# MPM2D(10年级数学)

Course Title: Principles of Mathematics

Course code: MPM2D

Credit value: 1.0

Pilot course: MPM1D or MFM1P or MPM1H

Course Description

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.

Overall Curriculum Expectations

 A. Quadratic Relations of the Form y = ax2 + bx + c A1 determine the basic properties of quadratic relations; A2 relate transformations of the graph of y = x2 to the algebraic representation y = a(x - h)2 + k; A3 solve quadratic equations and interpret the solutions with respect to the corresponding relations; A4 solve problems involving quadratic relations. B. Analytic Geometry B1 model and solve problems involving the intersection of two straight lines; B2 solve problems using analytic geometry involving properties of lines and line segments; B3 verify geometric properties of triangles and quadrilaterals, using analytic geometry. C. Trigonometry C1 use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity; C2 solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem; C3 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.