M’Learnin Student Centre

 COURSE OUTLINE COURSE TITLE Principles of Mathematics COMMON COURSE CODE MPM2D GRADE 10 COURSE TYPE Academic CREDIT VALUE 1.0 PREREQUISITE Grade 9 Academic Math CURRICULUM POLICY The Ontario Curriculum: Mathematics (Revised 2005) OTHER DOCUMENT Growing Success (First Edition, 2010) DEPARTMENT Mathematics DEVELOPMENT DATE January 2020 REVISION DATE Ongoing NUMBER OF SCHEDULED 110 HOURS

COURSE DESCRIPTION/RATIONALE

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

Throughout this course, students will:

1. PROBLEM SOLVING
• develop, select, apply, and compare a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
1. REASONING AND PROVING
• develop and apply reasoning skills (e.g., recognition of relationships, generalization through inductive reasoning, use of counter-examples) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;

1. REFLECTING
• demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
1. SELECTING TOOLS AND COMPUTATIONAL STRATEGIES
• select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
1. CONNECTING
• make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
1. REPRESENTING
• create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
1. COMMUNICATING
• communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.

OUTLINE OF COURSE UNITS

 Unit Descriptions Time and Sequence Unit# 1 Quadratic Relations of the Form y ax2 = + bx + c 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. 36 hours Unit# 2 Analytic Geometry   By the end of this unit, 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. 36 hours Unit# 3 Trigonometry By the end of this course, students will: • 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. 38 hours Final Assessment 3 hours final exam culminating activity, worth 30% of the final grade, meant as a summative evaluation of all strands. TOTAL 110 hours