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Courses in Mathematics, Grades 9 and 10

Strands

Grade 9 Courses

Strands and Subgroups in the Grade 9 Courses

The strands in the Grade 9 courses are designed to build on those in Grade 8, while at the same time providing for growth in new directions in high school. The strand Number Sense and Algebra builds on the Grade 8 Number Sense and Numeration strand and parts of the Patterning and Algebra strand. 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.

In the Foundations course, it covers operations with polynomials involving one variable and the solving of first-degree equations with non-fractional coefficients. The strand in the

Foundations course also includes expectations that follow from the Grade 8 Proportional

Reasoning strand, providing an opportunity for students to deepen their understanding of proportional reasoning through investigation of a variety of topics, and providing them with skills that will help them meet the expectations in the Linear Relations strand.

 

Grade 9 and Grade 10 Mathematics Courses Offered:

 

9 Essential Mathematics (Locally Developed) MAT1LK

9 Principles of Mathematics Academic MPM1D

9 Foundations of Mathematics Applied MFM1P

 

10 Essential Mathematics (Locally Developed) MAT2LK

10 Principles of Mathematics Academic MPM2D

  • -Prerequisite: Grade 9 Mathematics, Academic

    10 Foundations of Mathematics Applied MFM2P 

  • -Prerequisite: Grade 9 Mathematics, Academic or Applied

Academic courses develop students’ knowledge and skills through the study of theory and abstract

problems. These courses focus on the essential concepts of a subject and explore related concepts as well. They incorporate practical applications as appropriate.

Applied courses focus on the essential concepts of a subject, and develop students’ knowledge and skills through practical applications and concrete examples. Familiar situations are used to illustrate ideas, and students are given more opportunities to experience hands-on applications of the concepts and theories they study.

Essential courses focus on essential numeracy skills required in everyday life. All concepts are taught with concrete and practical skills and examples. Students are given many opportunities for hands-on applications of concepts.

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.

 

Foundations of Mathematics, Grade 9, Applied (MFM1P)

 

This course enables students to develop an understanding of mathematical concepts related to

introductory algebra, proportional reasoning, and measurement and geometry through investigation,

the effective use of technology, and hands-on activities. Students will investigate

real-life examples to develop various representations of linear relations, and will determine

the connections between the representations. They will also explore certain relationships that

emerge from the measurement of three-dimensional figures and two-dimensional shapes.

Students will consolidate their mathematical skills as they solve problems and communicate

their thinking.

 

Principles of Mathematics, Grade 10, Academic (MPM2D)

 

This course enables students to broaden their understanding of relationships and extend their

problem-solving and algebraic skills through investigation, the effective use of technology, and

abstract reasoning. Students will explore quadratic relations and their applications; solve and

apply linear systems; verify properties of geometric figures using analytic geometry; and investigate

the trigonometry of right and acute triangles. Students will reason mathematically and

communicate their thinking as they solve multi-step problems.

 

Foundations of Mathematics, Grade 10, Applied (MFM2P)

 

This course enables students to consolidate their understanding of linear relations and extend

their problem-solving and algebraic skills through investigation, the effective use of technology,

and hands-on activities. Students will develop and graph equations in analytic geometry;

solve and apply linear systems, using real-life examples; and explore and interpret graphs of

quadratic relations. Students will investigate similar triangles, the trigonometry of right

triangles, and the measurement of three-dimensional figures. Students will consolidate their

mathematical skills as they solve problems and communicate their thinking.

 

 

Courses in Grade 11 and Grade 12

 

Four types of courses are offered in the senior mathematics program: university preparation,

university/college preparationcollege preparation, and workplace preparation. Students

choose course types on the basis of their interests, achievement, and postsecondary goals.

 

The course types are defined as follows:

 

University preparation courses are designed to equip students with the knowledge and

skills they need to meet the entrance requirements for university programs.

 

University/college preparation courses are designed to equip students with the knowledge

and skills they need to meet the entrance requirements for specific programs offered at

universities and colleges.

 

College preparation courses are designed to equip students with the knowledge and

skills they need to meet the requirements for entrance to most college programs or for

admission to specific apprenticeship or other training programs.

 

Workplace preparation courses are designed to equip students with the knowledge and

skills they need to meet the expectations of employers, if they plan to enter the workplace

directly after graduation, or the requirements for admission to many apprenticeship or

other training programs.

 

University Preparation Courses

 

Grade 11 FUNCTIONS (MCR3U)

A. Characteristics of Functions

B. Exponential Functions

C. Discrete Functions

D. Trigonometric Functions

 

Grade 12 ADVANCED FUNCTIONS (MHF4U)

A. Exponential and Logarithmic Functions

B. Trigonometric Functions

C. Polynomial and Rational Functions

D. Characteristics of Functions

 

Grade 12 MATHEMATICS OF DATA MANAGEMENT (MDM4U)

A. Counting and Probability

B. Probability Distributions

C. Organization of Data for Analysis

D. Statistical Analysis

E. Culminating Data Management Investigation

 

Grade 12 CALCULUS AND VECTORS (MCV4U)

A. Rate of Change

B. Derivatives and Their Applications

C. Geometry and Algebra of Vectors

 

The Grade 11 university preparation course, Functions, builds on the concepts and skills developed in the Grade 9 and 10 academic mathematics courses. The course is designed to prepare students for Grade 12 mathematics courses that lead to one of many university programs, including science, engineering, social sciences, liberal arts, and education.

The concept of functions is introduced in the Characteristics of Functions strand of this course and extended through the investigation of two new types of relationships in the Exponential Functions and Trigonometric Functions strands. The Discrete Functions strand allows students, through the study of different representations of sequences and series, to revisit patterning and algebra concepts introduced in elementary school and make connections to financial applications involving compound interest and ordinary simple annuities.

The Grade 12 university preparation course Advanced Functions satisfies the mathematical prerequisite for some universities in areas that include business, social science, and health science programs. The strands in this course help students deepen their understanding of functions by revisiting the exponential and trigonometric functions introduced in Grade 11 to address related concepts such as radian measure and logarithmic functions and by extending prior knowledge of quadratic functions to explore polynomial and rational functions. The Characteristics of Functions strand addresses some of the general features of functions through the examination of rates of change and methods of combining functions.

The Grade 12 university preparation course Calculus and Vectors is designed to prepare students for university programs, such as science, engineering, and economics, that include a calculus or linear algebra course in the first year. Calculus is introduced in the Rate of Change strand by extending the numeric and graphical representation of rates of change introduced in the Advanced Functions course to include more abstract algebraic representations. The Derivatives and Their Applications strand provides students with the opportunity to develop the algebraic and problem-solving skills needed to solve problems associated with rates of change. Prior knowledge of geometry and trigonometry is used in the Geometry and Algebra of Vectors strand to develop vector concepts that can be used to solve interesting problems, including those arising from real-world applications.

 

The Grade 12 university preparation course Mathematics of Data Management is designed to satisfy the prerequisites for a number of university programs that may include statistics courses, such as those found in the social sciences and the humanities.

The expectations in the strands of this course require students to apply mathematical process skills developed in prerequisite courses, such as problem solving, reasoning, and communication, to the study of probability and statistics. The Counting and Probability strand extends the basic probability concepts learned in the elementary school program and introduces counting techniques such as the use of permutations and combinations; these techniques are applied to both counting and probability problems. The Probability Distributions strand introduces the concept of probability distributions; these include the normal distribution, which is important in the study of statistics. In the Organization of Data for Analysis strand, students examine, use, and develop methods for organizing large amounts of data, while in the Statistical Analysis strand, students investigate and develop an understanding of powerful concepts used to analyse and interpret large amounts of data. These concepts are developed with the use of technological tools such as spreadsheets and Fathom, a ministry-licensed dynamic statistical program. The Culminating Data Management Investigation strand requires students to undertake a culminating investigation dealing with a significant issue that will require the application of the skills from the other strands of the course.

University/College Preparation and College Preparation Courses

 

Grade 11 FUNCTIONS AND APPLICATIONS (MCF3M)

A. Quadratic Functions

B. Exponential Functions

C. Trigonometric Functions

The Grade 11 university/college preparation course, Functions and Applicationsprovides preparation for students who plan to pursue technology-related programs in college, while also leaving the option open for some students to pursue postsecondary programs that require the Grade 12 university preparation course Mathematics of Data Management.

The Functions and Applications course explores functions by revisiting key concepts from the Grade 10 mathematics curriculum and by using a more applied approach with less emphasis on abstract concepts than in the Grade 11 university preparation course, Functions. The first strand, Quadratic Functions, extends knowledge and skills related to quadratics for students who completed the Grade 10 applied mathematics course and reviews this topic for students entering from the Grade 10 academic course. The strand also introduces some of the properties of functions. The other two strands, Exponential Functions and Trigonometric Functions, emphasize real-world applications and help students develop the knowledge and skills needed to solve problems related to these applications.

College Preparation Courses

 

Grade 11

FOUNDATIONS FOR COLLEGE MATHEMATICS (MBF3C)

A. Mathematical Models

B. Personal Finance

C. Geometry and Trigonometry

D. Data Management

 

Grade 12

FOUNDATIONS FOR COLLEGE MATHEMATICS (MAP4C)

A. Mathematical Models

B. Personal Finance

C. Geometry and Trigonometry

D. Data Management

 

The Grade 11 college preparation course, Foundations for College Mathematicsincludes a blend of topics needed by students who plan to pursue one of a broad range of college programs. The course has been designed with four strands that address different areas of mathematics. The Mathematical Models strand uses the concepts connected to linear and quadratic relations developed in the Grade 9 and 10 applied mathematics courses to revisit quadratic relations and introduce exponential relations. The Personal Finance strand focuses on compound interest and applications related to investing and borrowing money and owning and operating a vehicle. Applications requiring spatial reasoning are addressed in the Geometry and Trigonometry strand. The fourth strand, Data Management, explores practical applications of one-variable statistics and probability.

 

The Grade 12 college preparation course Foundations for College Mathematics satisfies the mathematical prerequisites for many college programs, including programs in business, human services, hospitality and tourism, and some of the health sciences. The four strands of this course focus on the same areas of mathematics addressed in the Grade 11college preparation course, Foundations for College Mathematics. The Mathematical Models strand extends the concepts and skills that related to exponential relations introduced in Grade 11 and provides students with an opportunity to revisit all of the relations they have studied in the secondary mathematics program by using a graphical and algebraic approach. The Personal Finance strand focuses on annuities and mortgages,

renting or owning accommodation, and designing budgets. Problem solving in the

Geometry and Trigonometry strand reinforces the application of relationships associated with a variety of shapes and figures. The fourth strand, Data Management, addresses practical applications of two-variable statistics and examines applications of data management.

Workplace Preparation Courses

 

Grade 11 MATHEMATICS FOR WORK AND EVERYDAY LIFE (MEL3E)

A. Earning and Purchasing

B. Saving, Investing, and Borrowing

C. Transportation and Travel

 

Grade 12 MATHEMATICS FOR WORK AND EVERYDAY LIFE (MEL4E)

A. Reasoning With Data

B. Personal Finance

C. Applications of Measurement

 

The Grade 11 workplace preparation course, Mathematics for Work and Everyday Life, is designed to help students consolidate the basic knowledge and skills of mathematics used in the workplace and in everyday life. This course is ideal for students who would like to take the Grade 12 workplace preparation course before graduating from high school and entering the workplace. The course also meets the needs of students who wish to fulfill the senior mathematics graduation requirement but do not plan to take any further courses in mathematics. All three strands, Earning and Purchasing; Saving, Investing, and Borrowing; and Transportation and Travel, provide students with the opportunity to use proportional reasoning to solve a variety of problems.

 

The Grade 12 workplace preparation course, Mathematics for Work and Everyday Life, extends the knowledge and skills developed in Grade 11. The gathering, interpretation, and display of one-variable data and the investigation of probability concepts are the main components of the Reasoning With Data strand. Topics in the Personal Finance strand address owning or renting accommodation, designing a budget, and filing an income tax return. A variety of problems involving metric and imperial measurement are presented in the Applications of Measurement strand. The expectations support the use of hands-on projects and other experiences that make the mathematics more meaningful for students.