Page 30 - Math 9-10 (2009)

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Principles of Mathematics, Grade 9, Academic (MPM1D)
This course enables students to develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. 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.