The Ontario Curriculum

Ministry of Education

The Ontario Curriculum Grades 11 and 12

REVISED

Mathematics

2007

CONTENTS

INTRODUCTION

3

Secondary Schools for the Twenty-first Century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

The Importance of Mathematics in the Curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Roles and Responsibilities in Mathematics Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

THE PROGRAM IN MATHEMATICS

7

Overview of the Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Curriculum Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Courses and Strands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

THE MATHEMATICAL PROCESSES

17

Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Reasoning and Proving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Reflecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Selecting Tools and Computational Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Connecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Representing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Communicating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

ASSESSMENT AND EVALUATION OF

STUDENT ACHIEVEMENT

23

Basic Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

The Achievement Chart for Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Evaluation and Reporting of Student Achievement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Reporting on Demonstrated Learning Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

SOME CONSIDERATIONS FOR

PROGRAM PLANNING IN MATHEMATICS

30

Instructional Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Planning Mathematics Programs for Students With Special Education Needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Program Considerations for English Language Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Une publication ?quivalente est disponible en fran?ais sous le titre suivant : Le curriculum de l'Ontario, 11e et 12e ann?e ? Math?matiques, 2007.

This publication is available on the Ministry of Education's website, at .on.ca.

Antidiscrimination Education in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Literacy and Inquiry/Research Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 The Role of Information and Communication Technology

in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Career Education in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 The Ontario Skills Passport and Essential Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Cooperative Education and Other Forms of Experiential Learning . . . . . . . . . . . . . . . . . . . 38 Planning Program Pathways and Programs Leading to a

Specialist High-Skills Major . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Health and Safety in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39

COURSES

41

Grade 11

Functions, University Preparation (MCR3U) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Functions and Applications, University/College Preparation (MCF3M) . . . . . . . . . . . . . . 57

Foundations for College Mathematics, College Preparation (MBF3C) . . . . . . . . . . . . . . . 67

Mathematics for Work and Everyday Life, Workplace Preparation (MEL3E) . . . . . . . . . 77

Grade 12

Advanced Functions, University Preparation (MHF4U) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Calculus and Vectors, University Preparation (MCV4U) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Mathematics of Data Management, University Preparation (MDM4U) . . . . . . . . . . . . 111

Mathematics for College Technology, College Preparation (MCT4C) . . . . . . . . . . . . . . . 123

Foundations for College Mathematics, College Preparation (MAP4C) . . . . . . . . . . . . . . 135

Mathematics for Work and Everyday Life, Workplace Preparation (MEL4E) . . . . . . . 147

INTRODUCTION

This document replaces The Ontario Curriculum, Grade 11: Mathematics, 2006, and the Grade 12 courses in The Ontario Curriculum, Grades 11 and 12: Mathematics, 2000. Beginning in September 2007, all Grade 11 and Grade 12 mathematics courses will be based on the expectations outlined in this document.

SECONDARY SCHOOLS FOR THE TWENTY-FIRST CENTURY

The goal of Ontario secondary schools is to support high-quality learning while giving individual students the opportunity to choose programs that suit their skills and interests. The updated Ontario curriculum, in combination with a broader range of learning options outside traditional classroom instruction, will enable students to better customize their high school education and improve their prospects for success in school and in life.

THE IMPORTANCE OF MATHEMATICS IN THE CURRICULUM

This document provides a framework outlining what students are expected to know and be able to do by the end of each of the courses in the Grade 11?12 mathematics curriculum. The required knowledge and skills include not only important mathematical facts and procedures but also the mathematical concepts students need to understand and the mathematical processes they must learn to apply.

The principles underlying this curriculum are shared by educators dedicated to the success of all students in learning mathematics. Those principles can be stated as follows:1

Curriculum expectations must be coherent, focused, and well-articulated across the grades. Learning mathematics involves the meaningful acquisition of concepts, skills, and processes and the active involvement of students in building new knowledge from prior knowledge and experience. Learning tools such as manipulatives and technologies are important supports for teaching and learning mathematics. Effective teaching of mathematics requires that the teacher understand the mathematical concepts, procedures, and processes that students need to learn, and use a variety of instructional strategies to support meaningful learning. Assessment and evaluation must support learning, recognizing that students learn and demonstrate learning in various ways.

1. Adapted from Principles and Standards for School Mathematics, developed by the National Council of Teachers of Mathematics (Reston, VA: NCTM, 2000).

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