 20

The inversion property states that all integers have an inverse number that when added equal zero. 

3 + (-3) = 0

Although complicated young children can play with inversion when they become interested in, and work flexibly with equations.

3 + 2 - 2 = 3

So how can early childhood educators encourage children to participate in activities that promote early algebra? Here are some simple activities that can be used regularly to build children's confidence, ability and interest in number sense.

Equation Line


Provide children with a variety of subitizing cards and math symbols (addition sign, subtraction sign, equal sign). Encourage children to arrange the cards in different ways in order to create equivalencies.

 Make 5 (or 10)

Show children a total number of cubes (starting with 5 and then 10 is helpful). Hide the cubes behind your back and remove some. Show children the remaining number of cubes and encourage them to calculate how many are hiding.

Singing Songs with a Five/Ten Frame

When singing popular songs and finger plays with children (e.g., 5 Little Monkeys, 10 in the Bed) add a five or ten frame as a visual and manipulate the number of counters in the frame to match the number being sang. 

Counting Beads

A string of counting beads can easily be made using two colours of wooden beads secured on a pipe cleaner. Encourage children to use these when playing number games or engaging in number talks.

Domino Sort

Provide a mat for children (here a foam shamrock has been used but any shape will work). Write numbers on individual mats. Encourage children to sort dominoes and match their quantities to the mats in order to represent the many different dot arrangements possible for each number.

Roll a Ring

Seasonal rings are a fun tool to use in math games. Provide children with dice and encourage them to roll and add (or subtract) the numbers. Children can then wear the corresponding number of rings on their fingers. If two players play the game, they can each roll and wear rings and then compare hands to see who has more or less.

Name Equations

We enjoy representing children's names with boxes and encouraging them to think about the number, size and shape of the letters. These boxes are also fun to represent at equations so that children can play with their names and integrate a bit of math into literacy.

Calendar-based Number Talks

Morning message is a great time to encourage a daily number talk. We often represent the date in different ways (e.g., dice faces, dominoes, tallies, frames) and then encourage children to calculate the number by paying careful attention to the representations and operation signs used.

Which One Is Wrong?


Another favourite number talk is 'Which One is Wrong'. Different equations are displayed and children are challenged to explore each one using manipulatives (e.g., cubes, bead strings) to find the incorrect one. 

What other activities do you use to help children with early algebra? Let's connect on social media @McLennan1977!

Friday, September 2, 2022

Creating a Sensory Wall for Children

In our classroom we have a discovery area where children are invited to explore materials that focus specifically on the senses. We enjoy including resources that support exploration of light and colour (e.g., light table, sensory jars). Many loose parts are also in this area (e.g., stones, shells). The materials are stored on a small wooden shelf so they are easily accessible for children.

The shelf floats in the middle of the room as an anchor for the space. The back was covered in blue felt. We wanted to maximize all areas of this space and because there are many children with sensory needs in the class we decided to turn the felt area into a sensory wall.

The first step was to measure the space and plan out how the materials would fit together. I found this easiest to do on a flat working space. This way I could piece the material together like a puzzle and ensure they were diverse and interesting to explore.

Once I was satisfied with the way it looked I attached each piece to the felt wall using hot glue. I know that over time as children explore the pieces may fall off, but I am hopeful that I will be able to quickly and easily reattach them. I love how the sensory wall is low enough for all children to access. They will be able to sit and explore, or touch it while they walk by. The materials also match the colour scheme and decor in this calming space and do not stand out.

I found myself enjoying the materials and know that the children will too!

Tuesday, August 23, 2022

Documenting Children's Learning Using Instagram Reels

It was my absolute pleasure speak as keynote at the Canadian Early Mathematics Education Conference in quaint Kingston, Ontario on August 22, 2022. In addition to being able to stroll the downtown area and marvel at the beautiful campus of Queen's University, I meet many amazing educators who connected with me regarding early math learning, humbled me with kind comments about my work, and fascinated me with interesting questions regarding the teaching and learning of mathematics in the early years.


My presentation focused on sharing stories from my classroom in hopes of inspiring educators to consider how they might create opportunities for joyful math in all areas including art, literacy, the classroom environment, routines, and outdoor learning. I also shared information regarding the documentation I collect regarding math learning and how children can help co-create this documentation as part of assessment process. 

Throughout my presentation I shared many Instagram reels that I had created this past school year. These were often meant to be quick, easy and entertaining ways to make the learning visible for children, families and the community. I embedded the clips throughout the presentation to help highlight specific ways math could easily be integrated into other subject areas. I also spoke to how Instagram reels could be used as a form of documentation.

I was not surprised that the majority of conversations I had with educators after my presentation were regarding Instagram reels. Many people were curious to learn more. As a result I thought it might be helpful to blog about this and share the ideas beyond the conference.

There are many reasons why I would encourage any educator to consider creating reels as a form of communication regarding learning and special events happening in the classroom. I can think of many more, but here are my top ten:

1. Instagram reels are an engaging way to share information in a format that appeals to a viewer's senses and emotions. Catchy sound effects, music, text, stickers, hashtags and filters can be used to enhance photos and videos that help amplify the message you are hoping to send. In this reel I'm hoping to show in a humorous way how messy kindergarten children can get when exploring the outdoors, and that it's normal and healthy.

2. Instagram reels can help educators share best practices with others using social media, helping them reach beyond their immediate learning community and idea share with many others. I like to post reels that explain teaching strategies or that challenge traditional ideas or routines that others might be curious about. For example here is a reel that encourages educators to think beyond traditional 'calendar' during morning message.

3. Instagram reels can help explain the steps behind a specific activity so others can try it themselves. This way of explaining the process appeals to visual learners who would rather watch a video than read steps. The size of reels also mean that the instructions should be succinct. This reel explains how to create textured watercolours using simple materials.
4. Instagram reels can help educators unpack activities for families and the community so the learning can be made visible. This might be especially helpful for experiences that families might be unsure about including messy sensory experiences. I tried to use this reel to explain the rich learning that happens in mud play.
5. Instagram reels can help change a viewer's perception of a non-preferred subject or task. For example I try to use reels to show the beauty and wonder of mathematics because so many people still default to their negative experiences and consider it a cold and solitary experience. I want to portray math as beautiful and interconnected to nature and our everyday experiences. This reel shows a few examples of math integrated in areas of the classroom.
6. Instagram reels can be co-created with children and used as a form of communication to provide a summary of the week's experiences. They can very effectively replace weekly newsletters or bulletins meant to share news from the classroom. Children can suggest clips to include and educators can chose salient videos that highlight the rich learning that has occurred. This reel highlights some of the events that happened in one week in the spring.
7. Instagram reels can be used to give families and the community tours of the classroom and other school spaces. I have shared tours of my classroom during kindergarten registration when potential families are viewing the school, during Covid closures so families could virtually step into their children's learning space, and also as a way to share with other educators who might be looking for new ways of organizing their space. This reel is a flashback to a previous classroom I had in hopes the ideas sparked conversations and starting points for educators.
8. Instagram reels are a fun way to share a bit about yourself to your school community. I like to create a few personal ones that show my interests, pets and family in order to humanize me to my school community and make myself relatable. This definitely depends on one's comfort level to allow others to take a small step into your life and might not be for everyone. This reel was created on a sunny, lazy Sunday in my backyard.
9.  Instagram reels help educators connect with a 'professional learning community' or PLC. Use a rich wording when describing your work. Adding hashtags to your reel will also help audiences find your work as well as having it appear in the reels section of the app. It can be liked, shared or commented upon by others. Many times creating reels will help an educator connect with other like-minded people, and it's very enriching to view reels created by others. An Instagram PLC will provide endless opportunities for networking and collaboration! This reel piggybacked on a sound trend and was meant to show math in very different ways.
10. Instagram reels are a fun, creative outlet! I am always engrossed in creating these and love the challenge they provide. Involving students in their creation helps a class become producers and not just consumers of information. When co-creating and reflecting upon reels, children engage in digital documentation and can appreciate the depths of their work and understanding, and plan next steps for action. I love how this reel coordinates a fun song with the child's math game.
Tips to get started:
*find educators to follow on Instagram that work in your field, or share interests - use hashtags to help locate experts and other interesting people
*watch the reels stream in your Instagram wall - even though many of these videos are not related to education, they are entertaining and can spark ideas for your reel creation
*use up to 30 hashtags to describe your work - the more you use, the better viewers can locate your work
*capture as many videos and photos as you can in your classroom - you never know what might turn out to be interesting and important to include in a reel
*ask children to share ideas for photos and videos, or invite them to include their own work to make reels authentic and meaningful
*take photos and film videos vertically to make them fit properly into the Instagram formatting. Horizontal images and videos can still be used, but they have a large black frame around them which makes them appear small and harder to view
*use filters, stickers, locations, text, etc. to enhance your work
*jump on trends and modify them for educational use in order to help your reels be discovered by others
*reels (unless they have sound copyright or restrictions) can be saved to your phone or computer, and mashed with other tech - you can share these saved videos on twitter, in digital documentation programs like Edsby or Seesaw, or added to a blog (like I have here) to get the most out of your work

To see more of my reels and connect on Instagram please follow @McLennan1977!

Sunday, July 24, 2022

A Writer's Dream Come True

“Every morning you have two choices: continue to sleep with your dreams, or wake up and chase them.” 

For as long as I can remember I have always wanted to be an author. I dreamed of writing books that would inspire people. I especially hoped to help educators and children overcome their hesitations and fears regarding math learning, and view math as a beautiful and complex subject that could be discovered everywhere in the world around us.

It was with much excitement that my dream became reality. I was thrilled to publish multiple books regarding both math pedagogy and practice. I was thrilled to find out this summer that many of my books are now available through a favourite Canadian bookstore of mine - Indigo. Thank you to all of you who have helped to support my writing; from those who have proofread and given suggestions for improvement, to those who use the books in their classrooms each day - I am forever grateful!

You can find the books at Indigo here:

Thursday, April 28, 2022

The Wonder of Trees

"Between every two pines is 

a doorway to a new world."

John Muir


"Look at me!" Kyle called as he stood on his tiptoes.  "I can reach so high. If I jump I can reach even higher!"

"That's nothing. I bet I can reach higher," Asher responded.

"Ok, let's see you do it!" Kyle laughed. "I can reach this high." He jumped and slapped a spot on the tree.

Asher copied the movements, jumping and tapping the tree in a different place.

"Who was higher?" they called to me.

"I'm not sure," I answered. "It's hard to tell where you each touched and compare the spots. You'll have to think of a way to mark and measure to be accurate."

Harper had been standing next to me watching the boys. 

"I know," she said. "What if you each hold a piece of chalk in your hand. When you jump you can touch the tree and leave a mark."

"Oh good idea!" I answered. "And we can check our wonder wagon to see if we have any tools that measure."

"Like a measuring stick!" Harper answered.

Spending time outside in nature each day is important for children's growth and development. There is a misconception that a robust outdoor program needs numerous tools and materials in order to be successful. However in my practice I have found that often the best inquiries spark from examining and exploring natural elements in our play yard. One of the most intriguing artifacts that children love to explore is a tree. Trees are usually easy to find, diverse, and offer endless possibilities for child-centred inquiry. Responding to children's observations and wonderings about trees can inspire rich math, literacy and science work. 

Interested in exploring the trees in your surroundings with children? Here are some ideas for getting started. 

Tell stories about the interesting markings you find on trees.  Children love to hypothesize about unique things. Ask children to imagine how a spot ended upon a tree, or look for the math within the markings (here the knot on the tree appears to be made from concentric circles).

Explore the different textures you feel on trees. Many children are sensory learners who enjoy exploring their surroundings through touch. Encourage children to feel different parts of a tree (e.g., bark, leaves, blossoms) and describe what they feel. Sensations can be categorized and sorted (e.g., making a pile of smooth leaves).

Research the different objects that grow on trees. The life cycle of trees often results in the creation of flowers and fruit. This growth pattern can be observed and tracked over time.

Inquire about what living things make their homes in trees. Each area is unique with specific animals and insects using trees as shelters. Nests can be observed and described (e.g., a robin's nest is perfectly circular). Children can be encouraged to draw pictures detailing what they see.

Hypothesize the age of a tree using different clues. The rings on a stump can help determine the age of a tree as well as its type and size. Look for stumps and ask children to count as many of the concentric circles as they can see. They can estimate the age of the tree. If a tree is still standing children can estimate how tall or old it might be.

Build gross motor skills and perseverance by climbing trees. Building resiliency, grit and perseverance helps children in all aspects of their learning. Climbing trees encourages these skills as well as being a great physical experience that many children enjoy.

Investigate how trees change over time by exploring decomposition. Logs left over time provide a wonderful opportunity for children to become curious about how it has transitioned from tree to rotting wood. Many insects make their homes in and under logs. Ask children to tell stories about what they think might have happened to fell the tree, or investigate who has been using it as shelter.

Search for clues on the tree to guess who might have visited before you. Holes in the bark can tell stories of what animals have been searching for food in the bark, or using the tree as shelter. Children can observe bark for changes over time and conduct research.

Ponder why some trees stay green all year while others lose their leaves. Coniferous trees do not usually drop their needles. Ask children to describe and categorize the trees in the yard or neighbourhood, and observe them over the course of several weeks or months.

Use materials gathered from the tree as loose parts for imaginative play. Pinecones, twigs, leaves, needles and acorns are great manipulatives for math or creative work outdoors. These can be collected from the yard or donated by families, adding variety and interest to process-based play.
Measure, record and compare the sizes and shapes of different trees. Find the largest or smallest tree in your area and challenge children to find different ways to measure the trunk's circumference. Keep track of the measurements by recording them in a nature notebook or chart paper.
These suggestions are just a starting point for using trees as the basis for rich inquiry during outdoor learning. Listening to the observations and wonderings of children can spark amazing projects. Children often have the best ideas!

Monday, January 10, 2022

Stand Up Sit Down

Due to the great feedback I've received I have turned the 'Stand Up Sit Down' slides into a video that educators can use in their physical or virtual classrooms. This fun activity can be an icebreaker for a new group of students, a minds-on activity before a main lesson, or used during transition times.  


Check it out on YouTube: Stand Up Sit Down


See, Think, and Wonder Math Routine Using Videos

Math is all around us! As an educator I love helping children discover the authentic ways we use math in our everyday lives! As children recognize the integrated, meaningful ways math helps our world work, their interest and confidence in the subject will grow. Exploring the authentic math that exists in our surroundings may help nurture children’s interest and confidence, building a strong foundation for subsequent experiences. 

The ‘see, think, and wonder’ routine is a specific sequence of steps that guides children’s thinking regarding a specific observation. Children first describe what they see, focusing on their power of observation. Next, they interpret these observations and articulate connections to what they have seen. Finally, they share a question or wondering about the object in order to guide their future thinking work.

The 'Winter Day - See, Think and Wonder' video can be used in physical or virtual learning spaces to help facilitate math conversations. At first children can be invited to carefully observe each photo and share what they see. Ask children to use rich description as they articulate their observations. Next, ask children to make personal connections to the information presented in the text and photos. They can articulate what they think about the question prompts in the text, or make inferences about the information shared in the photos. Finally, ask children to share what they wonder about the text and photos. Educators can pause the video at any point to give children more time to engage in math conversation about their observations and wonderings.

As children engage in conversation, reflect upon their ideas. What are children curious about? What do they notice in the foreground, and background of each photo? What connections can they make to the video? What experiences do they have that relate to the objects or situations being presented? Is there something they are interested in learning further? How might they go about conducting mathematical research if they have access to these objects or scenarios in real life? What knowledge do they need to have in order to research their question? What tools and supports might help them in their quest? How can they share their findings with others?

After the children have explored the video, consider asking them to co-create their own version of the media in the form of a 'See, Think, and Wonder' class book. Children can illustrate pictures and write their own narratives. Invite children to look around their homes and communities for other seasonal situations to explore. Perhaps children can digitally document what they find and add these to their own Winter Day book. Images can also be gathered and shared in a video form. The possibilities are as endless as the questions children ask.

YouTube link is Here: Winter Day - See, Think and Wonder

Saturday, January 8, 2022

Math-ercise Videos

Interactive videos can be a great way to engage children in virtual learning spaces, or can be used in the physical classroom as warm ups to lessons, during transition times, or even during lunch times when children are finished eating (especially during Covid when only half the children can be eating at once and the other half of the class requires something to work on).

I have created some simple math-ercise videos that educators and families can use to help engage children in exploring math concepts. These ask children to look at a math equation and complete the exercise that corresponds to the answer they feel is correct. Children complete the exercise for 20 seconds and then get 5 seconds of rest as the correct answer is displayed. I feel that the physical nature of the videos will be engaging for children and add a kinesthetic feature to math learning. Videos can be paused and mini number talks can occur if educators wish.

The first video explores adding to 10.

 Math-ercise Workout - Adding up to 10

The second video explores adding to 20.

The third video explores subtracting from 10.
The third video explores subtracting from 20.

I will continue to create videos and add them to this blog post over time. I am hoping to explore subtraction, multiplication and division facts.

Educators may wish to create their own videos/presentations to explore other math concepts (e.g., number patterns, doubles). 

Get a copy of the files here to use at your own pace in your physical or virtual classroom. This gives you the option to pause the power point and explore each slide or personalize it to best meet the needs of your students. Music and transition times are embedded within the presentation so all educators need to do is change the equations and answers on each slide. Playing the presentation should run it without the need to manually forward each slide. 

This version is not animated: PDF Math-ercise File

Get a copy of the Power Point file here: PPTX Math-ercise File.

Get a copy of the Google Slides file here: Google Slides Math-ercise File 

Feel free to share with others! Feedback in the comments always appreciated!

Wednesday, January 5, 2022

Stand Up Sit Down

Here is a fun activity to get children moving as they respond to a prompt. Look at the photo and respond to the 'stand up if you..." prompt accordingly. Children can then create their own statements for their peers to consider. Providing time for children to reflect upon and discuss their ideas regarding the stand up/sit down prompts can encourage rich oral language as children consider the photos and verbal prompts and make connections to their own lives and experience.

Get a copy of the slides to use in your classroom here: Stand Up Sit Down

Thursday, November 11, 2021

Using End Pages to Inspire Math Conversations

"I think all of these have four wheels."
"No, the truck in the middle has 8. You just can't see the other four because they are on the other side."
"I like the red car best. It goes faster than the others."
"The red car has a number 5 on it. That's because it came in fifth place."
"No, the number five is because there are five cars on these pages. The other ones just don't have numbers on them."
* * * * * * * * * *
Have you ever taken time to appreciate the beautiful art that exists on the end pages of books? This year my goal has been to really slow down and enjoy books together with the children. Sometimes my literacy appetite is so great that I just can't wait to read all these wonderful books in my collection - we rush through book after book each day, gorging ourselves without slowing down to appreciate their intricacies. It's hard not to - there are so many amazing children's books in the world and I'm eager to share as many of them with my class as possible. However the educator in me knows it's important to take our time so we really get as much out of each book as possible. Appreciating the book's design, the illustrations, text, even choice of font, can all help empower children as well rounded readers. There is so much to be discovered within books when we appreciate each text.

Kassia Wedekind, co-author of Hands Down, Speak Out: Listening and Talking Across Literacy and Math, challenges us to think about "how we can mathematize end pages of books". She gives the example from the book Creepy Pair of Underwear by Aaron Reynolds. The end pages feature an array of mini underwear pictures (always a perfectly humorous topic for any elementary school student!). Kassia suggests that children can examine the array and use different strategies for calculating the total number of objects. Children can then be challenged to write different equations to show a deeper understanding of their thinking.

Looking to extend this idea we read Count on Me by Miguel Tanco. This book helps readers uncover the beautiful math that exists in the world around us (e.g., geometric shapes on playgrounds, sharing during dinner time). After reading the book for pleasure, I reintroduced it again to children and asked them to take notice of the cover and end pages specifically. They immediately noticed the vibrant pattern on the inside cover, and made the connection that a small portion of the pattern was also visible on the spine.
Count on Me | San Francisco Book Review

Participating in their discussion while honouring their ideas by including them in an idea web is always challenging for me. It's hard to listen attentively, talk, and record what is being said at the same time. I tried my best to capture some of their thinking on a large chart paper. Most children were eager to discuss the intricate crisscross pattern and curious about what other objects in our yard had this same design (e.g., many noted the fence also looked like this). Towards the end of our conversation the idea of quantity arose, and children wondered if the estimate of 30 diamonds was correct. Many felt this number was too small and thought counting by rows would be an easier way to find out. A next step for us might be to place the book along with different loose parts (e.g., gems, buttons), chart paper and a hundreds chart and challenge children to see how many diamonds they can count in the pattern. I also wonder if helping children to calculate a large quantity by creating groups of counters using a friendly number such as 5 or 10 might work. It's okay if we don't arrive at an answer to this question - the process of working towards it is just as important in my opinion. 

Interested in exploring end pages with children in order to provoke deeper math thinking and exploration? After you find a book that is meaningful for children and has beautiful end page art, consider using some of these question prompts: 
  • What do you see?
  • What do you think about ____?
  • What does this remind you of?
  • What do you like/dislike about these pages?
  • Why did the author/illustrator choose this design for the inside of the book?
  • What meaning does this end page have now that we've read the story? 
  • What connections to this design can you make?
  • What math do you see?
  • What math questions do you have?
  • How might we find an answer to your question?
  • If you were the author/illustrator how would you have designed the end pages?
  • How would you improve this design?
  • How would you change this design to emphasize patterning/quantity/shape/colour/etc. more prominently? 
  • Can you draw your own unique end page for a book you've written?
  • What would you ask the author/illustrator personally about this piece?
Connecting math and literacy is a wonderful way to help children appreciate how connected the world is and find authentic problems to explore in their lives!

Thursday, November 4, 2021

10 Math Concepts that Children Learn from Puddle Play

"Childhood is that state which ends the moment a puddle is first viewed as an obstacle instead of an opportunity."

K. Williams


Puddle play is an incredibly rich learning activity that many children enjoy. Spending time outdoors exploring many natural elements helps children recognize that there is no such thing as bad weather. There is beauty and wonder to be found in every aspect of nature. Sometimes in early childhood education we need to help our families and school community understand the authentic learning that can happen when children play with sensory materials like puddle water outdoors. Demonstrating the meaningful math connections that emerge in this type of play can build support for outdoor exploration and learning. Sharing this through regular communication including documentation can be incredibly helpful in cultivating positive partnerships and support for messy play outdoors.

Here are ten math ideas that can be introduced and strengthened when children play in the puddles:

1. Patterning

When rain drops fall into water their impact disturbs the surface tension of the water. The ripples spread outward from this impact point. This reaction forms concentric circles which are two or more circles that have the same center point. Each subsequent circle is larger than the last, creating a growing geometric pattern for children to explore.

2. Opposites (Float and Sink)

Children love to place objects in water and experiment with what happens to them. A favourite outdoor activity for our children is to place many different objects in water and see if they float or sink. An object's density determines whether it stays above or below the water. The object will float in the puddle if it is less dense than the water. If it sinks, it is more dense than the water. 

 3. Temperature

The temperature of puddles can vary depending on the ground and air temperature. Children enjoy feeling the water with their hands and describing how hot or cold it seems. An engaging activity is to provide kid-friendly thermometers to children and challenge them to read the temperature of the different puddles in the yard. Are the larger ones a different temperature than the smaller ones? Does the temperature of a single puddle change over the course of the day? Ask children to generate theories about why this is happening.

4. Measurement

Sensory experiences are vital for children's growth and development. Most children love to play in mud using cooking items and utensils. A favourite activity for us is to use the puddles for water play. Not only do we not have to worry about a wet floor indoors, children are captivated using cups, spoons, funnels and bowls to collect the water. Challenge children to measure how much water they can collect. Ask them to see if they can empty a puddle and calculate how much water it had altogether. 
5. Cause and Effect
Cause and effect activities help children realize that every action they take has a reaction. When children jump in puddles, the water splashes. Experimenting with cause and effect helps children play with variables that can control the reactions in different ways. For example, and bigger jump in the puddle usually results in a larger splash of water. Children can change their actions (e.g., increasing movement, decreasing movement, modifying direction) and observe the results.

6. Comparison
Puddle water can look many different ways. Some puddles are clear while others are muddy and filled with debris. Children can travel the yard and observe/describe what they see as they compare puddles to one another. They can also experiment with the different materials and observe the reactions that occur. For example when water is added to soil, the soil appears a darker colour. This occurs because wetter soil has less oxygen compares to drier soil. Some puddles are so saturated with dirt that there is a layer of mud that settles on the bottom and a layer of water that has risen to the top. As children explore different puddles they can notice and name what they see, and compare the properties of each to one another.

7. STEAM (science, technology, art, engineering, art, math)

STEAM challenges are highly motivating for children. Puddles offer many opportunities for educators to ask children to design and build an object to be used with the puddles. A favourite in our classroom is to ask children to create a puddle boat from loose parts (e.g., wooden craft sticks, cardboard, foam, aluminum foil) that floats. Another highly motivating construction activity is for children to build a bridge over the puddle for the mini cars to use to cross the puddle. 

8. Counting

In our yard we often have very large puddles when the rain falls due to the slope and drainage of the playground pavement. A fun activity is for children to crowd in and count how many can fit in the area of the puddle. Great math questions emerge in this activity - can the same number of children fit in the different sized puddles in the yard? How many boots altogether are in the puddle? Can we count the boots by 2s?

9. Reflection

Water is a reflective surface. When the water in a puddle is still, the surface is flat and can easily reflect light. If the wind is blowing and ripples appear, the reflection can become distorted. The harder the wind is blowing the more distorted the reflection appears. This type of reflection also offers an exploration of symmetry as children can identify the line of symmetry and see how each side appears. This symmetry is often curious for children who notice that the reflected side appears lighter/faded than the real object. Children can experiment with reflective symmetry by placing and moving different materials into the puddle and seeing the result.

10. Area and Perimeter

The size and shape of a puddle can often inspire conversation about its area and perimeter as children wonder about how big or small it might be. Sometimes we will use loose parts to help us measure (e.g., How many rocks fit around the outside of the puddle?  How many leaves can float on top of the puddle?). The distance across a puddle is also interesting to measure as children leap across the puddle and measure how far they've jumped, or build bridges to help the mini cars cross the puddle.
What other math have you explored in the puddles? Tweet me and share your awesome ideas and experiences! @McLennan1977

Looking for a resource to read with kids to support authentic math play in the puddles? Check out my new book Puddle Math: See, Think and Wonder! 
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