Sunday, September 30, 2018

Puddle Play - Rethinking the 'Math Classroom'

We are always looking for opportunities to head outside and enjoy the weather, even when it might be a little wet or cold. Last week our area enjoyed quite a bit of heavy autumn rain. The children spent much of the morning peering through the window and marveling at how much rain was falling. After a few hours they noticed a giant puddle forming in the corner. As the rain continued to fall and the puddle grew, the children became concerned that their outdoor play time would be hampered by the rain.

Fortunately by the early afternoon the rain tapered and the children were able to head outdoors. We are lucky to have a class set of rain boots purchased by the school parent council for use in our outdoor classroom. This way children can enjoy playing in our school yard, even when they might forget to bring their boots to school that day. We are always prepared and the children ready to explore the world outdoors. Even the giant puddle would be no problem that day!

The children scurried outside after eating lunch - many wearing mismatched school boots because they couldn't get them on their feet fast enough because they were so eager to explore the water.


As I approached them I was amazed by the authentic math talk developing in this natural and authentic learning environment. As I listened into their conversations I overhead children wondering with each other about amazingly big math ideas...

How many children could fit in the puddle?  Did each person's feet have to be touching to be counted? Did children who were jumping in and out of the puddle count too?

How deep was the water? How much water was there really in the big puddle? Could it fill a bath tub? How could it even be measured?

Who could make the biggest splash? How would they even judge how big the splash was? Could it be measured? Was the biggest splash the one that soaked the most children standing nearby?

Could the water be used to make soup? How much water was needed in the recipe? Would anyone even want to eat mud soup?

How much water was in one's rain boots after a big splash? How long did it take to dump it out? How did all that water get in there in the first place?

How much more water was needed to cover the stump? Was the stump floating or sinking in the water?  How tall was the stump? What if it rained more...would the stump be under water?

How long would it take to run across the puddle? Who could run the fastest over the water? How could we measure and record the puddle races?

The children were making connections between their puddle play and math in the world around them. The questions they were posing about their experiences in the water were meaningful to them, supporting and strengthening their productive disposition towards math. As an educator involved in their play, I was able to listen to their questions and facilitate conversation and critical thinking about the big math ideas. How could we figure out who could make the biggest splash? What experiences did the children have measuring the size of something irregular. What tools and resources were available to help support this inquiry? Could technology play a role? Would children be interested in revisiting these math questions at a later time or would their interest only occur when playing in the puddles?

As the children and I engaged in conversations about their questions they were developing adaptive reasoning skills - this is the capacity for logical thought, reflection and justification in their math thinking. As children connected what they were observing and experiencing in the puddle play to their own unique experiences and ideas, they were engaged in rich learning as they reflected upon and justified their questions, ideas and strategies to solve the puddle math problems.

Even though many of the children's questions were not answered, the purposeful outdoor math exploration encouraged children to develop a strong conceptual understanding of a variety of developmentally appropriate math topics related specifically to our curriculum including measurement, counting, capacity, classification, time and quantity. I was able to support their conversations and provide suggestions and strategies in the moment. I became a play participant together with them by playing in the puddles myself.

What had originally looked to be a damper on our outdoor fun turned into a complex and layered opportunity for rich math thinking during an activity that most children love to do - explore the rain. It just shows that math can happen anywhere, anytime, when we are willing to rethink what the 'math classroom' should look like.

Sunday, September 16, 2018

Anchor of Five

Anchor of 5

A successful math program for children will have an emphasis on number sense as its foundation. Number sense is a natural part of all other strands (e.g., geometry, patterning, data management). Exploring number relationships help children build fluency, accuracy and confidence. Five frames provide a visual reference to the anchor of 5. Five is a 'friendly number' for children. They associate five with the most natural of math 'manipulatives' that they always have available...fingers on one hand! The number system that we use in Canada encourages an understanding of place value that is dependent on groupings of 10, and understanding groups of 5 will evolve into 10. This is a key foundation for future place value work. Here is a review of some of our math work this week. 
Read alouds
We used many engaging, patterned texts during our whole group circle time that focused on groups of 5. In books like 'Five Busy Beavers' a group of 5 beavers slowly decreases to 1 as each beaver leaves the water for other adventures. Children can see the group decrease by 1 each time, and predict what the new number will be. They can subitize the new number as they observe the number of beavers on each page, or follow along and use their fingers to chant along with the text. This book can then be added to a math centre where manipulatives can be provided to further enhance the text and encourage children to play with the numbers 1 through 5.
A Number Station
During free choice time the children had the opportunity to visit a math centre where various manipulatives and tools were made available for children to play with the numbers. A number line, wooden and mirror numbers, five frames, finger tracers, and natural materials were available for children to explore. Students matched, counted, sorted, patterned, and ordered the manipulatives, often composing groups of 5.
Morning Message
Each morning we start our day with a morning message. One of the most important words that children first learn to read and write are their names (their own, and those of their peers). We used our 'star of the day' to model how our names fit into five frames (and sometimes beyond the five frame if the name has more than five letters). This helped us conceptualize the anchor of five and also introduced some concepts of print too (e.g., that words are composed of letters and that letters represent sounds).
Number Line
We brought a number line outdoors with us during our outdoor play time. It was interesting to see how the children created their own games without adult prompting. Some children gathered natural materials and placed them next to the numbers (e.g., 7 stones next to the number 7). Others used the line as a tool in a jumping game, starting at the 0 and seeing who could jump the furthest and reach the biggest number!
How Many are Hiding?
Whole group time is also a great opportunity to introduce meaningful math games that children can then play in small groups or during free choice play time. To help children compose to the anchor of five, we used a group of five unifix cubes. Children are first shown the five in a line. The player then hides some cubes behind his/her back and shows the group the remaining cubes. The group has to calculate how many cubes are hidden, encouraging them to subitize and compose to the anchor of 5. They indicate the missing quantity by holding their fingers up to the player who then reveals the missing quantity.


We love to sing each day. Our children loved the fingerplay "Five Little Monkeys Swinging in a Tree". To enrich the experience with meaningful math, we added a magnetic five frame to the song. As the children sang along and used their fingers to decompose the number 5 to 1, we removed counters from the frame as they count. During play time many children enjoyed leading their peers in a singing of the song!

Pentomino Challenge
Pentominoes are a wonderful math manipulative that encourage spatial reasoning and use an anchor of five as each unique piece is created using five small squares. A challenge that encouraged perseverance and spatial logic this week involved challenging the children to fill a standard cookie tray with pieces, leaving no gaps in the puzzle. 

We love learning from others! Share your favourite math activities that encourage an exploration of the anchor of 5 in the comments below!

Thursday, May 10, 2018

Printable Pentominoes

In our kindergarten classroom children enjoy spending time working with math manipulatives 
that encourage playful explorations with shape in a variety of ways. One of our favourite tools are 
versatile pentominoes.

Pentominoes are polygons made of five, equal-sized squares connected edge-to-edge. There are twelve 
different pentominoes in one set. You can purchase pentominoes from educational resource stores, or 
print paper copies on card stock and laminate for children’s use here:

There are many reasons why pentominoes are an essential math tool for any early childhood classroom. 

1. are gamelike in nature and promote a positive attitude towards math
2. encourage cooperation and collaboration among children 
3. Promote math thinking in a variety of areas including spatial reasoning (logic when solving
 puzzles, symmetry, reflection, rotation, design), measurement (considering the area and perimeter 
of designs), and number sense (counting the number of tiles or squares in a design, calculating the 
total number of squares using the anchor of 5)
 We have used pentominoes in many classroom activities. To see what we've done and follow our math journey, follow us on twitter @McLennan1977. Share your favourite pentomino activities in the comment section below!

Wednesday, May 9, 2018

Flipped Hundred Chart

Helping children conceptualize numbers and find meaningful ways to think about their relationships is a goal in our kindergarten classroom. We encourage problem solving and working with number strategies in daily number talks, and are always on the lookout for interesting ways to compliment the rich math learning opportunities we are observing in the children's play.

Recently I became a member of the National Council of Teachers of Math (NCTM A highlight of membership is that I have access to the journal Teaching Children Mathematics, which is filled with research-based articles outlining interesting and developmentally appropriate practice for the early years. In the December 2017 (24, 3) issue there is a fascinating article by Jennifer M. Bay-Williams and Graham Fletcher called A Bottom-Up Hundred Chart? In this piece the authors challenge educators to consider the potential for enriching children's learning if the popular math tool is flipped upside down.

Bay-Williams and Fletcher share that a flipped hundred chart makes sense because when children use the chart to solve equations, the language they use to describe direction on the chart matches their understanding of the operation - if adding the number appears to get taller, bigger and greater as physically modeled when children track the addition sentence by moving up on the chart and if subtracting the number appears to shrink, moving downwards and getting smaller by descending the chart (e.g., if a child is solving 13 + 12 s/he would first point to the thirteen, move upward one space and then to the right two). The authors also suggest a number of different activities for exploring the chart including cutting one into a 'number puzzle', encouraging children to find mystery numbers, and assigning children a number and challenging them to find all the number's 'neighbours'. These activities are great ways for children to physically and mentally manipulate the chart, helping them to become more comfortable working with the numbers.

After reflecting upon our math program I have created five additional activities that I believe will continue to challenge children and encourage them to strengthen their understanding and confidence working with the numbers 1 - 100.

Guess my number!

Display a flipped hundred chart and mentally think of a number that the children will have to guess. Give children one clue at a time to help guide them to your number (e.g., my number is less than 50, my number doesn't have a 6 in it, my number is odd). The children can consider the clues and cross out the numbers that don't follow the clues. With additional clues more numbers will be crossed off the chart until children guess the correct one. Reverse roles and invite the children to think of a number and give the clues to you!

Pentomino Trace

Our children love to manipulate pentominoes - using them to fill frames and trays and solving intricate puzzles. Children can also be encouraged to use them as tracers, matching them to the chart and outlining the numbers contained within. Once a collection of numbers has been traced, encourage children to find something that all numbers have in common (e.g., they each have a 4 in them; they are all greater than 36). Tip - ensure your flipped hundred chart is printed to the same size as your pentomino set to ensure an accurate match.

Dry Erase Number Write

Our children love to write with dry erase markers. Create a variety of 'missing number' flipped charts, laminate, and invite the children to practise filling in the missing numbers.

Flipped Hundred Chart Coding

We spend a lot of time coding in our classroom and see potential for incorporating coding directions and spatial reasoning into exploring the flipped hundred chart. Display the chart and determine a starting number. Provide children with a series of verbal or written coding directions as they move from the starting number and reach the end number. Once the final number is determined encourage children to create an statement or equation that describes the relationship between the two numbers.

Start at 3.
Move up 4.
Move right 5.
The number is 48!

 What do you know about 3 and 48? (48 - 3 = 45, 3 + 45 = 48, 3 + 5 + 40 = 48)

Roll, Subtract and Race!

Use an enlarged copy of the flipped hundred chart as a board game. Two (or more players) can use recycled board game pieces and place them on the starting point 100 spot. Each player takes a turn rolling one die and moving their player backwards on the chart (or 2 to make the game more difficult). Students can be encouraged to think in equations (If I start at 100 and roll 5, 100 - 5 places me on the 95 spot). First player to move off the board into the 0 spot wins!

What other ways can children learn with the flipped hundred chart? 
Feel free to share other ideas in the comment section below or tweet #flipped100schart!

Thursday, May 3, 2018

Playing with Shape

I had the great pleasure of hearing Dr. Nathalie Sinclair (@geometry4yl) speak at the recent ETFO Kindergarten Conference in Toronto on April 14, 2018. Her engaging presentation involved discussing how educators can create opportunities for children to explore geometry in integrated and playful ways.
As many of you know early years mathematics is an absolute passion of mine. Exploring what role math has in an emergent program, and what attuned educators can do to introduce and support children's evolving understandings, drives my everyday pursuits in the classroom. I tend to look at everything we do through a mathematical lens and am always interested in learning how we can delve even more deeply into our classroom understandings and interactions regarding math. It is for these reasons that I found Dr. Sinclair's presentation so fascinating.

"Play is exactly what mathematicians do.”

In her work Dr. Sinclair discusses how math relates naturally to play - both encourage children to step outside of reality, create order and beauty in the immediate world, are bound within time and space, and are governed by a set of rules. Dr. Sinclair reminds us that play is not aimless or spontaneous but a highly constructed reality that guides children in layered roles and representations. It is rehearsal for reality where children can experiment with different situations, problem-solve within the parameters of the play, and then try out different solutions to the problems within a supportive and safe learning environment. 

Something that I found particularly interesting in the presentation was Dr. Sinclair's discussion of shape learning in early years classrooms. She shared that often children identify with only the 'prototypical representation' of a shape and assume all other shapes by that name look the same.  Consider the typical representation of a triangle on many of the pre-made, purchased learning materials teachers might use in the classroom. Many look this this little guy - a smiling, upwards standing equilateral triangle. Over time many children assume that this is what all triangles look like, and when faced with variations aren't sure what shape to classify them as.

 Image result for triangle with a happy face
 Dr. Sinclair invited the audience to reflect upon what geometric models we were using in our practice and consider a number of alternative activities to help children play with shapes in order to better understand their interesting properties and build understanding when variance occurs. 

When I returned to my classroom I decided to conduct a small experiment in order to determine my students' thoughts regarding triangles. I created a survey using our morning 'sign in' that asked children to sign their name under the shapes they felt were triangles. Even though three of the four were triangles, most children chose only the typical equilateral triangle. I also noticed that the children assumed only one shape could be a triangle, so when they decided on the equilateral, they stopped examining the other shapes. They assumed that there was only one right answer.
I brought the survey to our whole group morning meeting time where we were able to explore the question together. I invited the children to share why they chose their shape and explain their thinking. Most children stated that the felt their triangle of choice was the right one because it had "three sides", "three corners", "straight sides", and "looked like a triangle". When we explored each of the shapes on the survey most children appeared surprised that there were also two other triangles that fulfilled their criteria. To extend on this thinking I decided to use a read aloud to help us explore shapes further. Linking literacy to math is a great way to make abstract ideas more tangible to children while hooking them emotionally within a story.
 In Marilyn Burns' 'The Greedy Triangle" children are introduced to a triangle who continues to change its shape after meeting with a shapeshifter until it is no longer a triangle but a circle. It was interesting to note the children's observations of the shapes in the story, especially the triangle, as Burns portrays many variations and they were quick to notice that these differed from the ones depicted on our initial sign in survey.

To compliment the text I then invited the children to play a shape sorting game with me. Using various shapes cut from construction paper, the children had to sort each based on whether or not they felt it was a triangle. It was interesting to listen to their descriptions of the shapes as they determined which grouping to place them within. At the conclusion of the activity we had a large collection of different triangles and the children determined that was made a triangle was a shape with "three sides and three corners" regardless of size.
Moving forward we will continue to explore geometry in our classroom in new and exciting ways. Some ideas for you to try with your students can include:

Using read alouds to inspire shape art - books like Perfect Square and Scribble can be read to children and then added to the art centre with various materials and tools to inspire creative exploration and manipulation of shape.
         Image result for The Perfect Square            

Playing with shapes using technology - the website Geometry for Young Learners from Simon Fraser University allows users to manipulate shapes in many different ways directly on the website using a sketchpad. No need to download any programs.

Creating shapes kinesthetically - children can use their bodies to create different shapes, especially in the outdoor classroom or gym!

Print making with found shapes - children can be invited to search the classroom for various shapes and use these to create prints with paint.

Locating shapes in the school and beyond - children can go on a shape hunt, record what they find on a tally chart or take photos with the class iPad, and then print out the photos and outline what they see on the print itself. 

What other shape activities and games have you tried with children? Leave your ideas in the comments section below!

Friday, April 13, 2018

Coding Stories and Games

We are pleased to have presented our workshop  Creating Coding Stories and Games at the 2018 ETFO Kindergarten Conference!





Here is our presentation for those interested in what we shared.

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