Facilitating Math Talks with Young Children - Printables to Support the Math Talk Books

Math talks are a great way to engage children in open-ended explorations that invite them to think critically and creatively about a concept. Math talks are like number talks, yet include any area of math that an educator would like children to explore. An effective math prompt to facilitate a rich math discussion will be layered; it should be open-ended with multiple entry points for engagement. Even children as young as kindergarten are capable of participating in complex math conversations. In our classroom I aim to invite children into a math talk at least once a day; I sometimes use the numerical date on our morning message as the spark for exploration. Other times an interesting photo or collection of loose parts will be engaging and incite children into further exploration. I try to vary the invitations I provide in order to diversify the math we discuss and to reach as many learning interests as possible. 

In our program we have a morning circle time. This circle is our first whole group gathering time for the day and helps set a positive atmosphere in our classroom. It is also a time to celebrate being together, and share news from our homes. We often use it as an opportunity to read a story and discuss any new and exciting activities or additions to our classroom space about which the children should know in order to be successful for the day. 

When I first started teaching kindergarten many years ago it was expected that the morning circle would begin with 'calendar time' where children would put a sticky number on a large grid to depict the day and there would be an extensive discussion about the calendar (e.g., day of the week, month, year). However over the years I realized that this was a very teacher-directed task and not as meaningful a use of our time. After reading Sherry Parrish's work on number talks I was inspired to use our morning message as an anchor for math talks. Wanting to still introduce the date to students, the numerical representation of the date became the foundation for our number talks most days. Sometimes I would use other prompts depending on the events and interests emerging in our classroom. If you would like to read more about number talks in kindergarten, you can access an article I wrote for the Journal of Teaching and Learning here: Joyful Number Talks in Kindergarten. 

 

Over the years I have shared my math talks on social media and have been asked repeatedly to create a guide to support educators who wish to engage their students in math talks. This inspired my collection of monthly math talk books. Each book contain 25 prompts to engage children in regular conversations in the classroom. The prompts do not need to be followed in order. In order to help educators I have also created free downloadable PDFs that can be printed and used with students. 

 

Click on the book's image to be linked to where it can be purchased. 

 

Click on the printable to be linked to where it can be printed.

Printables that can be used to support this book:

 

Printables that can be used to support this book:

      

       

 

Printables that can be used to support this book:

 

  

  

Cultivating a Mathematically Rich Learning Space

It's almost Labour Day! 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 weeks of summer and return soon to our classrooms with open eyes, minds and hearts.

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 ideas 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.

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 Instagram @McLennan1977 for regular ideas from my classroom!

Book Review

"Exploring trees outdoors is an enjoyable experience that children love to do! Swinging from a branch, exploring leaves and bark, and observing gnarled roots are all favourite activities that also integrate rich learning. Heading outside to explore the yard uses children's excitement and enthusiasm for sensory and nature experiences to inspire rich mathematical and scientific inquiries about what they are seeing and experiencing."

 

I was excited to see a review of my book Tree Math in the MAMT Spring Journal! You can access the review here!

Five Free Printables to Use with Tree Math

 "Trees are poems that the earth writes upon the sky."

-Khalil Gibran

During outdoor play children are drawn to the trees in the school yard. They love to feel bark with their hands and wrap their arms around the trunk. They collect artifacts for exploration including sticks and leaves and search for insects in the bark's crevices. Trees offer so many rich opportunities for wonder and discovery as children notice how they change with the weather and seasons.

To help supplement my book Tree Math (available from Amazon and Indigo) here are five easy, free printables that can be used to support children's work in nature!

1. My Favourite Tree

Encourage children to spend time in nature and observe the tree they like best. Ask them to consider what it is they appreciate about this tree? Children can then sketch the tree on this page and compare their tree with others.

2. My Tree and the Four Seasons

Over time children can observe the same tree and draw what they notice changing during the four seasons. This page can be kept over time and added to as the months change. Children can also draw on it at one sitting and hypothesize what the tree might look like in each season, especially after conducting research about how trees adapt to the weather.

3. Tree Circumference

Children can use a variety of materials to measure how big around a tree's trunk is (e.g., measuring tape, hand spans, links) and record it on this tracking page. Drawing a picture can help explain their math thinking.

4. Tree Bark Patterns

Exploring the texture of bark appeals to many children who enjoy sensory experiences. Children can use magnifying glasses to examine the patterns in bark up close, or place a paper on top of the bark and use crayons to create a rubbing. Children can then describe what they see and compare their rubbings to others. 

5. A Tree is a Home

Encourage children to explore many trees in the school yard and neighbourhood. Ask children to observe what living things they observe on and in the trees (e.g., birds, insects, mould) and record their observations on the tracking paper. They can hypothesize how the tree might be a home for many living things at the same time.

Ten Free Printables to Supplement the 'Autumn Math Walk' Book

 "Autumn is a second spring when every leaf is a flower."

Albert Camus

Autumn is my favourite time of year. Once we have settled into the new school year it's amazing to head outdoors and appreciate the interesting changes happening in nature. There is so much potential for math learning outside of the classroom. 

To celebrate the 1500th copy of Autumn Math Walk being published here are ten free printables to use with children during outdoor math exploration. Autumn Math Walk is available through Amazon. Enjoy!

 1. Hundred Chart Printable

Print and laminate this page so that children can bring it outdoors and see how many objects they can collect. Challenge children to find 100 of the same objects (e.g., acorns, leaves). If children's collections are made of different objects challenge them to see how many of each there are and total these to 100 (e.g., 20 acorns + 15 rocks + 12 leaves...)

2. See, Think, Wonder

Provide a copy of this page for each child. During time outdoors ask children to focus on something that piqued their interest. This page can be used to delve more deeply into the observation using the 'see, think, wonder' thinking routine.

 

 

3. Magnifying Glass

 

This page can be used to help children observe and represent something more closely. For example if children are curious about the vein patterns on the back of a leaf, they can represent what they see in a large format inside the magnifying glass.  

4. Scavenger Hunt

Before heading out on a math walk children can predict what they might see and draw these in the left column. For the walk have children attach the page to a clipboard and track how many of each object is observed using check marks or tallies.

5. Idea Web

This graphic organizer can be used to help children represent all the interesting things they observed on their autumn math walk. Papers can be distributed for individual use or a large one can be printed and used by the class when reflecting after their walk.

6. Autumn Colouring Page

Colouring can be a soothing activity. This fun page can be used by children during quieter moments of rest and reflection. It can also be sent home at the end of the day. 

 7. Autumn Counting

Ask children to look for different numbers or groups of objects on their walk. As they notice different arrangements of things they can fill them out on this page (e.g., 1 duck, 2 trees, 3 ladybugs...).

 8. Favourite Part

This template can be used once children return from their math walk. It asks children to reflect upon their favourite part of the walk by drawing a picture of what they saw, and completing a sentence to further explain their thinking.

9. Big and Little Objects

As children explore outdoors ask them to consider the size of objects they find. This template can be printed and laminated for children to use outdoors as they place objects directly in each column (e.g., small acorns, leaves, flowers, sticks). Children can also reflect upon their walk and draw pictures of small and large objects on the paper once returning from the walk.

10. Five and Ten Frames

These five and ten frames can be printed, laminated and brought out with children on their explorations outdoors. Challenge children to use the frames to count different collections of objects that they find. (The frames can be enlarged on a photocopier before laminated to accommodate very large objects). 

Creating a Space that Cultivates Math Learning

 

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. 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 list isn't all inclusive, I thought it might spark some ideas to support and inspire as we enjoy the first weeks of school and start back in our classroom with open eyes, minds and hearts this month.

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.

Eight Way to Encourage Math Learning During Risky Outdoor Play

This month I have a blog post featured on the National Association for the Education of Young Children's (NAEYC) website regarding how to engage children in math learning during risky, outdoor play. You can read the article here: Eight Ways to Encourage Math Learning During Risky Outdoor Play.

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!