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Course Outline | Math | Advanced Functions | MHF4U

Explorer Hop Academy

  • DEPARTMENT: Mathematics 
  •  DEPARTMENT HEAD: Hasina Lookman
  • COURSE DEVELOPMENT DATE: August 2021(Revision August 2022) COURSE: Advanced Functions, Grade 12 
  • COURSE TYPE: Online
  • PREREQUISITE: Functions, Grade 11 or Mathematics for College Technology, Grade 12 

COURSE CURRICULUM: Ontario Curriculum:  Grades 11 and 12 Mathematics 2007 (Revised). A copy of this document is available online at: 


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. 

CURRICULUM EXPECTATIONS                                                                              By the end of this course, students will: • demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically;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;make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems;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; solve problems involving polynomial and simple rational equations graphically and algebraically;demonstrate an understanding of solving polynomial and simple rational inequalities; demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point;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; compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.


  1. Polynomial and Rational Functions (30hours): Students will investigate polynomial functions (shape, x intercepts, leading coefficient, end behavior, etc.) in standard form and factored form. Students will  graph polynomial functions and apply the roles of the parameters a, k, d, and c in functions of the  form form y = af[k(x − d)] + c. They will compare properties of odd and even polynomial functions  and determine polynomials to be even, odd, or neither. Students will investigate properties of rational  functions that are reciprocals of linear and quadratic functions. They will graph rational functions  using its key features. 
  2. Solving Polynomial/Rational Equations and Inequalities (25hours) : Students will investigate the remainder  theorem and the factor theorem and apply these skills to factor polynomial expressions. They will solve polynomial equations in one variable by selecting the correct factoring strategies. Students will  determine solutions to polynomial inequalities and to simple rational inequalities in one variable by  graphing and using interval tables. 
  3. Exponential and Logarithmic Functions  (25hours): Students will be introduced to the concept of logarithms  and make connections to exponential equations. They will apply the laws of logarithms to solve  problems. Students will graph logarithmic functions and apply the roles of the parameters a, k, d, and  c in functions of the form y = alog10[k(x − d)] + c, and identify key features using correct  terminology. Students will apply their understanding to solve exponential and simple logarithmic  equations in one variable algebraically. 
  4. Trigonometry in Radian Measure  (20hours): Students will explore the concept of radian measure and determine the trigonometric ratios for special angles. They will apply this to sketch the graphs of  f(x) = sinx and f(x) = cosx and describe key properties using correct terminology. Students will  graph trigonometric functions and apply the roles of the parameters a, k, d, and c in functions of the  form y = a sin[k(x − d)] + c and y = a cos[k(x − d)] + c and pose problems based on real life  applications.
  5. Trigonometric Identities and Equations  (10hours): Students will apply trigonometric identities including  compound angle formulas to determine exact values of trigonometric ratios and prove trigonometric  identities through the application of reasoning skills. They will solve linear and quadratic  trigonometric equations for the domain of real values from 0 to 2π.
  6. Characteristics of Functions (10hours): Students will investigate rates of change in real life applications  (average and instantaneous rates of change) and explore the terms secant and tangent in graphs.  Students will investigate key features of combined graphs created by adding, subtracting,  multiplying, or dividing functions, as well as compositions of two functions. 


The course will cover the following strand as outlined in The Ontario Curriculum:  Grades 11 and 12 Mathematics 2007. A copy of this document is available online at: 

The details of the strands are included in the above link.

  • A. Exponential and Logarithmic Functions

  • B. Trigonometric Functions

  • C. Polynomial and Rational Functions

  • D. Characteristics of Functions

Teaching and Learning Strategies

Throughout the course, students are exposed to a variety of genres, and they develop skills to

evaluate the effectiveness of texts which include short stories, non-fiction texts, poems, videos, and other media and texts from a wide range of resources and periods.

Students will identify and use various strategies that include building vocabulary, learning to understand the organization of texts, and developing knowledge of conventions. Throughout the course, students develop into stronger readers, writers, and oral communicators by connecting literature and language to real world experiences. 

Teachers will differentiate instruction to meet the diverse learning needs of students. Through the resources in the learning management system and weekly meets, students will have the opportunity to track their growth and progression, to reflect on the achievements, and to set goals for the journey ahead in order to develop their 21st century skills.

Using a variety of instructional strategies, teachers will provide numerous opportunities for students to develop skills of inquiry, problem solving, and communication as they investigate and learn fundamental concepts. The integration of critical thinking and critical literacy will provide a powerful tool for reasoning and problem solving, and will be reflected in a meaningful blend of both process and content. 

Throughout the course, students will:

- Think Critically: students will learn to critically analyze texts and to use implied and stated evidence

from texts to support their analyses. Students use their critical thinking skills to identify perspectives in

texts, including biases that may be present.

- Generate ideas and topics: students will be encouraged to design their own approaches to the material

by maintaining frequent online communication with teachers who will facilitate choice in how students

respond to topics and questions, and by encouraging students' independent thinking through discussions.

- Research: various approaches to researching will be practiced. Students will learn how to cite sources

and provide a Works Cited page at the end of longer assignments using MLA formatting.

- Identify and develop skills and strategies: through modeling of effective skills, students will learn to

choose and utilize varied techniques to become effective readers, writers, and oral communicators.

- Communicate: numerous opportunities will be given to students to write and communicate orally, as well as develop listening skills.

- Produce published work and make presentations: students will engage in the editing and revising

process, including self-revision, peer revision, and teacher revision all of which strengthen texts with

the aim to publish or present student work.

- Reflecting: through the use of weekly reflections, drafts, discussions, and other elements of the course,

students will reflect on the learning process, focus on areas for improvement, set goals, and make

extensions between course content and their personal experiences.


Our school's assessment and evaluation policy is based on seven fundamental principles, and follows the guidelines in the Ontario Ministry of Education’s Growing Success document. Teachers are expected to understand and follow these seven principles in order to guide the collection of purposeful information that will guide instructional decisions, promote student engagement, and improve student learning.

To ensure that assessment, evaluation, and reporting are valid, reliable, and they lead to the improvement of all students, teachers use assessment and evaluation strategies that:

  1. are fair, transparent, and equitable for all students
  2. support all students
  3. are related to curriculum expectations, learning goals, and whenever possible, are related to the

interests, learning styles, preferences, needs, and experiences of students

  1. are clearly communicated to students and parents at critical points throughout the academic year
  2. are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities

for students to demonstrate the potential and learning

  1. provide descriptive feedback that is meaningful and timely to support learning, growth, and


  1. develop student self-assessment skills to enable them to assess their own learning, set goals, and plan

next steps for their learning

There are three forms of assessment that will be used throughout this course:

Assessment for Learning: Assessment for learning will directly influence student learning by reinforcing the connections between assessment and instruction, and provide ongoing feedback to the student. Assessment for learning occurs as part of the daily teaching process and helps teachers form a clear picture of the needs of the students because students are encouraged to be more active in their learning and associated assessment. Teachers gather this information to shape their classroom teaching.

Assessment as Learning: Assessment as learning is the use of a task or an activity to allow students the opportunity to use assessment to further their own learning. Self and peer assessments allow students  to reflect on their own learning and identify areas of strength and need. These tasks offer students the chance to set their own personal goals and advocate for their own learning.

The purpose of assessment as learning is to enable students to monitor their own progress towards achieving their learning goals.

Assessment of Learning: Assessment of learning will occur at or near the end of a period of learning; this summary is used to make judgments about the quality of student learning using established criteria, to assign a value to represent that quality and to communicate information about achievement to students and parents. 

Evidence of student achievement for evaluation is collected over time from three different sources – observations, conversations, and student products. Using multiple sources of evidence will increase the reliability and validity of the evaluation of student learning.

For a full explanation of assessment, evaluation, and reporting, kindly refer to the Growing Success document ( 

Course Expectation: This course is based on curriculum expectations found in The Ontario Curriculum:  Grades 11 and 12 Mathematics 2007. A copy of this document is available online at: 

Program Planning Considerations


To make new learning more accessible to students, teachers build new learning upon the knowledge and skills students have acquired in previous years – in other words, they help activate prior knowledge. It is important to assess where students are in their mathematical growth and to bring them forward in their learning. 

In order to apply their knowledge effectively and to continue to learn, students must have a solid conceptual foundation in mathematics. Successful classroom practices engage students in activities that require 

Students in a mathematics class typically demonstrate diversity in the ways they learn best. It is important, therefore, that students have opportunities to learn in a variety of ways – individually, cooperatively, independently, with teacher direction, through investigation involving hands-on experience, and through examples followed by practice. In mathematics, students are required to learn concepts, acquire procedures and skills, and apply processes 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. For example, even at the secondary level, manipulatives can be important tools for supporting the effective learning of mathematics. These concrete learning tools, such as connecting cubes, measurement tools, algebra tiles, and number cubes, invite students to explore and represent abstract mathematical ideas in varied, concrete, tactile, and visually rich ways. Other representations, including graphical and algebraic representations, are also a valuable aid to teachers. By analysing students’ representations of mathematical concepts and listening carefully to their reasoning, teachers can gain useful insights into students’ thinking and provide supports to help enhance their thinking. 

All learning, especially new learning, should be embedded in well-chosen contexts for learning – that is, contexts that are broad enough to allow students to investigate initial understandings, identify and develop relevant supporting skills, and gain experience with varied and interesting applications of the new knowledge. Such rich contexts for learning open the door for students to see the “big ideas” of mathematics – that is, the major underlying principles or relationships that will enable and encourage students to reason mathematically throughout their lives.

Promoting Positive Attitudes Towards Learning Mathematics:

Students’ attitudes have a significant effect on how students approach problem solving and how well they succeed in mathematics. Students who enjoy mathematics tend to perform well in their mathematics course work and are more likely to enrol in the more advanced mathematics courses. 

Students develop positive attitudes when they are engaged in making mathematical conjectures, when they experience breakthroughs as they solve problems, when they see connections between important ideas, and when they observe an enthusiasm for mathematics on the part of their teachers. With a positive attitude towards mathematics, students are able to make more sense of the mathematics they are working on, and to view themselves as effective learners of mathematics. They are also more likely to perceive mathematics as both useful and worthwhile, and to develop the belief that steady effort in learning mathematics pays off. 

It is common for people to feel inadequate or anxious when they cannot solve problems quickly and easily, or in the right way. To gain confidence, students need to recognize that, for some mathematics problems, there may be several ways to arrive at a solution. They also need to understand that problem solving of almost any kind often requires a considerable expenditure of time and energy and a good deal of perseverance. To counteract the frustration they may feel when they are not making progress towards solving a problem, they need to believe that they are capable of finding solutions. Teachers can encourage students to develop a willingness to persist, to investigate, to reason, to explore alternative solutions, to view challenges as opportunities to extend their learning, and to take the risks necessary to become successful problem solvers. They can help students develop confidence and reduce anxiety and frustration by providing them with problems that are challenging but not beyond their ability to solve. Problems at a developmentally appropriate level help students to learn while establishing a norm of perseverance for successful problem solving. 

Collaborative learning enhances students’ understanding of mathematics. Working cooperatively in groups reduces isolation and provides students with opportunities to share ideas and communicate their thinking in a supportive environment as they work together towards a common goal. Communication and the connections among ideas that emerge as students interact with one another enhance the quality of student learning.


Classroom teachers are the key educators of students who have special education needs. They have a responsibility to help all students learn, and they work collaboratively with special education teachers, where appropriate, to achieve this goal. Special Education Transformation: The Report of the Co-Chairs with the Recommendations of the Working Table on Special Education, 2006 endorses a set of beliefs that should guide program planning for students with special education needs in all disciplines. Those beliefs are as follows: 

  • All students can succeed. 
  • Universal design and differentiated instruction are effective and interconnected means of meeting the learning or productivity needs of any group of students. 
  • Successful instructional practices are founded on evidence-based research, tempered by experience. 
  • Classroom teachers are key educators for a student’s literacy and numeracy development. 
  • Each student has his or her own unique patterns of learning. 
  • Classroom teachers need the support of the larger community to create a learning environment that supports students with special education needs. 
  • Fairness is not sameness. 

In any given classroom, students may demonstrate a wide range of learning styles and needs. Teachers plan programs that recognize this diversity and give students performance tasks that respect their particular abilities so that all students can derive the greatest possible benefit from the teaching and learning process. The use of flexible groupings for instruction and the provision of ongoing assessment are important elements of programs that accommodate a diversity of learning needs. 

In planning mathematics courses for students with special education needs, teachers should begin by examining the current achievement level of the individual student, the strengths and learning needs of the student, and the knowledge and skills that all students are expected to demonstrate at the end of the course in order to determine which of the following options is appropriate for the student: 

  • no accommodations or modifications; 
  • or accommodations only; 
  • or modified expectations, with the possibility of accommodations; 
  • or alternative expectations, which are not derived from the curriculum expectations for a course and which constitute alternative programs and/or courses.

If the student requires either accommodations or modified expectations, or both, the relevant information, as described in the following paragraphs, must be recorded in his or her Individual Education Plan (IEP). More detailed information about planning programs for students with special education needs, including students who require alternative programs and/or courses, can be found in The Individual Education Plan (IEP): A Resource Guide, 2004 (referred to hereafter as the IEP Resource Guide, 2004). For a detailed discussion of the ministry’s requirements for IEPs, see Individual Education Plans: Standards for Development, Program Planning, and Implementation, 2000 (referred to hereafter as IEP Standards, 2000). (Both documents are available at 

Students Requiring Accommodations Only 

Some students are able, with certain accommodations, to participate in the regular course curriculum and to demonstrate learning independently. Accommodations allow access to the course without any changes to the knowledge and skills the student is expected to demonstrate. The accommodations required to facilitate the student’s learning must be identified in his or her IEP (see IEP Standards, 2000, page 11). A student’s IEP is likely to reflect the same accommodations for many, or all, subjects or courses. 

Providing accommodations to students with special education needs should be the first option considered in program planning. Instruction based on principles of universal design and differentiated instruction focuses on the provision of accommodations to meet the diverse needs of learners. 

There are three types of accommodations: 

  • Instructional accommodations are changes in teaching strategies, including styles of presentation, methods of organization, or use of technology and multimedia. 
  • Environmental accommodations are changes that the student may require in the classroom and/or school environment, such as preferential seating or special lighting. 
  • Assessment accommodations are changes in assessment procedures that enable the student to demonstrate his or her learning, such as allowing additional time to complete tests or assignments or permitting oral responses to test questions. 

If a student requires “accommodations only” in mathematics courses, assessment and evaluation of his or her achievement will be based on the appropriate course curriculum expectations and the achievement levels outlined in this document. The IEP box on the student’s Provincial Report Card will not be checked, and no information on the provision of accommodations will be included. 

Students Requiring Modified Expectations 

Some students will require modified expectations, which differ from the regular course expectations. For most students, modified expectations will be based on the regular course curriculum, with changes in the number and/or complexity of the expectations. Modified expectations represent specific, realistic, observable, and measurable achievements and describe specific knowledge and/or skills that the student can demonstrate independently, given the appropriate assessment accommodations. 

It is important to monitor, and to reflect clearly in the student’s IEP, the extent to which expectations have been modified. As noted in Section 7.12 of the ministry’s policy document Ontario Secondary Schools, Grades 9 to 12: Program and Diploma Requirements, 1999, the principal will determine whether achievement of the modified expectations constitutes successful completion of the course, and will decide whether the student is eligible to receive a credit for the course. This decision must be communicated to the parents and the student. 

When a student is expected to achieve most of the curriculum expectations for the course, the modified expectations should identify how the required knowledge and skills differ from those identified in the course expectations. When modifications are so extensive that achievement of the learning expectations (knowledge, skills, and performance tasks) is not likely to result in a credit, the expectations should specify the precise requirements or tasks on which the student’s performance will be evaluated and which will be used to generate the course mark recorded on the Provincial Report Card. 

Modified expectations indicate the knowledge and/or skills the student is expected to demonstrate and have assessed in each reporting period. The student’s learning expectations must be reviewed in relation to the student’s progress at least once every reporting period, and must be updated as necessary. 

If a student requires modified expectations in mathematics courses, assessment and evaluation of his or her achievement will be based on the learning expectations identified in the IEP and on the achievement levels outlined in this document. If some of the student’s learning expectations for a course are modified but the student is working towards a credit for the course, it is sufficient simply to check the IEP box on the Provincial Report Card. If, however, the student’s learning expectations are modified to such an extent that the principal deems that a credit will not be granted for the course, the IEP box must be checked and the appropriate statement from the Guide to the Provincial Report Card, Grades 9–12, 1999 (page 8) must be inserted. The teacher’s comments should include relevant information on the student’s demonstrated learning of the modified expectations, as well as next steps for the student’s learning in the course. 


Young people whose first language is not English enter Ontario secondary schools with diverse linguistic and cultural backgrounds. Some English language learners may have experience of highly sophisticated educational systems, while others may have come from regions where access to formal schooling was limited. All of these students bring a rich array of background knowledge and experience to the classroom, and all teachers must share in the responsibility for their English-language development. 

Teachers of mathematics must incorporate appropriate adaptations and strategies for instruction and assessment to facilitate the success of the English language learners in their classrooms. These adaptations and strategies include: 

  • modification of some or all of the course expectations so that they are challenging but attainable for the learner at his or her present level of English proficiency, given the necessary support from the teacher; 
  • use of a variety of instructional strategies (e.g., extensive use of visual cues, scaffolding, manipulatives, pictures, diagrams, graphic organizers;attention to clarity of instructions); 
  • modelling of preferred ways of working in mathematics; previewing of textbooks; pre-teaching of key vocabulary; peer tutoring; strategic use of students’ first languages); 
  • use of a variety of learning resources (e.g., visual material, simplified text, bilingual dictionaries, materials that reflect cultural diversity); 
  • use of assessment accommodations (e.g., granting of extra time; simplification of language used in problems and instructions; use of oral interviews, learning logs, portfolios, demonstrations, visual representations, and tasks requiring completion of graphic organizers or cloze sentences instead of tasks that depend heavily on proficiency in English). 

When learning expectations in any course are modified for English language learners (whether or not the students are enrolled in an ESL or ELD course), this must be clearly indicated on the student’s report card. 

Although the degree of program adaptation required will decrease over time, students who are no longer receiving ESL or ELD support may still need some program adaptations to be successful. 

For further information on supporting English language learners, refer to The Ontario Curriculum, Grades 9 to 12: English As a Second Language and English Literacy Development, 2007 and the resource guide Many Roots Many Voices: Supporting English Language Learners in Every Classroom (Ministry of Education, 2005). 


To ensure that all students in the province have an equal opportunity to achieve their full potential, the curriculum must be free from bias, and all students must be provided with a safe and secure environment, characterized by respect for others, that allows them to participate fully and responsibly in the educational experience. 

Learning activities and resources used to implement the curriculum should be inclusive in nature, reflecting the range of experiences of students with varying backgrounds, abilities, interests, and learning styles. They should enable students to become more sensitive to the diverse cultures and perceptions of others, including Aboriginal peoples. By discussing aspects of the history of mathematics, teachers can help make students aware of the various cultural groups that have contributed to the evolution of mathematics over the centuries. Finally, students need to recognize that ordinary people use mathematics in a variety of everyday contexts, both at work and in their daily lives. 

Connecting mathematical ideas to real-world situations through learning activities can enhance students’ appreciation of the role of mathematics in human affairs, in areas including health, science, and the environment. Students can be made aware of the use of mathematics in contexts such as sampling and surveying and the use of statistics to analyse trends. Recognizing the importance of mathematics in such areas helps motivate students to learn and also provides a foundation for informed, responsible citizenship. 

Teachers should have high expectations for all students. To achieve their mathematical potential, however, different students may need different kinds of support. Some boys, for example, may need additional support in developing their literacy skills in order to complete mathematical tasks effectively. For some girls, additional encouragement to envision themselves in careers involving mathematics may be beneficial. For example, teachers might consider providing strong role models in the form of female guest speakers who are mathematicians or who use mathematics in their careers. 


Literacy skills can play an important role in student success in mathematics courses. Many of the activities and tasks students undertake in mathematics courses involve the use of written, oral, and visual communication skills. For example, students use language to record their observations, to explain their reasoning when solving problems, to describe their inquiries in both informal and formal contexts, and to justify their results in smallgroup conversations, oral presentations, and written reports. The language of mathematics includes special terminology. The study of mathematics consequently encourages students to use language with greater care and precision and enhances their ability to communicate effectively. 

The Ministry of Education has facilitated the development of materials to support literacy instruction across the curriculum. Helpful advice for integrating literacy instruction in mathematics courses may be found in the following resource documents: 

  • Think Literacy: Cross-Curricular Approaches, Grades 7–12, 2003 Think Literacy: 
  • Cross-Curricular Approaches, Grades 7–12 – Mathematics: SubjectSpecific Examples, Grades 10–12, 2005 

In all courses in mathematics, students will develop their ability to ask questions and to plan investigations to answer those questions and to solve related problems. Students need to learn a variety of research methods and inquiry approaches in order to carry out these investigations and to solve problems, and they need to be able to select the methods that are most appropriate for a particular inquiry. Students learn how to locate relevant information from a variety of sources, such as statistical databases, newspapers, and reports. As they advance through the grades, students will be expected to use such sources with increasing sophistication. They will also be expected to distinguish between primary and secondary sources, to determine their validity and relevance, and to use them in appropriate ways. 

THE ROLE OF INFORMATION AND COMMUNICATION TECHNOLOGY IN MATHEMATICS Information and communication technologies (ICT) provide 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, allowing students to devote more of their efforts to thinking and concept development. Useful ICT tools include simulations, multimedia resources, databases, sites that give 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. 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 technologies can 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. 

Although the Internet is a powerful electronic learning tool, there are potential risks attached to its use. All students must be made aware of issues of Internet privacy, safety, and responsible use, as well as of the ways in which this technology is being abused – for example, when it is used to promote hatred. 

Teachers, too, will find the various ICT tools useful in their teaching practice, both for whole class instruction and for the design of curriculum units that contain varied approaches to learning to meet diverse student needs. 


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. 


Teachers planning programs in mathematics need to be aware of the purpose and benefits of the Ontario Skills Passport (OSP).The OSP is a bilingual web-based resource that enhances the relevancy of classroom learning for students and strengthens school-work connections. The OSP provides clear descriptions of Essential Skills such as Reading Text, Writing, Computer Use, Measurement and Calculation, and Problem Solving and includes an extensive database of occupation-specific workplace tasks that illustrate how workers use these skills on the job. The Essential Skills are transferable, in that they are used in virtually all occupations. The OSP also includes descriptions of important work habits, such as working safely, being reliable, and providing excellent customer service. The OSP is designed to help employers assess and record students’ demonstration of these skills and work habits during their cooperative education placements. Students can use the OSP to identify the skills and work habits they already have, plan further skill development, and show employers what they can do. 

The skills described in the OSP are the Essential Skills that the Government of Canada and other national and international agencies have identified and validated, through extensive research, as the skills needed for work, learning, and life. These Essential Skills provide the foundation for learning all other skills and enable people to evolve with their jobs and adapt to workplace change. For further information on the OSP and the Essential Skills, visit: 


Cooperative education and other workplace experiences, such as job shadowing, field trips, and work experience, enable students to apply the skills they have developed in the classroom to real-life activities. Cooperative education and other workplace experiences also help to broaden students’ knowledge of employment opportunities in a wide range of fields, including science and technology, research in the social sciences and humanities, and many forms of business administration. In addition, students develop their understanding of workplace practices, certifications, and the nature of employer-employee relationships. 

Cooperative education teachers can support students taking mathematics courses by maintaining links with community-based businesses and organizations, and with colleges and universities, to ensure students studying mathematics have access to hands-on experiences that will reinforce the knowledge and skills they have gained in school. Teachers of mathematics can support their students’ learning by providing opportunities for experiential learning that will reinforce the knowledge and skills they have gained in school. 

Health and safety issues must be addressed when learning involves cooperative education and other workplace experiences. Teachers who provide support for students in workplace learning placements need to assess placements for safety and ensure students understand the importance of issues relating to health and safety in the workplace. Before taking part in workplace learning experiences, students must acquire the knowledge and skills needed for safe participation. Students must understand their rights to privacy and confidentiality as outlined in the Freedom of Information and Protection of Privacy Act. They have the right to function in an environment free from abuse and harassment, and they need to be aware of harassment and abuse issues in establishing boundaries for their own personal safety. They should be informed about school and community resources and school policies and reporting procedures with regard to all forms of abuse and harassment. 

Policy/Program Memorandum No. 76A, “Workplace Safety and Insurance Coverage for Students in Work Education Programs” (September 2000), outlines procedures for ensuring the provision of Health and Safety Insurance Board coverage for students who are at least 14 years of age and are on placements of more than one day. (A one-day jobshadowing or job-twinning experience is treated as a field trip.) Teachers should also be aware of the minimum age requirements outlined in the Occupational Health and Safety Act for persons to be in or to be working in specific workplace settings. 

All cooperative education and other workplace experiences will be provided in accordance with the ministry’s policy document entitled Cooperative Education and Other Forms of Experiential Learning: Policies and Procedures for Ontario Secondary Schools, 2000. 


Mathematics courses are well suited for inclusion in programs leading to a Specialist High-Skills Major (SHSM) or in programs designed to provide pathways to particular apprenticeship or workplace destinations. In an SHSM program, mathematics courses can be bundled with other courses to provide the academic knowledge and skills important to particular industry sectors and required for success in the workplace and postsecondary education, including apprenticeship. Mathematics courses may also be combined with cooperative education credits to provide the workplace experience required for SHSM programs and for various program pathways to apprenticeship and workplace destinations. (SHSM programs would also include sector-specific learning opportunities offered by employers, skills-training centres, colleges, and community organizations.) 


Although health and safety issues are not normally associated with mathematics, they may be important when 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

Program Planning Considerations: These considerations are based on the directives mentioned in the Ontario Curriculum:  Grades 11 and 12 Mathematics 2007 (Revised). A copy of this document is available online at: 


Trillium bookstore:  McGraw-Hill Ryerson Advanced Functions 12 © 2008  

YouTube Resources 

The Infamous Bell:

Ms Havrot’s Canadian University Math Prerequisites: 

Explorer Hop Academy Program Materials


The primary purpose of assessment and evaluation is to improve student learning. The Achievement Chart for Mathematics will guide all assessment and evaluation.  

Term Evaluation = 70% of total grade broken up as follow:

Categories of Evaluation 

Term Work: 70% 

(based on conversations,  

observations, and products)

Final Summative: 30%

Knowledge and Understanding 


Final exam 30%

Thinking and Inquiry 






The final grade will be determined as follows: 

Term work and project  = 70% of final mark
Final exam = 30% of final mark


The six learning skills reported on the provincial report card are: Responsibility, Organization, Independent  Work, Collaboration, Initiative, and Self-Regulation. These are reported using a letter system of (E)  excellent, (G) good, (S) satisfactory and (N) needs improvement. These will be assessed using checklists,  student self-assessment, and teacher assessment. Learning skills assessment does not count toward the  course mark but proficiency with these skills is essential for achieving success.


Participating in online courses is a privilege. You are expected to behave in an appropriate manner while  logged into your online course(s). Any inappropriate use of language, use of the site facilities for purposes  other than course related activities or malicious actions taken against others through these facilities are not  permitted. These violations will be dealt with in a severe manner and may result in suspension or expulsion  from online learning. Please remember, your actions within the site can and will be monitored. Any  communications on the Internet, whether through email, private chat room, or other methods are not private.  Be aware that anything you communicate may be viewed by others. If you don't want it known, do not type it  into your computer. 


Students are expected to take responsibility in the completion of their course by creating a schedule in  advance and meeting deadlines. You are expected to write every test/evaluation as well as complete all  summative assessments. 

Notebooks need to be well kept and organized. You will get homework for every lesson. If you are having  trouble with the homework or with concepts covered in class, reach out to your instructor for support.

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