Mathematics 3 - Nova Scotia
Mathematics 3Guide2013
Website ReferencesWebsite references contained within this document are provided solely as a convenience and do not constitutean endorsement by the Department of Education of the content, policies, or products of the referenced website.The department does not control the referenced websites and subsequent links, and is not responsible for theaccuracy, legality, or content of those websites. Referenced website content may change without notice.Regional Education Centres and educators are required under the Department’s Public School ProgramsNetwork Access and Use Policy to preview and evaluate sites before recommending them for student use. If anoutdated or inappropriate site is found, please report it to curriculum@novascotia.ca .Mathematics 3 Crown copyright, Province of Nova Scotia, 2013, 2019Prepared by the Department of Education and Early Childhood DevelopmentThis is the most recent version of the current curriculum materials as used by teachers in Nova Scotia.The contents of this publication may be reproduced in part provided the intended use is for noncommercial purposes and full acknowledgment is given to the Nova Scotia Department of Education.
FT DRAMathematics 3DRAFTMay3201 DRACURRICULUM GUIDEArts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business EducationEnglish Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts EntrepreneurshipFamily Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health EducationInternational Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate LanguagesMathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Developmentand Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education PhysicalEducation Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled TradesSocial Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology EducationInformation and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and CommunicationTechnology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education BusinessEducation English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language ArtsEntrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family StudiesHealth Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education InternationalBaccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages MathematicsPersonal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and CareerEducation Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education SciencesSkilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social StudiesTechnology Education Information and Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Informationand Communication Technology Arts Education Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology ArtsEducation Business Education English Language Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education EnglishLanguage Arts Entrepreneurship Family Studies Health Education International Baccalaureate Languages Mathematics Personal Development and Career Education Physical Education Sciences Skilled Trades Social Studies Technology Education Information and Communication Technology Arts Education Business Education English Language Arts EntrepreneurshipFT
Mathematics 3Implementation DraftMay 2013
Website ReferencesWebsite references contained within this document are provided solely as a convenience and do not constitutean endorsement by the Department of Education and Early Childhood Development of the content, policies, orproducts of the referenced website. The Department does not control the referenced websites and subsequentlinks, and is not responsible for the accuracy, legality, or content of those websites. Referenced website contentmay change without notice.School boards and educators are required under the Department’s Public School Programs’ Internet Access andUse Policy to preview and evaluate sites before recommending them for student use. If an outdated orinappropriate site is found, please report it to links@EDnet.ns.ca.Mathematics 3, Implementation Draft Crown Copyright, Province of Nova Scotia, 2013Prepared by the Department of Education and Early Childhood DevelopmentThe contents of this publication may be reproduced in part provided the intended use is for noncommercial purposes and full acknowledgment is given to the Nova Scotia Department of Education andEarly Childhood Development. Where this document indicates a specific copyright holder, permission toreproduce the material must be obtained directly from that copyright holder. Please note that allattempts have been made to identify and acknowledge information from external sources. In the eventthat a source was overlooked, please contact English Program Services, Nova Scotia Department ofEducation, eps@EDnet.ns.ca.Cataloguing-in-Publication Data
AcknowledgementsAcknowledgementsThe Nova Scotia Department of Education and Early Childhood Education wishes to express its gratitudeto the following organizations for granting permission to adapt their mathematics curriculum in thedevelopment of this guide.Manitoba EducationThe Western and Northern Canadian Protocol(WNCP) for Collaboration in EducationNew Brunswick Department of EducationNewfoundland and Labrador Department ofEducationWe also gratefully acknowledge the contributions of the following individuals toward the developmentof the Nova Scotia Mathematics 3 curriculum.Arlene AndrecykCape Breton-Victoria Regional School BoardMark MacLeodSouth Shore Regional School BoardSharon BoudreauCape Breton Victoria Regional School BoardRebecca McDonaldChignecto-Central Regional School BoardGaston ComeauSouth Shore Regional School BoardSonya O’SullivanHalifax Regional School BoardBob CraneMi'kmaw Kina'matneweyNovadawn OultonAnnapolis Valley Regional School BoardRobin HarrisHalifax Regional School BoardMark PettipasStrait Regional School BoardDarlene MacKeen HudsonChignecto-Central Regional School BoardSherene SharpeSouth Shore Regional School BoardPatsy Height LewisTri-County Regional School BoardFred SullivanStrait Regional School BoardJill MacDonaldAnnapolis Valley Regional School BoardMarlene UrquhartCape Breton-Victoria Regional School BoardMathematics 3, Implementation Draft, May 2013iii
ContentsContentsIntroduction . 1Background and Rationale . 1Purpose . 1Program Design and Components . 3Assessment . 3Time to Learn for Mathematics. 4Outcomes . 5Conceptual Framework for K–9 Mathematics . 5Structure of the Mathematics Curriculum . 5Mathematical Processes . 15Nature of Mathematics . 19Curriculum Document Format . 21Contexts for Learning and Teaching . 23Beliefs about Students and Mathematics Learning . 23StrandsNumber . 27Patterns and Relations . 101Measurement . 119Geometry . 143Statistics and Probability . 155Appendices . 167Appendix A: Additional Information . 169References . 221Mathematics 3, Implementation Draft, May 2013v
IntroductionIntroductionBackground and RationaleMathematics curriculum is shaped by a vision that fosters the development of mathematically literatestudents who can extend and apply their learning and who are effective participants in society. It isessential that the mathematics curriculum reflect current research in mathematics instruction. Toachieve this goal, Western and Northern Canadian Protocol’s (WNCP) The Common CurriculumFramework for K–9 Mathematics (2006) has been adopted as the basis for the new mathematicscurriculum in Nova Scotia.The Common Curriculum Framework was developed by the seven ministries of education (Alberta,British Columbia, Manitoba, Northwest Territories, Nunavut, Saskatchewan, and Yukon Territory) incollaboration with teachers, administrators, parents, business representatives, post-secondaryeducators, and others. The framework identifies beliefs about mathematics, general and specific studentoutcomes, and performance indicators agreed upon by the seven jurisdictions. The outcomes andperformance indicators have been adapted for Nova Scotia. This document is based on both nationaland international research by the WNCP and the National Council of Teachers of Mathematics (NCTM).There is an emphasis in the Nova Scotia curriculum on particular key concepts at each grade that willresult in greater depth of understanding and, ultimately, stronger student achievement. There is also agreater emphasis on number sense and operations concepts in the early grades to ensure studentsdevelop a solid foundation in numeracy.PurposeThis document provides sets of outcomes and performance indicators to be used as a mandatedcommon base for defining mathematics curriculum expectations. This common base should result inconsistent student outcomes in mathematics within the province of Nova Scotia. It should also enableeasier transfer for students moving within the province or from any jurisdiction that has adopted theWNCP framework. This document is intended to clearly communicate to all education partners acrossthe province the high expectations for students’ mathematical learning.Mathematics 3, Implementation Draft, May 20131
Program Design and ComponentsProgram Design and ComponentsAssessmentOngoing assessment for learning is essential to effective teaching and learning. Research has shown thatassessment for learning (formative assessment) practices produce significant and often substantiallearning gains, close achievement gaps, and build students’ ability to learn new skills (Black & Wiliam1998; OECD 2006). Student involvement in assessment promotes learning. Timely and effective teacherfeedback and student self-assessment allow students to reflect on and articulate their understanding ofmathematical concepts and ideas.Assessment in the classroom includes providing clear goals, targets, and learning outcomes using exemplars, rubrics, and models to help clarify outcomes and identify important features of thework monitoring progress towards outcomes and providing feedback as necessary encouraging self-assessment fostering a classroom environment where conversations about learning take place, where studentscan check their thinking and performance and develop a deeper understanding of their learning(Davies 2000)Assessment for learning practices act as the scaffolding for learning, which only then can be measuredthrough assessment of learning (summative assessment). Assessment of learning tracks studentprogress, informs instructional programming, and aids in decision making. Both forms of assessment arenecessary to guide teaching, stimulate learning, and produce achievement gains.Assessment of student learning should align with curriculum outcomes clearly define criteria for success make explicit the expectations for students’ performance use a wide variety of assessment strategies and tools yield useful information to inform instructionMathematics 3, Implementation Draft, May 20133
Program Design and ComponentsTime to Learn for MathematicsThe Time to Learn Strategy Guidelines for Instructional Time: Grades Primary–6 includes time formathematics instruction in the “Required Each Day” section. In order to support a constructivistapproach to teaching through problem solving, it is highly recommended that the 45 minutes requireddaily in grades primary–2 and the 60 minutes required daily for grades 3–6 mathematics instruction beprovided in an uninterrupted block of time.Time to Learn guidelines can be found fwww.ednet.ns.ca/files/ps-policies/instructional time guidelines p-6.pdf4Mathematics 3, Implementation Draft, May 2013
OutcomesOutcomesConceptual Framework for Mathematics Primary–9The chart below provides an overview of how mathematical processes and the nature of mathematicsinfluence learning outcomes.(Adapted with permission from Western and Northern Canadian Protocol, The Common CurriculumFramework for K–9 Mathematics, p. 5. All rights reserved.)Structure of the Mathematics CurriculumStrandsThe learning outcomes in the Nova Scotia Framework are organized into five strands across gradesprimary to 9. Number (N)Pa
Newfoundland and Labrador Department of Education The Western and Northern Canadian Protocol (WNCP) for Collaboration in Education We also gratefully acknowledge the contributions of the following individuals toward the development of the Nova Scotia Mathematics 3 curriculum. Arlene Andrecyk Cape Breton-Victoria Regional School Board
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