Grade 9 : Principles of Mathematics
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.
UNIT CONTENT AND COURSES OF DELIVERY
Number Sense and Algebra (25 hours)
It includes expectations describing numeric skills that students are expected to consolidate and apply, along with estimation and mental computation skills, as they solve problems and learn new material throughout the course. The strand includes the algebraic knowledge and skills necessary for the study and application of relations. In the Principles course, the strand covers the basic exponent rules, manipulation of polynomials with up to two variables, and the solving of first-degree equations.
Linear Relations (30 hours)
Students develop initial understandings of the properties of linear relations as they collect, organize, and interpret data drawn from a variety of real-life situations (applying knowledge gained in the Data Management strand of the elementary school program) and create models for the data. Students then develop, make connections among, and apply various representations of linear relations and solve related problems.
Analytic Geometry (25 hours)
Students will extend the initial experiences of linear relations into the abstract realm of equations in the form y = mx + b, formulas, and problems.
Measurement and Geometry (30 hours)
Extends students’ understandings from Grade 8 to include the measurement of composite two-dimensional shapes and the development of formulas for, and applications of, additional three-dimensional figures. Furthermore, in measurement, students investigate the effect of varying dimensions (length and width) on a measure such as area. Students in the Principles course conduct similar investigations in connection with volume and surface area. Examination of such relationships leads students to make conclusions about shapes and figures. In geometry, the knowledge students acquired in Grade 8 about the properties of two-dimensional shapes is extended through investigations that broaden their understanding of the relationships among the properties.
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