* The self directed learning modules are in the process of being standardized and made AODA compatible. If you need a transcript or closed caption for any of these modules, please contact us and we will expedite those sessions.

Measurement from a Spatial Perspective
Self-directed Learning Module
Suggested Audience: Teachers (K-12); Math Facilitators/Consultants/Coaches; Principals

Session 1 – What does it mean to Measure?

What exactly is measurement? And why do students, from elementary to secondary, find it so challenging, especially when it is used so often in daily life? Building on some of the thinking from the Small and Northern Board project, this session uses video, online facilitation and google sharing environments to describe key measurement milestones that develop across the grades, examine how measurement differs from counting and explore some rather shocking – but all too common – misconceptions that student may hold because they have lost measurement’s connection to spatial reasoning.

Session 2 – What is a Unit?

It seems basic enough, but deeply understanding the meaning of a unit lies at the heart of understanding what it means to measure. And it’s not as straightforward as we might imagine! In this session we will explore big ideas underpinning the concept of a unit and some strategies to help students move from comparing to measuring. We will look at the role of accuracy, precision and estimation, the challenge of gaps and overlap, the differences between standard and non-standard units and relationships between and among our metric system – all from a spatial perspective.

Session 3 – Scales and Measurement Tools

Tired of seeing students do the protractor shuffle as they try to figure out the measure of an angle? Shocked at hearing that well over half of our grade six students have significant difficulties measuring a length when given a broken ruler? Maybe it’s because using a measurement tool is far more complex than we thought and for many students there are critical concepts missing in their understanding. This session will delve deeper into this idea and have us build our own scales and measuring devices in order to better understand and help students use the tools of the measurement trade.

Session 4 – From Relationships to Formulas

In the minds of many people – and students – measurement comes down to memorizing disconnected formulas. And that’s unfortunate because any formula is really just the final “ah ha moment” of recognizing very cool spatial relationships that exist among shapes and between attributes. Together we will explore these relationships and strategies for how students can reduce their myriad of area and volume formulas to a singular idea.

Multiplication and Division involving Fractions

Self-directed Learning Module

Suggested Audience: Junior – Intermediate (Grades 4 through 10)

Multiplication and division of fractions is frequently taught solely based upon the algorithms. This strategy obscures the mathematics, particularly in the case of division where multiplication is used. Research in Ontario classrooms has uncovered the importance of purposeful representations for fractions instruction, especially in the learning of multiplication and division of fractions. This session will explore these learnings through classroom ready tasks.

TIPS4Math Grade 9 Applied

Self-Directed Learning Module

Suggested Audience: Teachers (Grade 9 Applied); Math Facilitators/Consultants/Coaches; Principals/Vice-Principals

Based on Ontario Mathematics Curriculum, current research and TIPS4RM, this Adobe Connect session will explore the classroom resource supporting educators with a mix of face-to-face and online learning. Grade 9 Applied mathematics blended learning units will be explored and discussed.

In this Adobe Connect session you will have opportunities to:

  • deepen knowledge of mathematics classroom resources aligned with the curriculum
  • deepen knowledge of concrete and digital learning resources for classroom instruction that builds conceptual understanding and develop procedural fluency
  • develop pedagogical knowledge for teaching mathematics that is a blend of face-to-face and online learning

Supporting Indigenous Learners, in Mathematics

Self-Directed Learning Module

Suggested Audience: Teachers (K-8); Indigenous Consultants/Coordinators; Math Facilitators/Consultants/Coaches; Principals/Vice-Principals; Indigenous Community Partners (ex., Elder, Knowledge Keeper, Artist, Education Liaison, etc.) Participants are encouraged to register as a team with Indigenous community partners.

This series focuses on a multi-year participatory community-based research project that has brought together artist, educators, Elders and community members of Pikwakanagan First Nation, non-Indigenous educators, and First Nations and non-Indigenous students to explore the mathematics inherent in First Nations cultural practices. Participants will learn through the lens of a shared journey done ‘in relation’ and discover the power of placing Indigenous culture at the heart of mathematics teaching and learning. As researchers, teachers, artists, and students have done, it is hoped that participants will broadened their understanding of culture and what it means to ‘do math’ and ‘think mathematically’.

In this series participants will develop an understanding of:

  •    The project Protocols and Framework for engagement and collaborative work with Indigenous partners
    •    Importance of doing the work “in a good way”
    •    Components of a cyclical and iterative process
    •    Ethnomathematics
  •    Learning Mathematics through culture to develop mathematical and cultural identity
    •    Authentic culturally responsive teaching and learning
    •    Robust mathematical thinking
    •    Connections to the Ontario mathematics curriculum
  •    The project in relation to the FNMI Framework
    •    Reflect on individual local context

Session 1

In this session, we will focus on the importance of relationships and the necessity for a framework for engagement and collaborative work that upholds the UN Declaration on the Rights for Indigenous Peoples and The Truth and Reconciliation Commission: Calls to Action. Through video, tasks and discussions, we will explore the design and creation of Algonquin bone pipe bracelets and looming in Primary classrooms and unpack how these activities within a cultural context support students’ mathematical thinking. Emphasis will be placed on Early Number Sense and Operation, unitizing, connections between spatial and numeric representations such as composing and decomposing quantity, patterning, algebraic balancing and the introduction to multiplicative thinking.

Session 2

Session two will focus on community engagement and protocols when working with First Nations communities, specifically the importance and role of tobacco, story and beads/beading. The co-plan and co-teach aspects of the framework for engagement will be discussed in detail and project partners from the Algonquin community of Pikwakanagan will share their views and key learnings from a leadership perspective within the work. Through tasks, videos and discussion we will continue to look at bead looming with a focus on Grade 3. Collectively we will look at the progression of complexity of thinking from early primary and the connection between repeating and growing patterns. We will further unpack thinking in relation to Spatial Reasoning and Number Sense, specifically multiplicative thinking with a focus on unitizing, “groups of” language.

Session 3

We will go deeper into the robust mathematical thinking in Grade 3 related to bead looming in this third session. The focus will be on proportional reasoning, transformations, and the transition from patterning to algebraic thinking with an emphasis on unitizing, multiplicative thinking, generalizing and making far predictions. Supporting community goals for the revitalization of Algonquin culture and language, as well as how Indigenous pedagogical approaches benefit both Indigenous and non-Indigenous students’ mathematical learning will be explored and discussed.

Session 4

In this final session of the series, we will transition the focus from Grade 3 to Grade 6 mathematical thinking in relation to bead looming with an emphasis on algebra, proportional, and spatial reasoning. The central role of design will be explored through a 20 x 20 template. The sharing and re-consulting phases of the framework will be emphasized and the impact on student mathematical and cultural identity explored and celebrated.

Unit Fractions

Self-Directed Learning Module

Suggested Audience: Junior – Intermediate (Grades 4 through 10)

Based on Paying Attention to Fractions and related research, this Adobe Connect session will explore the role that unit fractions play in developing a solid fraction number sense across K-12 learning.

In this Adobe Connect session you will have opportunities to:

  • understand what a unit fraction is and how this changes the way we think about fractions;
  • examine how unit fractions can support learning across number systems and algebraic contexts;
  • develop deeper understanding of fraction as a number by engaging in the actions of partitioning, iterating and disembedding.

Operation Sense: From Arithmetic to Algebra

Self-Directed Learning Module

Suggested Audience: Teachers (K-12); Math Facilitators/Consultants/Coaches; Principals

Session 1 – Making Sense of Addition and Subtraction

What does it mean to add and subtract? And more importantly, how can students learn to translate word problems and everyday situations into number sentences that they can solve? This session explores the various addition and subtraction “problem structures” that students need to encounter, the types of representations students can use to make the operations visible, and the moves educators can make to help students advance in their learning, regardless of whether students are adding whole numbers, fractions or other types of numbers.

Session 2 – Developing Flexible Addition and Subtraction Strategies

How do students learn to add and subtract? This session looks at how the development of magnitude in the early years helps foster a robust and flexible fluency with addition and subtraction in later years. It explores the role of practice and the types of practice that builds understanding as the foundation for fluency. And it looks at the strategies educators can use to help students develop more efficient strategies through the years.

Session 3 – Making Sense of Multiplication and Division

What does it mean to multiply and divide? What does a “multiplicative situation” look like and how does it connect to proportional reasoning? And how can students learn to recognize these situations and represent them with the appropriate operation? This session explores the types of multiplication and division “problem structures” that students need to encounter, the relationship between multiplication and division and the various models students can use to make the operations visible. Furthermore, it looks at the role of paraphrasing as a strategy to help students advance in their learning, regardless of whether students are multiplying whole numbers, fractions or other types of numbers.

Session 4 – Developing Fluency with Multiplication and Division

How do students learn to multiply and divide? Why do some students have trouble with their “multiplication facts”? And what types of instructional moves can help close these gaps and strengthen efficiency? This session looks at the development of multiplicative thinking through the years, the role that models can play in building understanding and fluency and important mathematical ideas (unitizing, the distributive and associative properties, our place value system) and the role they all play in developing fluency with multiplication and division.

Comparing Fractions

Self-Directed Learning Module  |   Resources

Suggested Audience: Primary – Intermediate (K-9)

Through a variety of classroom ready activities participants will gain a deeper understanding of purposeful selection of representations, foundations of equivalency and comparing fractions. Using both participant and student thinking, discussion will highlight mathematical thinking and anticipated responses. 


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