Archive for the ‘intermediate’ Category

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

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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

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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.

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BC K-5 Math Communication

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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!

~Janice

Vision, Mission and Values Project at Thompson Elementary

Posted on: March 20th, 2017 by jnovakowski No Comments

The Richmond School District is embarking on a legacy project, developing new Vision, Mission and Values statements for our district. Teachers were invited to engage in discussions with their students and collect artifacts to contribute to the district process of creating new VMV statements. Two intermediate classes and their teachers from Thompson agreed to do some special filming for a district video for this legacy project.

At the beginning of January, I was able to meet with classroom teachers Lyanne McCaskill (grades 5&6) and Kevin Dimmick (grades 6&7) to plan how this project might unfold. The teachers put a lot of thought into the experiences they wanted to provide for their students. I was fortunate to be able to attend three different learning experiences with the students and to capture the students’ thinking and ideas with photographs and videos.

On the first day, as is the usual routine, the students in both classes entered their rooms to the morning provocation: What do you imagine school could be? They were invited to respond to the question using loose parts. Some students focused on the physical environment while others focused on metaphors and ideas. Each class paused to go to each table group and have those students share what they had done. Students could go back to their spots to revisit their work, connecting to new ideas or inspiration. Students were then asked to reflect on their thinking using a familiar response form.

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In the grades 5&6 class…

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In the grades 6&7 class…

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On the second day, the teachers used the Vision, Mission and Values from the Vancouver Aquarium website to initiate discussion about what Vision, Mission and Values are. In one class, the students were asked to use a familiar response format (Notice, Connect, Wonder) as they discussed and thought about the Aquarium’s VMV statements while in the other class, they used the Vision, Mission, and Values framework and questions as a way to respond.

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In one of the classes, the students sorted different statements they had made in their own reflective writing about VMV – there were very interesting discussions that emerged as students distinguished between what was part of a vision, mission or values statement.

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The students worked in small groups to create charts of words and phrases that connected to Vision, Mission or Values and these were displayed in the classroom for students to read and discuss.

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On our third day together, the teachers began their days as they had the first day – with a morning provocation posted for the students to engage with and loose parts available. The original question of What do you imagine school could be? was now linked to Vision, Mission and Values. The students could choose one or all of the three areas to represent and record their ideas about.

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It was fascinating to watch how the students’ ideas evolved over time and how each class had its own particular culture it terms of what came out in the students’ representations – kindness, inclusion, community, diversity and collaboration were the five big ideas that stood out to me as I listened to and read the students’ contributions to the project.

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An short video compilation of the Thompson VMV experience can be viewed HERE.

What has stuck with me, while spending time in these classrooms is the wisdom of our students. Their lived experiences in different types of learning environments, their understanding of each other, the importance of collaboration and the purpose of schools within a society made my heart sing. Our future is in good hands.

~Janice

creating spaces for playful inquiry: January 2017

Posted on: March 9th, 2017 by jnovakowski No Comments

Richmond’s Playful Inquiry Mentors hosted their second dinner event of Creating Spaces for Playful Inquiry series. For this session, we focused on the theme of identity and its connection to the core competencies as well as curricular competencies and content in BC’s curriculum. As sixty Richmond educators joined us in the Grauer multipurpose room, the playful inquiry mentors had set out provocations to engage in.

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A handout of the provocation questions and curricular connections can be downloaded HERE.

Three Richmond teachers (Kelly, Anna and Christy) who visited the Opal School in Portland last June shared how their visit to Opal has inspired their learning environments and their teaching practice.

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Kelly’s presentation on the impact her visit to Opal on her own teaching was summed up in two words – her presentation can be seen HERE.

 

 

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Christy’s presentation on Fine Arts Provocations with her grades 5&6 students can be viewed HERE

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For our professional learning area of focus for the evening, Marie and Hieu shared their thinking about using loose parts as an inclusive practice that particularly supports English Language Learners in our classrooms.

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After dinner together, we broke out into mentor groups to discuss specific areas of interest and to collaborate and plan together.

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Some of the playful inquiry mentors along with some of the participants in this series will be attending a Lower Mainland Study Tour to the Opal School in Portland over spring break and will bring back new sources of inspiration for playful inquiry to share with teachers in Richmond.

~Janice

investigating mathematical big ideas at Hamilton

Posted on: March 9th, 2017 by jnovakowski No Comments

In January, I spent some time in the two grades 4 & 5 classrooms at Hamilton Elementary. Coverage was provided to teachers so that they could observe and take part in math lessons in another teacher’s classroom. Teacher were then able to teach this lesson to their own classes, having seen and heard how another class responded and thus, anticipating and planning for their own students. This form of “adapted lesson study” is a common structure we use in professional learning in our district, with time to plan together, observe and discuss and then enact and debrief. The teachers at Hamilton had requested a focus on teaching through the big ideas in the curriculum.

For both classes we focused our planning around these big ideas:

Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.

Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.

To focus the students’ thinking, connection-making and our discussions, the question we posed for the students to investigate was: What is the relationship between multiplication and division?

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For each class we began with a game, to activate students’ thinking, get them talking about mathematics and to practice computing multiplication facts. In one class we played Product Gameboard and in the other, the card game Salute.

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IMG_9770After discussing the strategies the students used in each game, a problem was introduced to each class. Both of the problems were taken from the book: Good Uestions for Math Teaching. Using different strategies, I facilities meaning-making of the problems with the students and then the students began to engage in problem-solving. They had an opportunity to “turn and talk” and share their strategies and were encouraged to approach the problem in different ways.

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The students all began with the same problem but could adjust the number of students in the school (in the problem context) they were working with. They used whiteboard to show their different approaches to solving the problem.

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As students shared their solutions and strategies, we asked the students to listen to each other and build on or connecting to each others’ thinking as part of the discourse.

In the second class, a related problem was presented.

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What was interesting to notice as students engaged with this problem is that none of the students paid attention to the “four grades”- it was not required information to work through the problem but would have added an extra layer of complexity and context. We did pause near the end of our time together and this was pointed out, and if I had been with the class the next day, I might have had them re-visit this problem, being mindful of the “four grades” context.

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What students did pay attention to in terms of sense-making for this problem was the types of sports students might be playing and the number of students that would make sense for each team. The students found a context (tennis) that made sense of having one person per team and two per team (doubles). The students shared their different solutions on the large whiteboard which we used as a starting point to compare and contrast their different solutions and strategies and have the students make connections to how both multiplication and division are related and could be used to engage with both of the problems posed to the classes.

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Teaching through the big ideas was also a topic of conversation during an afternoon of Hamilton’s professional development day in January. We will be continuing our conversation at Hamilton’s pro-d day in May and continue to think about ways to nurture ways for students to make connections between mathematical concepts and strategies.

~Janice

making pentominoes

Posted on: February 27th, 2017 by jnovakowski No Comments

Many of our schools have the brightly coloured flat plastic pentominoes tucked away in storage cupboards. I have always like pentominoes due to their affordances for puzzles, problem-solving and spatial reasoning.

One thing I’ve noticed is that they have not been particularly appealing to our younger learners and I wondered if it was because of their two-dimensionality. I thought something that was more tactile for them and that they could build with might be more appealing.

When I saw these cubes at the dollar store, my mind went to building pentominoes based on a task I had read about in the Taking Shape book by Joan Moss et al.

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How many different ways can 3 blocks be put together, with all edges and faces flush? How will you know if you have found all the ways? Are two objects congruent if their orientation is different?

With 4 blocks?

With 5 blocks? (pentominoes)

I have done this task with teachers, both as part of our BCAMT Reggio-Inspired Mathematics Collaborative Inquiry Project and as part of a session on the mathematics curricular competencies at our district conference.

Teachers have found this task touches upon so many areas in our curriculum – spatial reasoning, geometry, problem-solving, visualizing, reasoning and analyzing, communicating, etc.

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As an extension to the building task, using the little wood cubes, I glued sets of pentominoes together, using an image of the 12 pentominoes I found online to help me as a guide. I also left lots of blocks not glued to be used for building the different arrangements.

Pro-tip – don’t use liquid white glue on the coloured blocks….the dye runs and you’ll have a mess on your hands and elsewhere!

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One of the unique aspects of pentominoes is that they are able to fit together to form various rectangles. How many different rectangles can you make using some or all of the pentominoes?

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~Janice

elementary math focus afternoon 2017

Posted on: January 17th, 2017 by jnovakowski

We hosted this year’s Elementary Math Focus Afternoon on January 16 at Byng Elementary. Over 250 educators attended, from 14 schools.

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There were a range of sessions to choose from and a huge thank you goes out to all the teacher facilitators who shared with their colleagues. A special thank you to our colleagues from Surrey and Delta who shared with us.

Elementary Math Focus Afternoon Jan 16 2017 program FINAL updated Jan 13

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Rebeca Rubio shared some of the many math resources and kits from the District Resource Centre.

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Tracy, from the Canadian Federation for Economic Education, shared resources to support the financial literacy component of the math curriculum, particularly around the Talk With Our Kids About Money initiative.

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The schools attending each contributed a display of materials, documentation or resources sharing an area of professional inquiry amongst their staffs.

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QR code Math Tags were available with links to IGNITE videos, websites and blogs.

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Math Tags 2017

 

General Handouts:

BC K-5 Mathematics Big Ideas (one pager per grade)

BC 6&7 Mathematics Big Ideas

K-5 Math Connections between Core and Curricular Competencies

6-9 Math Connections between Core and Curricular Competencies

The Sum What Dice Game Jan2013

Product GameBoard

BCFinancialLiteracyResourcesShared

 

Session Handouts:

Fred Harwood Grid Algebra 1

Fred Harwood Grid Algebra 2

Barker & Schwartz Picture Books Math & Literacy

Bebluk & Blaschuk Formative Assessment

High-Yield Routines September 2015

Linear Measurement final  from Marie Thom’s K-2 Measurement session

Primary Math Routines (Carrusca, Wozney, Ververgaert)

DST Formative Assessment for All

Jacob Martens Numeracy Competencies Presentation

Sentence Frames for Math ELL

ELL Tier 2 words poster

Carrie Bourne Mental Math Poster – Faire 10

Carrie Bourne mental math poster – valeur de position

(contact Carrie for more Mental Math Strategy posters en francais)

MIchelle Hikida Grades 1-4 Mathematical Inquiry

Michelle Hikida Symmetry

Sandra Ball’s Power of Ten Frames presentation and handout

 

A big thank you to the Byng staff for hosting and to all the facilitators for sharing their experiences and inspiring their colleagues in their sessions.

~Janice

geometry tiles

Posted on: January 5th, 2017 by jnovakowski

Inspired by a post on Christopher Danielson’s (yes, the author of the book and teacher resource Which One Doesn’t Belong?) blog called Talking Math With Your Kids, I created a set of geometry tiles. Always up to a crafty challenge, I thought…hmmm, I could make those! Christopher has created a one-pager of instructions as part of his Math on a Stick project for the Minnesota State Fair.

I found some balsa slats at Michael’s (teachers get a discount with a teacher card, just ask) and cut them to a 2 to 1 ratio which fortunately, gave me a set of smaller tiles of the same proportions.

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I painted front and back sides and edges with diluted acrylic paint although they could also be left plain. I marked the midpoint of one long side with a sharpie and used regular adhesive tape to tape off from the midpoint to each corner.

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I used black acrylic paint to paint in the triangles creating by the taping.

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And when the tiles were dry, I played around with what I could create with them. So much composing and decomposing of shapes!

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I used these geometry tiles as part of our mathematical tablescape at our Provincial Numeracy Project meetings to oohs and aahs.

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I’m looking forward to seeing how some students investigate these tiles!

~Janice

 

 

 

inclusive practices in mathematics for grades 6-9

Posted on: October 30th, 2016 by jnovakowski

Building on interest from an ILC (Inclusive Learning Community) project Shelley Moore and I facilitated with grade 8 teachers at Boyd Secondary, we held an after school session in October looking at inclusive practices in mathematics for grades 6-9 teachers. These practices are particularly mindful of the personal, social, intellectual and physical needs of students in the middle school age range.

Shelley began the session by sharing Richmond’s history with inclusive education and sharing some frameworks she has developed for thinking about inclusion (bowling pins, Fisher-Price stacker toy, planning pyramid, etc). She refers to inclusions lenses – personal, social and intellectual as well as places – different classrooms and places in the school as well as out of the school.

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In using the planning pyramid, Shelley considers goals, tasks and questions for all students, some students and a few students, starting where ALL students can access the unit or lesson. And here’s Shelley doing the tree pose – using the analogy that everyone/all could start this yoga pose by using the wall for support!

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Shelley shared the two year project with the grade 8 teachers and students at Boyd, with the first year addressing the Shape and Space curriculum and the second year examining the linear equations part of the curriculum. One example of a planning framework for an initial lesson on geometry looks like this:

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We shared photographs and video from the Boyd ILC project to share how the project unfolded with the students. Blog posts about the project and be found HERE and HERE.

I shared some of the practices and structures that we considered during the ILC project at Boyd and that can be used as a guide for planning mathematics lessons and units with inclusion in mind.

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Some of the choices that students were provided were what types of materials they might use. For example, during our lesson together about the volume of prisms, some students built prisms with cubes, some students used centimetre graph paper to create nets for their prisms and other drew 3D drawings that represented the measurements they were working with. Another choice was the range within the concept being addressed – for example, in the geometry lessons, identification of basic 2D shapes (faces) was an access point for all while some students investigated a range of 3D prisms. In the study of linear equations, choices of equations to investigate and represent with balances and other materials were provided, increasing in complexity or number of operations. Students were also provided with choices in how they processed or representing their thinking, for example, iPad technology was available and students could use the camera to take video or photos and then use a choice of screencasting apps to provide evidence of their understanding of the concept. Non-permanent vertical surfaces (NPVS) aka whiteboards or windows provide another choice for students who may not want to sit and work at a desk or table or use paper and pencil. The research-based practice of using NPVS has been shown to increase engagement and mathematical discourse, particularly at the middle-school age range.

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I shared the idea of mathematical routines such as number talks as inclusive practices with starting points for all and a way to build an inclusive mathematical community in the classroom. These routines also focus on the nurturing and development of the curricular competencies which are the same for grades 6-9. One of the routines shared was WODB (Which One Doesn’t Belong?). This routine has become very popular in Richmond classrooms as it provides an opportunity for the clear connection between curricular competencies and content. Four items are presented and they all belong to a set/group of some sort – integers, polygons, etc but each item is unique is some way. The goal of the routine is for the students to analyze and use reasoning to justify or defend which one they think doesn’t belong in the set and why. WODBs for geometry, number, graphs, etc are available at WODB.CA  - a site curated by an Ontario secondary math teacher.

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Shelley has posted a pdf version of our slides from the session on her blog. They can be found HERE.

Because of interest, we will be facilitating a repeat of this session on December 6 from 3:30-5:00pm at IDC – register on our district’s event page with further follow-up sessions planned in the new year.

~Janice

BCAMT Fall Conference 2016

Posted on: October 21st, 2016 by jnovakowski

On Friday, October 21, our Provincial PSA day, I had the honour of sharing the work we have been doing in the Richmond School District as we have been enacting BC’s redesigned curriculum. This year’s BCAMT conference had over 900 attendees and speakers. Fawn Nguyen shared an amazing keynote address with us, reminding us that we are a gift to our students and to honour their time with us.

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“that’s me in the front row!”

In the morning I was part of Curriculum Focus Session with a three-member panel – Ray Appel, Marc Garneau and myself. We shared aspects of the redesigned curriculum and then broke off into primary, intermediate and grades 8&9 focused breakout sessions.

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During the primary session, I shared snapshots and stories from Richmond classrooms. The handout from this primary breakout session can be dowloaded > bcamt-overview-primary-focus-oct-2016

One of the particular areas I shared was looking at the connections between the core competencies and curricular competencies in mathematics. My begin thinking around this can be downloaded > k-5-math-connections-between-core-and-curricular-competencies

I also shared the link between the heightened focus on computational fluency in the curriculum and the importance of regular number talks in classrooms.

Some info on Number Talks can be downloaded >

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I also shared some of the BC Curriculum summary pages that reflect the work in the Richmond School District. They can be downloaded >

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The next primary-focused session I presented was on Mathematical Routines such as counting collections, number talks and WODB.

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The handout from this Mathematical Routines session can be downloaded > bcamt-2016-mathematical-routines

There are many blogs posts about Mathematical Routines available on this blog – use the search tool to search for number talks, counting collections, WODB etc.

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Apparently, Counting Collections are taking over BC!

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During my last session called Playful Mathematical Inquiry for grades K-5 teachers, I shared the thinking I have been doing with teachers in our district around frameworks to think about inquiry in mathematics and how playful inquiry encompasses the curricular competencies in mathematics.

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The handout from this Playful Mathematical Inquiry session can be downloaded > playful-mathematical-inquiry-bcamt-2016

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As always, it is great to re-connect with colleagues and a special thank you to the teachers who participated in my sessions! Thanks to Rick Hikida for this photo from the back of a very crowded room and for his tech support!

~Janice

introducing WODBs to grades 4&5 at Westwind

Posted on: October 16th, 2016 by jnovakowski

I was invited into a grades 4&5 classroom at Westward to introduce the mathematical routine, Which One Doesn’t Belong? Teacher Carlos Victoria has emailed me to let me know the students had been learning about place value and different ways to represent numbers.

I began with a geometry WODB (found at wodb.ca ) and began the conversation about how these shapes are all the same, how they belong to a set or group. The students used the term shapes, then 2D shapes and with some guidance got to the term polygons. Then we looked at ways each shape was different than the others…unique. The students then turned and talked about if they had to choose just one shape, which one did they think didn’t belong? and WHY! We talked about how justification is a big part of being a mathematician.

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We then moved on to the following WODB – one I often start with regardless of grade level because there are so many ways to analyze and compare the numbers. Same questions as before – how are they the same (numbers, numbers under 100, numbers between o-50, etc) and then how are they different. So many creative responses! As students described and defended their choices, I highlighted the mathematical language students were using such as “digits” and modelled new language for them such as the term “square numbers”.

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After our two introductory WODBs, I shared our learning intentions for our time together:

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And then we moved on to two WODBs that focused on the mathematical content the class was learning about. The students were given a quiet minute to examine the WODB on their own and then were asked to turn and talk to their table group about which one doesn’t belong? Some students focused on form (a visual entry point) while other focused on the numbers.

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The students were then invited to work together to create their own WODBs. This is not as easy as it seems! I provided some guiding questions for the students to go back to as they were working through the process. As students completed their WODBs, the moved to a part of the classroom together to discuss and try and solve each others’.

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And as I said goodbye to the students, I know their teacher will continue the WODB routine with his class, as he just received our district’s WODB kit from the DRC – full of WODBs from the website as well as Christopher Danielson’s new WODB books  (picture book and teacher guide).

I am looking forward to hearing about more of their WODB experiences!

~Janice