## Introduction

#### Preface

This curriculum policy presents the compulsory Grade 9 mathematics course, 2021 (MTH1W). This course supersedes the two Grade 9 courses outlined in *The Ontario Curriculum, Grades 9 and 10: Mathematics, 2005* as well as *The Ontario Curriculum: Mathematics – Mathematics Transfer Course, Grade 9, Applied to Academic, 2006. *Effective September 2021, all mathematics programs for Grade 9 will be based on the expectations outlined on this site.

The Grade 9 mathematics curriculum focuses on key mathematics concepts and skills, as well as on making connections between related math concepts, between mathematics and other disciplines, and between mathematics and the lived experiences of students. This curriculum is designed to support all students in developing an understanding of, and the ability to apply, the range of mathematical knowledge and skills appropriate for the grade level. Consequently, this curriculum is intended to support all students in continuing to build confidence in approaching mathematics, develop a positive attitude towards mathematics, think critically, work collaboratively, and feel that they are reflected in mathematics learning.

### Vision and Goals of the Grade 9 Mathematics Course

The needs of learners are diverse, and all learners have the capacity to develop the knowledge, concepts, skills, and perspectives they need to become informed, productive, and responsible citizens in their own communities and within the world.

How mathematics is contextualized, positioned, promoted, discussed, taught, learned, evaluated, and applied affects the learning experiences and academic outcomes of all students. Mathematics can be appreciated for its innate beauty, as well as for its role in making sense of the world. Having a solid foundation in, a deep appreciation for, and excitement about mathematics, as well as recognizing their identities, lived experiences, and communities in their mathematics learning, will help ensure that all students grow more confident and capable as they step into the future.

All students bring their mathematical experiences from various contexts to school. Educators can value and build on these lived experiences so that mathematics classrooms become spaces that honour diverse mathematical ideas and thoughts, and incorporate multiple ways of knowing and doing. Such spaces allow all students to become flexible and adaptive learners in an ever-changing world.

The vision of this mathematics course is to support all students as they develop healthy and strong identities as mathematics learners and grow to be mathematically skilled, to enhance their ability to use mathematics to make sense of the world around them, and to enable them to make critical decisions while engaged in mathematical thinking. This vision is attained in a mathematics classroom filled with high academic expectations and deep engagement that generates enthusiasm and curiosity – an inclusive classroom where all students receive the highest-quality mathematics instruction and learning opportunities, are empowered to interact as confident mathematics learners, and are thereby supported in reaching their full potential.

The goal of the Ontario mathematics curriculum is to provide all students with the key skills required to:

- understand the importance of and appreciate the beauty and wonder of mathematics;
- recognize and appreciate multiple mathematical perspectives;
- make informed decisions and contribute fully to their own lives and to today’s interconnected local and global communities;
- adapt to changes and synthesize new ideas;
- work both independently and collaboratively to approach challenges;
- communicate effectively;
- think critically and creatively to connect, apply, and leverage mathematics within other areas of study including science, technology, engineering, the arts, and beyond.

A strong foundation of mathematics is an important contributor to students’ future success and an essential part of becoming an informed citizen. In order to develop a strong understanding of mathematics and the ability to apply mathematics in real life, all students must feel that they are connected to the curriculum – to what is taught, why it is taught, and how it is taught.

### The Importance and Beauty of Mathematics

Mathematics is integral to every aspect of daily life – social, economic, cultural, and environmental. It is embedded into the rich and complex story of human history. People around the world have used, and continue to contribute, mathematical knowledge, skills, and attitudes to make sense of the world around them and to develop new mathematical thinking and appreciation for mathematics. Mathematics is conceptualized and practised in many different ways across diverse local and global cultural contexts. It is part of diverse knowledge systems composed of culturally situated thinking and practices. From counting systems, measurement, and calculation to geometry, spatial sense, trigonometry, algebra, functions, calculus, and statistics, mathematics has been evident in the daily lives of people and communities across human histories.

Today, mathematics is found all around us. For example, mathematics can be found in sports performance analysis, navigation systems, electronic music production, computer gaming, graphic art, quantum physics, climate change modelling, and so much more. Mathematics skills are necessary when we buy goods and services online, complete our taxes, do beading, construct buildings, and play sports. Mathematics also exists in nature, storytelling, music, dancing, puzzles, and games. Proficiency with mathematical ideas is needed for many careers, including but not limited to engineering, health care and medicine, psychology, computer science, finance, landscape design, fashion design, architecture, agriculture, ecology, the arts, the culinary arts, and many other skilled trades. In fact, in every field of pursuit, the analytical, problem-solving, critical-thinking, and creative-thinking skills that students develop through the study of mathematics are evident. In the modern age of evolving technologies, artificial intelligence, and access to vast sources of information and big data, knowing how to navigate, interpret, analyse, reason, evaluate, and problem solve is foundational to everyday life.

Mathematics can be understood as a way of studying and understanding structure, order, patterns, and relationships. The power of mathematics is evident in the connections among seemingly abstract mathematical ideas. The applications of mathematics have often yielded fascinating representations and results. As well, the aesthetics of mathematics have also motivated the development of new mathematical thinking. The beauty in mathematics can be found in the process of deriving elegant and succinct approaches to resolving problems.

At times, messy problems and seeming chaos may culminate in beautiful, sometimes surprising, results that are both simple and generalizable. Elegance and chaos are both integral to the beauty of mathematics itself and to the mathematical experience. In other words, the beauty of mathematics is illustrated and enhanced by students’ diverse interpretations, strategies, representations, and identities – not diminished by them. Most importantly, students can experience wonder and beauty when they make exciting breakthroughs in problem solving. Therefore, these two aspects of mathematics, aesthetics and application, are deeply interconnected.

The Grade 9 mathematics course strives to equip all students with the knowledge, skills, and habits of mind that are essential to understanding and enjoying the importance and beauty of mathematics. Learning in Grade 9 mathematics begins with a focus on the fundamental concepts and foundational skills. This leads to an understanding of mathematical structures, operations, processes, and language that provides students with the means necessary for reasoning, justifying conclusions, and expressing and communicating mathematical ideas.

When educators put student learning at the centre, provide relevant and meaningful learning opportunities, and use technology strategically to enhance learning experiences, all students are supported as they learn and apply mathematical concepts and skills within and across strands and other subject areas.

The Grade 9 mathematics course emphasizes the importance of establishing an inclusive mathematical learning community where all students are invited to experience the living practice of mathematics, to work through challenges, and to find beauty and success in problem solving. As students engage with the curriculum, they are supported in incorporating their lived experiences and existing mathematical understandings, and then integrating the new ideas they learn into their daily lives. When students recognize themselves in what is taught and how it is taught, they begin to view themselves as competent and confident mathematics learners who belong to the larger mathematics community. As students develop mathematical knowledge and skills, they grow as mathematical thinkers. As students explore histories of mathematics and comprehend the importance and beauty of mathematics, they develop their mathematical agency and identity, at the same time as they make connections to other subjects and the world around them.

### Human Rights, Equity, and Inclusive Education in Mathematics

Research indicates that there are groups of students (for example, Indigenous students, Black students, students experiencing homelessness, students living in poverty, students with LGBTQ+ identities, and students with special education needs and disabilities) who continue to experience systemic barriers to accessing high-level instruction in and support with learning mathematics. Systemic barriers, such as racism, implicit bias, and other forms of discrimination, can result in inequitable academic and life outcomes, such as low confidence in one’s ability to learn mathematics, reduced rates of credit completion, and leaving the secondary school system prior to earning a diploma. Achieving equitable outcomes in mathematics for all students requires educators to be aware of and identify these barriers, as well as the ways in which they can overlap and intersect, which can compound their effect on student well-being, student success, and students’ experiences in the classroom and in the school. Educators must not only know about these barriers, they must work actively and with urgency to address and remove them.

Students bring abundant cultural knowledges, experiences, and competencies into mathematical learning. It is essential for educators to develop pedagogical practices that value and centre students’ prior learning, experiences, strengths, and interests. Such pedagogical practices are informed by and build on students’ identities, lived experiences, and linguistic resources. When educators employ such pedagogy, they hold appropriate and high academic expectations of students, applying the principles of Universal Design for Learning and differentiated instruction to provide multiple entry points and maximize opportunities for all students to learn. By acknowledging and actively working to eliminate the systemic barriers that some students face, educators create the conditions for authentic experiences that empower student voices and enhance their sense of belonging, so that each student can develop a healthy identity as a mathematics learner and can succeed in mathematics and in all other subjects. Mathematics learning that is student-centred allows students to find relevance and meaning in what they are learning and to make connections between the curriculum and the world outside the classroom.

In mathematics classrooms, teachers also provide opportunities for cross-curricular learning and for teaching about human rights. To create anti-racist, anti-discriminatory learning environments, all educators must be committed to equity and inclusion and to upholding and promoting the human rights of every learner. Students of all identities and social locations have the right to mathematics opportunities that allow them to succeed, personally and academically. In any mathematics classroom, it is crucial to acknowledge students’ intersecting social identities and their connected lived realities. Educators have an obligation to develop and nurture learning environments that are reflective of and responsive to students’ strengths, needs, cultures, and diverse lived experiences – identity-affirming learning environments free from discrimination. In such learning environments, educators set appropriate and high academic expectations for all.

**Culturally Responsive and Relevant Pedagogy in Mathematics**

High-quality instruction that emphasizes deep mathematical thinking and cultural and linguistic knowledge and that addresses issues of inequity is the foundation of culturally responsive and relevant pedagogy (CRRP) in mathematics. In CRRP classrooms, teachers reflect on their own identities and pay attention to how those identities affect their teaching, their ideas, and their biases. Teachers also learn about students’ identities, identifications, and/or affiliations and connected lived experiences. Teachers develop an understanding of how students are thinking about mathematical concepts according to their cultural backgrounds and experiences, and make connections with these cultural ways of knowing in their pedagogy. This approach to pedagogy develops social consciousness and critique while valorizing students’ cultural backgrounds, communities, and cultural and linguistic competences. Teachers build on students’ experiences, ideas, questions, and interests to support the development of an engaging and inclusive mathematics classroom community.

In mathematics classrooms, educators use CRRP to create teaching and learning opportunities to engage students in shaping much of the learning and to promote mathematical agency investment in the learning. When students develop agency, they are motivated to take ownership of their learning of, and progress in, mathematics. Teaching about diverse mathematical approaches and figures in history, from different global contexts, can offer opportunities for students to feel that they are reflected in mathematical learning – a key factor in developing students’ sense of self – and to learn about others, and about the multiple ways mathematics exists in all aspects of the world around them.

Mathematics is situated and produced within cultures and cultural contexts. The curriculum is intended to expand historical understanding of the diversity of mathematical thought. In an anti-racist and anti-discriminatory environment, teachers know that there is more than one way to develop a solution, and students are exposed to multiple ways of knowing and encouraged to explore multiple ways of finding answers.

Indigenous pedagogical approaches emphasize holistic, experiential learning, teacher modelling, and the use of collaborative and engaging activities. Teachers differentiate instruction and assessment opportunities to encourage different ways of learning, to allow students to learn from and with each other, and to promote an awareness of and respect for the diverse and multiple ways of knowing that are relevant to and reflective of students’ lived experiences in classrooms, schools, and the world. When making connections between mathematics and real-life applications, teachers are encouraged to work in partnership with First Nations, Inuit, and Métis individuals, communities, and/or nations. Teachers may respectfully incorporate culturally specific examples that highlight First Nations, Inuit, and Métis cultures, histories, present-day realities, ways of knowing, and contributions, to** **infuse Indigenous knowledges and perspectives meaningfully and authentically into the mathematics program. In this way, culturally specific examples centre Indigenous students as mathematical thinkers, and strengthen learning and course content so that all students continue to learn about diverse cultures and communities in a respectful and informed way. Students’ mind, body, and spirit are nourished through connections and creativity.

More information on equity and inclusive education can be found in the “Human Rights, Equity, and Inclusive Education” subsection of “Considerations for Program Planning”.

### Principles Underlying the Grade 9 Mathematics Curriculum

**A mathematics curriculum is most effective when it values and honours the diversity that exists among students and within communities.**

The Grade 9 mathematics curriculum is based on the belief that all students can and deserve to be successful in mathematics. In particular, an inclusive curriculum is built on the understanding that not all students necessarily learn mathematics in the same way, use the same resources (e.g., tools and materials), or learn within the same time frames. Setting high academic expectations and building a safe and inclusive community of learners requires the purposeful use of a variety of instructional and assessment strategies and approaches that build on students’ prior learning and experiences, and create an optimal and equitable environment for mathematics learning. The curriculum emphasizes the need to eliminate systemic barriers and to serve students belonging to groups that have been historically disadvantaged and underserved in mathematics education.**A robust mathematics curriculum is essential for ensuring that all students reach their full potential.**The Grade 9 mathematics curriculum challenges all students by including learning expectations that build on students’ prior knowledge and experience; involve higher-order thinking skills; and require students to make connections between their lived experiences, mathematical concepts, other subject areas, and situations outside of school. This learning enables all students to gain a powerful knowledge of the usefulness of the discipline and an appreciation of the histories and importance of mathematics.

**A mathematics curriculum provides all students with the fundamental mathematics concepts and foundational skills they require to become capable and confident mathematics learners.**The Grade 9 mathematics curriculum provides a balanced approach to the teaching and learning of mathematics. It is based on the belief that all students learn mathematics most effectively when they can build on prior knowledge to develop a solid understanding of the concepts and skills in mathematics, and when they are given opportunities to apply these concepts and skills as they solve increasingly complex tasks and investigate mathematical ideas, applications, and situations in everyday contexts. As students continue to explore the relevance of mathematics, they further develop their identity and agency as capable mathematics learners.

**A progressive mathematics curriculum includes the strategic integration of technology to support and enhance the learning and doing of mathematics.**The Grade 9 mathematics curriculum strategically integrates the use of appropriate technologies to support all students in developing conceptual understanding and procedural fluency, while recognizing the continuing importance of students’ mastering the fundamentals of mathematics. For some students, assistive technology also provides an essential means of accessing the mathematics curriculum and demonstrating their learning. Students develop the ability to select appropriate tools and strategies to perform particular tasks, to investigate ideas, and to solve problems. The curriculum sets out a framework for learning important skills, such as problem solving, coding, and modelling, as well as opportunities to develop critical data literacy, information literacy, and financial literacy skills.

**A mathematics curriculum acknowledges that the learning of mathematics is a dynamic, gradual, and continuous process, with each stage building on the last.**The Grade 9 mathematics curriculum is dynamic, continuous, and coherent and is designed to support all students in developing an understanding of the interconnected nature of mathematics. Students come to understand how concepts develop and how they build on one another. As students communicate their reasoning and findings, they move towards new understandings. Teachers observe and listen to all students and then responsively shape instruction in ways that foster and deepen student understanding of important mathematics. The fundamental concepts, skills, and processes introduced in the elementary grades support students in extending their learning in the secondary grades.

**A mathematics curriculum is integrated with the world beyond the classroom.**The Grade 9 mathematics curriculum provides opportunities for all students to investigate and experience mathematical situations they might find outside the classroom and develop an appreciation for the beauty and wide-reaching nature and importance of mathematics. The overall curriculum integrates and balances concept development and skill development, including social-emotional learning skills, as well as the use of mathematical processes and real-life applications.

**A mathematics curriculum motivates students to learn and to become lifelong learners.**The Grade 9 mathematics curriculum is brought to life in the classroom, where students develop mathematical understanding and are given opportunities to connect their knowledge and skills to wider contexts and other disciplines. Making connections to the world around them stimulates their interest and motivates them to become lifelong learners with healthy attitudes towards mathematics. Teachers bring the mathematics curriculum to life using their knowledge of:

- the mathematics curriculum;
- the backgrounds and identities of all students, including their past and ongoing experiences with mathematics and their learning strengths and needs;
- mathematical concepts and skills, and the ways in which they are connected across the strands, other grades, other disciplines, and the world outside the classroom;
- instructional approaches and assessment strategies best suited to meet the learning needs of each student;
- resources designed to support and enhance the achievement of and engagement with the curriculum expectations, while fostering an appreciation for and joy in mathematics learning.

### Roles and Responsibilities

#### Students

It is essential that all students continue to develop a sense of responsibility for and ownership of their own learning as they begin their journey through secondary school. Mastering the skills and concepts connected with learning in the mathematics curriculum requires a commitment to:

- continual and consistent personal reflection and goal setting;
- a belief that they are capable of succeeding in mathematics;
- developing the skills to persevere when taking on new challenges;
- connecting prior experiences, knowledge, skills, and habits of mind to new learning;
- a willingness to work both independently and collaboratively in an inclusive environment;
- dedication to ongoing practice;
- a willingness and an ability to receive and respond to meaningful feedback and ask questions to clarify understanding;
- a willingness to explore new learning in mathematics and share insights and experiences.

Through ongoing practice and reflection, all students can develop a strong and healthy mathematical identity whereby they value and appreciate mathematics as a discipline, feel themselves to be confident and competent mathematics learners, and understand what successful mathematics learning and being an effective mathematician look like.

Students’ experiences influence their attitudes towards mathematics education and can have a significant impact on their engagement with mathematics learning and their subsequent success in achieving the expectations. Students who are engaged in their learning and who have opportunities to solve interesting, relevant, and meaningful problems within a supportive and inclusive learning environment are more likely to adopt practices and behaviours that support mathematical thinking. More importantly, they are more likely to be successful in their learning, which contributes to their enjoyment of mathematics and increases their desire to pursue further mathematics learning.

With teacher support and encouragement, students learn that they can apply the skills they acquire in mathematics to other contexts and subjects. For example, they can apply the problem-solving skills they develop in mathematics to their study of the science and Canadian and world studies curricula. They can also make connections between their learning and life beyond the classroom. For example, when presented with an issue or a contextually relevant STEM-based (science, technology, engineering, and mathematics–based) problem, they can look for potential applications of mathematical modelling. They can also begin to identify how mathematical modelling can be used to answer important questions related to global health, the environment, and sustainable, innovative development, or to address various issues that are relevant to their lives and communities.

#### Parents

Parents are significant role models for their children and play an integral part in their children’s experiences with mathematics. It is important for schools and parents, and in some situations, caring and trusted adults in students’ lives who are not their parents, to work together to ensure that they provide a mutually supportive framework for young people’s mathematics education. Research assures us of the positive impact of parent engagement and parent-child communication about mathematics on student success.

Parents can play a role in their children’s success by speaking positively about mathematics and modelling the attitude that mathematics is enjoyable, worthwhile, and valuable. By encouraging their children to acknowledge challenges, to persevere when solving problems, and to believe that they can succeed in mathematics, parents help them build self-confidence and a sense of identity as mathematics learners.

Parents can support their children’s mathematics success by showing an interest in what their children are learning. Parents are encouraged to engage with mathematics alongside their children by asking about their experiences in class and by finding ways to apply what is being learned in class to everyday contexts. Mathematics is everywhere, and parents can help their children make connections between what they are learning at school and everyday experiences at home and in the community, using tasks such as making appropriate choices when shopping, or saving for future needs. Parents can include their children in the things they do themselves that involve mathematics, such as estimating the amount of material needed to redecorate or renovate a room, or the quantities of ingredients needed to cook a meal. Through family activities, such as enjoying mathematics-based puzzles and games, making crafts, and beading jewelry together, parents can create opportunities for mental mathematics estimations and calculations and for making predictions. Parents can support their children’s learning by encouraging them to complete their mathematics tasks, to practice new skills and concepts, to apply new mathematics learning to experiences at home, and to connect mathematical experiences at home to learning at school.

As students begin their journey through secondary school, parents can help them consider how mathematics may play a role in their future by talking about education and career goals or connecting with community partners to gather information. Parents can help their children make connections between what they are learning, potential careers, and their future choice of postsecondary pathways – such as apprenticeship, skilled trades, community living, college, university, or the workplace.

Schools offer a variety of opportunities for parents t