Archive for the ‘primary’ Category

summer professional reading: Teaching Mathematical Thinking

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

IMG_6362Teaching Mathematical Thinking: Tasks & Questions to Strengthen Practices and Processes

by Marian Small

foreward by Linda Dacey

published by Teachers College Press, 2017

 

 

In this recently published book, well known math educator and author Marian Small highlights an important aspect of the discipline of mathematics – the thinking practices and processes that are “the doing of mathematics” when engaging in mathematical problems and learning content.

For those wanting clear examples of practices such as mathematical modeling, structure and argument are – the author clearly defines these with examples from across grade bands (K-2, 3-5 and 6-8).

For each practice/process, the author includes:

1) a definition with examples

2) where that practice/process is seen in K-8 mathematics

3) examples of problems, across grade bands, that might bring out that practice/process, often with examples of student responses

4) assessment questions for the educator to use to help notice and reflect on the students’ use of the practice/process

5) a short summary

I can’t think of another book that makes such careful nods to the Canadian mathematics education landscape. Although the focus is on the eight American Common Core standards for mathematical practice, the author connects these to our mathematical processes/competencies in Canada (with slight differences in different provinces/regions). Because our Canadian emphasis on visualization and mental math and estimation is not explicit in the American practices, the author has added a final chapter dedicated to these processes.

The problems are chosen to connect to each practice/process but should not be considered practice-specific. There are different types of problems – if you are familiar with Marian Small’s other books, you will understand the type of open-ness, differentiation and complexity built into the problems provided. For each practice/process she provides at least one problem for each grade band and then discusses how students take up the problems, with student examples.

I highly recommend this book. So so many wonderful problems for K-8 students and great information for teachers to help us think about the discipline of mathematics.

~Janice

playful storytelling celebration

Posted on: June 13th, 2017 by jnovakowski No Comments

We held our year end celebration for our Playful Storytelling through the First Peoples Principles of Learning project on June 1 at Grauer. Teachers and school teams came together to share what they had been working on during this school year. It is always interesting to hear how each school makes the project its own.

An overview of our session at the beginning of the year is HERE

After an acknowledgement of territory and a welcome to some visiting educators from Manitoba, in circle each teacher introduced themselves and shared the principle that they have most connected to this school year.

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A group of us involved in this project visited the Vancouver Art Gallery in early May to see the Susan Point exhibit. We made so many connections between her work and story and came up with several questions to guide our practice when having students engage with art. We shared this with the group and also shared how some teachers had already taken up these ideas with their classes.

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School teams then shared how they have investigated playful storytelling in their schools.

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We noticed a clear move to many classes taking storytelling outdoors and this will be something we continue to investigate next year.

After a lovely dinner together prepared by Marie Thom, we moved to The Studio at Grauer to engage in some sensory experiences with materials that can be used to enhance the storytelling experience. Experiences with clay, watercolour and wet felting were provided, for teachers to consider – what stories live in these materials?

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We all left inspired by each other and full of new ideas to enact with our students. Looking forward to continue this work in our district next year!

~Janice

The Studio at Grauer

Posted on: June 11th, 2017 by jnovakowski 2 Comments

The Studio at Grauer came to be based on a need we felt existed in our district – a space to engage in professional learning experiences for teachers as well as for a learning environment for students that could be left  “set up”. My office partner, Marie Thom, and I have been talking about this for the last couple of years. The notion of a “pop-up” classroom emerged and Andrew Ferguson, the principal at Grauer, was approached to see if we could use one of the school’s unused classrooms.

December 16 2018 – Room 102

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Room 102 was being used as a storage room until we began our transformation of it in January 2017. Blending Marie’s background in learning environments and my understanding of mathematics teaching and learning, we developed a space focused on mathematics, filled with inspiring materials in a learning environment designed for learners K-Adult. Our goal was to create a flexible, responsive and inclusive learning environment.

Room 102 – January 10 2017

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January 13 2017

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The learning environment is set up to create opportunities for choice, collaboration, personalized learning and inquiry. More specifically for mathematics, our hope was to broaden understanding of what mathematics is and what the teaching and learning of mathematics can be. Often school mathematics is perceived as “arithmetic” and mathematics is a much broader discipline that this. We wanted students and teachers to see math all around them and be inspired to think about mathematics in different ways – to see mathematical ideas in the materials, in pinecones, in buildings and structures, in images of our community, in art, in stories.

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As we discussed how we were going to use the space, we decided to call it The Studio, inspired the notion of an atelier, a studio space used in the early childhood schools of Reggio Emilia.

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Classes from Grauer, as well as visiting classes on “math field trips” visit The Studio to engage in mathematical inquiry. Marie and I take on the role of atelierista, working with the classroom teacher to facilitate learning experiences through different materials in the space. We have intentionally curated both mathematically structured materials like pattern blocks and Cuisenaire rods alongside materials often known as loose parts such as ribbons, gems, rocks, pinecones, etc. We also have art materials available to the students such as paint, clay, charcoal, yarn and wool so that students can express themselves and think using different languages. Students also have access to various tools to support their investigations such as measuring tapes, protractors, grids and ten frames.

The first class to visit The Studio – the grades 3&4 students from Grauer on January 18 2017

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The learning environment is intentionally flexible with choices in seating and tables available for both students and adults. Interestingly, although we have some chairs available, none of the students using The Studio have used them, preferring instead to stand or sit and lie on the carpet or use pillows. We have observed the flow of movement in the space and intentionally have large open spaces for students to move through. Shelves filled with baskets of materials are open and accessible to students. Students can choose the materials they want to use and take them to where they would like to engage.  We took doors off of some cupboards to create more open shelving. All of the furniture, except for four small Ikea open shelves, was found in school storage rooms and thrift shops.

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Provocations are set up on tables for students (and educators) to inspire mathematical thinking and inquiry. Inspired by one of the students’ interests in optical illusions, the grades 3&4 students from Grauer investigated the mathematics embedded in optical illusions. I gathered materials and tools that I hoped would provoke their thinking about optical illusions and the students also accessed and were inspired by other materials in The Studio.

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As we have more classes through The Studio, we have developed documentation to share in the space. Panels, photographs and photobooks are available for students and educators to engage with, to reflect upon and to inspire new experiences.

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One area of pedagogical intention in The Studio has been on noticing, naming and nurturing the Core Competencies and the Mathematics Curricular Competencies from our BC curriculum framework. A focus has been on both communication and creative thinking in mathematics. We intentionally create opportunities for students to engage in different types of communication and to reflect on how they are doing.

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We have had many groups of educators also visit The Studio. Our District Support Team, educators attending our Playful Inquiry professional learning series and teams from schools in our district. Many BC educators involved with our BCAMT Reggio-Inspired Mathematics project have visited the space as well. We have also had visitors from Manitoba and Sweden! We often focus the visits with the questions – what do you notice? what do you wonder?

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We also have a dedicated professional learning library with the teacher resources we recommend around teaching and learning mathematics, the use of loose parts and the importance of the learning environment.

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We had hoped The Studio would inspire similar learning environments in our district but recognize that many schools do not have access to a dedicated room for a studio space – we hope that teachers will be inspired by elements of The Studio for their own classroom learning environments. What has been exciting for Marie and I is that this little project has had a huge ripple effect at Grauer, in our district, and beyond!

~Janice

 

 

creating spaces for playful inquiry: April 2017

Posted on: May 28th, 2017 by jnovakowski No Comments

For our third session of our Creating Spaces for Playful Inquiry dinner series, Richmond educators came together at Grauer Elementary to share and learn together. This year at our sessions we have focused on broad themes or big ideas that cut across curriculum areas and grade levels, beginning with community, then identity and for our third time together this year, we chose to focus on place. Those that attended our Lower Mainland study tour to  the Opal School in Portland created panels reflecting on their experience. Many of our playful inquiry mentors set up either pedagogical provocations or shared provocations they developed to engage their students.

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Four teachers shared their experiences visiting Opal for the first or second time – what had an impact on them and how it is affecting their practice. Thank you to April, Louesa, Laurie and Karen for your thoughtful and passionate presentations!

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Based on feedback from the mentor groups during our January session, Michelle Hikida and I did a short professional learning presentation on playful mathematical inquiry and how we plan around a big idea, use provocations and projects based on students’ interests and curiosities and how we extend and sustain a math inquiry.

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After dinner together, we spent time in our mentor groups, zooming in on an area of interest and sharing and learning from each other.

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We are looking forward to continuing working together next year to support professional learning and building a playful inquiry community across our district.

~Janice

primary teachers study group: sixth session

Posted on: May 28th, 2017 by jnovakowski No Comments

For our sixth and final session of the year, the primary teachers study group met at Blair Elementary. Thank you to Karen, Robyn and Tanyia for hosting us!

We broke into small groups and worked on our environmental inquiry visual – still a work in progress! Lots of great feedback from the group.

We then toured the outdoor learning spaces at Blair. I was the teacher-librarian at Blair for three years when I introduced Spuds in Tubs to the school – since then the school has embraced school gardens and many of the teachers have made outdoor learning and integral part of their programs. April and Karen shared how they use some of the typical suburban school spaces around the school for outdoor learning and also shared how they involved the district Works Yard employees in creating an outdoor classroom space and storage.

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There was much talk about school gardening as a way to get students outdoors and feeling connected. We left thinking about ways to continue our work around environmental inquiry and creating opportunities for students to take action and take care of the outdoor spaces at their schools.

Next year, our primary teachers study group will be entering its fifteenth year as a professional learning structure in our school district!

~Janice

primary teachers study group: fifth session

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

For our after spring break session, we met at Steves Elementary, hosted by Kathleen Paiger. After sharing some of the outdoor learning experiences we were engaging in, we began to co-construct a visual of sorts to show the process of environmental inquiry that we have been working towards together this school year. For many teachers in the group – the first stages have been the focus: getting outside, noticing and naming local plants and animals, being curious and connecting. Drawing upon the work of David Suzuki, Ann Pelo and many others, we know these initial stages are essential if children are to care about the environment.

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What we discussed, and connecting to last year’s Natural Curiosity seminar that some of us attended, was that getting outdoors and gardening, although important, is not the overall goal of environmental inquiry. We want to find opportunities for students to take action, to take up a concern or issue that emerges or that they are noticing in their environment.

Kathleen regularly takes her kindergarten students for walks in their neighbourhood which includes the west dyke. We ventured out together and learned about some of the story of this place – the farmland, the coyotes and the birds that frequent the wetland areas.

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And as the weather eventually warms up, we know there will be lots of opportunities for our classes to get outside, to notice and wonder. We are using these three picture books this spring to inspire us.

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~Janice

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

Provincial Numeracy Project in Richmond – year two

Posted on: April 24th, 2017 by jnovakowski

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.

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Several routines such as Counting Collections (see tedd.org) 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.

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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.”

*****

~Janice

investigating numbers with the Kindergarten class at Garden City

Posted on: March 20th, 2017 by jnovakowski

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

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