Secondary Math Learning Overview

​"The mathematical processes cannot be separated from the knowledge and skills that students acquire throughout the course. Students must problem solve, communicate, reason, reflect, and so on, as they develop the knowledge, the understanding of concepts, and the skills required in the course."

The Ontario Curriculum, Grades 9 and 10: Mathematics

​ The mathematical processes are:

• problem solving
• reasoning and proving
• reflecting
• selecting tools and computational strategies
• connecting
• representing
• communicating​

Taken and adapted from The Ontario Curriculum, Grades 9 and 10: Mathematics

​*For more information about the seven mathematical processes, watch the video "Targeted Implementation and Planning Supports for Revised Mathematics (TIPS4RM): Mathematical Processes​".

"This course enables students to consolidate, and continue to develop, an understanding of mathematical concepts related to number sense and operations, algebra, measurement, geometry, data, probability, and financial literacy. Students will use mathematical processes, mathematical modelling, and coding to make sense of the mathematics they are learning and to apply their understanding to culturally responsive and relevant real-world situations. Students will continue to enhance their mathematical reasoning skills, including proportional reasoning, spatial reasoning, and algebraic reasoning, as they solve problems and communicate their thinking."

(from The Ontario Curriculum, Grades 9 Mathematics)

The new Grade 9 math course builds on the 2020 elementary (Grades 1 to 8) mathematics curriculum. In this course, students will learn math concepts and skills to prepare them for their future. Below are the areas of focus:

Social-emotional learning (SEL) skills in mathematics

Students will:

• build their social-emotional learning skills, such as learning to recognize and identify emotions that support mathematical learning

• build their confidence and develop a healthy relationship with math

Mathematical thinking and making connections

Students will:

• use their problem-solving, communication and reasoning skills as they develop their mathematical knowledge

• make connections between what they learn in math and their real-life experiences

Number

Students will: 

• work with different types of numbers, such as powers with positive and negative exponents

• solve problems involving positive and negative fractions, decimal numbers, and integers

• build their knowledge and skills related to percentages, ratios, rates and proportions, and make connections to real-life situations (for example, comparing costs)

Algebra

Students will: 

• develop their understanding of algebraic expressions and equations

• apply coding skills to understand complex math concepts and make predictions

• learn about various linear and non-linear relations

• increase their understanding of rates of change and apply it to make sense of real-life situations (for example, analysing motion of a car or rates of pollution)

Data

Students will: 

• build their data literacy skills to examine the collection, representation, and use of data including how data is used to inform decisions

• continue to apply mathematical modelling to analyse real-life situations, such as the impact of social media on the economy

Geometry and measurement

Students will: 

• make connections between geometric shapes and their applications in architecture, engineering, and design

• analyse and create designs to increase understanding of geometric relationships

• solve real-life problems that involve applying their knowledge of perimeter, area, surface area, and volume, such as planning and creating models of a community garden

Financial literacy

Students will:  

• build their financial literacy by learning to manage finances, such as working with budgets and understanding appreciation and depreciation of assets

• analyse various financial situations and learn how math can be applied to make informed decisions (for example, understanding shifts in the stock market)

• examine how interest rates, down payments, and other factors impact purchasing decisions

"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"

The Ontario Curriculum, Grades 9 and 10: Mathematics

Quadratic Relations of the Form y = ax2 + bx + c

• investigate the basic properties of quadratic relations₁
• relate the graph of y = x2 and its transformations₂
• solve quadratic equations₃
• solve problems involving quadratic relations

Analytic Geometry

• use linear systems₄ to solve problems
• solve problems involving properties of line segments
• use analytic₅ geometry to verify geometric properties

Trigonometry

• investigate similarity and solving problems involving similar triangles₆
• solve problems involving the trigonometry of right₇ triangles
• solve problems involving the trigonometry of acute₈ triangles

Taken and adapted from The Ontario Curriculum, Grades 9 and 10: Mathematics​​

1 Quadratic Relation. A relation whose equation is in quadratic form; for example, y = x2 + 7x + 10. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 63)

2 Transformation. A change in a figure that results in a different position, orientation, or size.The transformations include translation, reflection, rotation, compression,and stretch. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 64

3 Quadratic Equation. An equation that contains at least one term whose exponent is 2, and no term with an exponent greater than 2; for example, x2 + 7x + 10 = 0. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 63)

4 System of Linear Equations.Two or more linear equations involving two or more variables.The solution to a system of linear equations involving two variables is the point of intersection of two straight lines. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p.64)

5 Analytic Geometry. A geometry that uses the xy-plane to determine equations that represent lines and curves. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 60)

6 Similar Triangles. Triangles in which corresponding sides are proportional. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 64)

7 Right Triangle. A triangle containing one 90º angle. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 63)

8 Acute triangle. A triangle in which each of the three interior angles measures less than 90º. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 60)

​"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."

The Ontario Curriculum, Grades 9 and 10: Mathematics

Measurement and Trigonometry

• solve problems involving similar triangles₁
• solve problems involving the trigonometry of right triangles₂
• solve problems involving surface area and volume, using imperial and metric systems of measurement

Modelling Linear Relations

• manipulate and solving algebraic equations
• graph and writing equations of lines
• solve and interpreting systems of linear equations₃

Quadratic Relations of the Form y = ax2 + bx + c

• manipulate quadratic expressions
• identify characteristics of quadratic relations₄
• solve problems by interpreting graphs of quadratic relations

Taken and adapted from The Ontario Curriculum, Grades 9 and 10: Mathematics​​​

1 Similar Triangles. Triangles in which corresponding sides are proportional. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 64)

2 Right Triangle. A triangle containing one 90º angle. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 63)

3 System of Linear Equations.Two or more linear equations involving two or more variables.The solution to a system of linear equations involving two variables is the point of intersection of two straight lines. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p.64)

4 Quadratic Relation. A relation whose equation is in quadratic form; for example, y = x2 + 7x + 10. (The Ontario Curriculum Grades 9 and 10, Mathematics, 2005, p. 63)

​"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.​"

Prerequisite: Principles of Mathematics, Grade 10, Academic​

​Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics

"The Grade 11 university/college preparation course, Functions and Applications, provides 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."

Prerequisite: Principles of Mathematics, Grade 10, Academic, or Foundations of Mathematics, Grade 10, Applied

​ ​Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics​

"The Grade 11 college preparation course, Foundations for College Mathematics, includes 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."

Prerequisite: Foundations of Mathematics, Grade 10, Applied

​Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics​

"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."

Prerequisite: Principles of Mathematics, Grade 9, Academic, or Foundations of Mathematics, Grade 9, Applied, or a ministry-approved locally developed Grade 10 mathematics course

​ ​Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics​​

"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."

Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation 

​  ​Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics

"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."

Note: The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U).​

​ ​Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics​ 

"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 13THE PROGRAM IN MATHEMATICS 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."

Prerequisite: Functions, Grade 11, University Preparation, or Functions and Applications, Grade 11, University/College Preparation

​  ​Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics​

"The Grade 12 college preparation course Mathematics for College Technology provides excellent preparation for success in technology-related programs at the college level. It extends the understanding of functions developed in the Grade 11 university/college preparation course, Functions and Applications, using a more applied approach, and may help students who decide to pursue certain university programs to prepare for the Grade 12 university preparation course Advanced Functions. Exponential and trigonometric functions are revisited, developing algebraic skills needed to solve problems involving exponential equations and extending the skills associated with graphical representations of trigonometric functions. The Polynomial Functions strand extends to polynomial functions concepts that connect graphs and equations of quadratic functions. Finally, students apply geometric relationships to solve problems involving composite shapes and figures and investigate the properties of circles and their applications." 

Prerequisite: Functions and Applications, Grade 11, University/College Preparation, or Functions, Grade 11, University Preparation

​  ​Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics​​ 

"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 11 college 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."

Prerequisite: Foundations for College Mathematics, Grade 11, College Preparation, or Functions and Applications, Grade 11, University/College Preparation​

Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics​​​  

"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."

Prerequisite: Mathematics for Work and Everyday Life, Grade 11, Workplace Preparation

 ​Taken and adapted from The Ontario Curriculum, Grades 11 and 12, Mathematics​​​