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Ontario Curriculum

Acquiring mathematical knowledge is a continuous process. The Ontario curriculum for mathematics recognizes all the benefits that  technologies in today's communities can bring to the fundamentals of math. It therefore integrates the use of appropriate technologies, while recognizing the continuing importance of students’ mastering essential arithmetic skills. The development of mathematical knowledge is a gradual process. A continuous, cohesive progam throughout the grades is necessary to help students develop an understanding of the “big ideas” of mathematics – that is, the interrelated concepts that form a framework for learning mathematics in a coherent way.The fundamentals of important concepts, processes, skills, and attitudes are introduced in the primary grades and fostered through the junior and intermediate grades. The program is continuous, as well, from the elementary to the secondary level.

The following guidelines and expectations were taken from the Ministry of Education for the Government of Ontario. A complete list of expectations and guidelines can be found by visiting the Ministry of Education website. You can also see the detailed documents in pdf format by clicking on the appropriate links below.



Elementary (Gr.1-8) 

Mathematics - It's Role in Society

In a society filled with technology and new innovations, people best equipped to handle everyday challenges are those that acquire problem-solving, critical thinking and communication skills. The Ontario math curriculum for elementary students provides students with the tools they need to achieve these standards.


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Grade 1 


In Grade 1, students are expected to:



  • investigate and apply strategies to solve problems.
  • apply reasoning skills such as pattern recognition to help understand mathematics by discussing with other students and teacher.
  • demonstrate that they understand how to solve a problem by explaining their reasoning to others
  • read whole numbers up to 50, and count different money amounts using various different techniques.
  • solve addition and subtraction questions of single-digit numbers.
  • represent information in graphs and pictographs;
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Grade 2 


In Grade 2, students are expected to:


  • demonstrate that they can think and clarify their their reasoning as they work on and solve problems.
  • use a selection of visual and electronic learning tools to investigate and solve problems;
  • communicate mathematical thinking orally, visually, and in writing, using everyday language, a developing mathematical vocabulary, and a variety of representations.
  • read, represent, compare, and order whole numbers to 100, and use concrete materials to represent fractions and money amounts to 100¢;
  • demonstrate an understanding of magnitude by counting forward to 200 and backwards from 50, using multiples of various numbers as starting points;
  • solve problems involving the addition and subtraction of one- and two-digit whole numbers, using a variety of strategies, and investigate multiplication and division.
  • estimate, measure, and record length, perimeter, area, mass, capacity, time, and temperature, using non-standard units and standard units;
  • identify two-dimensional shapes and three-dimensional figures and sort and classify them by their geometric properties;
  • demonstrate an understanding of the concept of equality between pairs of expressions, using concrete materials, symbols, and addition and subtraction to 18.
  • read and describe primary data presented in tally charts, concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers;
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Grade 3 


In Grade 3, students are expected to:

  • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by explaining to others why they think their solution is correct);
  • make connections among simple mathematical concepts and procedures, and relate mathematical ideas to situations drawn from everyday contexts;
  • communicate mathematical thinking orally, visually, and in writing, using everyday language, a developing mathematical vocabulary, and a variety of representations.
  • read, represent, compare, and order whole numbers to 1000, and use concrete materials to represent fractions and money amounts to $10;
  • compare two-dimensional shapes and three-dimensional figures and sort them by their geometric properties;
  • demonstrate an understanding of equality between pairs of expressions, using addition and subtraction of one- and two-digit numbers.
  • read, describe, and interpret primary data presented in charts and graphs, including vertical and horizontal bar graphs;
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Grade 4 


In Grade 4, students are expected to:

  • develop and apply reasoning skills (e.g., classification, recognition of relationships, use of counter-examples) to make and investigate conjectures and construct and defend arguments;
  • make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, sports);
  • communicate mathematical thinking orally, visually, and in writing, using everyday language, a basic mathematical vocabulary, and a variety of representations, and observing basic mathematical conventions.
  • read, represent, compare, and order whole numbers to 10 000, decimal numbers to tenths, and simple fractions, and represent money amounts to $100;
  • demonstrate an understanding of magnitude by counting forward and backwards by 0.1 and by fractional amounts;
  • estimate, measure, and record length, perimeter, area, mass, capacity, volume, and elapsed time, using a variety of strategies;
  • identify quadrilaterals and three-dimensional figures and classify them by their geometric properties, and compare various angles to benchmarks;
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Grade 5 


In Grade 5, students are expected to:

  • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
  • make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, sports);
  • communicate mathematical thinking orally, visually, and in writing, using everyday language, a basic mathematical vocabulary, and a variety of representations, and observing basic mathematical conventions.
  • demonstrate, through investigation, an understanding of the use of variables in equations.
  • determine the relationships among units and measurable attributes, including the area of a rectangle and the volume of a rectangular prism.
  • identify and classify two-dimensional shapes by side and angle properties, and compare and sort three-dimensional figures;

  • read, represent, compare, and order whole numbers to 100 000, decimal numbers to hundredths, proper and improper fractions, and mixed numbers;
  • solve problems involving the multiplication and division of multi-digit whole numbers, and involving the addition and subtraction of decimal numbers to hundredths, using a variety of strategies;
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Grade 6 


In Grade 6, students are expected to:

  • make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, sports);
  • create a variety of representations of mathematical ideas (e.g., by using physical models, pictures, numbers, variables, diagrams, graphs, onscreen dynamic representations), make connections among them, and apply them to solve problems;
  • communicate mathematical thinking orally, visually, and in writing, using everyday language, a basic mathematical vocabulary, and a variety of representations, and observing basic mathematical conventions.
  • read, represent, compare, and order whole numbers to 1 000 000, decimal numbers to thousandths, proper and improper fractions, and mixed numbers;
  • solve problems involving the multiplication and division of whole numbers, and the addition and subtraction of decimal numbers to thousandths, using a variety of strategies;
  • demonstrate an understanding of relationships involving percent, ratio, and unit rate.
  • classify and construct polygons and angles;
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Grade 7 


In Grade 7, students are expected to:


  • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
  • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
  • represent, compare, and order numbers, including integers;
  • demonstrate an understanding of addition and subtraction of fractions and integers, and apply a variety of computational strategies to solve problems involving whole numbers and decimal numbers;
  • demonstrate an understanding of proportional relationships using percent, ratio, and rate.
  • report on research into real-life applications of area measurements;
  • construct related lines, and classify triangles, quadrilaterals, and prisms;
  • model real-life linear relationships graphically and algebraically, and solve simple algebraic equations using a variety of strategies, including inspection and guess and check.
  • make and evaluate convincing arguments, based on the analysis of data;
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Grade 8 


In Grade 8, students are expected to:


  • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
  • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
  • solve problems involving whole numbers, decimal numbers, fractions, and integers, using a variety of computational strategies;
  • research, describe, and report on applications of volume and capacity measurement;
  • determine the relationships among units and measurable attributes, including the area of a circle and the volume of a cylinder.
  • demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric properties in the real world;
  • represent transformations using the Cartesian coordinate plane, and make connections between transformations and the real world.

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Secondary (Gr.9-12) 
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Grade 9 

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.

In this course, students are expected to:


  • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
  • make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
  • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
  • communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
  • 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.
  • apply data-management techniques to investigate relationships between two variables;
  • demonstrate an understanding of the characteristics of a linear relation;
  • 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;
  • verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.
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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.

In this course, students are expected to:


  • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
  • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
  • communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
  • simplify numerical and polynomial expressions in one variable, and solve simple first-degree equations.
  • demonstrate an understanding of constant rate of change and its connection to linear relations;
  • connect various representations of a linear relation, and solve problems using the representations.
  • determine, through investigation, the optimal values of various measurements of rectangles;
  • solve problems involving the measurements of two-dimensional shapes and the volumes of three-dimensional figures;
  • determine, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.
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Grade 10 


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.

In this course, students are expected to:


  • develop, select, apply, and compare a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
  • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
  • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
  • determine the basic properties of quadratic relations of the form y=ax^2+bx+c;
  • relate transformations of the graph of y = x2 to the algebraic representation y = a(x – h)2 + k;
  • solve quadratic equations and interpret the solutions with respect to the corresponding relations;
  • model and solve problems involving the intersection of two straight lines;
  • solve problems using analytic geometry involving properties of lines and line segments;
  • solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
  • solve problems involving acute triangles, using the sine law and the cosine law.
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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.


In this course, students are expected to:


  • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
  • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
  • communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
  • use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
  • solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
  • solve problems involving the surface areas and volumes of three-dimensional figures, and use the imperial and metric systems of measurement.
  • manipulate and solve algebraic equations, as needed to solve problems;
  • graph a line and write the equation of a line from given information;
  • solve systems of two linear equations, and solve related problems that arise from realistic situations.
  • solve problems by interpreting graphs of quadratic relations.
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Grade 11
Functions and Applications 

University/College Preparation MCF3M

This course introduces basic features of the function by extending students’ experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modelling real-world situations. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems.


In this course, students are expected to:


  • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
  • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
  • make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
  • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
    • expand and simplify quadratic expressions, solve quadratic equations, and relate the roots of a quadratic equation to the corresponding graph;
    • demonstrate an understanding of functions, and make connections between the numeric, graphical, and algebraic representations of quadratic functions;
    • simplify and evaluate numerical expressions involving exponents, and make connections between the numeric, graphical, and algebraic representations of exponential functions;
    • demonstrate an understanding of periodic relationships and the sine function, and make connections between the numeric, graphical, and algebraic representations of sine functions;
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    Foundations for College 

    College Preparation MBF3C

    This course enables students to broaden their understanding of mathematics as a problemsolving tool in the real world. Students will extend their understanding of quadratic relations; investigate situations involving exponential growth; solve problems involving compound interest; solve financial problems connected with vehicle ownership; develop their ability to reason by collecting, analysing, and evaluating data involving one variable; connect probability and statistics; and solve problems in geometry and trigonometry. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.


    In this course, students are expected to:


    • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used,by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
    • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
    • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
    • make connections between the numeric, graphical, and algebraic representations of quadratic relations, and use the connections to solve problems;
    • demonstrate an understanding of exponents, and make connections between the numeric, graphical, and algebraic representations of exponential relations;
    • describe and represent exponential relations, and solve problems involving exponential relations arising from real-world applications.
    • compare simple and compound interest, relate compound interest to exponential growth, and solve problems involving compound interest;

    • solve problems involving trigonometry in acute triangles using the sine law and the cosine law,including problems arising from real-world applications.
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    Mathematics for Work and Everyday Life 

    Workplace Preparation MEL3E

    This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel in a variety of situations. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.


    In this course, students are expected to:


    • develop, select, apply, compare, and adapt a variety of problem-solving  strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
    • develop and apply reasoning skills (e.g., use of inductive reasoning, deductive reasoning, and counter-examples; construction of proofs) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
    • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
    • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
    • make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
    • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
    • communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
    • interpret information about different types of remuneration, and solve problems and make decisions involving different remuneration methods;
    • describe and compare services available from financial institutions;
    • demonstrate an understanding of simple and compound interest, and solve problems involving related applications;
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    Functions 

    University Preparation MCR3U

    This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

    In this course, students are expected to:


    • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
    • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
    • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
    • communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
    • demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.
    • evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways;
    • demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle;
    • demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems;
    • determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;
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    Grade 12 

    Advanced Functions 

    University Preparation MHF4U

    This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.


    In this course, students are expected to:


    • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
    • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
    • communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
    • solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.
    • demonstrate an understanding of the meaning and application of radian measure;
    • solve problems involving trigonometric equations and prove trigonometric identities.
    • identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;
    • identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;
    • determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems;
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    Calculus and Vectors 

    University Preparation MCV4U

    This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in threedimensional
    space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.


    In this course, students are expected to:


    • develop, select, apply, compare, and adapt a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
    • develop and apply reasoning skills (e.g., use of inductive reasoning, deductive reasoning, and counter-examples; construction of proofs) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
    • communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
    • demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit;
    • graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative;
    • make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching;
    • solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.
    • demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;
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    Mathematics of Data Management 

    University Preparation MDM4U

    This course broadens students’ understanding of mathematics as it relates to managing data. Students will apply methods for organizing and analyzing large amounts of information; solve problems involving probability and statistics; and carry out a culminating investigation that integrates statistical concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. Students planning to enter university programs in business, the social sciences, and the humanities will find this course of particular interest.


    In this course, students are expected to:


    • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
    • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
    • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
    • solve problems involving the application of permutations and combinations to determine the probability of an event.
    • demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications;
    • describe the characteristics of a good sample, some sampling techniques, and principles of primary data collection, and collect and organize data to solve a problem.
    • analyse, interpret, and draw conclusions from two-variable data using numerical, graphical, and algebraic summaries;
    • communicate the findings of a culminating investigation and provide constructive critiques of the investigations of others.
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    Mathematics for CollegeTechnology 

    College Preparation MCT4C

    This course enables students to extend their knowledge of functions. Students will investigate and apply properties of polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for a variety of college technology programs.


    In this course, students are expected to:


    • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
    • make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
    • create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
    • communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
    • solve problems involving exponential equations algebraically using common bases and logarithms, including problems arising from real-world applications.
    • recognize and evaluate polynomial functions, describe key features of their graphs, and solve problems using graphs of polynomial functions;
    • make connections between the numeric, graphical, and algebraic representations of polynomial functions;

    • determine the values of the trigonometric ratios for angles less than 360º, and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;
    • represent vectors, add and subtract vectors, and solve problems using vector models, including those arising from real-world applications;
    • determine circle properties and solve related problems, including those arising from real-world applications.
    ________________________________________________________________________________________________________

    Foundations for College Mathematics 

    College Preparation MAP4C

    This course enables students to broaden their understanding of real-world applications of mathematics. Students will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; solve financial problems connected with annuities, budgets, and renting or owning accommodation; simplify expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades.


    In this course, students are expected to:


    • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
    • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
    • evaluate powers with rational exponents, simplify algebraic expressions involving exponents, and solve problems involving exponential equations graphically and using common bases;
    • describe trends based on the interpretation of graphs, compare graphs using initial conditions and rates of change, and solve problems by modelling relationships graphically and algebraically;
    • make connections between formulas and linear, quadratic, and exponential relations, solve problems using formulas arising from real-world applications, and describe applications of mathematical modelling in various occupations.
    • demonstrate an understanding of annuities, including mortgages, and solve related problems using technology;
    • explain the significance of optimal dimensions in real-world applications, and determine optimal dimensions of two-dimensional shapes and three-dimensional figures;
    • collect, analyse, and summarize two-variable data using a variety of tools and strategies, and interpret and draw conclusions from the data;
    ________________________________________________________________________________________________________

    Mathematics for Work and Everyday Life 

    Workplace Preparation MEL4E

    This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will investigate questions involving the use of statistics; apply the concept of probability to solve problems involving familiar situations; investigate accommodation costs, create household budgets, and prepare a personal income tax return; use proportional reasoning; estimate and measure; and apply geometric concepts to create designs. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.


    In this course, students are expected to:


    • collect, organize, represent, and make inferences from data using a variety of tools and strategies, and describe related applications;
    • determine and represent probability, and identify and interpret its applications.
    • gather, interpret, and compare information about owning or renting accommodation and about the associated costs;
    • interpret, design, and adjust budgets for individuals and families described in case studies;
    • demonstrate an understanding of the process of filing a personal income tax return, and describe applications of the mathematics of personal finance.
    • determine and estimate measurements using the metric and imperial systems, and convert measures within and between systems;
    • apply measurement concepts and skills to solve problems in measurement and design, to construct scale drawings and scale models, and to budget for a household improvement;
    • identify and describe situations that involve proportional relationships and the possible consequences of errors in proportional reasoning, and solve problems involving proportional reasoning, arising in applications from work and everyday life.
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