Grade: Grade 10
Course Title: Principles of Mathematics
Course code: MPM2D
Course Type: Academic
Credit value: 1.0
Pilot course: MPM1D or MFM1P or MPM1H
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.
Unit Titles and Descriptions
Linear relationships are not only important to understand for everyday use - understanding the interplay between distance and time for the calculation of speed, or rates of change in business, for example. Linear relationships are also fundamental to more complex forms of mathematics. This unit reviews the concepts of linear algebra that were developed in Grade 9, and expands upon important procedures such as rearranging equations and developing accurate graphs.
Expanding upon the foundation built in the last unit, the equations of lines and line segments will be examined. Developing logical and mathematical methods for determining line segment length and midpoint, based upon an equation or upon coordinates, will enable a deeper study of geometric shapes and properties.
To progress beyond a certain point in any mathematics, some rather advanced algebraic skills must first be mastered. In this unit, students will consider various operations on monomials, binomials and polynomials. Factoring of binomials and trinomials will be studied.
Until this point, all algebraic relations that have been considered have been linear. In this unit, second-order functions are introduced. The concept of the function will be studied; the domain, range and simple transformations of quadratic functions will be explored; and students will learn how to complete the square.
Having explored quadratic functions graphically, the algebra of quadratic equations will be considered. The Quadratic Formula, which will be used extensively throughout all future math courses, will be derived and used.
Triangles have a particularly significant role to play in mathematics. This unit is all about triangles and how they can be used to describe many phenomena in the universe. A review of Pythagorean Theorem will start the discussion, which will lead the student through sine, cosine and tangent ratios, the sine law and cosine law, and the ability to solve problems using these tools.
This is a proctored exam worth 30% of your final grade.
Overall Curriculum Expectations
A. Quadratic Relations of the Form y = ax2 + bx + c
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.
B. Analytic Geometry
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.
Teaching and Learning Strategies:
The over-riding aim of this course is to help students use the language of mathematics skillfully, confidently and flexibly, a wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests, and ability levels. The following mathematical processes are used throughout the course as strategies for teaching and learning the concepts presented.
● Problem Solving: This course scaffolds learning by providing students with opportunities to review and activate prior knowledge (e.g. reviewing order of operations from prior mathematics courses), and build off of this knowledge to acquire new skills. The course guides students toward recognizing opportunities to apply knowledge they have gained to solve problems.
● Connecting: This course connects the concepts taught to real-world applications (e.g. connecting quadratic equations to projectile motion problems).
● Representing: Through the use of examples, practice problems, and solution videos, the course models various ways to demonstrate understanding, poses questions that require students to use different representations as they are working at each level of conceptual development - concrete, visual or symbolic, and allows individual students the time they need to solidify their understanding at each conceptual stage.
● Self-Assessment: Through the use of interactive activities (e.g. multiple choice quizzes, and drag-and-drop activities) students receive instantaneous feedback and are able to self-assess their understanding of concepts.