Page 12 - Math 9-10 (2009)

THE PROGRAM IN MATHEMATICS 11
The strands in the two Grade 10 courses have similarities, but there are significant differences between them in terms of level of abstraction and degree of complexity. Both courses contain the strand Quadratic Relations in the Form y = ax2 + bx + c. The difference between the strand in the Principles course and its counterpart in the Foundations course lies in the greater degree of algebraic treatment required in the Principles course. Both strands involve concrete experiences upon which students build their understanding of the abstract treatment of qua- dratic relations. In the Foundations course, problem solving relates to the interpretation of graphs that are supplied to students or generated by them using technology. In the Principles course, problem solving involves algebraic manipulation as well as the interpretation of sup- plied or technologically generated graphs, and students also learn the techniques involved in sketching and graphing quadratics effectively using pencil and paper.
Both Grade 10 courses extend students’ understanding of linear relations through applications (in the Analytic Geometry strand of the Principles course and in the Modelling Linear Relations strand of the Foundations course). Students in the Foundations course begin by extending their knowledge into the abstract realm of equations in the form y = mx + b, for- mulas, and problems. While students in both courses study and apply linear systems, students in the Principles course solve multi-step problems involving the verification of properties of two-dimensional shapes on the xy-plane. The topic of circles on the xy-plane is introduced in the Principles course as an application of the formula for the length of a line segment.
In both the Trigonometry strand of the Principles course and the Measurement and Trigonometry strand of the Foundations course, students apply trigonometry and the proper- ties of similar triangles to solve problems involving right triangles. Students in the Principles course also solve problems involving acute triangles. Students in the Foundations course begin to study the imperial system of measurement, and apply units of measurement appropriately to problems involving the surface area and volume of three-dimensional figures.