Bound for Success Scope and Sequence Statements

MATHEMATICSWorking Mathematically(Note that this strand should be addressed simultaneously with all mathematics content strands)Concept In Year 1the student:In Year 2the student:In Year 3the student:In Year 4the student:In Year 5the student:In Year 6the student:In Year 7the student:In Year 8the student:In Year 9the student:Contextualisingand Posingquestions• Talks about where they seenumbers, shapes andmeasurements and givesexamples of some of theways they and theirfamilies use numbers (e.g.says “there are numberson our phone and on footyjumpers”)• Knows that numbers areused for differentpurposes; some to tell howmany (cardinal), others aslabels (nominal) and othersto describe order (ordinal)• Describes some of theways they and their friendsand families use numbers,shapes and measurements(e.g. says “we use thenumbers on the clock totell us when to havelunch” and “Mummeasures the flour whenshe makes a cake”)• Identifies and distinguishesbetween different purposesfor numbers andmeasurements (i.e.cardinal, nominal andordinal numbers; startingtimes, finishing times andelapsed time)• Identifies familiarmathematical features intheir activities and those oftheir community (e.g. findsout about and reports onthe mathematics used bypeople they know at homeand at work, and identifiesmeasuring tools from othercultures and times such asabacus, sundials, systemsof knots)• Identifies and describesmathematical features inthe built, creative andnatural environmentincluding those of othercultures and societies (e.g.shapes in buildings,pentagons in flowers,tessellations in paving,shapes in artworks)• Compares the ways thatfamiliar mathematics isdone in their own andother communities (e.g.compares how time isexperienced in WesternCultures- by measuringstart and finish times- withthose in some Indigenouscultures- by the quality ofthe experience; the yeardivided into four ‘western’seasons compared withthat divided into 6 seasons;including the wet and thedry)• Researches and reports ondifferent ways numbers areused in society (e.g.Dewey system, labellingsections in a paper, cricketovers, petrol prices, 10-point type face) andexplains why they aredifferent and yetappropriate for differentcircumstances)• Knows and respectsdifferences betweenWestern Mathematics andother ways of imposingorder in society throughnaming, ordering, valuingand pattern (e.g. usingperimeter to delineateboundaries for ownershipcompared with the use ofphysical features such asrivers and mountains todelineate territory; use oflatitude and longitude tolocate places comparedwith an affinity with theland)• Poses questions (withprompting) that can beanswered using numbers(e.g. asks “How old areyou?”)• Poses questions that can beanswered by counting,ordering, matching andclassifying (e.g. asks “Howmany jars are on the shelf?and “Why have you putthis shape with these othershapes?”)• Represents questions usingobjects, pictures, symbolsor mental images (e.g. for:Sam was picking 4 teamswith 3 players, how manypeople will Sam need?represents Sam’s teamswith shells or toy people)• Poses questions promptedby a number sentenceinvolving one operation(e.g. writes astory/question leading to15 x 3 such as “how muchwill 15 CDs cost if they are$3 each?”)• Poses questions suggestedby data they have collected(e.g. having gone on a‘shape walk’ they mightask “What shapes aremostly in buildings?”)• Generates simplemathematical questions forthemselves and others toinvestigate, stimulated by afamiliar context such as aphoto of a crowd at afootball match (e.g.” howmany people are in thecrowd?”)• Asks clarifying questionsto make sense ofinstructions and ensuresthat they know themathematical terms beingused (e.g. says “when yousay that I should draw anisosceles triangle youmean I should draw atriangle with two sides thesame length?”)• When given a list of theirown or someone else’squestions used in anattempt to make sense of asituation, can eliminatethose which won’t provideinformation that helps• Suggests questions leftunanswered by theirmathematical work (e.g.says “the method workedfor all the shapes I usedbut I’m not sure it wouldwork for triangles”)• Discriminates betweenimportant and incidentalinformation in a context orsituation and states relatedassumptions/conditions,varying these in a contextif needed (e.g. questionsthe level of accuracyneeded and decides as aresult to calculate to 4decimal places whenworking with currencyconversions)• Respond to ‘what wouldhappen if…?’-typequestions duringmathematical activities(e.g. says “it would beheavier”)• Asks ‘what if…?’questions and makessimple conjectures aboutthem and attempts toexplain their reasoning(e.g. says “what wouldhappen if we covered theplate with bigger biscuits?I think we wouldn’t needas many biscuits becausethey are bigger”)• Makes conjectures aboutoperations on numbers,shapes and measurements(e.g. says “I think thiscontainer will hold morethan that one” ;“If 3 + 6 =9 then 13 + 6 must equal19”, and “You can onlymake a triangle if you onlyhave three sticks”)• Makes and tests simpleconjectures (e.g. that everyrectangle made using thesame number of identicalsquares has the sameperimeter) and explains theapproach taken and theconclusions reached (e.g.says “the perimeterbecomes smaller as thelength and width becomecloser to each other insize”)• Makes their ownconjectures and designssimple experiments to testthem (e.g. conjectures thatthe sum of the angles of apentagon equals 450º anddraws a pentagon,measures its angles,decides they were wrongand can explain why)• Collects data to help themwhen making and testingconjectures about numbers(e.g. to find what happenswhen you add two oddnumbers tries different oddnumbers and conjecturesthat they always give asum that is even)• Generates newmathematical questionsand conjectures based ontheir results (e.g. “what ifwe had used a line graphinstead of a bar graph –would our results havebeen different?”, and “Ithink this will work forpentagons too becausethey are also regularpolygons”)• Tests and checks thevalidity of propositions byidentifying counterexamples(e.g. tests theclaim that all dice beingused are biased, or allnumbers [such as 4n – 1]are even)MathematicalStrategies• Shows some selfcorrectingbehaviourduring mathematicalactivities (e.g. whensharing out lollies realiseswhen one person has toomany and takes it away)• Represents a problem withconcrete materials (e.g.given a bag of lollies canshare them out between agroup of friends, or canattempt to find out howmany children are at theschool by using a box torepresent every classroomand putting stones intoeach box to represent thechildren)• Represents a problem withconcrete materials andmanipulates these to find asolution; represents aproblem with a drawing• Represents a problem withan appropriate numberoperation (e.g. represents‘there are three teams withfour players in each; howmany players are there?’with 3 x 4)• Responds to questionssuch as “What do weknow?”, “What do wewant to know?”, “What arewe trying to find out?”,“Can you say it in yourown words?”• Attempts to understand theessential features of aproblem by askingthemselves organisingquestions such as “Whatdo we know?”, “What dowe want to know?” ,“Whatare we trying to findout?”, “Can you say it inyour own words?” in anattempt to get started;When using ‘guess andcheck’ as a strategy, writesdown the guesses so thatthey know they’ve triedthem already; Uses adictionary to find out whata word means in a problemor asks others if they know• Makes organised listswhen examiningmathematical situations(e.g. when examining andclassifying some 3Dshapes, labels each shapeusing digits 1 to 10, andexamines the shapes oneby one using tabularheadings: ‘faces, edges,vertices/corners’ withoutbeing asked to do so;Recognises and crosses outirrelevant information in aproblem)• Systematically generatesand lists possibilities, andexplains why they thinkthey have listed them all;Produces a systematicapproach to solving aproblem (e.g. for getting agroup of people over ariver)• Plans and conductsinquiries that require themto pose questions andformulate propositions,hypotheses or conjecturesrelated to a given contextand uses a range ofstrategies (e.g. considersthe safety of surfconditions at a givenlocation on a particular dayand time in terms of windand current strength anddirection and tide height);Chooses and uses aspectsof mathematics to carryout investigations, modelsituations and solveproblems (e.g. analysesdata from a data logger orBound for Success Scope and Sequence Statements V2 Page 24 Working Document Semester One 2007