Mathematics 6
Mathematics 6Curriculum Guide 2015
TABLE OF CONTENTSTable of ContentsAcknowledgements . . iiiForeword . .vIntroduction . . . . .1Background . . .2Beliefs About Students and Mathematics Learning . .1Affective Domain . .2Goal for Students . .2Conceptual Framework for K–9 Mathematics.3Mathematical Processes . . .3Nature of Mathematics . . .7Essential Gradutaiton Learnings . . .10Strands.11Outcomes and Achievement Indicators . .12Summary . . .12Assessment and Evaluation . . .13Assessment Strategies . . . 15Instructional FocusPlanning for Instruction . . . 17Teaching Sequence . .17Instruction Time per Unit . . . 17Resources .18General and Specific Outcomes.19Unit 1: Numeration. . .19Unit 2: Number Relationships. . . .41Unit 3: Patterns in Mathematics . . . . . .71Unit 4: Data Relationships. . . . .99Unit 5: Motion Geometry. .133Unit 6: Ratio & Percent. . .157Unit 7: Fractions. . .185Unit 8: Multiplication and Division of Decimals. . .207Unit 9: Measurement. . .229Unit 10: 2D Geometry. . .261Unit 11: Probability. . .283AppendixOutcomes with Achievement Indicators Organized by Stand.297References . . . .311MATHEMATICS 6 CURRICULUM GUIDE 2015i
TABLE OF CONTENTSiiMATHEMATICS 6 CURRICULUM GUIDE 2015
ACKNOWLEDGEMENTSAcknowledgementsThe Department of Education would like to thank the Western and Northern Canadian Protocol (WNCP)for Collaboration in Education, The Common Curriculum Framework for K-9 Mathematics - May 2006 andThe Common Curriculum Framework for Grades 10-12 - January 2008, which has been reproduced and/oradapted by permission. All rights reserved.We would also like to thank the provincial Mathematics 6 curriculum committee, the Alberta Department ofEducation, the New Brunswick Department of Education, and the following people for their contribution:Trudy Porter, Program Development Specialist Mathematics, Division of ProgramDevelopment, Department of EducationLinda Stacey, Program Development Specialist Mathematics, Division of ProgramDevelopment, Department of Education and Early Childhood DevelopmentColin Barry, Teacher St. Matthew’s Elementary, St. John’sAnnette Bull, Teacher Glovertown Academy, GlovertownWanda Bussey, Teacher Queen of Peace Middle School, Happy Valley Goose BayAlvin Dominie, Teacher Sacred Heart Academy, MarystownLarry Doyle, Teacher Numeracy Support Teacher, Nova Central School DistrictGuy Dupasquier, Teacher St. Edward’s Elementary, Conception Bay SouthRegina Hannam, Teacher Lakewood Academy, GlenwoodCherry Harbin, Teacher St. Peter’s Academy, Benoit’s CoveAngela Hayden, Teacher Millcrest Academy, Grand Falls-WindsorPaulette Jayne, Teacher Sprucewood Academy, Grand Falls-WindsorElaina Johnson, Teacher Bishop White School, Port RextonGina Keeping, Teacher Larkhall Academy, St. John’sAnnette Larkin, Teacher Topsail Elementary, Conception Bay SouthDamien Lethbridge, Teacher St. John Bosco, St. John’sJohn Power, Teacher Numeracy Support Teacher, Eastern School DistrictSandra Rennie, Teacher St. Lawrence Academy, St. LawrenceDaryl Rideout, Teacher Mary Queen of Peace, St. John’sRoxanne Roberts, Teacher Beachy Cove Elementary, Portugal Cove St-Philip’sMillie Walsh, Teacher Baie Verte Academy, Baie VerteMegan Wamboldt, Teacher Queen of Peace Middle School, Labrador CityMATHEMATICS 6 CURRICULUM GUIDE 2015iii
ACKNOWLEDGEMENTSivMATHEMATICS 6 CURRICULUM GUIDE 2015
INTRODUCTIONINTRODUCTIONBackgroundThe curriculum guidecommunicates highexpectations for students.The Mathematics curriculum guides for Newfoundland and Labradorhave been derived from The Common Curriculum Framework for K-9Mathematics: Western and Northern Canadian Protocol, 2006. Theseguides incorporate the conceptual framework for Grades Kindergartento Grade 9 Mathematics and the general outcomes, specific outcomesand achievement indicators established in the common curriculumframework. They also include suggestions for teaching and learning,suggested assessment strategies, and an identification of the associatedresource match between the curriculum and authorized, as well asrecommended, resource materials.Mathematics 6 was originally implemented in 2010.Beliefs AboutStudents andMathematicsStudents are curious, active learners with individual interests, abilitiesand needs. They come to classrooms with varying knowledge, lifeexperiences and backgrounds. A key component in developingmathematical literacy is making connections to these backgrounds andexperiences.Mathematicalunderstanding is fosteredwhen students build ontheir own experiences andprior knowledge.Students learn by attaching meaning to what they do, and they needto construct their own meaning of mathematics. This meaning is bestdeveloped when learners encounter mathematical experiences thatproceed from the simple to the complex and from the concrete to theabstract. Through the use of manipulatives and a variety of pedagogicalapproaches, teachers can address the diverse learning styles, culturalbackgrounds and developmental stages of students, and enhancewithin them the formation of sound, transferable mathematicalunderstandings. Students at all levels benefit from working with avariety of materials, tools and contexts when constructing meaningabout new mathematical ideas. Meaningful student discussions provideessential links among concrete, pictorial and symbolic representationsof mathematical concepts.The learning environment should value and respect the diversityof students’ experiences and ways of thinking, so that students feelcomfortable taking intellectual risks, asking questions and posingconjectures. Students need to explore problem-solving situations inorder to develop personal strategies and become mathematically literate.They must come to understand that it is acceptable to solve problemsin a variety of ways and that a variety of solutions may be acceptable.MATHEMATICS 6 CURRICULUM GUIDE 20151
INTRODUCTIONAffective DomainTo experience success,students must learn to setachievable goals and assessthemselves as they worktoward these goals.A positive attitude is an important aspect of the affective domain andhas a profound impact on learning. Environments that create a sense ofbelonging, encourage risk taking and provide opportunities for successhelp develop and maintain positive attitudes and self-confidence withinstudents. Students with positive attitudes toward learning mathematicsare likely to be motivated and prepared to learn, participate willinglyin classroom activities, persist in challenging situations and engage inreflective practices.Teachers, students and parents need to recognize the relationshipbetween the affective and cognitive domains, and attempt to nurturethose aspects of the affective domain that contribute to positiveattitudes. To experience success, students must learn to set achievablegoals and assess themselves as they work toward these goals.Striving toward success and becoming autonomous and responsiblelearners are ongoing, reflective processes that involve revisiting,asssessing and revising personal goals.Goals ForStudentsMathematics educationmust prepare studentsto use mathematicsconfidently to solveproblems.The main goals of mathematics education are to prepare students to: use mathematics confidently to solve problems communicate and reason mathematically appreciate and value mathematics make connections between mathematics and its applications commit themselves to lifelong learning become mathematically literate adults, using mathematics tocontribute to society.Students who have met these goals will:2 gain understanding and appreciation of the contributions ofmathematics as a science, philosophy and art exhibit a positive attitude toward mathematics engage and persevere in mathematical tasks and projects contribute to mathematical discussions take risks in performing mathematical tasks exhibit curiosity.MATHEMATICS 6 CURRICULUM GUIDE 2015
MATHEMATICAL PROCESSESCONCEPTUALFRAMEWORKFOR K - 9MATHEMATICSMathematicalProcesses Communication [C] Connections [CN] Mental Mathematicsand Estimation [ME] Problem Solving [PS] The chart below provides an overview of how mathematical processesand the nature of mathematics influence learning outcomes.There are critical components that students must encounter in amathematics program in order to achieve the goals of mathematicseducation and embrace lifelong learning in mathematics.Students are expected to: communicate in order to learn and express their understanding connect mathematical ideas to other concepts in mathematics, toeveryday experiences and to other disciplines demonstrate fluency with mental mathematics and estimation develop and apply new mathematical knowledge through problemsolvingReasoning [R] develop mathematical reasoning Technology [T] Visualization [V]select and use technologies as tools for learning and for solvingproblems develop visualization skills to assist in processing information,making connections and solving problems.This curriculum guide incorporates these seven interrelatedmathematical processes that are intended to permeate teaching andlearning.MATHEMATICS 6 CURRICULUM GUIDE 20153
MATHEMATICAL PROCESSESCommunication [C]Students need opportunities to read about, represent, view, write about,listen to and discuss mathematical ideas. These opportunities allowstudents to create links between their own language and ideas, and theformal language and symbols of mathematics.Students must be able tocommunicate mathematicalideas in a variety of waysand contexts.Communication is important in clarifying, reinforcing and modifyingideas, attitudes and beliefs about mathematics. Students should beencouraged to use a variety of forms of communication while learningmathematics. Students also need to communicate their learning usingmathematical terminology.Communication helps students make connections among concrete,pictorial, symbolic, oral, written and mental representations ofmathematical ideas.Connections [CN]Through connections,students begin to viewmathematics as useful andrelevant.Contextualization and making connections to the experiencesof learners are powerful processes in developing mathematicalunderstanding. When mathematical ideas are connected to each otheror to real-world phenomena, students begin to view mathematics asuseful, relevant and integrated.Learning mathematics within contexts and making connections relevantto learners can validate past experiences and increase student willingnessto participate and be actively engaged.The brain is constantly looking for and making connections. “Becausethe learner is constantly searching for connections on many levels,educators need to orchestrate the experiences from which learners extractunderstanding Brain research establishes and confirms that multiplecomplex and concrete experiences are essential for meaningful learningand teaching” (Caine and Caine, 1991, p.5).4MATHEMATICS 6 CURRICULUM GUIDE 2015
MATHEMATICAL PROCESSESMental Mathematics andEstimation [ME]Mental mathematics andestimation are fundamentalcomponents of number sense.Mental mathematics is a combination of cognitive strategies thatenhance flexible thinking and number sense. It is calculating mentallywithout the use of external memory aids.Mental mathematics enables students to determine answers withoutpaper and pencil. It improves computational fluency by developingefficiency, accuracy and flexibility.“Even more important than performing computational procedures orusing calculators is the greater facility that students need—more thanever before—with estimation and mental math” (National Council ofTeachers of Mathematics, May 2005).Students proficient with mental mathematics “. become liberated fromcalculator dependence, build confidence in doing mathematics, becomemore flexible thinkers and are more able to use multiple approaches toproblem solving” (Rubenstein, 2001, p. 442).Mental mathematics “. provides the cornerstone for all estimationprocesses, offering a variety of alternative algorithms and nonstandardtechniques for finding answers” (Hope, 1988, p. v).Estimation is used for determining approximate values or quantities orfor determining the reasonableness of calculated values. It often usesbenchmarks or referents. Students need to know when to estimate, howto estimate and what strategy to use.Estimation assists individuals in making mathematical judgements andin developing useful, efficient strategies for dealing with situations indaily life.Problem Solving [PS]Learning through problemsolving should be the focusof mathematics at all gradelevels.Learning through problem solving should be the focus of mathematicsat all grade levels. When students encounter new situations and respondto questions of the type, “How would you know?” or “How couldyou .?”, the problem-solving approach is being modelled. Studentsdevelop their own problem-solving strategies by listening to, discussingand trying different strategies.A problem-solving activity requires students to determine a way to getfrom what is known to what is unknown. If students have already beengiven steps to solve the problem, it is not a problem, but practice. Atrue problem requires students to use prior learning in new ways andcontexts. Problem solving requires and builds depth of conceptualunderstanding and student engagement.Problem solving is a powerful teaching tool that fosters multiple,creative and innovative solutions. Creating an environment wherestudents openly seek and engage in a variety of strategies for solvingproblems empowers students to explore alternatives and developsconfident, cognitive mathematical risk takers.MATHEMATICS 6 CURRICULUM GUIDE 20155
MATHEMATICAL PROCESSESReasoning [R]Mathematical reasoninghelps students thinklogically and make sense ofmathematics.Mathematical reasoning helps students think logically and make senseof mathematics. Students need to develop confidence in their abilitiesto reason and justify their mathematical thinking. High-order questionschallenge students to think and develop a sense of wonder aboutmathematics.Mathematical experiences in and out of the classroom provideopportunities for students to develop their ability to reason. Studentscan explore and record results, analyze observations, make and testgeneralizations from patterns, and reach new conclusions by buildingupon what is already known or assumed to be true.Reasoning skills allow students to use a logical process to analyze aproblem, reach a conclusion and justify or defend that conclusion.Technology [T]Technology contributesto the learning of a widerange of mathematicaloutcomes and enablesstudents to exploreand create patterns,examine relationships,test conjectures and solveproblems.Technology contributes to the learning of a wide range of mathematicaloutcomes and enables students to explore and create patterns, examinerelationships, test conjectures and solve problems.Technology can be used to: explore and demonstrate mathematical relationships and patterns organize and display data extrapolate and interpolate assist with calculation procedures as part of solving problems decrease the time spent on computations when other mathematicallearning is the focus reinforce the learning of basic facts develop personal procedures for mathematical operations create geometric patterns simulate situations develop number sense.Technology contributes to a learning environment in which the growingcuriosity of students can lead to rich mathematical discoveries at allgrade levels.6MATHEMATICS 6 CURRICULUM GUIDE 2015
NATURE OF MATHEMATICSVisualization [V]Visualization “involves thinking in pictures and images, and the abilityto perceive, transform and recreate different aspects of the visual-spatialworld” (Armstrong, 1993, p. 10). The use of visualization in the studyof mathematics provides students with opportunities to understandmathematical concepts and make connections among them.Visualization is fosteredthrough the use of concretematerials, technologyand a variety of visualrepresentations.Visual images and visual reasoning are important components ofnumber, spatial and measurement sense. Number visualization occurswhen students create mental representations of numbers.Being able to create, interpret and describe a visual representation ispart of spatial sense and spatial reasoning. Spatial visualization andreasoning enable students to describe the relationships among andbetween 3-D objects and 2-D shapes.Measurement visualization goes beyond the acquisition of specificmeasurement skills. Measurement sense includes the ability todetermine when to measure, when to estimate and which estimationstrategies to use (Shaw and Cliatt, 1989).Nature ofMathematics Change Constancy Number Sense Relationships Patterns Spatial Sense UncertaintyMathematics is one way of trying to understand, interpret and describeour world. There are a number of components that define the natureof mathematics and these are woven throughout this curiculum guide.The components are change, constancy, number sense, patterns,relationships, spatial sense and uncertainty.ChangeIt is important for students to understand that mathematics is dynamicand not static. As a result, recognizing change is a key component inunderstanding and developing mathematics.Change is an integral partof mathematics and thelearning of mathematics.Within mathematics, students encounter conditions of change and arerequired to search for explanations of that change. To make predictions,students need to describe and quantify their observations, look forpatterns, and describe those quantities that remain fixed and those thatchange. For example, the sequence 4, 6, 8, 10, 12, can be describedas: the number of a specific colour of beads in each row of a beadeddesign skip counting by 2s, starting from 4 an arithmetic sequence, with first ter
MATHEMATICS 6 CURRICULUM GUIDE 2015 5 Problem Solving [PS] MATHEMATICAL PROCESSES Mental Mathematics and Estimation [ME] Mental mathematics and estimation are fundamental components of number sense. Learning through problem solving should be the focus of mathematics at all grade levels. Mental mathematics is a combination of cognitive .
IBDP MATHEMATICS: ANALYSIS AND APPROACHES SYLLABUS SL 1.1 11 General SL 1.2 11 Mathematics SL 1.3 11 Mathematics SL 1.4 11 General 11 Mathematics 12 General SL 1.5 11 Mathematics SL 1.6 11 Mathematic12 Specialist SL 1.7 11 Mathematic* Not change of base SL 1.8 11 Mathematics SL 1.9 11 Mathematics AHL 1.10 11 Mathematic* only partially AHL 1.11 Not covered AHL 1.12 11 Mathematics AHL 1.13 12 .
as HSC Year courses: (in increasing order of difficulty) Mathematics General 1 (CEC), Mathematics General 2, Mathematics (‘2 Unit’), Mathematics Extension 1, and Mathematics Extension 2. Students of the two Mathematics General pathways study the preliminary course, Preliminary Mathematics General, followed by either the HSC Mathematics .
2. 3-4 Philosophy of Mathematics 1. Ontology of mathematics 2. Epistemology of mathematics 3. Axiology of mathematics 3. 5-6 The Foundation of Mathematics 1. Ontological foundation of mathematics 2. Epistemological foundation of mathematics 4. 7-8 Ideology of Mathematics Education 1. Industrial Trainer 2. Technological Pragmatics 3.
2. Further mathematics is designed for students with an enthusiasm for mathematics, many of whom will go on to degrees in mathematics, engineering, the sciences and economics. 3. The qualification is both deeper and broader than A level mathematics. AS and A level further mathematics build from GCSE level and AS and A level mathematics.
Enrolment By School By Course 5/29/2015 2014-15 100 010 Menihek High School Labrador City Enrolment Male Female HISTOIRE MONDIALE 3231 16 6 10 Guidance CAREER DEVELOPMENT 2201 114 73 41 CARRIERE ET VIE 2231 32 10 22 Mathematics MATHEMATICS 1201 105 55 50 MATHEMATICS 1202 51 34 17 MATHEMATICS 2200 24 11 13 MATHEMATICS 2201 54 26 28 MATHEMATICS 2202 19 19 0 MATHEMATICS 3200 15 6 9
The Nature of Mathematics Mathematics in Our World 2/35 Mathematics in Our World Mathematics is a useful way to think about nature and our world Learning outcomes I Identify patterns in nature and regularities in the world. I Articulate the importance of mathematics in one’s life. I Argue about the natu
1.1 The Single National Curriculum Mathematics (I -V) 2020: 1.2. Aims of Mathematics Curriculum 1.3. Mathematics Curriculum Content Strands and Standards 1.4 The Mathematics Curriculum Standards and Benchmarks Chapter 02: Progression Grid Chapter 03: Curriculum for Mathematics Grade I Chapter 04: Curriculum for Mathematics Grade II
Advanced Engineering Mathematics Dr. Elisabeth Brown c 2019 1. Mathematics 2of37 Fundamentals of Engineering (FE) Other Disciplines Computer-Based Test (CBT) Exam Specifications. Mathematics 3of37 1. What is the value of x in the equation given by log 3 2x 4 log 3 x2 1? (a) 10 (b) 1(c)3(d)5 E. Brown . Mathematics 4of37 2. Consider the sets X and Y given by X {5, 7,9} and Y { ,} and the .
