Archive for the ‘primary’ Category

investigating numbers with the Kindergarten class at Garden City

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

I visited the kindergarten class at Garden City twice over January and February, introducing different routines to develop number sense and to investigate numbers. Teacher Lori Williams had initially asked me to come to her class to introduce counting collections to her students and after that lesson, I suggested some other routines or practices she might try with her students.

To introduce counting collections to the class, the students and I sat in a circle together. The class’ “special helper” and I counted a collection in different ways, taking suggestions from the suggestions. I intentionally modelled working together as a “team” – taking turns, taking on different roles (one of us moving the items, the other counting, etc) and having each of us support each other when we were unsure or “stuck”. We counted a collection by 1s in different ways – each of us placing an item in a container taking turns while counting, putting the items in a line and counting them together, moving the items from one pile to another taking turns counting as we moved the items one by one. I asked the students if they could think of any other ways they might count their collections and they had some new ideas as well as some suggesting that they count by 2s or 10s. Pairs of students then went off to choose a collection to count, with the expectation that they count it in at least two or three different ways.

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The students and I came together after about 30 minutes of counting and I invited some pairs of students to share what they counted and how they counted their collections. I encouraged the students to listen and make connections in their mind as to how they had counted their collections.

For my next visit, I introduced the clothesline and explained that it was another way to investigate counting, particularly ordering numbers.

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The students took turns placing different representations of numbers on the clothesline – they were asked to explain their placement decisions. We followed this routine with an invitation to investigate ordering and sequencing numbers using a variety of materials.

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The students were creative in their use of materials and the inspiration of the materials often nudged them beyond their familiar counting range and what the curricular expectation are for kindergarten in BC (number concepts, including counting from 0-10).

For the classroom teacher, this was a time to notice her students engaging in new routines with different materials and to think about how she might incorporate them into her classroom. It is always a conundrum for kindergarten teachers – there are always more materials to add to the classroom but we also have to let things go and put things away, even if temporarily, to create open access to the materials students will use regularly and purposefully.

~Janice

investigating patterns with the grade 3s at Garden City

Posted on: March 18th, 2017 by jnovakowski No Comments

I visited the grade three class at Garden City Elementary twice in February, focusing on ways to teach mathematics through the big ideas in BC’s new curriculum.

Teacher Stella Santiago asked that we do some work around patterning together and we began with a class discussion around the question: What makes a pattern a pattern? The students shared their developing ideas about patterns, which included many examples of patterns, and then the students were provided with a choice of materials with which to investigate different types of pattens with. We asked them to push their thinking about what patterns were and to investigate different types of patterns and what makes them patterns.

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The students mostly began with repeating patterns but used different formats for their patterns such as going around the circumference of a table instead of just in a straight line. Blank grids were provided for students to investigate and some students engaged with those.

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Students also explored using different shape frameworks to create patterns with.

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And they played with seeing patterns in three-dimensions, from different perspectives.

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About half an hour in to the work with materials, we asked the students to pause and walk around and notice what other students were doing – to be inspired, to capture an idea, to make connections.

As the students created their patterns, I recorded the questions I was asking them during their investigations, meant to provoke their thinking about what makes a pattern a pattern.

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It was these questions that I came back to in the end as students shared their findings about patterns. We were able to come to consensus as a group that a pattern is predictable and generalizable, that there is regularity in it. Big words for a big mathematical idea.

On my next visit to the class we connected the idea of patterns to the students’ current study of multiplication. We began with a number talk, using a grid to support students in visualizing the patterns in multiplication. We played with the idea of decomposing numbers to support us in calculating multiplication questions. After our number talk, the students were provided a choice of materials and tools with which to investigate the focus question: Where do patterns live in multiplication?

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One of the tools provided to students was a 100 chart and students used gems to cover multiples of different numbers on the chart to investigate what visual patterns might emerge.

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Some students started with their understanding of multiplication – equal groupings of objects and then used the materials to create different visual patterns with these groupings.

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Some students connected the idea of growing patterns with multiplication and used different materials to represent this connection.

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The students were very curious about the geoboards, as they are not a regular item in their classroom. One student wasn’t sure where to start with the geoboard and I showed him how to stretch a band to make a square. He made another square and then I added a third. By then, he was making his own connections and began an investigation of square numbers.

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Another student used the geoboard to create arrays. She played with the idea of halving and doubling the arrays, including using diagonals to create triangles.

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A group of three students chose to use the magnetic grids to play with patterns and multiplication, using alternating colour patterns.

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The students again had an opportunity to walk around the class and see what other students were doing to investigate patterns and multiplication and then go back to their own materials, adding new ideas if inspired to do so.

We met together as a class in a “math congress” to report out our findings and make connections between what we had found out about patterns and multiplication. Students used the terms growing and increasing but identified the regular-ness of the patterns involved in multiplication. Some students focused more on the spatial relationship of arrays and how those change as factors increase or decrease.

As the students continue to study multiplication and division, I am looking forward to hearing what relationships and patterns they find.

~Janice

primary teachers study group: fourth session

Posted on: March 10th, 2017 by jnovakowski No Comments

For our fourth session together this year, we gathered after school at Errington Elementary to share what outdoor inquiry experiences we had engaged in with students. There were many attempts at freezing bubbles, tracking different animals’ movements in the snow, looking closely at ice, snow and their affects on the environment, investigating melting of ice and snow and creating new experiences for students to experience the outdoors in winter.

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Our discussions took several turns…self-regulations, navigating how much we share about our personal choices such as vegetarianism with our students, the benefits of risky play. Here is a link to the UBC research that study group member Megan Zeni referred to as we discussed the benefits of outdoor risky play.

We ended our session discussing the upcoming forecast for more snow and the eventual arrival of spring!

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Thank you to Stephanie (Merrick) Rubio for hosting us in her lovely classroom!

~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

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 No Comments

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

primary teachers study group: third session

Posted on: January 17th, 2017 by jnovakowski No Comments

The Primary Teachers Study Group had their third session of the year at Woodward Elementary, hosted by Anne-Marie Fenn. Anne-Marie shared the school’s plan for an outdoor learning space and then we went outside to imagine how the current garden space will be transformed.

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Teachers were able to purchase pictures books that are intended to inspire students’ wondering about winter. Sizing Up Winter is a book that inspires mathematical inquiry around measurement, In The Snow: Who’s Been Here? has students consider ways to know whether an animal has visited different parts of the environment and Curious About Snow shares factual information and photographs of snow – sure to inspire lots of questions, particularly with the very wintery weather we have had this year.

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Teachers shared ways that had been engaging their students in inquiry about the outdoors and winter – freezing bubbles, looking for tracks, creating icy sun catchers, learning about animal behaviour in winter.

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Jenn Lin from Maple Lane shared how she had guest speakers in from the Institute for Urban Ecology atDouglas College to teach her class about the important role bees play in the environment and then the students made bee containers/nests.

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What are your students wondering about this winter? Where do the bees go? Where do the raccoons and birds find food? What do the snow geese eat when the ground is frozen and covered with snow? Do trees freeze? Are your students making connections between how the weather and seasons are affecting other living things around them?

~Janice

geometry tiles

Posted on: January 5th, 2017 by jnovakowski No Comments

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

 

 

 

primary teachers study group: second session

Posted on: December 7th, 2016 by jnovakowski

A summary of our first primary teachers study group session and goals for the year can be found HERE.

For our second session of the school year, the primary teachers study group met at the Richmond Nature Park. We read and discussed the story of this place and learned about the formation of the bog environment and the uniqueness of this ecosystem. We connected this to the video of the formation of the delta from the online Musqueam teachers resource developed by the MOA and the Musqueam Nation which can be found HERE.

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We visited different parts of the Nature Park, thinking about how we could engage students in different spaces. The Nature Park has a covered area with picnic benches for eating or journalling as well as other seating areas.

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Another favourite spot is the bird watching area where there are many bird feeders set up that are visited by a variety of birds and squirrels. Makes for excellent observing and a chance look closely at animal behaviour! I like to take video to share with students after a trip to “re-live” and discuss what they noticed.

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We walked through along the board walk and took a short trail loop to notice and talk about the variety of trees and plants in the park and ways to engage students. We also bounced on the bog!

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One of the plants we looked closely at was Labrador Tea, a common local bog plant, turning the leaves over to help identify it. Traditional local indigenous uses for this plant include making a tea infusion to treat colds and sore throats.

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We looked at the variety of bat and bird houses and discussed these as a great ADST project for students to consider and design based on the needs of their local environment. “Bug hotels” or pollinator houses are another design option as well for school garden spaces.

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As it got dark, we visited the Nature House where one of the staff members shared some interesting information about local snakes with us.

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Teachers who have brought classes to the Nature Park shared some of their experiences and the Blair team shared how they were doing a self-guided trip with three classes the following week and were doing three different inquiry-based stations during their trip.

We will be meeting again in January, registration is still open on the Richmond Professional Learning Events site.

I am curious what sort of questions our students are having about the impact of the snow and cold on the living things around their schools?

~Janice

introducing clothesline to the kindergarten students at General Currie

Posted on: November 29th, 2016 by jnovakowski 1 Comment

Last Tuesday, I made another visit to the kindergarten classrooms at General Currie Elementary. During each visit I introduce a new mathematical “routine” to the students and teachers and then extend the routine with some related learning experiences.

I introduced the “clothesline” introduced to me via Twitter by Andrew Stadel last year. There is a website dedicated to sharing information about clothesline math HERE. Most of the work I have seen done with the clothesline is at the middle school level and I can see great uses for it in exploring equivalent fractions, decimal fractions and percentages with our intermediate students. In looking at the kindergarten mathematics curriculum  for BC, sequencing and representing numbers from 0-10 is an important learning standard and connects to the use of the clothesline, a form of interactive numberline.

We began with just the numeral cards and the students came up on a a time (in random order) to place their cards on the clothesline. They were asked to state their reasoning for why they put their cards where they did.

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After the 0-10 cards were in place, we took them off and then I shuffled them with the ten frame and tally cards and handed one card out to each student. Again, the students came up one or two or three at a time and placed their cards, explaining their reasoning. When there was an equivalent representation already in place, they just placed the card on top of the other.

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The tent cards I created can be downloaded here:

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When I asked the first class of kindergarten students one way of showing “seven”, one little guy held up seven fingers. I hope to take some photos of the students finger combinations next week when I visit to include these on a set of cards.

I can also see great potential for the clothesline to look at multiple representations of numbers in grades 2-5 to help students think about place value.

After each class worked with the clothesline, the students could choose from several related learning experiences, all that focused on sequencing numbers or representing quantities to 10.

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The students were highly engaged with the materials and were able to share their thinking about why it was important to know how to order numbers –  ”to count, to be organized”. In one of the kindergarten classes we looked around the classroom for ways that numbers in order or sequence were used. The students found the 100-chart, the calendar and the clock.

Next week, we are going to do some number talks with dot cards and ten frame  cards and investigate the idea of parts-whole relationships in numbers by decomposing and composing quantities.

~Janice