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Program of Studies Elementary Schools Mathematics Interim RRICULUM STANDARDS BRANCH QA 14 cee A3 A31218 1994 /dlbcrra ECS-gr06 R 1994 EDUCATION CURRGDHT CX LIBRIS UNIVERSITATIS ALBERT/ENSIS MATHEMATICS PROGRAM OVERVIEW A. RATIONALE As students acquire an understanding of mathematical concepts, they further Mathematics is a common and essential human demonstrate: activity. To buy groceries, plan a trip, or carry • a willingness to take risks and accept out countless other everyday tasks, people need challenges mathematics to understand the world and function in it. When students learn • asense ofaccomplishment • a positive attitude toward mathematics mathematics, they have knowledge, skills and learning. attitudestomakedecisionsindaily life. Mathematics learningisanintegratedprocessin PHILOSOPHY which students develop and demonstrate understandingby solvingproblems. The mathematics program of studies is built uponthefollowingprinciples. Students develop mathematical understanding by building on a solid foundation of previous learnings and derive meaning from suitable • Students learn mathematics and apply it bysolvingreal-lifeproblems. problem-solvingexperiences intheenvironment. Students learn a new concept by solving As students solve problems, they use problems that contain key aspects of the manipulatives and diagrams to develop their understanding of concepts and make the concept. They are then able to apply their understandingto newproblem situations. connection with associated spoken terms and writtensymbols. • Communication is essential for developing and demonstrating Students demonstrate mathematical conceptualunderstanding. understanding by applying their knowledge to solve real-life problems, to justify solutions, and Students understand mathematics when toverifyforcorrectness. they reflect upon, explain and defend their As students apply the knowledge learned they ideas, using manipulatives (concrete mode), demonstrate their understanding of spoken diagrams (pictorial mode) and spoken terms andwrittensymbols(symbolicmode). terms and written symbols by using manipulativesanddiagrams. Mathematics (Elementary) A.l (Interim October 1994) Reasoning is required for understanding Problem solvingapplies mathematics to real-life mathematics. situations, as well as to problems arising from the investigation of mathematical ideas. When Students reason when they analyze solving problems, students must choose situations, make choices, draw conclusions appropriate operations and calculation methods; and justify processes as they work toward e.g., estimation, mental calculation, paper and solutions. pencil, calculator. Some problems, however, cannot be solved by simply adding, subtracting, Making connections is required for multiplying or dividing. They may require the understandingmathematics. use of other strategies, such as role playing, drawingadiagram, usinga pattern or collecting Students understand mathematics by data. makingconnectionswith, betweenoramong: - what they already know and new Students develop and demonstrate their learning understandingofconceptsasthey solveproblems - mathematicsandreal-lifeproblems and apply the associated skills, strategies and - concrete, pictorialand/or symbolic modes attitudeswithinandacrossstrands. ofrepresentation - conceptual understanding and As students learn and apply mathematics, they proceduralknowledge focus on four integrated aspects of problem - thevariousstrandsinmathematics solving: mathematicsand othersubjectareas. • learningabouthowtosolveproblems,by: - understandingtheproblem Integrating assessment with instruction - developingandcarryingoutaplan is necessary to maximize the progress of - lookingback each student. • learning concepts through problem solving, by: Assessing for conceptual understanding, - beginning with a problem that contains using a variety of strategies, facilitates keyaspectsoftheconcept learningwheninstructional decisions can be - connectingtheconcretewiththeabstract built upon what students already know and • applying the concepts learned to new cando. problemsituations • creating problems that exemplify the Technology is changing mathematics conceptslearned. learning. Students are able to solve a wide variety of PROGRAMORGANIZATION problems and focus attention upon mathematics understanding when there is The program of studies provides learner appropriate use of calculators and expectations for each grade level from Pre-grade computers. 1 toGrade6. PROBLEM SOLVING The general learnerexpectations, whichprovide an overview, are described in greater detail through related specific learner expectations. The primary thrust of the program of studies is Students achieve these expectations by solving on developing and increasing problem-solving problems related to the concepts in each of five confidence and competence. Students need to strands. learn many different skills and strategies to apply in a variety of old and new situations. Also, they need to express a desire to solve problems and demonstrate perseverance in carryingoutsolutions. UNlVERSHMtUBBfiRfcs(Elementary) A.2 UNlVERSiTttflfe&Bflflfcber 1994) Strands Measurement For clarity, the mathematics program has been As they solve problems, students develop and describedinstrands. However, inpractice, these demonstrate understanding of time, length, strands should be integrated during instruction, capacity, mass, temperature, money, perimeter, learningandassessment. Thestrandsare: area, volume and angles. The emphasis is on estimating before measuring. When students • numeration estimate and then measure to check how close • operationsandproperties their estimate is, they deepen their • measurement understandingofthemeasurementprocess. • geometry • datamanagement. The successive stages in the measuring process include: Numeration • makingcomparisonsbetweenobjects • comparinganobjectwithanonstandardunit As they solve problems, students develop and • comparinganobjectwithastandardunit demonstrate understanding of patterns, • choosing measurement units for specific numbers and place value (whole numbers, tasks. fractions, decimals); number relationships (comparing, ordering, rounding); and estimation ofquantity. Geometry Numeration concepts form the foundation for all As they solve problems, students develop and theotherstrands. demonstrate their understanding of the attributes of geometric shapes and spatial relationships. Building on their intuitive OperationsandProperties understanding of concepts, students move from the concrete to the abstract. They study three- As they solve problems, students develop and dimensionalobjects andtwo-dimensional figures demonstrate understanding of addition, by moving, sorting, classifying, constructing and subtraction, multiplication and divisionofwhole describing them. The emphasis is on making numbers anddecimals. Avarietyofmethodscan connections between three-dimensional objects be used to solve problems; including estimating, andtwo-dimensionalfigures. mental calculation, algorithms; and the use of calculators or computers, with a lesser emphasis onpaperandpencil calculations. DataManagement A solidknowledge ofnumberfactsisessentialfor As they solve problems, students develop and developing number sense and estimation skills. demonstrate understanding of probability and Competence in a variety ofestimation strategies statistics, including graphing. They explore the enables students to determine the concepts of chance through probability reasonableness of answers obtained, including experiments; and in statistics, they collect, thosefromcalculatorsandcomputers. organize, display and interpret data to solve problems. To enhance their understanding of operations and mental calculations, students use the commutative, associative and distributive SPECIFIC LEARNER EXPECTATIONS properties andtheuniqueeffectof and 1. The specific learner expectations, in each ofthe five strands and across the grade levels, further expand the mathematical understandings expressedinthegeneral learnerexpectations. Mathematics (Elementary) A.3 (Interim October 1994) Mathematics (Elementary) A.4 (Interim October 1994) LEARNER EXPECTATIONS B. PROBLEM SOLVING: IntegraltoAllMathematics As students progress through the grade levels, they are challenged by problems that reflect the increasingcomplexityoftheknowledgeandskillswithinandacrossthestrands. Problem-solvingstrategiesandskillsforallgrade levelsaredescribed inthefollowingchart. GeneralLearner GradeLevel Expectations Related Specific LearnerExpectations P 1 2 3 4 5 6 Thestudentusesa DemonstratingTraitsofa Successful Problem varietyofstrategies Solver tosolve problemsand justifythe solution Thestudent: process. The problemsintegrate • demonstrateswillingnesstofindasolutionto kf conceptsacrossthe theproblem strands. • perseveresinfindinga solutiontotheproblem • demonstratesflexibilityinfindingsolutionsto fk problems • presentsideasinanunderstandableway fk • worksbothindividuallyandinagroup. k UnderstandingtheProblem Thestudent: • interpretspicturesanddiagrams • understandswordsandphrases • understandsthequestionasked • identifiesgiveninformation • understandswhat informationis implied • understandswhat informationismissing • understandswhatinformationisextraneous • restatestheproblem in ownwords. Developingand CarryingOuta Plan Thestudent: • usestheprocess ofelimination(logical kf reasoning) • usesroleplaying kf Mathematics(Elementary) B.l Problem Solving (Interim October 1994) GeneralLearner GradeLevel Expectations Related Specific LearnerExpectations P 1 2 3 4 5 6 1 i 1 • usesmanipulativesandtrialanderror techniques • looksforandcontinuespatterns • drawspicturesanddiagrams f • collectsandusesdata : : : k • choosesandcarriesoutanappropriate ' • : fc operation,usinganappropriatemethod • doesasimplerbutrelatedproblem • usesestimation,guessesandchecks k • usestablesorlists h • worksbackward h : ! i ! " • monitorstheprocessincarryingouttheplan. LookingBack Thestudent: • statestheanswer(s) totheproblem • determinesiftheanswerisreasonable • discussesthe solutionprocesswithothers • retellstheproblemwiththesolution • looksforotherwaystosolvetheproblem • doessimilarproblems • alterstheproblemandfindsthe effect • generalizesthesolution • createsproblemsthatexemplifytheconcepts learned. Mathematics (Elementary) B.2 (Interim October 1994) ProblemSolving PRE-GRADE 1 PROBLEM SOLVING Through problem solving, students develop and apply knowledge and skills within and across the strands. Strategies and skills for problem solving are presentedinthechartonpagesB.l andB.2. NUMERATION GeneralLearner Expectations Related SpecificLearnerExpectations Inaproblem-solvingcontext, thestudent: Patterns In solvingproblems, the usestwoormoredifferentactionsandmanipulativesto: studentrecognizesand - identifyapattern usespatterns. -' reproduceapattern - create apattern - extend a pattern; e.g., 2 red buttons, 3 blue buttons, 2 red buttons, 3bluebuttonsand2 claps, 3snaps, 2claps, 3snaps WholeNumbers Insolvingproblems, the • sortsobjects intosetsaccordingtoattributesand describesthese studentdemonstrates attributes understandingofsetsand wholenumbers1 to9. • matches members of two sets of manipulatives, and describes the relationship between the two sets, using the terms more than, greater than, fewer than, less than, the same as/equal to (nowrittensymbols) • countsthenumberofobjectsinaset • representsnumbers, by: - creating sets, using manipulatives and diagrams, and making the connection with their spoken terms and written symbols - illustrating spoken terms and written symbols, using manipulativesanddiagrams • orderssets,basedonthenumberofobjectsinthesets. Mathematics(Elementary) B.3 PGl/Numeration (Interim October 1994) OPERATIONSAND PROPERTIES GeneralLearner Expectations Related Specific LearnerExpectations Inaproblem-solvingcontext, thestudent: Additionand SubtractionofWholeNumbers Insolvingproblems, the • represents the processes of addition and subtraction through studentdemonstrates roleplayingandtheuseofmanipulatives. awarenessofadditionand subtraction. Mathematics (Elementary) B.4 (Interim October 1994) PGl/Operationsand Properties