E Of M 10 12 - British Columbia
This document represents an updating of the 2000 IRP. This updating has beenundertaken for the purpose of clarifying the Prescribed Learning Outcomes introducing Suggested Achievement Indicators addressing content overloadResources previously recommended for the 2000 version of the curriculum,where still valid, continue to support this updated IRP. (See the LearningResources section in this IRP for additional information.)Essentials ofMathematics 10 to 12Integrated Resource Package 2006IRP 137
Library and Archives Canada Cataloguing in Publication DataMain entry under title:Essentials of mathematics 10 to 12 : integrated resourcepackage 2006. – Rev. ed.Also available on the Internet.ISBN 07726550061. Mathematics – Study and teaching (Secondary).2. Business mathematics – Study and teaching (Secondary).I. British Columbia. Ministry of Education.QA39.3.E87 2006510.7'12C2006-9600287Copyright 2006 Ministry of Education, Province of British Columbia.Copyright NoticeNo part of the content of this document may be reproduced in any form or by any means, including electronicstorage, reproduction, execution, or transmission without the prior written permission of the Province.Proprietary NoticeThis document contains information that is proprietary and confidential to the Province. Any reproduction,disclosure, or other use of this document is expressly prohibited except as the Province may authorizein writing.Limited Exception to Non-ReproductionPermission to copy and use this publication in part, or in its entirety, for non-profit educational purposeswithin British Columbia and the Yukon, is granted to (a) all staff of BC school board trustees, includingteachers and administrators; organizations comprising the Educational Advisory Council as identifiedby Ministerial Order; and other parties providing, directly or indirectly, educational programs to entitledstudents as identified by the School Act, R.S.B.C. 1996, c.412, or the Independent School Act, R.S.B.C. 1996, c.216,and (b) a party providing, directly or indirectly, educational programs under the authority of the Minister ofthe Department of Education for the Yukon Territory as defined in the Education Act, R.S.Y. 2002, c.61.
Table of ContentsAcknowledgmentsAcknowledgments. IIIPrefacePreface. VIntroduction to Essentials of Mathematics 10 to 12Rationale. 3Requirements and Graduation Credits . 4Graduation Program Examination. 4Goals for Essentials of Mathematics 10 to 12. 4Curriculum Organizers. 5Mathematical Processes. 6Essentials of Mathematics 10 to 12: At a Glance. 9Suggested Timeframe. 10Considerations for Program DeliveryAlternative Delivery Policy.Instructional Focus.Fostering the Development of Positive Attitudes .Applying Mathematics .Involving Parents and Guardians.Confidentiality.Inclusion, Equity, and Accessibility for All Learners . .Working with the School and Community .Working with the Aboriginal Community . .Information and Communications Technology .Copyright and Responsibility .1313131414141415151516Prescribed Learning OutcomesIntroduction.Wording of Prescribed Learning Outcomes.Domains of Learning.Essentials of Mathematics 10 Prescribed Learning Outcomes.Essentials of Mathematics 11 Prescribed Learning Outcomes.Essentials of Mathematics 12 Prescribed Learning Outcomes.191919202224Student AchievementIntroduction.Classroom Assessment and Evaluation.Key Elements.Achievement Indicators.Essentials of Mathematics 10Key Elements.Suggested Achievement Indicators.292932323435Essentials of Mathematics 10 to 12
Table of ContentsEssentials of Mathematics 11Key Elements . .Suggested Achievement Indicators.Essentials of Mathematics 12Key Elements . .Suggested Achievement Indicators.44455253Learning ResourcesIntroduction. 61Essentials of Mathematics 10 to 12 Grade Collections. 61GlossaryGlossary. 65II Essentials of Mathematics 10 to 12
AcknowledgmentsMany people contributed their expertise to this document. The Project Co-ordinator was Mr. RichardDeMerchant of the Ministry of Education, working with other ministry personnel and our partnersin education. We would like to thank all who participated in this process.Essentials of Mathematics 10 to 12 IRP Refinement TeamBarb Lajeunesse, School District No. 36 (Surrey )Preliminary ReviewSandra Stevenson, School District No. 61 (Victoria)Preliminary ReviewHold Fast Consultants Inc.IRP writing and editingEssentials of Mathematics 10 to 12 III
PrefaceThis Integrated Resource Package (IRP)provides basic information teachers willrequire in order to implement Essentials ofMathematics 10 to 12. This document supersedesthe Essentials of Mathematics 10 to 12 portionof the Mathematics 10 to 12 Integrated ResourcePackage (2000).The information contained in this documentis also available on the Internet atwww.bced.gov.bc.ca/irp/irp.htmThe following paragraphs provide briefdescriptions of the components of the IRP.IntroductionThe Introduction provides general informationabout Essentials of Mathematics 10 to 12, includingspecial features and requirements.Included in this section are a rationale for teaching Essentials ofMathematics 10 to 12 in BC schools the curriculum goals descriptions of the curriculum organizers –groupings for prescribed learning outcomesthat share a common focus a suggested timeframe for each curriculumorganizer a graphic overview of the curriculum contentConsiderations For Program DeliveryThis section of the IRP contains additionalinformation to help educators develop their schoolpractices and plan their program delivery to meetthe needs of all learners.Prescribed Learning OutcomesThis section contains the prescribed learningoutcomes, the legally required content standardsfor the provincial education system. The learningoutcomes define the required knowledge, skills,and attitudes for each subject. They are statementsof what students are expected to know and be ableto do by the end of the course.Student AchievementThis section of the IRP contains information aboutclassroom assessment and measuring studentachievement, including sets of specific achievementindicators for each prescribed learning outcome.Achievement indicators are statements thatdescribe what students should be able to do inorder to demonstrate that they fully meet theexpectations set out by the prescribed learningoutcomes. Achievement indicators are notmandatory; they are provided to assist in theassessment of how well students achieve theprescribed learning outcomes.Also included in this section are key elements –descriptions of content that help determine theintended depth and breadth of the prescribedlearning outcomes.Learning ResourcesThis section contains general information onlearning resources, and provides a link to titles,descriptions, and ordering information for therecommended learning resources in the Essentialsof Mathematics 10 to 12 Grade Collections.GlossaryThe glossary defines selected terms used in thisIntegrated Resource Package.Essentials of Mathematics 10 to 12
IntroductionEssentials of Mathematics 10 to 12
Introduction to Essentials of Mathematics 10 to 12This Integrated Resource Package (IRP) setsout the provincially prescribed curriculumfor Essentials of Mathematics 10 to 12. Thedevelopment of this IRP has been guided by theprinciples of learning: Learning requires the active participationof the student. People learn in a variety of ways and atdifferent rates. Learning is both an individual and a groupprocess.In addition to these three principles, this documentrecognizes that British Columbia’s schools includeyoung people of varied backgrounds, interests,abilities, and needs. Wherever appropriate for thiscurriculum, ways to meet these needs and to ensureequity and access for all learners have beenintegrated as much as possible into the learningoutcomes and achievement indicators.The Achievement Indicators were developed, inpart, using the following documents: Mathematics 10 to 12 Integrated Resource Package(British Columbia Ministry of Education, 2000) Essentials of Mathematics 10 ProvincialExamination Specifications (British ColumbiaMinistry of Education, 2004)This document represents an updating of the 2000IRP. This updating has been undertaken for thepurpose of clarifying the prescribed learning outcomes introducing suggested achievement indicators addressing content overloadResources previously recommended for the 2000version of the curriculum continue to support thisupdated IRP. (See the Learning Resources sectionlater in this IRP for additional information.)Essentials of Mathematics 10 to 12, in draft form,was available for public review and responsefrom November to December, 2005. Feedbackfrom educators, students, parents, and othereducational partners informed the developmentof this updated IRP.RationaleMathematics is increasingly important in ourtechnological society. Students today requirethe ability to reason and communicate, to solveproblems, and to understand and use mathematics.Development of these skills helps students becomenumerate.Numeracy can be defined as the combinationof mathematical knowledge, problem solvingand communication skills required by allpersons to function successfully withinour technological world. Numeracy is morethan knowing about numbers and numberoperations. (British Columbia Associationof Mathematics Teachers, 1998)Becoming numerate involves developing the abilityto explore, conjecture, reason logically, and use avariety of mathematical methods to solve problems.It also involves the development of self-confidenceand the ability to use quantitative and spatialinformation in problem solving and decisionmaking. As students develop their numeracy skillsand concepts, they generally grow more confidentand motivated in their mathematical explorations.This growth occurs as they learn to enjoy andvalue mathematics, to think analytically, and tounderstand and appreciate the role of mathematicsin everyday life.The provincial mathematics curriculum emphasizesthe development of numeracy skills and conceptsand their practical application in higher educationand the workplace. The curriculum placesemphasis on probability and statistics, reasoningand communication, measurement, and problemsolving. To ensure that students are prepared forthe demands of both further education and theworkplace, the graduate years of the mathematicscurriculum (Grades 10 to 12) help students developa more sophisticated sense of numeracy.Essentials of Mathematics 10 to 12
Introduction to Essentials of Mathematics 10 to 12Requirements and Graduation CreditsEssentials of Mathematics 10 and 11 or 12 are twoof the courses available for students to satisfy theGraduation Program mathematics requirement.Essentials of Mathematics 10, 11, and 12 are eachdesignated as four-credit courses, and must bereported as such to the Ministry of Education fortranscript purposes. Letter grades and percentagesmust be reported for these courses. It is not possibleto obtain partial credit for these courses.The course codes for Essentials of Mathematics 10to 12 are EMA 10, EMA 11, and EMA 12. Thesecourses are also available in French (Mathématiquesde base 10, Mathématiques de base 11, Mathématiquesde base 12; course codes EMAF 10, EMAF 11,EMAF 12).Graduation Program ExaminationEssentials of Mathematics 10 has a GraduationProgram examination, worth 20% of the final coursemark. Students are required to take this exam toreceive credit for the course. There is no provincialexam for Essentials of Mathematics 12.For more information, refer to the Ministryof Education examinations web site:www.bced.gov.bc.ca/exams/Goals for Essentialsof Mathematics 10 to 12In order to meet the challenges of society, highschool graduates must be numerate. Studentsfollowing this pathway will have opportunitiesto improve their numeracy skills and concepts.Developing a sense of numeracy will help them tounderstand how mathematical concepts permeatedaily life, business, industry, and government.Students need to be able to use mathematics notjust in their work lives, but also in their personallives as citizens and consumers. It is intended thatstudents will learn to value mathematics andbecome confident in their mathematical abilities.Goals for Essentials of Mathematics 10 to 12The aim of Essentials of Mathematics 10 to 12 is to provide students with the necessary numeracy skillsand concepts to be successful in their daily lives, business, industry, and government.Students will become numerate citizens with the ability to explore, conjecture, reason logically, and use a variety ofmathematical methods to solve problems develop self-confidence and the ability to use quantitative and spatial information in problem solvingand decision making learn to enjoy and value mathematics, to think analytically, and to understand and appreciate the roleof mathematics in everyday life be prepared for the demands of both further education and the workplace and develop a moresophisticated sense of numeracy Essentials of Mathematics 10 to 12
Introduction to Essentials of Mathematics 10 to 12Curriculum OrganizersA curriculum organizer consists of a set ofprescribed learning outcomes that share a commonfocus. The prescribed learning outcomes forEssentials of Mathematics 10 to 12 progress inage-appropriate ways, and are grouped underthe following curriculum organizers andsuborganizers.Note that the ordering of these organizers andsuborganizers is not intended to imply an orderof instruction.Curriculum Organizers and SuborganizersEssentials of MathematicsNumber Business Plan Government Finances Income and Debt Investments Owning andOperating a Vehicle Personal Banking Personal Finance Personal Income Tax Spreadsheets Wages, Salaries, andExpensesPatterns and Relations Rate, Ratio, andProportion Relations andFormulas Variation andFormulasNumberIn this organizer students apply a range of numberoperations and problem solving skills to solveproblems involving personal and business finances.The Number organizer includes the followingsuborganizers: Business Plan – research and design a businessplan Government Finances – understandgovernment finances and implication onpayroll deductions and taxes Income and Debt – understand proceduresand apply mathematics related to moneymanagement Investments – make sound financial decisionstaking into account a variety of factors Owning and Operating a Vehicle – make sounddecisions related to acquiring and maintaininga motor vehicleShape and Space Design andMeasurement Geometry Project MeasurementTechnology Trigonometry Statistics andProbability Probability andSampling Data Analysis andInterpretationPersonal Banking – understand and use theservices and facilities of banks, trust companies,and credit unionsPersonal Finance – analyse various typesof insurance and mortgage scenariosPersonal Income Tax – understand how toprepare an income tax returnSpreadsheets – design and use spreadsheetsto mak
Mathematics 10 to 12 Integrated Resource Package (British Columbia Ministry of Education, 2000) Essentials of Mathematics 10 Provincial Examination Specifications (British Columbia Ministry of Education, 2004) This document represents an updating of the 2000 IRP. This updating has been undertaken for the purpose of
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Analytic Geometry and Calculus I Exam 1 Practice Problems Solutions 2/19/7 Question 1 Write the following as an integer: 2log4(9) log2(5) We have: 2log4(9) log2(5) 2log4(9) 2log2(5) 5 2log4(9) 5 41 2 log 4(9) 5 4log4(9) 1 2 5(9)12 5(3) 15: Here we used the properties: a b c a ac; aloga(b) b; (ab) c abc (a )b: Question 2 Eliminate the parameter t to nd a Cartesian equation .
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