Page 47 - Math 9-10 (2009)

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Principles of Mathematics, Grade 10, Academic (MPM2D)
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 inves- tigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Mathematical process expectations. The mathematical processes are to be integrated into student learning in all areas of this course.
Throughout this course, students will:
PROBLEM SOLVING
REASONING AND PROVING
REFLECTING
SELECTING TOOLS AND COMPUTATIONAL STRATEGIES
CONNECTING
REPRESENTING
COMMUNICATING
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develop,select,apply,andcompareavarietyofproblem-solvingstrategiesastheyposeand solve problems and conduct investigations, to help deepen their mathematical under- standing;
developandapplyreasoningskills(e.g.,recognitionofrelationships,generalization through inductive reasoning, use of counter-examples) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
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);
selectanduseavarietyofconcrete,visual,andelectroniclearningtoolsandappropriate computational strategies to investigate mathematical ideas and to solve problems;
makeconnectionsamongmathematicalconceptsandprocedures,andrelatemathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
createavarietyofrepresentationsofmathematicalideas(e.g.,numeric,geometric,alge- braic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
communicatemathematicalthinkingorally,visually,andinwriting,usingmathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.