### Introduction to the Coast Metro Elementary Math Framework

After a successful spring 2022 professional learning series with Dr. Marian Small, the Coast Metro Consortium invited educators from the Lower Mainland Math Contacts (LMMC) group to develop an elementary math framework to support teachers in the Coast Metro region in the teaching and assessment of elementary mathematics. A team of teachers from the LMMC collaborated over the summer of 2022 using suggested elements from the Coast Metro Consortium to develop a shared vision for elementary mathematics education, grounded in the BC K-7 mathematics curriculum. This collaborative work continued through to March 2023 and is being made available to all BC educators. The following K-7 resources are focused on Number and Number Operations and the corresponding curricular competencies.

#### Considerations for developing a mathematics community in your classroom

In building a mathematics community in your classroom there are several things to consider including developing mathematical habits of mind, nurturing positive dispositions in mathematics, and engaging in mathematical problem solving and discourse. Building strong foundational content knowledge and developing mathematical competencies happen in tandem, through a range of mathematics learning experiences, tasks, and problems.

We hope that students learning mathematics in our classrooms will:

- believe in themselves
- take risks and learn from mistakes
- persevere when solving problems
- ask questions and investigate ideas
- think creatively, critically, and reflectively
- show and communicate thinking in different ways
- value the process of learning and engage in collaboration
- have agency through personal choices such as accessing materials, technology or tools as needed

Diversity—of students’ understanding, skills, experiences, and backgrounds—enriches the teaching and learning of mathematics. A classroom rich in mathematics provides all students with mathematical experiences to help them see themselves as mathematicians with interesting and important ideas of their own.

#### Structure of a Math Class and Lesson Structures

Daily math instruction is suggested for K-7 classrooms. This would consist of a one-hour math lesson with other opportunities for mathematics and numeracy experiences throughout the school day. The daily math lesson is focused on a learning goal (comprised of both content and competency standards) and this learning goal is often developed over one or two weeks. An example of a learning goal for grade 3 is “Students will demonstrate an understanding of fractions concepts by representing fractions in concrete, pictorial and symbolic forms.” Evidence-based practice supports a three-part lesson model for mathematics. Within this three-part lesson structure there are opportunities for exploration, investigation, explicit instruction, discourse and collaboration.

Three-Part Lesson Structure for Mathematics

The following is a description of the three-part lesson structure drawn from the work of Dr. John van deWalle and Dr. Marian Small. We have provided examples for clarity.

**Before:**provide opportunities to activate prior knowledge and language, explore materials and ideas; this part of the lesson could involve an instructional routine or introduction of a material

*Provide each table group of students with a tub of Cuisenaire Rods. On the whiteboard, provide the prompts: “What can you find out about this math material?” “What fraction relationships can you find?” Invite students to share their findings.*

During this stage, the teacher circulates to listen for student understanding. While students are sharing their findings, the teacher highlights fractional relationships the students notice and extends or elaborates fraction concepts and language as necessary.

**During:**Students investigate a mathematics concept, develop competencies, engage in mathematics tasks or problem-solving (the main component of the lesson – for example, about 40 minutes)

*Invite students to collaborate with a partner. Provide a set of Cuisenaire Rods and ask students to build one half (½) in as many different ways as they can. Have students record their findings using pictures and fraction symbols. Pause to do a gallery walk for students to see fractions created by their classmates. Students can continue to add to their ways to make one-half or choose a new fraction to build and record.*

During this stage, the teacher circulates and notices what students are doing and records observations and notes. The teacher may provide prompts to clarify, develop or extend student thinking.

**After:**opportunities to consolidate and reflect on learning and thinking through discussion and sharing.

*Students come together on the carpet and are invited to share how using Cuisenaire Rods has supported their understanding of fraction concepts and the connections they have made to other learning experiences and materials. *

The teacher facilitates sharing and discussion, selecting specific student examples that will support students’ understanding and move their thinking forward. The teacher records key concepts and language that students have used to share their findings and asks students to reflect upon what their goals are for the next steps in their learning of fractions.

Different lesson types provide instructional variety and different learning opportunities for students. Using problems, materials and different contexts provides openings for students to transfer their understanding of concepts to new situations and demonstrate their learning. In other words, students can use what they know and can do in new situations.

Problem-Based Lesson

What is a ‘problem’? A problem is anything problematic – in other words, where the solution is not immediately clear. A “word” problem is not necessarily a problem. Problem solving requires reasoning and creative thinking to solve. A problem-based lesson is a lesson that involves students engaged in the problem-solving process, discussing their strategies, and sharing their solutions and thinking.

Materials-Based Inquiry Lesson

In this lesson structure, students are invited to investigate a mathematical concept through materials as a way to make connections, and transfer previous learning to new contexts. The lesson may begin by having students share what they know about the concept. The students are then provided with a choice of materials to investigate the concept, both mathematically structured (like Cuisenaire Rods or pattern blocks) and unstructured materials (like clay or wire) and are invited to record and share their findings.

Math Workshop Lesson (centres/stations)

In this lesson structure, students explore new mathematics concepts and/or have a chance to revisit and practice previous content/competencies. Stations are set up around the room with a variety of opportunities for students to apply their learning and practice independently or in small groups. Once the structure is established with the students, the teacher is able to monitor the class as well as stay at one station to provide small group differentiated instruction related to the learning goal.

In any of these lesson types, new ideas and experiences and prior knowledge are connected, integrated and built on each other over time. There are ongoing opportunities within these lesson types for formative assessment by the teacher and self-assessment and reflection by the student.

#### Considerations for setting up your math classroom

As you set up your physical space, you consider your students’ needs as well as the tasks, routines and materials your plan to use for teaching and learning mathematics. You are setting up an environment to support student learning, encourage discourse and collaboration and provide student access to materials and tools. A math classroom can be a place of inspiration and joy.

#### Flexible spaces for whole class, small group, partner activities

**Implications for furniture**- Not cluttered

- Able to re-arrange

- Flexible options

**Space to engage in problem solving**- Tables or desks-put together

- Floor space

- Vertical non-permanent surfaces (whiteboards, Wipebooks)

#### Visuals

- Grade appropriate number line

- Can be flexible - add/remove numbers throughout year

- Word wall with visual definitions/representations

- Bulletin board that periodically highlights student voices/ideas (eg. problems with different approaches, open question, today’s number)

- Selection of posters, for example:

■ Inspirational/affective, eg. YouCubed posters [visual cue of classroom culture to reinforce/reference]

■ Culturally diverse representation (people, ideas like how different cultures understand number, history)

■ Big Ideas

■ Curricular Competencies

#### Possible Teacher Materials

- LCD projector & screen/white board

- Clear white board space

- Document camera

- Teacher manipulatives (larger, magnetic)

- Ten frames, number lines, etc.

#### Technology & Tools

- Cart (eg. iPad or Mac) available, or at least enough for two-to-one collaboration

- Calculators

#### Picture Books

#### Other Text Resources

- Math dictionary

- Math biographies

- Collection of infographics

#### Student Materials

- White boards & dry erase markers or sleeves

- Personal tool kit (varies by grade),with items like:

■ Pencil, markers

■ Hundred chart, ten frames, grids, number lines

■ Ruler

■ Protractor & compass

■ Calculator (Intermediate)

- Accessible manipulatives (varies by grade)

■ Coloured tiles

■ Pattern blocks

■ Cuisenaire rods

■ Unifix cubes

■ Numicon shapes

■ Sumblox

- Counting materials (e.g. for counting collections)

■ Different things to count

■ Containers to sort collections (sort by attribute or to unitize)

- Natural materials (eg. land-based or placed connected)

- Base ten materials

- Multi-link cubes (or Unifix cubes)

- Two colour counters

- Ten frames

- Blank with counters in primary grades

- Ten-frame & hundred frame templates starting in Grade 2

- Attribute blocks

- Dice (regular dice/multi-sided), spinners, etc

- Money

#### Considerations for Planning, Instruction and Assessment

Drawing upon mathematics education and cognitive science research and the goals and design of the BC K-7 mathematics curriculum, key considerations for planning, instruction and assessment include:

- Introduce number concepts that are new or foundational to a grade level and computational fluency practice in the first part of the school year so there are multiple opportunities to revisit them over time. This allows for spaced practice and learning.
- Computational fluency practice is regular and ongoing. Build in time each week for practice with addition, subtraction, multiplication, and division facts relevant to your grade level.
- Weave in other areas of mathematics learning such as probability, geometry and measurement in each term so that in each period of assessment and evaluation, students are able to show what they know and can do across a range of mathematics concepts as well honouring a holistic engagement with mathematics.
- Draw upon an understanding of First Peoples Principles of Learning to consider Indigenous ways of knowing and being as you design for mathematics learning. Weave authentic experiences connecting Indigenous knowledge and cultural practices to mathematics throughout units of study and across different areas of mathematics learning.
- Create opportunities for all learners to see themselves as part of the mathematics experience in the classroom. Create access points with your students in mind and provide choices in how students engage with mathematical tasks and ideas and how they show what they know and can do.

#### Components of framework at each grade level

A framework has been developed to support teachers’ planning, instruction and assessment of grade-level learning standards in the BC K-7 mathematics curriculum.

Each grade level framework includes the following components:

- Key Concepts: key math concepts for each grade
- Learning Story for the grade: this places the concept in context, explaining how it has been experienced before the grade level and how it will continue and extend beyond the grade level; indicates new concepts or shifts for the grade level, shares the big picture of mathematics at the grade level
- For each of the key concepts:
- Overview – describes the concept, why it is important and how it is developed at the grade level
- Math Foundations – supporting concepts and related competencies that are needed to develop this grade level concept
- Progression – the key concept at the grade level and how it is developed over time
- Week at a glance – a sample of a week plan for the concept and how it is developed over the week through a variety of lesson types; a brief description of what happened before this week and what might happen after this week is included
- Assessment – expectations are provided as to what students are able to do by the end of this grade; what students will know and can do is described
- Resources – web links and books related to the lessons in the week overview

- Year overview: how these concepts fit into a suggested year plan with multiple opportunities to develop understanding over the year. Please note that the complete curriculum framework for each grade level can be found here: https://curriculum.gov.bc.ca/curriculum/mathematics