intermediate numeracy project: Flags 4 Rights

Posted on: June 20th, 2020 by jnovakowski

On February 25, on what would be our last face to face time together, I spent the morning with the grades 5&6&7 class at Quilchena. At that time, I was still thinking I was going to Reggio Emilia, Italy for a study group on spring break and I shared a project from that community with the students to connect to their class’ Agents of Change and Human Rights project. In Reggio Emilia, the community has organized a Flags 4 Rights project where local children, as well as children from around the world, have submitted artwork sharing their thinking about children’s rights. The artwork was then transferred to large flags that were hung throughout the community.

A primary class from Grauer created artwork that was sent to Reggio Emilia. The following is just one example:

We invited the intermediate students at Quilchena to engage in a plan and design numeracy task, considering creating flags for their school, what size they would, where they would be hung and what their budget would be.

The students measured, estimated, visualized and drew their plans to think about about where they would hang the flags and what size they could be.

The students shared and compared their plans. It would have been great to have been able to follow through on this task and think about what students could design and create for their school after spring break but alas, that was not to be!


intermediate numeracy project: numbers in the news

Posted on: June 20th, 2020 by jnovakowski

On January 29, I spent the morning with the grades 5&6&7 class at Quilchena thinking about numbers in the news. We connecting this idea to our study of infographics and how numbers can be used to inform, persuade or evoke emotion in us. We wondered how headlines might use numbers to pull us into a news article and how we can use numbers to make sense of the world around us.

We began by asking the students what their sources of news were. Many replied hearing it on the radio when they were driving with their parents. We shared sources of both local and national/international news.

We then shared some different current headlines with the students and asked them to analyze them with the following questions:

We then invited students to choose a current event that they were interested in, either local or global, and to find a news article about it that included the use of numbers, whether it be quantities, measurements or percentages.

The students investigated their news articles individually or in pairs or triads. The events of most interest to the students included the wildfires in Australia and the recent plane crash involving Kobe Bryant.

The students shared their findings at the end of their time together and compared data from different sources.

The COVID-19 virus outbreak was just beginning to be a focus in the news and some students were interested in learning more and chose this as their current news. Who could have ever predicted at the end of January what this would have meant for us here in Richmond and all the mathematical modelling that has been involved with our public health guidelines in the province?


SD38 Math Play Space 2019-2020

Posted on: June 20th, 2020 by jnovakowski

The Richmond School District’s Math Play Space popped up at several school and community events this school year.

In the fall we were at Blundell Elementary for their Meet the Teacher Night/Open House:

We visited Kingswood Elementary during one of their afternoons of parent-teacher conferences:

Gilmore Elementary invited us to their school during an afternoon of conferences with families:

We set up in the school gym at Diefenbaker Elementary during an afternoon of conferences with families. We set up earlier in the afternoon so some of the classes could come by for a Math Play Space experience as well.

Our last school visit of the year was at Walter Lee Elementary where the Math Play Space was set up in one of their wings during an afternoon of student-led conferences:

We also set up on the main floor of the Brighouse branch of the Richmond Public Library for two afternoons:

October 17

February 13 – What different ways can you make a heart with the materials? (and other playful creations)

A public blog with an events calendar and information for parents related to the Math Play Space can be found HERE.

Unfortunately due to the COVID-19 pandemic, our events needed to be cancelled in the spring. We look forward to re-imagining how the Math Play Space might be experienced as we move forward with new health and safety protocols.


Math for Action

Posted on: June 20th, 2020 by jnovakowski

Just before spring break, I was fortunate to collaborate with secondary colleagues from our department, Shaheen Musani and Baren Tsui on a professional learning series for secondary school teams. The series is called Math for Action and looks at the intersection of mathematics and social issues with a focus on student agency. A goal of the series is to elevate the importance of numeracy across curricular areas.

A variety of resources were shared. A book list that supports this series can be downloaded here:

We looked at this Social Justice Lens, as created by the BCTF’s Social Justice committee.

A close up of a sign

Description generated with very high confidence

It felt like we just got started with this thinking together and then in-school instruction was suspended. We look forward to continuing this series in some format when we return to school in the fall.


virtual manipulatives

Posted on: June 19th, 2020 by jnovakowski

updated September 3 2020

Although I believe nothing replaces the physical and sensory interaction with materials such as math manipulatives, in this time of COVID-19 and its many health and safety precautions and protocols, we are turning to the use of virtual manipulatives or e-manipulatives more then ever. Students can use them on their computers or devices at home or in-school so that students do not need to physically share and use materials that would need to be regularly sanitized.

The use of widely-used commercial mathematically structured manipulatives originated with the design and creation of Cuisenaire Rods in the early 1950s , although many other math materials, such as Froebel’s gifts and some Montessori math materials had been in use before this. Unifix Cubes were developed soon after this in 1953, by a family of educational suppliers who had worked with both Froebel and Montessori. Over time there have been “overhead projector” and magnetic versions of these manipulatives and since the 1990s virtual manipulatives have been developed using flash or java apps or applets.

One of the first collections of virtual manipulatives was the National Library of Virtual Manipulatives hosted by Utah State University, launched in 1999. You can find manipulatives sorted by math topic and grade band. The site can be accessed HERE.

A book sharing ways to teach mathematics with the manipulatives from the NLVM was published in 2010. I found it still available for purchases HERE.

The following are suites of free, accessible virtual manipulatives:

(please note that all image below are screenshots from the websites and do not link to the apps/sites. there is a link for each website embedded in the description)

The Math Learning Center

The Math Learning Center provides a suite of virtual manipulatives that are available as web-based apps, iOS apps and are also available in the Chrome Store. The Math Learning Center iOS apps have been loaded to our district-configured sets of iPad devices. Some of the apps have a new sharing features that allows teachers to pose problems or design investigations specific to their class of students. The pages hosting the apps and more information about them can be found HERE. Some of the apps available are pictured below.

Didax Education

Didax Education has created virtual manipulatives of their widely used physical manipulatives such as Unifix Cubes. The manipulatives, instructions, learning activities, and ways to embed the manipulatives in online platforms can be found HERE. Some of the virtual manipulatives that can be found on the Didax site are pictured below.


Mathies Learning Tools have been developed in Ontario, including Canadian money manipulatives. Information is available in English and French and the tools are available for different platforms. The pages hosting their virtual manipulatives and other tools can be found HERE.


Mathigon hosts a “polypad” which is like a web-based whiteboard screen that their suite of virtual manipulatives can be used on. The page can be accessed HERE.

Toy Theater

Toy Theater hosts a page of virtual manipulatives. The site also includes a range of number charts like 100 and 120 chart and Canadian money manipulatives. The page of virtual manipulatives can be found HERE.

The following suites of virtual manipulative are added from Twitter suggestions. With thanks to Karla Pearce, Alistair Carratt and Sean K for their suggestions.

Mathsbot Manipulatives

Mathsbot hosts a page of virtual manipulatives within their site found HERE. There are standard math manipulatives like tangrams, pattern blocks and Cuisenaire rods but also tools like discs, dice, counters, a visual fraction wall, geoboards and many other visual supports for learning, doing and thinking about mathematics. It is the only suite that I have found that includes prime factor tiles, number frames and Hungarian frames.


Geogebra create a specific page to host tools to support remote learning, including an array of whiteboards (dots, grids, isometric, etc) as well as virtual manipulatives such as algebra tiles, protractors, fraction circles, prism creators, and many others that can be used across the grades. This page can be found HERE.

The Geogebra home page also takes you to several math apps, tasks, simulations, games and other classroom resources.

Some online resources on the research and use of virtual manipulatives:

As part of the NCTM 100 Days of Learning series, Chrissy Newell presented a webinar, sharing different ways to use virtual manipulatives. The recorded webinar can be accessed HERE. And the presentation slides can be downloaded here:

What are Virtual Manipulatives? article published in Teaching Children Mathematics, NCTM, 2002

A meta-analysis of the effects of virtual manipulatives on student achievement and mathematics learning, 2013


Big Math Ideas in Grades 3-5: professional learning series 2020

Posted on: June 16th, 2020 by jnovakowski

This year’s Big Math Ideas for Grades 3-5 series used Tracy Zager’s book, Being The Math Teacher you Wished You’d Had, as our core resource. Teachers read chapters between our sessions and we shared our highlights at the beginning of each session along with exploring some of the resources, websites and math tasks from the book.

The publisher’s companion website for the book, with supporting materials, can be found HERE.

In our first session, we explored the idea of what mathematicians do and shared some of the picture books that Tracy highlights in her book along with some others from my collection. We watched a video “How to Snakes” by mathematician/artist Vi Hart, in which she exemplifies the playful, curious nature of doing mathematics. You can find the video HERE.

Other areas of focus during the series included computational fluency and using math games for purposeful practice.

In our second session, we looked at the big idea of spatial relationships.

And introduced the instructional routine of Same but Different.

In our third session together, we looked at the big ideas of number, specifically around fractions and also the big ideas around data analysis.


2019-2020 primary teachers study group: continuity of learning during term three

Posted on: June 16th, 2020 by jnovakowski

Much like our students, teachers learned “at-home” during term three, during our province’s continuity of learning during the global COVID-19 pandemic. We joined together on Zoom for our next scheduled session in April and the group decided it would like to continue to connect every two weeks.

We shared and collected resources to provide to families during this new way of teaching and learning and have posted some of them on a page at the top of this blog, called PTSG Outdoor Learning Opportunities. A direct link can be found HERE.

An area we focused on during our Zoom discussions with communication with families. We compiled the different ways teachers in the group were successfully communicating with students and their families.

In June, the teachers in the group completed an online survey to provide feedback on this year and to plan for next year. Areas of interest include teaching and learning through the First Peoples Principles of Learning, the core competencies, student agency and a continued focus on outdoor learning.

Take care and have a wonderful summer,


2019-2020 primary teachers study group: session four

Posted on: June 16th, 2020 by jnovakowski

For our fourth (and what turned out to be our final in-person time together) session, the primary teachers study group met at Anderson Elementary.

We began our time together by investigating the materials included in the Bog Ecology Kit, available through our district resource centre (DRC).

Inspired by some cards in the kit, the group decided it wanted to create plant cards on a ring that teachers could take outside with their students. Each teacher in the group will take on a local plant to photograph and research with their students.

The teachers from Anderson took us out to visit their outdoor learning area and garden and then we walked over to Garden City Park, where we used Anne-Marie Fenn’s nature finding list to observe the area.

Thank you to the Anderson teachers for hosting us!


2019-2020 primary teachers study group: session three

Posted on: June 16th, 2020 by jnovakowski

For our third session of our primary teachers study group, we came together at Spul’u’kwuks Elementary to think together about land-based art and the connection to language.

We chose to intersect creating land-based art with the idea of exploring landscape – sky, land, water. January is also often a tumultuous time of year for weather, so we extended the idea of landscape to connect to ideas of weather through the language of place. Jess created weather word cards using vocabulary from the Online Musqueam Teaching Kit.

The weather word cards can be downloaded here:

We walked from the school down to the edge of the river, where the river meets the ocean. Small groups of teachers created landscapes with materials they found on the land and some added the weather word cards to their landscapes.

Some of the resources shared during our session:

Musqueam Place Name Map
The Origin of the Name Musqueam

Musqueam Language and Culture Department Online Book Collection
Teacher resource guide below virtual books

Virtual hən̓q̓əmin̓əm̓ Alphabet Cards

Teacher resource guide below virtual books

Water Words (2014) Public Art
By: Joanne Arnott and Spul’u’kwuks Elementary School

Online Musqueam Teacher’s Kit: Musqueam: giving information about our teachings
The kit can be booked through the Museum of Anthropology or through our SD38 District Resource Center 

Our current Aboriginal Education Enhancement Agreement:

Many teachers were interested in further development of their understanding of the hən̓q̓əmin̓əm̓ language. If you are a SD38 teacher and would like the keyboard for the hən̓q̓əmin̓əm̓ language, you need to fill in a tech work order and ask for the North American Phonetic Alphabet keyboard to be installed.

Thank you to the teachers at Spul’u’kwuks for hosting us for this inspiring session.


tessellating tiles indoors and outdoors

Posted on: June 10th, 2020 by jnovakowski

As we have moved to a blended model of teaching and learning in June 2020, I had the pleasure of spending time with two small groups of grades 1&2 students at Grauer while they were at the school for in-school instruction. To connect to the different online math studio projects we had been doing this spring, I wanted to do something that connected math and art. The classroom teachers and I decided to explore tessellations with sidewalk chalk.

With the first class, it was raining quite heavily so we decided to stay indoors and practice create tessellating tiles from old library cards. The students drew a line from corner to corner on the bottom of the card, cut along the line and then “slide” that piece to the top of the card. Then using masking tape, the student taped the two pieces together. They were asked to imagine what that new shapes could be? What had they transformed the rectangle into?

Each student was given a large piece of paper to trace and tessellate their tiles and add details, patterns or character or animal features.

Later in the week, I visited the second class on a dry day outside. I demonstrated how to create a tessellating tile and the students were given a letter-size piece of manilla tag/cardstock. I had prepared individual bags of sidewalk chalk that students would use and then keep in their personal tote boxes for the rest of the month.

We headed outside and found an area of concrete where students could physically distance themselves. One student drew a circle around her space. The students traced and tessellated their tiles using sidewalk chalk and then added character features.

The following week, when it was dry outside the classroom teacher from the first class made larger tiles with them and they took them outside to tessellate using sidewalk chalk.

Usually with tessellating with primary students, we focus on collaborative tessellating with materials like pattern blocks but in this time of physical distancing and not using shared materials, this was a great task to focus on transformational geometry, positional language and spatial reasoning in our lead up to World Tessellation Day on June 17!