AVAILABILITY: Full-time – All Campuses, Part-time – All campuses, Private – All campuses, Blyth Academy Online

THE ONTARIO CURRICULUMMathematics

## Course Overview

MPM2D online 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. In MPM2D online, students will reason mathematically and communicate their thinking as they solve multi-step problems. Whether taken as an online course or in-person on one of the Blyth campuses, this course will prepare students for future coursework in mathematics with a focus on real-world usage. Both online and in-person options for this class follow the same curriculum and answer the same six essential questions on topics ranging from linear systems, geometry, trigonometry, quadratic expressions, and quadratic equations.

## Course Outline

You will find a course outline below created by Blyth Academy for Principles of Mathematics – Grade 10. Whether taken online or in-person on one of the Blyth campuses, the course outline remains the same. The course, using code MPM2D, is divided into six units: linear systems, analytic geometry, similar triangles and trigonometry, quadratic expressions, quadratic equations part 1, and quadratic equations part 2. The six units cover key topics in mathematics with a focus on their real-world applications.

Take the time to read over the details of the six units in this math class and learn more about how the answer to each unit’s essential question provides a foundation for using math in real-world applications and continued study in mathematics.

### UNIT ONE Linear Systems

Essential Question: How can mathematical expressions be analyzed to help us understand our world?

In this unit, students will investigate how to determine the point of intersection of two lines algebraically and graphically. students will apply their knowledge to examine real-world scenarios that can be modelled using a linear system of equations and interpret the meaning of a point of intersection through the lens of the real-world application.

### UNIT TWO Analytic Geometry

Essential Question: How can Geometry be used to analyze relationships between variables?

In this unit, students will investigate a series of tools that are useful in geometric problem-solving scenarios. Students will apply their understanding of analytic geometry tools to classify quadrilaterals based on their determined properties. Students will also combine their understanding of analytic geometry tools with their understanding of linear relations to solve complex geometry problems.

### UNIT THREE Similar Triangles and Trigonometry

Essential Question: How do effective problem-solvers approach problems that involve multiple steps?

In this unit, students will learn to analyze and classify triangles as similar or congruent. Students will also investigate the relationship between sides and angles in both right and non-right triangles. Students will apply their understanding of trigonometric ratios to determine unknown sides and angles, as well as solve problems that are encountered in the real-world.

Essential Question: How does representing expressions in different ways help to solve problems?

In this unit, students will develop strategies for representing trinomial expressions in different forms. Students will learn to select the appropriate strategy for any given problem. These skills are important and considered foundational for the remainder of this course and future mathematics studies.

### UNIT FIVE Quadratic Equations (Part I)

Essential Question: How can models be used to make predictions in real-world scenarios?

In this unit, students will investigate the properties of the vertex form of a quadratic relation and apply these properties to graph quadratic relations. Students will also develop the skills necessary for converting standard form to vertex form. Students will apply these skills to solve real-world problems involving maximums and minimums of quadratic models.

### UNIT SIX Quadratic Equations (Part II)

Essential Question: How can observed patterns be summarized in order to make informed predictions?

In this unit, students will develop an understanding of how factoring can be used to determine the x-intercepts of a quadratic relation. Students will investigate how the quadratic formula can be used to determine the x-intercepts when factoring is not possible. Students will make connections between the x-intercepts of a quadratic and real-world context, while also applying their new skills to solve real-world problems involving maximums and minimums of quadratic models.

### Assessment

The culminating project, which can be worked on at any time during the course, will be 10% of the final grade; the final exam will be 20% of the final grade. Please take the time to review the details of the culminating project and when to schedule the final exam, which requires 1.5 hours.

Please consult our Frequently Asked Questions Page or the Exam section within your course for more details on final exams and the exam fee. More information can also be found in our Student Handbook

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