Principles of Mathematics – Canadian International Secondary School

Course ID

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.

Overall Curriculum Expectations

Number Sense and Algebra

demonstrate an understanding of the exponent rules of multiplication and division, and apply them to simplify expressions;
manipulate numerical and polynomial expressions, and solve first-degree equations.

Linear Relations

apply data-management techniques to investigate relationships between two variables;
demonstrate an understanding of the characteristics of a linear relation;
connect various representations of a linear relation.

Analytic Geometry

determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity;
determine, through investigation, the properties of the slope and y-intercept of a linear relation;
solve problems involving linear relations.

Measurement and Geometry

determine, through investigation, the optimal values of various measurements;
solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures;
verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.

A variety of assessments for and as learning are conducted on a regular basis to allow ample opportunities for students to improve and ultimately demonstrate their full range of learning.

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Students tend to learn best by engaging in a variety Students tend to learn best by engaging in a variety of teaching activities in a math course. It is important, therefore, that students be provided the opportunities to learn in a variety of ways – individually, cooperatively, independently, with teacher direction, through hands-on experience, through examples followed by practice. In mathematics, students are required to learn concepts, procedures, and processes and to acquire skills, and they become competent in these various areas with the aid of the instructional and learning strategies best suited to the particular type of learning. The approaches and strategies used in the classroom to help students meet the expectations of this curriculum will vary according to the object of the learning and the needs of the students.

Teaching Approaches

Teachers in mathematics programs are expected to:

Clarify the purpose for learning

Help students activate prior knowledge

Differentiate instruction for individual students and small groups according to need

Explicitly teach and model learning strategies

Encourage students to talk through their thinking and learning processes

Provide many opportunities for students to practise and apply their developing knowledge and skills

apply effective teaching approaches involve students in the use of higher-level thinking skill

Encourage students to look beyond the literal meaning of texts

Clarify the purpose for learning

The Role of Technology in Mathematics

Information and communication technology (ICT) provides a range of tools that can significantly extend and enrich teachers’ instructional strategies and support students’ learning in mathematics. Teachers can use ICT tools and resources both for whole-class instruction and to design programs that meet diverse student needs. Technology can help to reduce the time spent on routine mathematical tasks and to allow students to devote more of their efforts to thinking and concept development. Useful ICT tools include simulations, multimedia resources, databases, sites that gave access to large amounts of statistical data, and computer-assisted learning modules.

Applications such as databases, spreadsheets, dynamic geometry software, dynamic statistical software, graphing software, computer algebra systems (CAS), word-processing software, and presentation software can be used to support various methods of inquiry in mathematics. The technology also makes possible simulations of complex systems that can be useful for problem solving purposes or when field studies on a particular topic are not feasible.

Information and communications technology can also be used in the classroom to connect students to other schools, at home and abroad, and to bring the global community into the local classroom.

Career Education in Mathematics

Teachers can promote students’ awareness of careers involving mathematics by exploring applications of concepts and providing opportunities for career-related project work. Such activities allow students the opportunity to investigate mathematics-related careers compatible with their interests, aspirations, and abilities.

Students should be made aware that mathematical literacy and problem solving are valuable assets in an ever-widening range of jobs and careers in today’s society. The knowledge and skills students acquire in mathematics courses are useful in fields such as science, business, engineering, and computer studies; in the hospitality, recreation, and tourism industries; and in the technical trades.

Health and Safety in Mathematics

Although health and safety issues are not normally associated with mathematics, they may be important when the learning involves fieldwork or investigations based on experimentation. Out-of-school fieldwork can provide an exciting and authentic dimension to students’ learning experiences. It also takes the teacher and students out of the predictable classroom environment and into unfamiliar settings. Teachers must preview and plan activities and expeditions carefully to protect students’ health and safety.