Transcription

ISBN 0-7794-7940-8Ministry of Education04-165 Queen’s Printer for Ontario, 2005The Ontario CurriculumGrades 9 and 10REVISEDMathematicsPrinted on recycled paper2005

ContentsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3The Place of Mathematics in the Curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Roles and Responsibilities in Mathematics Programs . . . . . . . . . . . . . . . . . . . . . . . . . .4The Program in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6Curriculum Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8Strands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9The Mathematical Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12Reasoning and Proving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13Reflecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14Selecting Tools and Computational Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14Connecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15Representing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16Communicating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16Assessment and Evaluation of Student Achievement . . . . . . . . . . . . . . . . . . . . . . . . . .17Basic Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17The Achievement Chart for Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18Evaluation and Reporting of Student Achievement . . . . . . . . . . . . . . . . . . . . . . . . . . . .22Some Considerations for Program Planning in Mathematics . . . . . . . . . . . . . . . . . . .23Teaching Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23Planning Mathematics Programs for Exceptional Students . . . . . . . . . . . . . . . . . . . . . . .24English As a Second Language and English Literacy Development (ESL/ELD) . . . . . . . .25Antidiscrimination Education in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26Une publication équivalente est disponible en français sous letitre suivant : Le curriculum de l’Ontario, 9 e et 10 e année –Mathématiques, 2005.This publication is available on the Ministry of Education’swebsite, at http://www.edu.gov.on.ca.Every effort has been made in this publication to identify mathematics resources and tools (e.g., manipulatives) in generic terms. In cases where aparticular product is used by teachers in schools across Ontario, that product is identified by its trade name, in the interests of clarity.

2THE ONTARIO CURRICULUM, GRADES 9 AND 10: MATHEMATICSLiteracy and Inquiry/Research Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27The Role of Technology in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27Career Education in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28Health and Safety in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28CoursesPrinciples of Mathematics, Grade 9, Academic (MPM1D) . . . . . . . . . . . . . . . . . . . . . . .29Foundations of Mathematics, Grade 9, Applied (MFM1P) . . . . . . . . . . . . . . . . . . . . . . .38Principles of Mathematics, Grade 10, Academic (MPM2D) . . . . . . . . . . . . . . . . . . . . . .46Foundations of Mathematics, Grade 10, Applied (MFM2P) . . . . . . . . . . . . . . . . . . . . . .53Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60

3IntroductionThis document replaces The Ontario Curriculum, Grades 9 and 10: Mathematics, 1999.Beginning in September 2005, all Grade 9 and 10 mathematics courses will be based on theexpectations outlined in this document.The Place of Mathematics in the CurriculumThe unprecedented changes that are taking place in today’s world will profoundly affect thefuture of today’s students. To meet the demands of the world in which they will live, studentswill need to adapt to changing conditions and to learn independently. They will require theability to use technology effectively and the skills for processing large amounts of quantitativeinformation. Today’s mathematics curriculum must prepare students for their future roles insociety. It must equip them with essential mathematical knowledge and skills; with skills ofreasoning, problem solving, and communication; and, most importantly, with the ability andthe incentive to continue learning on their own. This curriculum provides a framework foraccomplishing these goals.The choice of specific concepts and skills to be taught must take into consideration new applications and new ways of doing mathematics. The development of sophisticated yet easy-to-usecalculators and computers is changing the role of procedure and technique in mathematics.Operations that were an essential part of a procedures-focused curriculum for decades cannow be accomplished quickly and effectively using technology, so that students can now solveproblems that were previously too time-consuming to attempt, and can focus on underlyingconcepts. “In an effective mathematics program, students learn in the presence of technology.Technology should influence the mathematics content taught and how it is taught. Powerfulassistive and enabling computer and handheld technologies should be used seamlessly in teaching, learning, and assessment.”1 This curriculum integrates appropriate technologies into thelearning and doing of mathematics, while recognizing the continuing importance of students’mastering essential numeric and algebraic skills.Mathematical knowledge becomes meaningful and powerful in application. This curriculumembeds the learning of mathematics in the solving of problems based on real-life situations.Other disciplines are a ready source of effective contexts for the study of mathematics. Richproblem-solving situations can be drawn from closely related disciplines, such as computerscience, business, recreation, tourism, biology, physics, or technology, as well as from subjectshistorically thought of as distant from mathematics, such as geography or art. It is importantthat these links between disciplines be carefully explored, analysed, and discussed to emphasizefor students the pervasiveness of mathematical knowledge and mathematical thinking in allsubject areas.1. Expert Panel on Student Success in Ontario, Leading Math Success: Mathematical Literacy, Grades 7–12 – The Report ofthe Expert Panel on Student Success in Ontario, 2004 (Toronto: Ontario Ministry of Education, 2004), p. 47. (Referred tohereafter as Leading Math Success.)

4THE ONTARIO CURRICULUM, GRADES 9 AND 10: MATHEMATICSThe development of mathematical knowledge is a gradual process. A coherent and continuousprogram is necessary to help students see the “big pictures”, or underlying principles, of mathematics. The fundamentals of important skills, concepts, processes, and attitudes are initiated inthe primary grades and fostered through elementary school. The links between Grade 8 andGrade 9 and the transition from elementary school mathematics to secondary school mathematics are very important in the student’s development of confidence and competence.The Grade 9 courses in this curriculum build on the knowledge of concepts and skills thatstudents are expected to have by the end of Grade 8. The strands used are similar to those ofthe elementary program, with adjustments made to reflect the new directions mathematicstakes in secondary school. The Grade 9 courses are based on principles that are consistent withthose that underpin the elementary program, facilitating the transition from elementaryschool. These courses reflect the belief that students learn mathematics effectively when theyare initially given opportunities to investigate ideas and concepts and are then guided carefullyinto an understanding of the abstract mathematics involved. Skill acquisition is an importantpart of the program; skills are embedded in the contexts offered by various topics in the mathematics program and should be introduced as they are needed.The Grade 9 and 10 mathematics curriculum is designed to foster the development of theknowledge and skills students need to succeed in their subsequent mathematics courses, whichwill prepare them for the postsecondary destinations of their choosing.Roles and Responsibilities in Mathematics ProgramsStudents. Students have many responsibilities with regard to their learning in school. Studentswho make the effort required and who apply themselves will soon discover that there is adirect relationship between this effort and their achievement, and will therefore be more motivated to work. There will be some students, however, who will find it more difficult to takeresponsibility for their learning because of special challenges they face. For these students, theattention, patience, and encouragement of teachers and family can be extremely importantfactors for success. However, taking responsibility for one’s progress and learning is an important part of education for all students, regardless of their circumstances.Successful mastery of concepts and skills in mathematics requires a sincere commitment towork and study. Students are expected to develop strategies and processes that facilitate learning and understanding in mathematics. Students should also be encouraged to actively pursueopportunities to apply their problem-solving skills outside the classroom and to extend andenrich their understanding of mathematics.Parents. Parents have an important role to play in supporting student learning. Studies showthat students perform better in school if their parents or guardians are involved in their education. By becoming familiar with the curriculum, parents can find out what is being taught inthe courses their children are taking and what their children are expected to learn. This awareness will enhance parents’ ability to discuss their children’s work with them, to communicatewith teachers, and to ask relevant questions about their children’s progress. Knowledge of theexpectations in the various courses also helps parents to interpret teachers’ comments on student progress and to work with them to improve student learning.

5INTRODUCTIONThe mathematics curriculum promotes lifelong learning not only for students but also fortheir parents and all those with an interest in education. In addition to supporting regularschool activities, parents can encourage their sons and daughters to apply their problemsolving skills to other disciplines or to real-world situations. Attending parent-teacher interviews,participating in parent workshops, becoming involved in school council activities (includingbecoming a school council member), and encouraging students to complete their assignmentsat home are just a few examples of effective ways to support student learning.Teachers. Teachers and students have complementary responsibilities. Teachers are responsiblefor developing appropriate instructional strategies to help students achieve the curriculumexpectations for their courses, as well as for developing appropriate methods for assessing andevaluating student learning. Teachers also support students in developing the reading, writing,and oral communication skills needed for success in their mathematics courses. Teachers bringenthusiasm and varied teaching and assessment approaches to the classroom, addressing different student needs and ensuring sound learning opportunities for every student.Recognizing that students need a solid conceptual foundation in mathematics in order to further develop and apply their knowledge effectively, teachers endeavour to create a classroomenvironment that engages students’ interest and helps them arrive at the understanding ofmathematics that is critical to further learning.Using a variety of instructional, assessment, and evaluation strategies, teachers provide numerous opportunities for students to develop skills of inquiry, problem solving, and communication as they investigate and learn fundamental concepts. The activities offered should enablestudents not only to make connections among these concepts throughout the course but alsoto relate and apply them to relevant societal, environmental, and economic contexts. Opportunities to relate knowledge and skills to these wider contexts – to the goals and concernsof the world in which they live – will motivate students to learn and to become lifelonglearners.Principals. The principal works in partnership with teachers and parents to ensure that eachstudent has access to the best possible educational experience. To support student learning,principals ensure that the Ontario curriculum is being properly implemented in all classroomsusing a variety of instructional approaches. They also ensure that appropriate resources aremade available for teachers and students. To enhance teaching and learning in all subjects,including mathematics, principals promote learning teams and work