Geometric Chalk Art in the Outdoor Classroom

Have masking tape and sidewalk chalk? Then you can invite children to create amazing geometric artwork outdoors in just a few steps! 

Create the outline of the art by placing tape on the ground in different designs. I personally like creating a large square or rectangle and then using various shapes to fill the area inside. 

Invite children to colour each section using a different colour of chalk. 

Remove the tape to reveal the gorgeous design!

Experiment with different designs...

...and encourage children to to use the art when inventing and playing their own games!

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.

 

 

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!

15 Easy Autumn Invitations for Learning

Autumn is a beautiful time of year! There is so much potential for encouraging rich, playful exploration with natural objects that children find fascinating to explore. In this post I will share 15 easy to create autumn invitations for learning that can be presented in the classroom as table top activities, or investigated during outdoor play. These sparks for learning integrate math, literacy and science while offering potential for additional inquiries depending on how children explore and manipulate the materials. 

Educators can observe each activity and provoke further discovery using a 'see, think, and wonder' learning routine. After watching the children play with the materials, ask them to share what they are noticing while playing by stating "I see...". They can then be asked to reflect upon their observations and begin to build their theories about the play by making connections in an "I think..." statement. Finally a question for further exploration can be crafted in an "I wonder..." open-ended query. As children pose questions and share their curiosities about the materials and the world around them, the educator can record observations, reflect upon how to support children in additional work, and gather materials to enhance and evolve the play. 

For example - "I see many different kinds of leaves. I think they might be different sizes. I wonder if I can order them from smallest to biggest."

Natural Objects Colour Matching - recycle paint chip strips by providing them to children and encouraging them to find objects in the yard or placed on a table that match each shade as closely as possible. Encourage children to explore the different shades of each colour.

Roll and Fill the Web - create a spider web by wrapping a shallow basket with thick yarn. Encourage children to roll a die (or multiple dice), add or subitize the pips, and add that many spiders to their web.

Spider Game - create mini catapults by securing a wooden clothespin to a solid block or piece of wood with an elastic. Children can manipulate the catapult and fire a plastic spider into the web. Every spider that lands on the web earns them a point! Children can record their points using tallies, and compare their scores to others.

Measuring Circumference - present a variety of interesting pumpkins and gourds to children. Ask them to suggest ways to measure the circumference of each object. Order the objects from smallest to largest circumference.

Counting Seeds - encourage children to use fine motor skills to remove the inside contents of a squash, gourd, or pumpkin. Provide a variety of tools (e.g., hundreds charts, ten frames) for the to use when calculating the total number of seeds they have removed.

Gourd Runs - present a variety of gourds and recycled floor boards to children. Encourage them to create a variety of ramps and runs to experiment with rolling the gourds down.

Geo-Pumpkins - encourage children to create their own shapes and designs on pumpkins by using pushpins and elastics. Children can push the pins into different places on the pumpkins and then stretch an elastic around them.

Gourd Catapults - present a variety of recycled tubes, wooden boards and mini pumpkins to children. Model how the tubes and boards can be used to make a catapult. Children can be encouraged to stomp on the catapult and launch the pumpkin as far as they can. Brainstorm with children how to record how far the pumpkin travels. Discussing safety rules beforehand is recommended (e.g., ensuring no one is standing in front of the catapult before launching a pumpkin).

Creepy Crawly Pick Up - provide a variety of seasonal trinkets to children in trays. Encourage children to pick up and move the materials using a variety of fine motor tools (e.g., chopsticks, tweezers). Children can sort the materials in the trays in different ways (e.g., by colour, size).

Roll and Fill - provide a template for children to use (grid paper also works). As children roll the dice and add the pips, they then colour the corresponding number of objects or squares on their paper. First to fill a line, section or the entire page wins. 

Big Body Spider Webs - encourage children to wind yarn or twine around natural materials outdoors (e.g., stumps, tree trunks, branches), creating a large spider web. If the web is large enough, children can move their bodies in and out of the web, avoiding the yarn as an obstacle course. Large plastic spiders can also be added and the web transformed into a dramatic playscape.

Pumpkin Weigh In - provide a variety of measuring tools (e.g., balance scales, digital scales) for children along with a collection of pumpkins and gourds. Encourage children to measure and record the weight of the objects. Provide challenges like asking children to find the lightest/heaviest pumpkin or ordering them from lightest to heaviest.

Hanging Leaves - attach yarn or twine between to objects (e.g., tree trunks, posts). Provide a variety of real or fabric leaves and clothespins. Encourage children to attach the leaves to the twine in a variety of ways (e.g., sorted by shade, in a pattern, smallest to largest). Children can explore the play yard for other interesting objects to hang on the line.

Natural Materials Sensory Table - fill a sensory table with autumn items found in the play yard or provided by families. Add tools including magnifying glasses, tweezers, scissors and sorting trays to enhance the play.

Which One Doesn't Belong - present a variety of different pumpkins to children. Ask them to explain which one they feel doesn't belong and articulate their thinking using math ideas and terminology.

Small World Play and Math

 "Old things are better than new things, because they've got stories in them."

Kami Garcia

What is hiding in your cupboards and closets? For 20 years now I have kept an old, beautiful china set from my grandmother high up on my shelves. I can honestly say that I haven't used it once; life with busy children doesn't lend itself to tea parties and fancy dinners. Each time I opened the particular cupboard in which these beautiful objects were stored, I'd feel a sense of guilt. They were treasured by my Nana and used for special gatherings. Now they collected dust.

As I look ahead to the next school year, I am eager to bring beautiful, inspiring materials back into our classroom. Covid has meant that many children have been home with their families, isolated from the world. I anticipate a higher than normal level of anxiety and stress as we return to school, even if we are eager and ready for this new chapter. Having beautiful, interesting materials in the classroom space can often welcome children and pique their curiosity, helping them transition into the space and overcome their feelings of anxiety.

Last week I cleaned the kitchen and as I handled the china, I wondered if it could be integrated into the classroom as play props. Not only would that give the bowls and cups a sense purpose, they would beautify our space. I liked the idea of being able to enjoy them on a regular basis; each time I look at them they remind me of my grandmother and I love feeling her presence in my life.

I had been eager to use a small teacup set (found at Value Village) in some way. I knew that the children loved small world play, and that imaginative mini playscapes held potential for rich math learning. I decided to turn my china into a tea garden. In each piece I placed small stones at the bottom for drainage. I planted succulents in the potting soil because of their hardiness and ease of care. 

     

I anticipate placing these materials on a low shelf in the classroom. They will be a semi-permanent fixture there. They will beautify our space when not in use, and be accessible enough that children can access them without needing to move them around the classroom. I have always felt comfortable integrating fragile materials into our space. My experience has been that when children feel empowered as learners, they care deeply for the materials and handle them gently. I'm also prepared for the possibility of accidents. The children are capable and careful when something breaks and I am willing to trade this risk with the reward of using these materials.

I am purposely not adding character props to this learning invitation. I would rather see how children integrate other materials we have into their play (e.g., mini animals, wooden clothespin dolls), or create their own fairies and other figures at the art center. I also see potential for creating a similar invitation outdoors in some way (e.g., fairy door in a stump). As I observe the children I will take note of their ideas and interests, and help to scaffold and support the math learning as it emerges. Some math ideas I think might present include:

• a discussion of proportional reasoning as children explore the size of the small world and create additional play props
• an observation of pattern as children see, think and wonder about what they find on the china
• practice with one to one correspondence as children set the table for a tea party and create additional props to support their storytelling (e.g., plates, forks, food)
• STEAM as children create their own figures to integrate in this play (e.g., dolls, fairies) or create their own mini worlds (e.g., dollhouses from boxes)
• observations of shape and size as teacups are compared to one another
• connections with capacity as children consider how much liquid might fit into the cups, or create their own tea parties while playing in the mud kitchen or water table

I'm sure as children explore the materials additional ideas will emerge. I can't wait to see what they discover! I'm eager to search my closets for other materials to upcycle and bring into our learning space!

Which One Doesn't Belong? Using Autumn Treasures to Inspire Math Talk

 The children were gathered for whole group. I displayed a collection of pumpkins and asked them a question - which one does not belong?

"I think this one doesn't belong. It's got the thickest stem. If you look at the others their stems are thinner. One pumpkin doesn't even have a stem."

 

"No, that one is green. All the other colours are normal pumpkin colours but that one isn't. Green is a dark colour and I don't even think pumpkins are supposed to be green."

 

"What if we make two piles - green and non-green?"

 

"What about this one? It's got the longest stem. That's different from the others. The stem is even longer than my hand if I put them next to each other."

 

"Yeah, but this one doesn't even have stem. That makes it different from the others. I wonder how it grew without a stem!"

 

"I know! This little one is different. It's the smallest. If I put the pumpkins in order by size this one would be on the end. It's teeny-tiny!"

 

"No. This is the one that is different. It's the only one with bumps."

 

Math talks can be incredible powerful experiences for young children; as they engage in interesting and meaningful conversations they uncover problems of importance (e.g., which pumpkin does not belong), engage in a problem-solving approach (e.g., using their senses to explore the pumpkins in depth and making connections between previous experiences and current explorations), and discover a variety of solutions (e.g., justifying why their chosen pumpkin does not belong using descriptive language). This builds confidence and agency in their work as mathematicians. They build theories about the world around them as they support their ideas with observations, draw upon previous experiences, listen to and consider the opinions of their peers, and revise their thinking as needed. Open ended math talks give children time and space to notice and wonder about something they find interesting and meaningful about the world around them. I purposely chose pumpkins for this math talk because the children have been quite excited about Halloween, and curious about the autumn artifacts we have placed around our classroom and outdoor space (e.g., leaves, gourds, decorative corn).

According to Antonia Cameron (2020) in addition to helping educators fulfill curriculum and assessment obligations, thinking routines included in regular math talks can be used to:

• develop specific content ideas
• meet different standards
• develop playful mindsets in children
• practice problem-solving models
• facilitate communication skills  

Children are natural researchers who engage playfully with the world around them. They are driven to answer questions that promote a curious and wondrous mindset. They test their theories and revise their understandings through conversation and experience. Math talks can become powerful learning routines that empower children and build community over time. Children can share their ideas, justify their thinking, consider the ideas of their peers and whether or not they agree with them, and use this information to advance their mathematical understandings.

 

West and Cameron (2013) suggest a number of reflective points for educators to consider when designing mathematical thinking routines including:

• what is the purpose of the math talk?
• what big mathematical ideas are you hoping to embed within the conversation?
• what are the needs of children and is the talk differentiated enough to include all?
• what directions do you anticipate the conversation taking?
• what assessment opportunities will the math talk provide?

A starting point for any math conversation is to provide a tangible artifact for children to explore (e.g., a pumpkin, piece of artwork, collection of loose parts) and ask them to notice and name what they see. Once they articulate their observations about characteristics of the object (e.g., shape, size, colour, texture, smell) they can make connections between these and the world around them (e.g., other objects, experiences, texts). Perhaps questions emerge in the conversation and children can wonder about some element of the object or conversation. This can lead to a research query to explore further. 

Giving children freedom to play with problems empowers them as mathematical learners. They grow their individual and collective mindset as they trust their abilities and engage in productive struggle. They question the world around them and delve deeply into complex wonderings and questions. This provides educators with rich opportunities to infuse complex math ideas into authentic moments of learning; building the big math ideas and spiralling curriculum as needed. Making time for regular math talk in the classroom celebrates children's thinking and empowers them as the amazing mathematicians they are! 

 

Cameron, A. (2020). Early childhood math routines: Empowering young minds to think. 

    Portsmouth, NH: Stenhouse Publishers.

 

West, L., & Cameron, A. (2013). Agents of change: How content coaching transforms 

    teaching and learning. Portsmouth, NH: Heinemann.

Mandalas

The children have been very interested in creating intricate, circular designs using a variety of loose parts and pattern blocks. We introduced the word 'mandala' to them. It has been interesting to see what shapes and patterns they can discover and identify.