Math Grade 4 - British Columbia

INTRODUCTION TO MATHEMATICS K TO 7"#03*(*/"- 1&341& 5*7&Aboriginal students in British Columbia come fromdiverse geographic areas with varied cultural andlinguistic backgrounds. Students attend schoolsin a variety of settings including urban, rural, andisolated communities. Teachers need to understandthe diversity of cultures and experiences of students.Aboriginal students come from cultures wherelearning takes place through active participation.Traditionally, little emphasis was placed upon thewritten word. Oral communication along withpractical applications and experiences are importantto student learning and understanding. It is also vitalthat teachers understand and respond to non-verbalcues so that student learning and mathematicalunderstanding are optimized. Depending on theirlearning styles, students may look for connectionsin learning and learn best when mathematics iscontextualized and not taught as discrete components.A variety of teaching and assessment strategies isrequired to build upon the diverse knowledge, cultures,communication styles, skills, attitudes, experiences andlearning styles of students. 5IF TUSBUFHJFT VTFE NVTU HP CFZPOE UIF JODJEFOUBM JODMVTJPO PG UPQJDT BOE PCKFDUT VOJRVF UP B DVMUVSF PS SFHJPO BOE TUSJWF UP BDIJFWF IJHIFS MFWFMT PG NVMUJDVMUVSBM FEVDBUJPO #BOLT BOE #BOLT "''& 5*7& %0."*/Bloom’s taxonomy of learning behaviours identifiedthree domains of educational activities, affective(growth in feelings or emotional areas – attitude),cognitive (mental skills – knowledge), and psychomotor(manual or physical skills – skills). The affectivedomain involves the way in which we perceive andrespond to things emotionally, such as feelings, values,appreciation, enthusiasms, motivations, and attitudes.A positive attitude is an important aspect of theaffective domain that has a profound effect onlearning. Environments that create a sense ofbelonging, encourage risk taking, and provideopportunities for success help students developand maintain positive attitudes and self-confidence.Research has shown that students who are moreengaged with school and with mathematics are far Mathematics Grade 4more likely to be successful in school and in learningmathematics. (Nardi & Steward 2003). Studentswith positive attitudes toward learning mathematicsare likely to be motivated and prepared to learn,participate willingly in classroom activities, persistin challenging situations, and engage in reflectivepractices.Substantial progress has been made in research in thelast decade that has examined the importance and useof the affective domain as part of the learning process.In addition there has been a parallel increase inspecific research involving the affective domain andits’ relationship to the learning of mathematics whichhas provided powerful evidence of the importanceof this area to the learning of mathematics (McLeod1988, 1992 & 1994; Hannula 2002 & 2006; Malmivuori2001 & 2006). Teachers, students, and parents needto recognize the relationship between the affectiveand cognitive domains, and attempt to nurture thoseaspects of the affective domain that contribute topositive attitudes. To experience success, studentsmust be taught to set achievable goals and assessthemselves as they work toward these goals.Students who are feeling more comfortable witha subject, demonstrate more confidence and havethe opportunity for greater academic achievement(Denton & McKinney 2004; Hannula 2006; Smith et al.1998). Educators can include opportunities for activeand co-operative learning in their mathematics lessonswhich has been shown in research to promote greaterconceptual understanding, more positive attitudes andsubsequently improved academic achievement fromstudents (Denton & McKinney 2004). By allowingthe sharing and discussion of answers and strategiesused in mathematics, educators are providing richopportunities for students mathematical development.Educators can foster greater conceptual understandingin students by having students practice certain topicsand concepts in mathematics in a meaningful andengaging manner.It is important for educators, students, and parentsto recognize the relationship between the affectiveand cognitive domains and attempt to nurture thoseaspects of the affective domain that contribute topositive attitudes and success in learning.

INTRODUCTION TO MATHEMATICS K TO 7/"563& 0' ."5)&."5* 4Number SenseMathematics is one way of trying to understand,interpret, and describe our world. There are anumber of components that are integral to thenature of mathematics, including change, constancy,number sense, patterns, relationships, spatial sense,and uncertainty. These components are woventhroughout this curriculum.Number sense, which can be thought of as intuitionabout numbers, is the most important foundation ofnumeracy (The Primary Program 2000, p. 146).ChangeIt is important for students to understand thatmathematics is dynamic and not static. As aresult, recognizing change is a key component inunderstanding and developing mathematics.Within mathematics, students encounterconditions of change and are required to search forexplanations of that change. To make predictions,students need to describe and quantify theirobservations, look for patterns, and describe thosequantities that remain fixed and those that change.For example, the sequence 4, 6, 8, 10, 12, can bedescribed as: skip counting by 2s, starting from 4 an arithmetic sequence, with first term 4 and acommon difference of 2 a linear function with a discrete domain(Steen 1990, p. 184).ConstancyDifferent aspects of constancy are described by theterms stability, conservation, equilibrium, steady stateand symmetry (AAAS–Benchmarks 1993, p. 270).Many important properties in mathematics and sciencerelate to properties that do not change when outsideconditions change. Examples of constancy include: the area of a rectangular region is the same regardlessof the methods used to determine the solution the sum of the interior angles of any triangle is 180 the theoretical probability of flipping a coin andgetting heads is 0.5Some problems in mathematics require students to focuson properties that remain constant. The recognition ofconstancy enables students to solve problems involvingconstant rates of change, lines with constant slope, directvariation situations or the angle sums of polygons.A true sense of number goes well beyond the skillsof simply counting, memorizing facts and thesituational rote use of algorithms.Number sense develops when students connectnumbers to real-life experiences, and use benchmarksand referents. This results in students who arecomputationally fluent, flexible with numbers and haveintuition about numbers. The evolving number sensetypically comes as a by-product of learning rather thanthrough direct instruction. However, number sensecan be developed by providing rich mathematical tasksthat allow students to make connections.PatternsMathematics is about recognizing, describingand working with numerical and non-numericalpatterns. Patterns exist in all strands and it isimportant that connections are made among strands.Working with patterns enables students to makeconnections within and beyond mathematics.These skills contribute to students’ interaction withand understanding of their environment.Patterns may be represented in concrete, visual orsymbolic form. Students should develop fluency inmoving from one representation to another.Students must learn to recognize, extend, create anduse mathematical patterns. Patterns allow studentsto make predictions, and justify their reasoningwhen solving routine and non-routine problems.Learning to work with patterns in the early gradeshelps develop students’ algebraic thinking thatis foundational for working with more abstractmathematics in higher grades.RelationshipsMathematics is used to describe and explainrelationships. As part of the study of mathematics,students look for relationships among numbers, sets,shapes, objects and concepts. The search for possiblerelationships involves the collection and analysisof data, and describing relationships visually,symbolically, orally or in written form.Mathematics Grade 4

INTRODUCTION TO MATHEMATICS K TO 7Spatial Sense(0"-4 '03 ."5)&."5* 4 , 50 Spatial sense involves visualization, mental imageryand spatial reasoning. These skills are central tothe understanding of mathematics. Spatial senseenables students to reason and interpret among andbetween 3-D and 2-D representations and identifyrelationships to mathematical strands.Mathematics K to 7 represents the first formal stepsthat students make towards becoming life-longlearners of mathematics.Spatial sense is developed through a variety ofexperiences and interactions within the environment.The development of spatial sense enables students tosolve problems involving 3-D objects and 2-D shapes.5IF .BUIFNBUJDT , DVSSJDVMVN JT NFBOU UP TUBSU TUVEFOUT UPXBSE BDIJFWJOH UIF NBJO HPBMT PG NBUIFNBUJDT FEVDBUJPO Spatial sense offers a way to interpret and reflect on thephysical environment and its 3-D or 2-D representations.Some problems involve attaching numerals andappropriate units (measurement) to dimensionsof objects. Spatial sense allows students to makepredictions about the results of changing thesedimensions. For example: knowing the dimensions of an object enablesstudents to communicate about the object andcreate representations the volume of a rectangular solid can be calculatedfrom given dimensions doubling the length of the side of a squareincreases the area by a factor of fourUncertaintyIn mathematics, interpretations of data and thepredictions made from data may lack certainty.Events and experiments generate statistical data thatcan be used to make predictions. It is important torecognize that these predictions (interpolations andextrapolations) are based upon patterns that have adegree of uncertainty.The quality of the interpretation is directly related tothe quality of the data. An awareness of uncertaintyallows students to assess the reliability of data anddata interpretation.Chance addresses the predictability of theoccurrence of an outcome. As students developtheir understanding of probability, the language ofmathematics becomes more specific and describesthe degree of uncertainty more accurately. Mathematics Grade 4(0"-4 '03 ."5)&."5* 4 , 50 using mathematics confidently to solveproblems using mathematics to better understand theworld around us communicating and reasoning mathematically appreciating and valuing mathematics making connections between mathematics andits applications committing themselves to lifelong learning becoming mathematically literate and usingmathematics to participate in, and contributeto, society4UVEFOUT XIP IBWF NFU UIFTF HPBMT XJMM gain understanding and appreciation of thecontributions of mathematics as a science,philosophy and art be able to use mathematics to make and justifydecisions about the world around us exhibit a positive attitude toward mathematics engage and persevere in mathematical tasksand projects contribute to mathematical discussions take risks in performing mathematical tasks exhibit curiosity

INTRODUCTION TO MATHEMATICS K TO 7 633* 6-6. 03("/*;&34A curriculum organizer consists of a set ofprescribed learning outcomes that share a commonfocus. The prescribed learning outcomes forMathematics K to 7 progress in age-appropriateways, and are grouped under the followingcurriculum organizers and suborganizers: VSSJDVMVN 0SHBOJ[FST BOE 4VCPSHBOJ[FSTMathematics K-7NumberPatterns and Relations Patterns Variables and EquationsShape and Space Measurement 3-D Objects and 2-D Shapes TransformationsStatistics and Probability Data Analysis Chance and UncertaintyThese curriculum organizers reflect the main areas ofmathematics that students are expected to address. Theordering of organizers, suborganizers, and outcomesin the Mathematics K to 7 curriculum does not implyan order of instruction. The order in which varioustopics are addressed is left to the professional judgmentof teachers. Mathematics teachers are encouraged tointegrate topics throughout the curriculum and withinother subject areas to emphasize the connectionsbetween mathematics concepts.NumberStudents develop their concept of the numbersystem and relationships between numbers.Concrete, pictorial and symbolic representationsare used to help students develop their numbersense. Computational fluency, the ability to connectunderstanding of the concepts with accurate,efficient and flexible computation strategiesfor multiple purposes, is stressed throughoutthe number organizer with an emphasis onthe development of personal strategies, mentalmathematics and estimation strategies.The Number organizer does not contain anysuborganizers.Patterns and RelationsStudents develop their ability to recognize, extend,create, and use numerical and non- numericalpatterns to better understand the world around themas well as the world of mathematics. This organizerprovides opportunities for students to look forrelationships in the environment and to describethe relationships. These relationships should beexamined in multiple sensory forms.The Patterns and Relations organizer includes thefollowing suborganizers: Patterns Variables and EquationsShape and SpaceStudents develop their understanding of objectsand shapes in the environment around them.This includes recognition of attributes that canbe measured, measurement of these attributes,description of these attributes, the identification anduse of referents, and positional change of 3-D objectsand 2-D shapes on the environment and on theCartesian plane.The Shape and Space organizer includes thefollowing suborganizers: Meas

Mathematics grade 4 : integrated resource package 200 Also available on the Internet. ISBN 978-0-7726-5718-3 1. Arithmetic - Study and teaching (Elementary) – British Columbia. 2. Mathematics - Study and teaching (Elementary) – British Columbia. 3. Education, Elementary – Curricu