This course enables students to broaden their understanding of relations, extend their skills in multi-step problem solving, and continue to develop their abilities in abstract reasoning. Students will model linear and quadratic relationships arising from a variety of contexts. Using trigonometric ratios and analytic geometry techniques, students will learn how to find exact measures in geometric contexts, as opposed to the approximate measures they have found using scale drawings and measurement tools. Geometric relationships investigated in Grade 9 will be confirmed, analytically, in specific cases, and students will be introduced to proof in general. Algebraic skills will be extended to generate factored, expanded, and completed square forms of quadratic expressions, and to solve linear systems and quadratic equations. Fundamental mathematical ideas of modelling, patterning, optimization, and superimposing a grid onto a geometric situation are reinforced. Connections among the various strands of the course are intentionally developed.

This course enables students to consolidate their understanding of key mathematical concepts through hands-on activities and to extend their problem-solving experiences in a variety of applications. Students solve proportions and recognize when it is appropriate to use proportional reasoning and when it is not. Correct use of proportions is a very important skill in many learning, working, and leisure activities. Percentage, ratio, and rate work from earlier grades is captured in this new light, as are linear relationships. Similar triangles and trigonometric models for right-triangle problems provide new applications of proportions. Quadratic applications serve as contrasts to proportional reasoning. New algebraic skills for quadratics are introduced and practiced. Algebraic skills are extended to include solution of linear systems and some quadratic equations, and some algebraic manipulation of quadratic expressions.

This Grade 10 Mathematics - is an essentially developed optional course, is designed to provide additional experiences in mathematics that may help the student in the Grade 11 Workplace Mathematics course. The students for whom this course is designed will have had varying degrees of success in learning mathematics. They are students from the Grade 9 Essential Mathematics course who intend to take the Grade 11 Workplace Mathematics course. They are students who have experienced significant difficulty in previous mathematics courses and may not be ready to work at the level demanded by the Grade 11 course. Students need to continue reinforcing and developing skills from Grade 9 and to continue building the necessary base for success in Grade 11. Repetition of skills, including repeated exposure to technology, in a diversity of contexts, is an important strategy to use since students may take longer to consolidate skills and concepts.
In order for students to complete their work thoroughly, and to achieve an appropriate level of understanding and a mastery of skills, it is beneficial for them to have more time to complete the assignments in a structured, well-organized environment. Students should be encouraged to work in pairs or in small groups, but increasing independence is the goal. This does not imply that a formal co-operative learning structure must be in place. At this level, students often find comfort and confidence when allowed to sit near a friend as they both complete the same assignment.
The Grade 11 Workplace course requires that students spend time solving authentic problems and using technology. A comfort level must be reached in these areas so that students are more willing to take risks and to try to solve authentic problems. Providing opportunities to work with mathematics within a real-life context of high student interest provides a vehicle that can help to make this happen. This context helps the students develop a strategy and apply it, allowing them to complete a solution which otherwise might be very abstract and intimidating.