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Course Outline | Math | Grade 10 | MPM2D

Explorer Hop Academy

DEPARTMENT: Mathematics     


COURSE DEVELOPMENT DATE: August 2021(Revision August 2022) 

COURSE: Principles of Mathematics, Grade 10 



PREREQUISITE: De-streamed Mathematics, Grade 9


COURSE CURRICULUM: Ontario Curriculum:  Grades 9 and 10 Mathematics (2005). A copy of this document is available online at:


This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract  reasoning. Students will explore quadratic relations and their applications; solve and apply linear  systems; verify properties of geometric figures using analytic geometry; and investigate the  trigonometry of right and acute triangles. Students will reason mathematically and communicate their  thinking as they solve multi-step problems. 


By the end of this course, students will: • determine the basic properties of quadratic relations; • relate transformations of the graph of y = x2 to the algebraic representation y=a(x–h)2 +k; • solve quadratic equations and interpret the solutions with respect to the corresponding relations; • solve problems involving quadratic relations; • model and solve problems involving the intersection of two straight lines; solve problems using analytic geometry involving properties of lines and line segments; • verify geometric properties of triangles and quadrilaterals, using analytic geometry;  • use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity; • solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem; • solve problems involving acute triangles,• using the sine law and the cosine law.

In September 2021, the ministry implemented a de-streamed Grade 9 mathematics course (MTH1W). Students who have earned a credit in this course are well prepared for success in Grade 10 mathematics.

To support students in their transition from MTH1W to MPM2D, the ministry is issuing this addecdum to MPM2D, effective September 2022. It includes three new specific expectations under an existing overall expectation. As set out on page 38 of Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools (2010), all specific expectations must be accounted for in instruction and assessment, but evaluation focuses on students’ achievement of the overall expectation.

Analytic Geometry Existing Overall Expectation

By the end of this course, students will:

  • model and solve problems involving the intersection of two straight lines.

New Specific Expectations

By the end of this course, students will:

  • identify the relationship between the slopes of parallel and perpendicular lines, and use this relationship to solve related problems;
  • develop the formula for the slope of a line (i.e., ), and use this formula to determine
    the equations of lines, given information about the lines (e.g., a graph of a line, a table of values, the coordinates of two points);
  • represent the equations of lines in different forms (e.g., y = mx + b, Ax + By + C = 0, Ax + By = D) and translate between these forms, as appropriate for the context.1


  1. Quadratic Functions (25 hours): In this unit students will explore properties of quadratic relations by graphing  parabolas and creating a table of values to determine the second differences. Students will identify  key features of a parabola and use technology to explore transformations of quadratic relations in  vertex form. Students will communicate their understanding of quadratic relation transformations  using key terminology (reflection, stretch/compression, translations), as well as domain and range. 
  2. Quadratic Equations (30 hours): Students will extend their learning of quadratic relations by expanding and  simplifying second-degree polynomials and factoring polynomial expressions involving common  factors, trinomials, difference of squares, and perfect square trinomials. Students will solve quadratic  equations using a variety of techniques such as graphing, factoring, quadratic formula, and  completing the square. Students will use their knowledge to connect these concepts to real life  scenarios (height of a ball over elapsed time). 
  3. Analytic Geometry (30 hours): Students will solve systems of two linear equations involving two variables  using substitution or elimination and solve problems that arise from realistic situations described in  words. Students will determine the midpoint/length of a line segment, determine the equation for a  circle, and solve problems to deepen understanding of geometric shapes and properties. 
  4. Trigonometry (25 hours) : Students will explore properties of similar triangles to solve problems in realistic  situations. Students will be introduced to the relationship between the ratio of two sides in a right  triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine,  cosine, and tangent ratios. Students will also explore sine and cosine laws in acute triangles and  determine the measures of sides and angles to solve problems. 

Course Strands

The course will cover the following strand as outlined in the Ontario Curriculum:  Grades 9 and 10 Mathematics (2005). A copy of this document is available online at:

The details of the strands are included in the above link.

Students who have earned a credit in de-streamed Grade 9 Mathematics (MTH1W) will bring with them supplementary learning compared to Grade 9, Academic (MPM1D). The chart below high- lights this learning as it relates to the strands in MPM2D.

Strands in MPM2D

Related Learning in MTH1W

Quadratic Relations of the Form y = ax2 + bx + c

In MTH1W, students:

represented and described characteristics of non-linear relations; collected and analysed data involving non-linear relations;

translated, reflected, and rotated lines defined by y = ax;

evaluated powers involving integer exponents;

compared algebraic expressions using various methods, including simplification.

Analytic Geometry

In MTH1W, students:

  • solved linear systems using the algebraic method of comparison in addition to the graphical method;
  • analysed the effects that positive and negative signs have on the value of rates in various contexts, including rates of change;
  • identified lines defined by equations and regions defined by inequalities;
  • analysed geometric relationships including properties of circles and triangles.


In MTH1W, students:

solved problems involving real-life applications of proportions in various contexts, including geometry.

Teaching and Learning Strategies

Throughout the course, students are exposed to a variety of genres, and they develop skills to

evaluate the effectiveness of texts which include short stories, non-fiction texts, poems, videos, and other media and texts from a wide range of resources and periods.

Students will identify and use various strategies that include building vocabulary, learning to understand the organization of texts, and developing knowledge of conventions. Throughout the course, students develop into stronger readers, writers, and oral communicators by connecting literature and language to real world experiences. 

Teachers will differentiate instruction to meet the diverse learning needs of students. Through the resources in the learning management system and weekly meets, students will have the opportunity to track their growth and progression, to reflect on the achievements, and to set goals for the journey ahead in order to develop their 21st century skills.

Using a variety of instructional strategies, teachers will provide numerous opportunities for students to develop skills of inquiry, problem solving, and communication as they investigate and learn fundamental concepts. The integration of critical thinking and critical literacy will provide a powerful tool for reasoning and problem solving, and will be reflected in a meaningful blend of both process and content. 

Throughout the course, students will:

- Think Critically: students will learn to critically analyze texts and to use implied and stated evidence

from texts to support their analyses. Students use their critical thinking skills to identify perspectives in

texts, including biases that may be present.

- Generate ideas and topics: students will be encouraged to design their own approaches to the material

by maintaining frequent online communication with teachers who will facilitate choice in how students

respond to topics and questions, and by encouraging students' independent thinking through discussions.

- Research: various approaches to researching will be practiced. Students will learn how to cite sources

and provide a Works Cited page at the end of longer assignments using MLA formatting.

- Identify and develop skills and strategies: through modeling of effective skills, students will learn to

choose and utilize varied techniques to become effective readers, writers, and oral communicators.

- Communicate: numerous opportunities will be given to students to write and communicate orally, as well as develop listening skills.

- Produce published work and make presentations: students will engage in the editing and revising

process, including self-revision, peer revision, and teacher revision all of which strengthen texts with

the aim to publish or present student work.

- Reflecting: through the use of weekly reflections, drafts, discussions, and other elements of the course,

students will reflect on the learning process, focus on areas for improvement, set goals, and make

extensions between course content and their personal experiences.


Our school's assessment and evaluation policy is based on seven fundamental principles, and follows the guidelines in the Ontario Ministry of Education’s Growing Success document. Teachers are expected to understand and follow these seven principles in order to guide the collection of purposeful information that will guide instructional decisions, promote student engagement, and improve student learning.

To ensure that assessment, evaluation, and reporting are valid, reliable, and they lead to the improvement of all students, teachers use assessment and evaluation strategies that:

  1. are fair, transparent, and equitable for all students
  2. support all students
  3. are related to curriculum expectations, learning goals, and whenever possible, are related to the

interests, learning styles, preferences, needs, and experiences of students

  1. are clearly communicated to students and parents at critical points throughout the academic year
  2. are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities

for students to demonstrate the potential and learning

  1. provide descriptive feedback that is meaningful and timely to support learning, growth, and


  1. develop student self-assessment skills to enable them to assess their own learning, set goals, and plan

next steps for their learning

There are three forms of assessment that will be used throughout this course:

Assessment for Learning: Assessment for learning will directly influence student learning by reinforcing the connections between assessment and instruction, and provide ongoing feedback to the student. Assessment for learning occurs as part of the daily teaching process and helps teachers form a clear picture of the needs of the students because students are encouraged to be more active in their learning and associated assessment. Teachers gather this information to shape their classroom teaching.

Assessment as Learning: Assessment as learning is the use of a task or an activity to allow students the opportunity to use assessment to further their own learning. Self and peer assessments allow students  to reflect on their own learning and identify areas of strength and need. These tasks offer students the chance to set their own personal goals and advocate for their own learning.

The purpose of assessment as learning is to enable students to monitor their own progress towards achieving their learning goals.

Assessment of Learning: Assessment of learning will occur at or near the end of a period of learning; this summary is used to make judgments about the quality of student learning using established criteria, to assign a value to represent that quality and to communicate information about achievement to students and parents. 

Evidence of student achievement for evaluation is collected over time from three different sources – observations, conversations, and student products. Using multiple sources of evidence will increase the reliability and validity of the evaluation of student learning.

For a full explanation of assessment, evaluation, and reporting, kindly refer to the Growing Success document ( 

Program Planning Considerations

Teaching Approaches:  Teachers can use multiple teaching approaches including: 

  • Use prior knowledge from previous years to assess where tehy are in their mathematical growth. 
  • Incorporating successful classroom practices that involve students in activities that require higher-order thinking, with an emphasis on problem solving, this includes  the inquiry model of problem solving and this approach is still fundamental in the Grade 9 and 10 program.
  • Use Diversity of teaching methods: The approaches and strategies used in the classroom to help students meet the expectations of this curriculum will vary according to the object of the learning and the needs of the students.
  • Using Manipulatives: These concrete learning tools invite students to explore and represent abstract mathematical ideas in varied, concrete, tactile, and visually rich ways. Manipulatives are also a valuable aid to teachers. By analysing students’ concrete representations of mathematical concepts and listening carefully to their reasoning, teachers can gain useful insights into students’ thinking and provide supports to help enhance their thinking.
  • Using Well-Chosen Contexts for learning:  Contexts that are broad enough to allow students to investigate initial understandings, identify and develop relevant supporting skills, and gain experience with varied and interesting applications of the new knowledge. Such rich contexts for learning open the door for students to see the “big ideas” of mathematics – that is, the major underlying principles, such as pattern or relationship. This understanding of key principles will enable and encourage students to use mathematical reasoning throughout their lives.

Promoting Positive Attitudes: 

  •  Students’ attitudes have a significant effect on how they approach problem solving and how well they succeed in mathematics. Teachers can help students develop the confidence they need by demonstrating a positive disposition towards mathematics, explaining that there are several ways to find a solution, and encouraging problem solving. 
  • Encouraging students to develop the willingness to persist, to investigate, to reason and explore alternative solutions, and to take the risks necessary to become successful problem solvers.
  • Encouraging collaborative learning that enhances students’ understanding of mathematics. Working cooperatively in groups reduces isolation and provides students with opportunities to share ideas and communicate their thinking in a supportive environment as they work together towards a common goal. 

Planning Mathematics Programs for Exceptional Students:

Teachers should determine which option is appropriate for exceptional students

  • no accommodations or modifications; 
  • accommodations only; 
  • modified expectations,with the possibility of accommodations.

If the student requires either accommodations or modified expectations, or both, the relevant information, as described in the following paragraphs, must be recorded in his or her Individual Education Plan (IEP). For a detailed discussion of the ministry’s requirements for IEPs, see Individual Education Plans: Standards for Development, Program Planning, and Implementation, 2000 (referred to hereafter as IEP Standards, 2000). More detailed information about planning programs for exceptional students can be found in the Individual Education Plan (IEP): A Resource Guide, 2004. (Both documents are available at

Students Requiring Accommodations Only.

With the aid of accommodations alone, some exceptional students are able to participate in the regular course curriculum and to demonstrate learning independently. (Accommodations do not alter the provincial curriculum expectations for the course.) 

The accommodations required to facilitate the student’s learning must be identified in his or her IEP (see IEP Standards, 2000, page 11). A student’s IEP is likely to reflect the same accommodations for many, or all, courses. 

There are three types of accommodations. 

  • Instructional accommodations are changes in teaching strategies, including styles of presentation, methods of organization, or use of technology and multimedia. 
  • Environmental accommodations are changes that the student may require in the “Accommodations” refers to individualized teaching and assessment strategies, human supports, and/or individualized equipment. classroom and/or school environment, such as preferential seating or special lighting. 
  • Assessment accommodations are changes in assessment procedures that enable the student to demonstrate his or her learning, such as allowing additional time to complete tests or assignments or permitting oral responses to test questions (see page14 of IEP Standards, 2000, for more examples). If a student requires “accommodations only” in mathematics courses, assessment and evaluation of his or her achievement will be based on the appropriate course curriculum expectations and the achievement levels outlined in this document. 

Students Requiring Modified Expectations. 

Some exceptional students will require modified expectations, which differ from the regular course expectations. For most of these students, modified expectations will be based on the regular course curriculum, with changes in the number and/or complexity of the expectations. It is important to monitor, and to reflect clearly in the student’s IEP, the extent to which expectations have been modified. 

As noted in Section 7.12 of the ministry’s policy document Ontario Secondary Schools, Grades 9 to 12: Program and Diploma Requirements, 1999, the principal will determine whether achievement of the modified expectations constitutes successful completion of the course, and will decide whether the student is eligible to receive a credit for the course.This decision must be communicated to the parents and the student. 

When a student is expected to achieve most of the curriculum expectations for the course, the modified expectations should identify how they differ from the course expectations.When modifications are so extensive that achievement of the learning expectations is not likely to result in a credit, the expectations should specify the precise requirements or tasks on which the student’s performance will be evaluated and which will be used to generate the course mark recorded on the Provincial Report Card. Modified expectations indicate the knowledge and/or skills the student is expected to demonstrate and have assessed in each reporting period (IEP Standards, 2000, pages 10 and 11). 

Modified expectations represent specific, realistic, observable, and measurable achievements and describe specific knowledge and/or skills that the student can demonstrate independently, given the appropriate assessment accommodations.The student’s learning expectations must be reviewed in relation to the student’s progress at least once every reporting period, and must be updated as necessary (IEP Standards, 2000, page 11). If a student requires modified expectations in mathematics courses, assessment and evaluation of his or her achievement will be based on the learning expectations identified in the IEP and on the achievement levels outlined in this document.

If some of the student’s learning expectations for a course are modified but the student is working towards a credit for the course, it is sufficient simply to check the IEP box. If, however, the student’s learning expectations are modified to such an extent that the principal deems that a credit will not be granted for the course, the IEP box must be checked and the appropriate statement from Guide to the Provincial Report Card, Grades 9–12, 1999 (page 8) must be inserted.The teacher’s comments should include relevant information on the student’s demonstrated learning of the modified expectations, as well as next steps for the student’s learning in the course

Anti discrimination education in Mathematics: 

  • To ensure that all students in the province have an equal opportunity to achieve their full potential, the curriculum must be free from bias and all students must be provided with a safe and secure environment, characterized by respect for others, that allows them to participate fully and responsibly in the educational experience.

  •  Learning activities and resources used to implement the curriculum should be inclusive in nature, reflecting the range of experiences of students with varying backgrounds, abilities, interests, and learning styles. They should enable students to become more sensitive to the diverse cultures and perceptions of others, including Aboriginal peoples. For example, activities can be designed to relate concepts in geometry or patterning to the arches and tile work often found in Asian architecture or to the patterns used in Aboriginal basketry design. By discussing aspects of the history of mathematics, teachers can help make students aware of the various cultural groups that have contributed to the evolution of mathematics over the centuries.

  •  Finally, students need to recognize that ordinary people use mathematics in a variety of everyday contexts, both at work and in their daily lives. Connecting mathematical ideas to real-world situations through learning activities can enhance students’ appreciation of the role of mathematics in human affairs, in areas including health, science, and the environment. Students can be made aware of the use of mathematics in contexts such as sampling and surveying and the use of statistics to analyse trends. 

  • Recognizing the importance of mathematics in such areas helps motivate students to learn and also provides a foundation for informed, responsible citizenship. Teachers should have high expectations for all students.To achieve their mathematical potential, however, different students may need different kinds of support. Some boys, for example, may need additional support in developing their literacy skills in order to complete mathematical tasks effectively. For some girls, additional encouragement to envision themselves in careers involving mathematics may be beneficial. For example, teachers might consider providing strong role models in the form of female guest speakers who are mathematicians or who use mathematics in their careers.

Literacy and Inquiry/Research Skills:

 Literacy skills can play an important role in student success in mathematics courses. Many of the activities and tasks students undertake in math courses involve the use of written, oral, and visual communication skills. For example, students use language to record their observations, to explain their reasoning when solving problems, to describe their inquiries in both informal and formal contexts, and to justify their results in small-group conversations, oral presentations, and written reports.

The language of mathematics includes special terminology.The study of mathematics consequently encourages students to use language with greater care and precision and enhances their ability to communicate effectively.The Ministry of Education has facilitated the development of materials to support literacy instruction across the curriculum. 

Helpful advice for integrating literacy instruction in mathematics courses may be found in the following resource documents: 

  • Think Literacy: Cross-Curricular Approaches, Grades 7–12, 2003
  • Think Literacy: Cross-Curricular Approaches, Grades 7–12 – Mathematics: Subject-Specific Examples, Grades 7–9, 2004

 In all courses in mathematics, students will develop their ability to ask questions and to plan investigations to answer those questions and to solve related problems. Students need to learn a variety of research methods and inquiry approaches in order to carry out these investigations and to solve problems, and they need to be able to select the methods that are most appropriate for a particular inquiry. 

Students learn how to locate relevant information from a variety of sources, such as statistical databases, newspapers, and reports. As they advance through the grades, students will be expected to use such sources with increasing sophistication.They will also be expected to distinguish between primary and secondary sources, to determine their validity and relevance, and to use them in appropriate ways.

The Role of Technology in Mathematics:

Information and communication technology (ICT) provides a range of tools that can significantly extend and enrich teachers’ instructional strategies and support students’ learning in mathematics.Teachers can use ICT tools and resources both for whole-class instruction and to design programs that meet diverse student needs.Technology can help to reduce the time spent on routine mathematical tasks and to allow students to devote more of their efforts to thinking and concept development. 

Useful ICT tools include simulations, multimedia resources, databases, sites that gave access to large amounts of statistical data, and computer-assisted learning modules. Applications such as databases, spreadsheets, dynamic geometry software, dynamic statistical software, graphing software, computer algebra systems (CAS), word-processing software, and presentation software can be used to support various methods of inquiry in mathematics.

The technology also makes possible simulations of complex systems that can be useful for problem-solving purposes or when field studies on a particular topic are not feasible. Information and communications technology can also be used in the classroom to connect students to other schools, at home and abroad, and to bring the global community into the local classroom.

Career Education in Mathematics:

Teachers can promote students’ awareness of careers involving mathematics by exploring applications of concepts and providing opportunities for career-related project work. Such activities allow students the opportunity to investigate mathematics-related careers compatible with their interests, aspirations, and abilities. 

Students should be made aware that mathematical literacy and problem solving are valuable assets in an ever-widening range of jobs and careers in today’s society.The knowledge and skills students acquire in mathematics courses are useful in fields such as science, business, engineering, and computer studies; in the hospitality, recreation, and tourism industries; and in the technical trades.

Health and Safety in Mathematics:

Although health and safety issues are not normally associated with mathematics, they may be important when the learning involves fieldwork or investigations based on experimentation. Out-of-school fieldwork can provide an exciting and authentic dimension to students’ learning experiences. It also takes the teacher and students out of the predictable classroom environment and into unfamiliar settings. Teachers must preview and plan activities and expeditions carefully to protect students’ health and safety.

Program Planning Considerations: These considerations are based on the directives mentioned in the Ontario Curriculum: Grades 9 and 10 document which can be found here 


  • TRILLIUM BOOKSTORE: Addison Wesley Principles of Mathematics 10 © 2000
  • YouTube Resources: Mr. Boghossian:   and  others
  • Explorer Hop Academy Program Materials


The primary purpose of assessment and evaluation is to improve student learning. The Achievement Chart for Mathematics will guide all assessment and evaluation.  

Term Evaluation = 70% of total grade broken up as follow: 

Categories of Evaluation 

Term Work: 70% 

(based on conversations,  

observations, and products)

Final Summative: 30%

Knowledge and Understanding 


Final exam 30%

Thinking and Inquiry 






The final grade will be determined as follows: 

Term work and project  = 70% of final mark
Final exam = 30% of final mark


The six learning skills reported on the provincial report card are: Responsibility, Organization, Independent  Work, Collaboration, Initiative, and Self-Regulation. These are reported using a letter system of (E)  excellent, (G) good, (S) satisfactory and (N) needs improvement. These will be assessed using checklists,  student self-assessment, and teacher assessment. Learning skills assessment does not count toward the  course mark but proficiency with these skills is essential for achieving success. 


Participating in online courses is a privilege. You are expected to behave in an appropriate manner while  logged into your online course(s). Any inappropriate use of language, use of the site facilities for purposes  other than course related activities or malicious actions taken against others through these facilities are not  permitted. These violations will be dealt with in a severe manner and may result in suspension or expulsion  from online learning. Please remember, your actions within the site can and will be monitored. Any  communications on the Internet, whether through email, private chat room, or other methods are not private.  Be aware that anything you communicate may be viewed by others. If you don't want it known, do not type it  into your computer. 


Students are expected to take responsibility in the completion of their course by creating a schedule in  advance and meeting deadlines. You are expected to write every test/evaluation as well as complete all  summative assessments. 

Notebooks need to be well kept and organized. You will get homework for every lesson. If you are having  trouble with the homework or with concepts covered in class, reach out to your instructor for support.

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