Archive for February, 2016

thinking about place value with grades 1&2 at Homma

Posted on: February 25th, 2016 by jnovakowski

about teaching mathematicsWhen I was in my first year of teaching (1991-1992), I began a diploma program in K-12 Math and Science Education. It was during this year that the classic Marilyn Burns book seen to the left, was published. I read it, used the ideas in my classroom and cited it in my papers and projects for my coursework. Over the years, I have recommended it to colleagues and used it as a recommended resource during the years I taught the math methodology course at UBC. I believe it is in its 4th edition now but I cherish my original, tattered copy because of the memories of how it brought joy to the teaching of math for me in my beginning years of teaching. I devoured anything by Marilyn Burns and continue to do so, also having been fortunate to hear her speak at several NCTM conferences.

I particularly like the chapter and assessment task that focuses on place value and I used these resource as a launching point for a lesson this month.

I have been working with Terra McKenzie and her grades 1 and 2 students at Homma Elementary this term. We have a planning session once a month and then I work in her classroom with her once a month, modelling different aspects of math instruction that she is curious about. Last month we did a Number Talk followed by some practice tasks focused on mental math strategies and this month we focused on the development of place value concepts. Terra has being doing some different tasks with her students and I was greeted by this provocation as I walked into the classroom.


Terra and I had discussed her class profile and that many of the students were still not consistently demonstrating an understanding of the teen numbers as ten and some more and that they had limited number sense around numbers larger than ten. I wanted to use tasks that would focus on building an understanding of “ten-ness” as well as the language of place value.

I began with the classic Stars game, asking students to predict how many starts they thought I could draw in one minute. I modelled a few different ways to draw stars, we discussed their estimates and then I turned my phone over to a student to use the timer to time me.


After I drew the stars, students adjusted their estimates before we counted. I asked how we could count and although some suggested we count by 2s, many also suggested counting by 10s stating they made that choice because “there are so many stars”. I circled groups of ten and then we counted how many groups of tens and “extra” ones and then counted by tens, counting on by 1s. I recorded how many group of tens and ones, then recorded the quantity in expanded form and then in standard form.

The students then pulled out their math notebooks and they played stars. The recording in different forms was new to the students.

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After the students finished recording, we had students respond to questions about the number of straws they drew. This was a way to quickly get some feedback around their understanding of both the concepts and mathematical language. For example, whose number has an even digit in the tens place?

Again, choosing one of my favourite games from the book, a student and I played Five Towers in front of the class. Each player takes turns rolling two dice, calculating the sum and then build a tower out of Unifix cubes that represents the sum. The players go back and forth until they have each made five towers. I have students estimate how many they think they have in total (and many have already counted or calculated this as they go) before we count.  The students then snap their cubes together and build one tall tower and then break it into groups of ten to count up the total. Again, we modelled recording in different forms.


I also shared the place value tents with the students (this are available for free downloads from different sources) and played with the ideas of tens and ones, expanded and standard form, etc.


The students then played the game with a partner and Terra and I were able to walk around and listen to the students as they talked and asked them questions to extend their thinking. As students finished their game, their recorded their results in their math notebooks.

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As our time together came to an end, Terra and I talked about what could be next. Terra was able to see what language students need to be developed to communicate their thinking and could see the value of regular practice with these games. We talked about Marilyn Burn’s game Race to 100 as a good next step, again focusing on making tens and counting up by tens and ones. I also suggested the Create a Creature task, with students first exploring with the base ten blocks and then creating creatures of a specified value. A post about this task can be found HERE.


intermediate storytelling at Blair

Posted on: February 22nd, 2016 by jnovakowski

Karen Choo, grades 4&5 teacher at Blair Elementary is part of our district’s Creating Spaces for Playful Inquiry series. In January, she shared her journey with a group of 50 educators – how she has been using morning provocations to uncover big ideas and big thinking in her classroom. She has a collection of loose parts in her classroom and along with art materials, provides opportunities for all her students to build and create ideas together.

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Karen and her students have been learning about Chinese Immigration to Canada, reading novels, information books and having rich discussions, many students making connections to their own families’ immigration stories. Although Karen’s students were familiar with using materials to represent and idea, they had not used them to create stories. We presented a table of materials along with the loose parts already available in the classroom.



Karen noticed the high engagement with her students and also commented on the richness of the language and the role-playing that emerged in the stories. Karen commented that the concepts came alive for the students through the storytelling. It was interesting to note how the students wove in metaphors and symbols in their stories – such as the Chinese and Canadian flags and “gold mountain”.



part of this story included how the head tax kept increasing


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Many of the stories involved travels across the ocean and the students created settings or symbols of the two worlds – China and Canada, separated by a journey.

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The students used the iPad camera to take photos of their stories and then use the 30Hands app to narrate their stories – often going outside to find a quiet place to record. As I listened to the students’ stories, I heard many connections to the students’ own personal experiences and their strong beliefs about social justice coming through.

Not only does storytelling create an opportunity for Social Studies and Science concepts to come alive for students, it also provides an opening for students to tell their stories, to share a bit of themselves.


grade 2 science: forces and motion

Posted on: February 20th, 2016 by jnovakowski

Based on feedback from teachers last spring, we have planned a series of after school sessions supporting new content in the K-7 science curriculum. Each session will look at the learning standards around a specific grade and content area and teachers will experience both the curricular content and competencies through an inquiry-based approach. Connections to the core competencies and First Peoples Principles of Learning will be also be woven throughout the sessions.

This month, the after school science series session focused on the grade 2 science curricular content of forces and motion. This is a content grade shift, most of which was previously at the grade 1 level but now with more emphasis on how forces affect motion.

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We looked at the big ideas, curricular competencies and content along with the elaborations and then considered ways the curriculum could become uncovered through investigating with materials



and supported with children’s information and fiction books.


The following are some resources to support this area of study:

Grade 2 Forces and Motion

Grade 2 Force and Motion Resources


intermediate storytelling at Homma

Posted on: February 20th, 2016 by jnovakowski

I visited two classes at Homma Elementary in February to introduce oral storytelling using materials to inspire stories that consider the First Peoples Principles of Learning.

Carrie Bourne and her grades 4&5 French Immersion students have been using loose parts to represent ideas. We combined their collection of loose parts with a table full of natural materials and fabrics to create story settings, paying attention to the big ideas of self, place and the power of story. We first came together in a circle and the students shared some of their thinking about stories. We discussed big ideas around immigration (a focus of what they were studying in Social Studies) and made connections to books they have been reading about Indian Residential Schools, like Shi-shi-etko by Nicola Campbell (which is available en francais). Students shared their ideas about coming, going, leaving, arriving, connecting and dis-connecting with a focus on place. Students could choose to work by themselves or with a partner, as they created stories, inspired by the materials.

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After about an hour of the class circle and creating their stories, we asked the students to share their stories with another classmate or partnership. As students orally “rehearse” their stories, they are playing with ideas and language, synthesizing the theme or message their story. The students then captured their story using iPad technology by taking still photographs and using the app 30Hands to orally narrate their stories.

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Here are two video clips students practicing their stories:


Grades 4&5 story

And here are some of the students’ stories that the captured using 30Hands and then posted to their Fresh Grade portfolios:

Grade 4&5 EFI Homma – place

Grade 4&5 EFI Homma – transition


In Peter Ritchie’s grades 6&7 classroom, we began by watching a short video of Dr. Jo-Ann Archibald telling the story of Lady Louse (can be found HERE). We asked the students to pay attention to her storytelling technique and the students shared their observations about how she used her hands, varied the use of her voice and how she repeated the theme or message of the story in different ways throughout the story. They also noted how the story didn’t have a typical resolution in stories like they are familiar with, but left you thinking.

Peter had collected various plants and mosses from his brother’s property in Squamish and the students used these along with various other materials to create settings for their stories. We discussed the importance of creating an authentic environment and if they were using animals in their stories, to consider the place of the animal within the ecosystem.

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sharing our worldMany of the students were aware of animals portraying values or metaphors in stories from different cultures and we referred to the book Sharing Our World, for students to consider animals they might want to include in their stories. Possibly inspired by the materials presented them,  many of the students’ stories involved environmental themes. I noticed the students at this age (and also very fluent with using iPad technology) were  focused on creating detailed settings and used different camera angles and backgrounds to make sure there weren’t distracting items or people in their photos. As with Carrie’s class, they used the 30Hands app to load their photos and narrate their stories.

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The following are some of the students stories:

The Story of the Fox

Appreciate What You Have

Listen to Elders – The Hike

On the February 19th professional development day, the staff led a morning of looking at teaching and learning through the First Peoples Principles of Learning, and storytelling with materials was something that the staff engaged in themselves.

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I’m looking forward to hearing many more stories from Homma Elementary!



intermediate storytelling at Cook

Posted on: February 14th, 2016 by jnovakowski

As a follow-up to an after school Leanne McColl and I held for grade 5 teachers (see post HERE) on Indian Residential Schools, I visited two of the grades 5&6 teachers at Cook Elementary to further explore the power of story with their students, making connections to self and place as part of their study of Indian Residential Schools, part of the redesigned Social Studies Curriculum. The teachers have been reading both picture books such as Shi-shi-etko and the novel Fatty Legs as part of this study, emphasizing the power of stories – stories that need to be told. Both Christy Rollo and Jo Fournier are also part of the Creating Spaces for Playful Inquiry series in our district and their students have been using loose parts to represent ideas and concepts.

sharing our worldWe gathered in a circle and discussed the power and purposes of stories, along with some questions to provoke and inspire their thinking. In both classes, the students were asked to consider a story they were familiar with or to think of their own story, something that was personal to them. For both contexts, the students were asked to pay particular attention to the setting or place. I read a few pages from the book Sharing Our World, which shares the significance and meaning animals portray in Aboriginal stories. Animal figures were provided as one of the choices for the students to use in their stories. The students were presented with a “buffet” of materials to choose from, to create their stories.

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The students had many choices to make – to work alone or with a partner or triad, what materials to choose, what type of story to create and tell. Some students sat with their choices and needed some time to think while others jumped to the materials and let the materials help to inspire their choices.


The following are some photographs from Christy’s class where we had a variety of stories – personal narratives, retellings of Aboriginal stories, retellings of the class novel, retellings of childhood favourites and stories created specifically around one of the northwest animals.




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The students had a chance to practice telling their stories and then tell their stories to another group. The students took photographs of their story settings using the iPad camera, then importing the photos into the app 30Hands, where the students could then orally narrate their stories.


The following week in Jo’s class, we narrowed the story choices to the focus of the Social Studies topic they were studying.

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The students were highly engaged with the materials, spending time developing an idea and setting for their stories. Where they needed the “nudging” was in the telling of their stories – thinking about ways to convey their message or theme. Many students drew upon familiar stories and how there was repetition of an idea throughout the story and they tried to weave this element into their own stories. Other students focused on characters’ actions and what they did and what happened to them. Some students embraced the ideas of self and place and created an interplay of these ideas in their stories.

In a few cases, students worked together to create their stories in their first language, often with much animation and expression. With support, they then practiced the main points of their story in English and recorded using the 30Hands app.

I also noticed that students at this age in general seemed more hesitant when sharing their stories with others compared to the excitement younger children show when asked to share their stories with each other. I wonder if using the iPad technology created an opportunity for students to record their stories in a such a way that seemed less “on display”? This is something I would like to ask the students about as we continue to learn about the importance of storytelling in the classroom. Christy and Jo both have the students engage in sharing circles and class discussions and have discourse structures in place to create a safe, connected community in their classrooms. I’m curious to hear how storytelling contributes to these communities and also how the existing communities provide the necessary environment for storytelling to flourish.


more math days at Debeck

Posted on: February 9th, 2016 by jnovakowski

Debeck Elementary is in their second year of their math goal and they are using some of their innovation grant funding to bring in TTOCs to release teachers to observe lessons in each others’ classrooms. I come in and do a lesson with one class with other teachers observing and then we are able to debrief about what the teachers noticed and what they are wondering about at lunch time. I’ve been back twice in February.

During the first visit, three of the four classes began with a WODB (Which One Doesn’t Belong). This routine, similar to the Sesame Street favourite – one of these things is not like the other – presents the students with four objects, images or numbers and the students have to choose and then justify which one doesn’t belong. The twist is though that each object/image/number could be the one that doesn’t belong so students need to think carefully about the attributes and properties of each and be prepared to justify their choice. Justification and “proof” is a large part of mathematics and a routine like WODB strengthens students’ abilities in thinking in this way.

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In the grades 2&3 class and the grades 4&5 class we began with the WODB above. The instant reaction is that 9 doesn’t belong because it is the only single-digit number but as students dig deeper and talk to each other, they uncover properties of all the numbers. The students were talking about prime and composite numbers, multiples, division, odd and even, patterns they noticed, square numbers and we even discussed digital sums.

In the grade 4&5 class, the students then created their own WODBs and had others solve them and in the grade 2&3 class, we moved on to a number talk.


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In the grade 6&7 class, the students had begun learning about circle graphs so I put up the following WODB and very rich discussion ensued.

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I then asked the students what the graphs could be about. They chose one of the graphs from the WODB and added a title/question, labels and a legend. Some students added an explanation or analysis.

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A Canadian math educator curates submissions of WODBs here:

One of the Debeck teachers commented on what a rich routine this was for getting students to think outside the box and to not just focus on getting an answer quickly, something that our students unfortunately often have a focus on in mathematics.

On my second visit, the four classes all focused on math journalling as communicating mathematical thinking is part of the school goal. We always begin with a number talk or a chance for students to turn and talk to each other for “oral rehearsal” as a way to sort out their thinking before they are asked to draw, diagram, write. When moving to a math journal, the phrase “use pictures, numbers and words to show your thinking” is part of the mathematical norms in the classroom.

In one of the grades 6&7 classes, we looked at the big idea of equivalence, as the students were studying algebra. I began with a prompt on the board and asked students to do a quiet write, responding to the questions. The majority of the students responded similarly in that they described the equals sign as what the answer to a math question goes after.


We played around with the order of different equations (with the = symbol in different locations within the equation) and then used the number balance to highlight the idea of equivalence. One student looked at me and said – “I get it, each side needs to stay balanced.” We then asked the students to add to their previous explanation or definition but using a different colour so we could see how their thinking had changed.




I returned to one of the grades 4&5 classes to look at a string of multiplication questions in a number talk and then have students choose from some related questions to record their strategies for in their math journals. Always popular, the students were invited to add to the “math graffiti” board for these questions.

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With the grade 1 class we did some more Flash It games with the ten frame cards – this time adding Make 11 and Make 12, building on Make 10 that we had done before. We begin by doing a quick review of all cards with the students calling out the value of each ten frame and then for the next round instead of the value they call out the amount needed to Make 10. Today we moved to Make 11, bridging over 10 and we modelled this using the large magnetic ten frame first. The students did really well with Make 11! Make 12 proved to be a bit hard for them to visualize quickly for a Flash It type game and we need to continue to work on those strategies that help students decompose numbers into parts to make ten and then some.

We then moved onto the focus problem of the day – What different ways can you make 10? And we asked students to focus on using ten frames as one of their strategies. I was happy to see some students playing around with three and four parts of 10.

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In one of the kindergarten classes, the students were stars with the ten frames and then I modelled stories about 10 using ten peg dolls I happened to have in my bag. We talked about different stories involving 10 people – watching a movie was a favourite example, going on a bus, train or airplane and other examples were shared by the students. The students then thought about a number story they could tell and chose “loose parts” to work with. This is a class that engages in story workshop with materials and the students quickly took to the idea of math stories. Some students chose to record their stories in their math journals.


“ten guys climbing all over each other – like at the circus”

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Over the two mornings at Debeck, we tried to stay focused on lessons that developed and valued mathematical thinking, considering the curricular competencies of our redesigned curriculum here in BC – reasoning, analyzing, solving, communicating, representing and connecting. Students made “math to math connections” as they shared and compared their strategies or approaches to their classmates or to other mathematical topics. Students were given various opportunities to communicate – with materials, orally to a partner or small group or in whole class discussion or by using pictures, number and words in their math journals.

Until my next visit…




primary teachers study group: inquiry in mathematics

Posted on: February 7th, 2016 by jnovakowski

In its thirteenth year, the Richmond Primary Teachers Study Group chooses a focus each year to guide their professional collaborative inquiry. This year, building on the focus on inquiry in BC’s redesigned curriculum, teachers wanted to investigate inquiry across curriculum areas and we’ve chosen one curriculum area as a focus for each term, beginning with mathematics.

We began our first session by looking at the definition of inquiry provided on BC’s curriculum website:

BC Curriculum Glossary

and from that, talking about the focus on a range of types of inquiry and the importance of student-generated questions. We also discussed how there can be different starting points for inquiry – the mathematics itself, an object, a book, an image, etc.

RPTSG thinking about inquiry Oct 2015

As a group, we chose one strand of mathematics (patterning) and collected some ideas for different types of inquiry-based experiences for our students.

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Teachers were asked to try one of these tasks or related ones and notice how their students responded.

what in the world This year, we are using a collection of children’s picture books to inspire inquiry and our first one is the newly released What in the World?: Numbers in Nature by Nancy Raines Day.

This book helps students see the world through a mathematical lens and provokes students to notice numerical sets in their world. This is a great book to read before going outside for a math walk with the prompt: I wonder what math/numbers/patterns/shapes/etc we will see?

A book list was also provided so that teachers had other potential starting points for inquiry with their students.

book list-mathematical inquiry


When we met together in November, teachers shared the different tasks they tried and we began to record some of the inquiry questions that inspired these tasks – some from the teachers and some from their students.


Screen Shot 2016-02-06 at 8.20.13 PMWe only meet every 4-6 weeks but we also have a conference site on Richnet, our intranet platform. Teachers are able to share ideas on this site. Here is a photo from one teacher’s classroom showing how she set up a provocation using our study group book:


Another teacher shared an emergent inquiry from her class. During a study of Canada and how animals adapt to different ecosystems in a grade 2&3 class, the students wondered how big a walrus really was. This led into an investigation of size, comparing the size of the walrus to themselves and using all sorts of different measuring tools and language. A short write up of this inquiry is included here:

Primary Walrus Math Investigation

This study group provides teachers with a community to share ideas, and build on each others’ thinking and questions and has become a “safe” support network for primary teachers over the years. Looking forward to continuing this professional collaborative inquiry into inquiry!


provincial numeracy project in Richmond

Posted on: February 6th, 2016 by jnovakowski

Richmond is one of the districts that is part of BC’s Provincial Numeracy Project. This is a pilot year for the project, with eight districts involved. The project’s goals focus on looking at balanced numeracy experiences in classrooms with a focus on developing number sense. Alongside this is looking at what types of professional learning experiences support teachers in developing and assessing these experiences. Many of the districts are basing their projects on BC’s Changing Results for Young Readers model.

In Richmond, we have teams from three schools participating – Byng, Westwind and Kidd. All three schools have goals around mathematics and have done school-wide numeracy assessments. Each school team is comprised of early primary teachers and a learning resource teacher. Teachers were asked to bring their class’ assessments and to think about one particular child they were curious about with regards to development of number sense.

number sense routines shumwayDuring our first session in January, we overviewed the goals and expectations of the project. Teachers were asked to consider a professional inquiry question that paralleled their questions about their focus student in some way. Each teacher was provided with the book Number Sense Routines by Jessica Shumway and we looked at the routines of quick images and counting around the circle on video. We discussed how their classes might respond to these routines, thinking especially about their focus students.


We also looked at the routine of Counting Collections and I shared some images and video from Richmond classrooms that have been using this routine. Again, teachers discussed and planned how this routine might be enacted in their classrooms.


For each of the routines, we “unpacked” the mathematics involved and what we could be looking and listening for. We also discussed how “guided math” supports students’ development by targeting instruction at students’ “just right” level and that many number sense routines could be the foundation of a guided math program. At the end of the session, the teachers completed a project recording form, including a “baseline” profile of their focus students.

During our second session in February, teachers shared what number sense routines they had tried and how their students responded. Two new number sense routines were introduced – numberlines or clotheslines (inspired by the work of Andrew Stadel) and Choral Counting, as found on the University of Washington site

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We focused on the big mathematical concept of place value, as related to these two routines, particularly looking at number patterns and the importance of being able to count on from tens. The teachers were provided with a foundational concept brochure about place value that was developed for the BCAMT Cross-District Collaborative Inquiry Reggio-Inspired Mathematics Project. You can find that document here:

Place Value vers 2

number concepts kathy richardsonThe teachers were also provided with the book How Children Learn Number Concepts by Kathy Richardson. This book clearly outlines the learning phases students go through as the develop number concepts such as counting and place value. It has examples of experiences that support student learning.

As we move forward with this project we will be looking at assessment tools, iPad apps and thinking more deeply about what balanced numeracy looks like in our classrooms.