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Big Mathematical Ideas for Grades 3-5: year four

Posted on: May 25th, 2017 by jnovakowski No Comments

This after school series is in its fourth year, focused specifically on the foundational mathematical concepts in grades 3-5 such as operations, place value and fractions. This year, we met once a term after school in Jennifer Plummer’s French Immersion grades 3&4 classroom at Homma Elementary (thank you for hosting Jennifer!).

For our first session in the fall, we focused on number sense and operations and the curricular competencies of reasoning and communication. I had recently been to the NCTM Regional Conference in Phoenix and shared a great game that I was reminded of in one of the sessions there.

The Product Gameboard

The Product Gameboard instructions


At our second session, in January, we focused on financial literacy and mathematical inquiry. I shared the new Pizza Co. game for the iPad from Osmo as well as some other resources and children’s books to support the financial literacy content in the BC Mathematics Curriculum.

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BC K-5 Mathematics Big Ideas


For our third session in April, teachers in the series requested a focus on assessment, place-based learning and connecting the core and curricular competencies.



BC K-5 Math Communication


We explored curricular content and competencies by investigating with power polygons.

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Looking forward to continuing the conversation around big mathematical ideas next year!


Provincial Numeracy Project in Richmond – year two

Posted on: April 24th, 2017 by jnovakowski No Comments

For the second year, Richmond is one of several districts in the province that are taking part of an adapted version of Changing Results for Young Readers in the form of Changing Results for Young Mathematicians. Provincially, this project is not just focused on young students but for K-12 students and their teachers and has been called the Provincial Numeracy Project.

This year, three school teams of primary teachers and a Learning Resource Teachers are participating – teams from Whiteside, Grauer and McNeely.


Several routines such as Counting Collections (see and High Yield Routines (book published by NCTM) were shared with teachers as elements that could be introduced as both whole class and small group instruction.The  importance of assessment to inform instruction was discussed and the importance of spending time being present with our students – listening, noticing and talking with them. This is a critical practice in this project – really zooming in on students’ mathematical thinking.

One of the handouts provided to teachers was a collection of Number Sense tasks and background information connected to the Kathy Richardson book we would be using. The handout package can be downloaded here: Didax Number Sense guide

number concepts kathy richardsonUnfortunately, our second session together was cancelled due to a lack of TTOCs. Between sessions, copies of Kathy Richardson’s book How Children Learn Number Concepts was delivered to each teacher in the project. Teachers were asked to zoom in on one section of the book and make connections to what they were noticing as their students engaged in counting or other number routines.

Each Orange Had 8 Slices Teachers were also provided with a copy of the classic math picture book Each Orange Had 8 Slices and were encouraged to share some of the pages with their students and engage in playful and joyful mathematics – counting, problem posing and problem solving.

The one-pager that was created to accompany the book to send home with students to engage in joyful math with their parents can be downloaded here: Each Orange Had 8 Slices.

For our third and final session in March, school teams shared what they had been trying and what they had been noticing in their classrooms.

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A specific focus on the reasoning and analyzing section of the curricular competencies was explored through estimation. Estimation is a good indicator of students’ number sense and is an important competency to develop and use in many contexts – both computational and with measurement. The estimation information and connections to literature that was developed as part of the BCAMT Reggio-Inspired Mathematics project can be downloaded here: Estimating final

We also looked at the curricular competency: “use reasoning to explore and make connections” through routines such as Number Talk Images and Clothesline.

How many ducks are there? How do you know? What different ways can you see the quantity?

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A blog post of how clothesline math has been used in kindergarten classes in Richmond can be found HERE.


Teachers in the project each received a copy of Which One Doesn’t Belong? by Christopher Danielson and connections to our BC curricular competencies in math were made – communication, reasoning, justifying and explaining.

As part of the project, teachers were asked to pay attention to a child who they were wondering about – a child whose math learning was causing questions for the teacher. Based on the findings from Changing Results for Young Readers, we felt that focusing on the learning of one child, and how that child  responds to new ways of approaching math learning, would influence the class’ learning as a whole. Teachers were asked to reflect on this as well as write a short professional narrative reflecting on their own professional inquiry during the project. A collection of excerpts from the teachers’ reflections are included below:

“We are having to unlearn the ways we learned math in order to think about ways we can help the students build a solid number sense foundation.”

“I noticed increased student ownership over their own learning. They are choosing collection at their just right level and are trying to figure out, on their own, ways to count their collection in multiple different ways. Students are beginning to be able to communicate their thinking about the strategies they use to count their collections.”

“I have a better understanding of number concepts and where to go next to help/challenge a student.”

“High Yield Routines had high engagement levels and encouraged a lot of math talk in our classroom.”

“I noticed that I was taking chances in my teaching during this project, allowing myself to learn alongside my students.”

“I learned that math is about exploring and sense-making.”

“Students were engaged with math talk images of actual objects rather than dots or ten frames.”

“My students are more engaged and more hands on with the math now as a result of the changes I made.”

“Students are now expected to voice and articulate and justify their thinking about why they feel their answer could be right.”

“I learned about recognizing the phases of mathematical development and how foundational skills contribute to deeper meaning and understanding for students in subsequent years.”

“I noticed that I need to step back and invest time to delve into student learning and understanding beyond the correct answer.”



looking for math outdoors

Posted on: January 4th, 2017 by jnovakowski

During my last visit of the year to the Kindergarten classes at General Currie Elementary, it was a snowy and icy day so we decided to venture outdoors with some iPads to capture images of things that inspired our mathematical thinking. We had a quick talk with the students about how to look for math outdoors – looking up, looking down, looking all around. We talked about what math might look like outdoors – the counting of items, the shape of things, patterns in the environment, as well as sources of inspiration for thinking about math.

One of the first mathematical ideas we played with was shadows – how does your position affect your shadow? what determines the height of your shadow? what do we need to think about if we wanted to put our shadows in height order?

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As with the case of all our school sites…there is a story that lives there. General Currie was one of the first one room school houses on what was originally called Lulu Island. We stopped briefly at the historic building that is still on the new school’s site and talked about the time elapsed – what school might have been like, what the neighbourhood might have looked like, etc.

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We ventured on to the field and took photos as we walking along noticing nests in trees, tracks in the snow, all sorts of ice and frozen leaves.

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The ice was a source of fascination and many questions for the students. They were also very interested in some footprints they found and wondered about the size of different footprints or tracks.

We came back into the classroom and the students used the app Skitch with one of the photographs they took. They labelled, circled or used arrows to show where they noticed math or what inspired a mathematical problem or question.

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Classroom teacher Kelly Shuto then showed some of the students “skitches” to the class to inspire further questions.

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The following week Kelly tweeted out about the class photo book they had created, based on the idea “What math lives here?”


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In this crisp wintery weather, what will your students notice outdoors? What math lives in the frozen puddles and tracks through the snow? How far do animals need to travel to find food? What might your students wonder about?


Science Jam 2016

Posted on: March 2nd, 2016 by jnovakowski

SJ 2016 logoThe Richmond School District is celebrating its thirteenth year of Science Jam, a featured event of Education Week.

Science Jam is BC’s largest non-competitive science fair, bringing together students in grades 4-7 from across our district to share their science inquiry projects. This year students from 11 schools participated choosing to do projects under three broad themes – environmental sustainability, going local and looking at the redesigned curriculum.

IMG_2732Two French Immersion students from William Bridge Elementary conducted the opening ceremonies with welcoming words from our mayor and superintendent, introduced our board of school trustees and honoured the event’s sponsors.




Science World started off Science Jam with a *bang* with a science surprises show.



And then it was time for our district’s young scientists to share their projects with “celebrity scientists”, parents, community members and each other.




A video with highlights of the event can be viewed HERE.


cedar weaving

Posted on: June 17th, 2015 by jnovakowski

Back in April, the Richmond School District’s Aboriginal Education department hosted Alice Guss of the Squamish Nation for a morning of cedar weaving. Alice is an artist, storyteller and drummer and has been involved in the field of education for over twenty years. She does workshops around the world in drum making and weaving.

More information about Alice can be found HERE.

We invited Alice back to Richmond as part of our National Aboriginal Day celebrations and this week she worked with two of our QTL (Playful Storytelling through First Peoples  Principles) classes at Steves and then joined teachers from the project after school.

Kathleen Paiger’s kindergarten class and Ellen Reid’s grades 1 and 2 class at Steves Elementary listened to Alice singing and drumming and learned about how cedar is harvested for the purposes of weaving and making practical items and regalia. Alice shared some of items that are made from different parts of the cedar tree.



The students learned how to weave a cedar bookmark and they were quite interested in the texture and smell of the wood.

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The students then enjoyed listening to Alice’s stories and she said them in some dancing to her drumming, with the students taking on different animal roles.


After school, a group of teachers involved in our QTL project along with some other interested educators, came together. Alice shared her family’s history and we learned about the story of The Chief in Squamish and  of the two-headed serpent, a story important to the Squamish people. The teachers then learned more about the importance of cedar and how cedar trees that have been culturally modified (stripped for cultural purposes) can not be cut down by logging companies. An article about culturally modified trees can be found HERE.






The teachers learned how to weave a small cedar basket. There was lots to be learned during the process about persistence and learning new things and also about the natural properties of the cedar. The completed projects were cherished by the teachers and were all one of a kind.


It was an honour to have Alice join us in Richmond again and we hope to have her back again next year!


learning about electricity with squishy circuits

Posted on: June 7th, 2015 by jnovakowski

We are continuing to pilot three Squishy Circuits in our district and this spring I was invited to use them with intermediate students at Homma and Blundell.

We opened with a short discussion around what the students already know about electricity. I then gave each group of three students a battery pack, 3 LEDs and a ball of conductive playdough and asked the students to examine the three components and then see what they could find out. The students usually place the LEDs in the ball of playdough, insert the positive and negative wires from the battery pack, turn the battery pack on then go hmmm, wondering why the lights don’t go on. It’s hard not to jump in but part of the inquiry process is for the students to problem solve and think through the different variables that could be the issue. Sometimes, if students seem really stalled and I think its because they might not have enough background knowledge, I sometimes prompt them to think about flow of electrons.




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Once the first group of students gets the LEDs to light up, this sends off a reaction in the class and the students get curious about what others have done. A conversation about the concept of the “path of least resistance” is really important here for students to understand the flow of the current. Some students want to know more about series and parallel circuits and use the materials to investigate this. I pass out beepers and motors to add another opportunity for students to investigate different ways of creating circuits.

Once students see the possibilities of using squishy circuits, the creative possibilities open up.


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More information about Squishy Circuits, including recipes for the conductive and insulating playdoughs, can be found here.


using visual tools to support early numeracy

Posted on: October 24th, 2014 by jnovakowski

I had the pleasure on the BC PSA day on Friday to share some of the work we are doing in Richmond in the area of early numeracy at the BCAMT fall conference in Surrey. My presentation shared the ways visual tools support strong number sense, the foundation of computational fluency. Examples of using Reggio-inspired practices, number talks and the use of iPad technology were shared from Richmond classrooms.


The handout with links and resources can be accessed through the following link:

BCAMT 2014 handout

Thanks to the many teachers attending my session for their contributions to our thinking and learning. Apologies to those of you who were crammed into the room, standing along the periphery or on the floor!


thinking about decimal fractions in grades 5&6

Posted on: October 22nd, 2014 by jnovakowski

I have spent two Thursday mornings in Gillian Ewart’s grades 5 & 6 class working with the students as they learn about decimal numbers (tenths, hundredths, thousandths) and how to represent them. Students at this grade level need a strong understanding of tenths and hundredths and then should be able to generalize this understanding to thousandths, ten thousandths, etc. Taking the time to work with concrete materials and visual tools to represent these numbers helps to develop strong conceptual understanding and sense about these numbers that will support students when they begin to apply operations (adding, subtracting, multiplying and dividing) to these numbers.

The iPad app, Skitch, was introduced as a way for students to capture representations of decimal numbers. The students took photographs of hundred grids in the classroom and then used the drawing and text tools within the app. The students saved their images to the iPad’s photo album.

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The students were then introduced to the screencasting app, ShowMe, and students were asked to show what they knew about decimal fractions/numbers by using the images they created in Skitch and then annotating the images further as they narrated their screencasts. Gillian quickly set up a class account on so the students could log in and save their screencasts to a shared site.



An example of one of the students first tries at a screencast is posted below:

A mathematics-based app that students used to start up their mathematical thinking at the beginning of our second session was Math Tappers: Numberline (an iPhone app). Students chose a range of numbers they felt comfortable working with and a type of numberline (different types of reference points) and then had to place a decimal number where they thought it should go. The students receive feedback as they play. The whole series of Math Tappers apps is excellent and they were developed by University of Victoria professors so they are particularly well suited to our curriculum.

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Next, we introduced the app Number Pieces. The students had been working on representing decimal numbers using base ten blocks and this app has students work with base ten blocks as a virtual manipulative and label and annotate their representations. The students then either used the Number Pieces app or a photo of a concrete representation with base ten blocks to import an image into ShowMe. The students then created a short screencast (we gave them an upper limit of one minute this time) to share their understanding of representing decimal numbers.

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By doing some oral rehearsal before recording, the students are getting more comfortable in communicating their mathematical understanding. The classroom teacher, Gillian Ewart has commented on the insights she gets into her students’ understanding and misconceptions as she listens to and views the screencasts which provide valuable information to plan what comes next in planning her instruction.


littleBits in grade 9 science at Cambie

Posted on: June 6th, 2014 by jnovakowski

We have been piloting the use of littleBits in our district to investigate the different ways that the components can be used to stimulate creative thinking within the domain of science. Last week I visited one of Karen Ibbott’s grade 9 science classes at Cambie, to see how grade 9 students might respond to the materials. In much the same way that we have been trying them out in elementary classrooms, I gave each group of 4 students a small tray of components and asked them to find out what they could about littleBits. The students were quick to figure out how the components worked together and manipulated different variables to see what they could do with the components.

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The students then worked in their groups to “create something that does something” and scrounged around the classroom for materials. We asked the students to document their project using a set of iPads I had brought in…taking photos, video and using apps like ShadowPuppet, 30Hands or Haiku Deck to share their project. Lots of creative thinking and problem solving was involved as students collaborated in their groups.

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As the groups worked on their projects, we asked them to create circuit diagrams.

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Here is a short video clip created on the Shadow Puppet app of the Keep the Guy Alive project:

We uploaded 6 projects to the littleBits website and each project post included a short video, photo and circuit diagram. The projects can be found on this page (scroll down page and search by littleBits user name jnovakowskisd38):

Campfire Monster

The Crane

Armed with Alarms


Keep the Guy Alive

Happy Face

What I noticed…what was the same and what was different about using littleBits in a secondary class:

the same

high level of engagement

collaboration amongst students

problem solving

time needed for investigation

vast variety of creative projects created

particular components were in high demand (ie. fan, dc motor, buzzer)


elementary students generally approached created the circuits with more of a “guess and test/check” approach while the secondary students were more intentional and applied what they knew about electricity when constructing their circuits

in general, the elementary students made inferences about what was happening in terms of electrical circuits while the secondary students knew, understood and could clearly explain what was happening

the secondary students were able to envision components that would be useful to have, i.e. “it would be cool if we had a __________”

On our last day together, I asked the students to provide some feedback using TodaysMeet and some of the comments included:

What did you like about using littleBits?

“It was simple and safe.” “Because its very interactive.” “Allows us to have fun and learn at the same time.” “littleBits are better than Lego.”

How do you think littleBits inspires creative thinking?

“It inspired us to invent something.” “It lets you have a sense of creativity.”

How did you use what you know about electricity while you were working with littleBits?

“Knowledge of how electrons flow.” “Making a series circuit.”

“littleBits is a fun little product that teaches others the concept of circuits…it’s fast and fun.”

Overall, the students’ feedback suggested that these materials were valuable and encouraged students to be creative and collaborative. Our District Resource Centre has purchased a workshop kit of 100 littleBits components to add to our collection, creating more opportunities for more students to work with these materials.


noticing and comparing plants at Blair

Posted on: May 11th, 2014 by jnovakowski

IMG_1038I visited Blair at the end of April and worked with the grades 2 & 3 students in Daisy Khare’s class. The students were beginning to learn about plants and we decided it was an ideal time to go outside and look closely at the school’s new garden beds. Some of the other classes’ plantings were growing so well already.


This gave us a great opportunity to discuss looking closely at plants – noticing the colours, the textures, the lines, the shapes, the markings, the size, etc. The students were asked to choose two different plants to observe and notice what was the same and what was different about them. The students enjoyed using magnifying glasses and loupes to really zoom in on the details.

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IMG_1027 IMG_1019 IMG_1018 IMG_1010The students took their science notebooks outside with them and recorded their observations with drawings and words. We left it up to the students how they would do this.

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It was interesting to listen in on some of the students’ conversations. Many of them wondered what the plants were exactly and looked for clues (like plant markers with the names on them!) to help them out. They were excited to see bright red radishes bulging up through the soil. One student noticed the tendrils on the pea plants and wondered what they were for.


This led to other questions from the students and they began recording their questions in their notebooks alongside their observations.

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We came back inside for students to focus on the recording of their experience in their science notebooks. It was impressive to see the variety of formats the students chose to show their learning.

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This experience for the students was connected to the primary teachers’ professional collaborative inquiry looking at taking science outdoors and making students’ learning visible through science notebooking.