Maths2014 Curriculum changes proof - Mathematics … · Changes to the Maths Curriculum: Year 1 ... 1999 curriculum, subjects are compared to the more detailed provisions that were

Detailed breakdown of changes in the core subjects

Maths

© Pearson 2014. This work is credited to the author Michael Tidd page 1

Changes to the Maths Curriculum: Year 1

Contents This document contains details breakdown comparisons of the new curriculum against the old national strategies and curriculum documentation. Rather than directly comparing against the 1999 curriculum, subjects are compared to the more detailed provisions that were made in more recent documents:

Maths Curriculum 2014 Primary Framework 2006

Year 1 Changes page 2






Maths Curriculum



Maths CurriculumChanges to the Maths Curriculum: Year 1

At a glanceHow does the new curriculum compare to the primary framework for Mathematics (2006)?

What’s gone? What’s been added?• Datahandling/StatisticsisremovedfromY1• Nospecificrequirementtodescribepatterns• Nospecificrequirementstodescribewaysofsolvingproblemsorexplainchoices

• Counting&writingnumeralsto100• Writenumbersinwordsupto20• Numberbondssecuredto20• Useofvocabularysuchasequal,morethan,lessthan,fewer,etc.

In detailA direct reference to the former objectives of the primary framework. Where an objective was covered in more than one block, it is only recorded once.

RedindicatesnolongerrequiredinYear1GreencontentisnewtoYear1

Use and apply mathematics

OutgoingNationalCurriculum(QCAunits) NewNationalCurriculum

Solveproblemsinvolvingcounting,adding,subtracting,doublingorhalvinginthecontextofnumbers,measuresormoney;recognisethevalueofcoins

“Solveone-stepproblemsthatinvolveaddition&subtraction,usingconcreteobjectsandpictorialrepresentations,andmissingnumberproblemssuchas7=[]–9”“Recogniseandknowthevalueofdifferentdenominationsofcoinsandnotes”

Describeaproblemusingnumbers,practicalmaterialsanddiagrams;usethesetosolvetheproblemandsetthesolutionbackintheoriginalcontext

Seeabove

Answeraquestionbyselectingandusingsuitableequipment,andsortinginformation,shapesorobjects;displayresultsusingtablesandpictures

Seeabove

Describesimplepatternsandrelationshipsinvolvingnumbersorshapes;decidewhetherexamplessatisfygivenconditions

NotexplicitlyrequiredinnewProgrammeofStudy

Describewaysofsolvingproblemsandexplainchoicesanddecisionsorallyorusingpictures

Counting & Number Relationships

OutgoingNationalCurriculum(QCAunits) NewNationalCurriculum

Countreliablyatleast20objectsrecognisingthatwhenrearrangedthenumberofobjectsstaysthesame;relateadditiontocountingonandcountonorbackinones,twos,fivesandtens;estimateanumberofobjectsthatcanbecheckedbycounting

Extendedtocountingto100

Similar




What’s gone? What’s been added?• Data handling/Statistics is removed from Y1• Nospecificrequirementtodescribepatterns• Nospecificrequirementstodescribewaysof solvingproblemsorexplainchoices

• Counting&writingnumeralsto100• Writenumbersinwordsupto20• Numberbondssecuredto20• Useofvocabularysuchasequal,morethan,lessthan, fewer,etc.


RedindicatesnolongerrequiredinYear1GreencontentisnewtoYear1


Outgoing National Curriculum (QCA units) NewNationalCurriculum

Solveproblemsinvolvingcounting,adding,subtracting,doublingorhalvinginthecontextofnumbers,measuresormoney;recognise the value of coins

“Solveone-stepproblemsthatinvolveaddition&subtraction,usingconcreteobjectsandpictorialrepresentations,andmissingnumberproblemssuchas 7 = [] – 9”“Recogniseandknowthevalueofdifferentdenominationsof coins and notes”

Describeaproblemusingnumbers,practicalmaterialsanddiagrams;usethesetosolvetheproblemandsetthesolutionbackintheoriginalcontext

Seeabove

Answeraquestionbyselectingandusingsuitableequipment,andsortinginformation,shapesorobjects;displayresultsusingtablesandpictures

Seeabove

Describesimplepatternsandrelationshipsinvolvingnumbersorshapes;decidewhetherexamplessatisfygivenconditions

NotexplicitlyrequiredinnewProgrammeofStudy

Describewaysofsolvingproblemsandexplainchoicesanddecisionsorallyorusingpictures



Countreliablyatleast20objectsrecognisingthatwhenrearrangedthenumberofobjectsstaysthesame;relateadditiontocountingonandcountonorbackinones,twos,fivesandtens;estimateanumberofobjectsthatcanbecheckedbycounting

Extendedtocountingto100

Similar

© Pearson 2014. This work is credited to the author Michael Tidd


page 3

Compareandordernumbers,usingtherelatedvocabulary;usetheequals(=)sign

Use + - and =

Readandwritenumeralsfrom0to20,thenbeyond;useknowledgeofplacevaluetopositionthesenumbersonanumbertrackandnumberline

Extendedtonumeralsto100;wordsto20

Saythenumberthatisonemoreorlessthananygivennumber,andtenmoreorlessformultiplesoften

SimilarUsethelanguageof:equalto,morethan,lessthan(fewer),most,least

Usethevocabularyofhalvesandquartersincontext “Recognise,findandnameahalfasoneoftwoequalpartsofanobject,shapeorquantity”“Recognise,findandnameaquarterasoneoffourequalpartsofanobject,shapeorquantity”

Number Facts


Deriveandrecallallpairsofnumberswithatotalof10andadditionfactsfortotalstoatleast5;workoutthecorrespondingsubtractionfacts

“Representandusenumberbondsandrelatedsubtractionfactswithin20”

Useknowledgeofcountingintwos,fivesandtenstoderivethemultiplesof2,5and10tothetenthmultiple

Countinmultiplesoftwos,fivesandtens

Recallthedoublesofallnumberstoatleast10 “Representandusenumberbondsandrelatedsubtractionfactswithin20”

Calculations


Recognisethatadditioncanbedoneinanyorderandusethistoaddmentallyaone-digitnumberoramultipleof10toaone-digitortwo-digitnumber

“Addandsubtractone-digitandtwo-digitnumbersto20,including zero”

Subtractone-digitnumbersfromone-digitandtwo-digitnumbersandamultipleof10fromatwo-digitnumber;applyadditionandsubtractionstrategies,e.g.countingontofindthedifference

“Addandsubtractone-digitandtwo-digitnumbersto20,including zero”

Understandsubtractionasboth'takingaway'and'difference'andusetherelatedvocabularyandsymbolstodescribeandrecordadditionandsubtractionnumbersentences

“Read,writeandinterpretmathematicalstatementsinvolvingaddition(+),subtraction(-)andequals(=)signs”

Solvepracticalproblemsthatinvolvecombininggroupsof2,5or10,orsharingintoequalgroups

“Solveone-stepproblemsinvolvingmultiplicationanddivision,bycalculatingtheanswerusingconcreteobjects,pictorialrepresentationsandarrayswiththesupportoftheteacher”

Position & Transformation


Visualise and name common 2-D shapes and 3-D solids and describetheirfeatures;usethemtomakepatterns

“Recognise and name common 2-D and 3-D shapes”



Identifyobjectsthatrotate;recogniseandmakewhole “Describeposition,directionsandmovements,includinghalf,quarterandthree-quarterturn”

Visualiseanddescribethepositionofobjectsanddirectionanddistancewhenmovingthem

Measure


Estimate,measure,weighandcompareobjects,choosingandusingsuitableuniformnon-standardorstandardunitsandmeasuringinstruments,e.g.aleverbalance,metrestickormeasuringjug

Compare,describe,measureandbegintorecordandsolvepracticalproblemsforlength/height/capacity/time

Usevocabularyrelatedtotime;orderdaysoftheweekandmonths;readthetimetothehourandhalfhour

“Recogniseanduselanguagerelatingtodates,includingdaysoftheweek,weeks,monthsandyears”“Tellthetimetothehourandhalfpastthehouranddrawthehandsonaclockfacetoshowthesetimes.”

Data handling


Answeraquestionbyrecordinginformationinlistsandtables;presentoutcomesusingpracticalresources,pictures,blockgraphsorpictograms

NostatisticsworkisincludedintheYear1programmeofstudy

Usediagramstosortobjectsintogroupsaccordingtoagivencriterion;suggestadifferentcriterionforgroupingthesameobjects




What’s gone? What’s been added?• Roundingtwo-digitnumberstothenearest10• Halving/doublingnolongerexplicitlyrequired• Usinglists/tables/diagramstosortobjects

*Was required in 2000 Programme of Study for KS1

• Solvingproblemswithsubtraction• Finding/writingfractionsofquantities(andlengths)• Addingtwo2-digitnumbers• Addingthree1-digitnumbers• Demonstratingcommutativityofaddition&multiplication• Describingpropertiesofshape(e.g.edges,vertices)• Measuring temperature in °C• Tell time to nearest 5 minutes• Makecomparisonsusing<>=symbols• Recognise£psymbolsandsolvesimplemoneyproblems*


RedindicatesnolongerrequiredinYear2BluecontenthasbeenmovedtoYear1GreencontentisnewtoYear2



Solveproblemsinvolvingaddition Solveproblemswithaddition&subtraction

Identifyandrecordthenumbersentencesinvolvedinaproblem

Moved to Y1

Followalineofenquiryandanswerquestionsbyselectingandusingsuitableequipmentandinformationandorganising and presenting the information in lists

Describepatternsandrelationshipsinvolvingnumbersorshapes

“Orderandarrangecombinationsofmathematicalobjectsin patterns”

Presentsolutionstoproblemsinanorganisedway;explaindecisions



Readandwritetwo-andthree-digitnumbersinfiguresandwords;describeandextendnumbersequencesandrecogniseoddandevennumbers

“Readandwritenumberstoatleast100innumeralsandinwords”“Recognisingoddandevennumbers”

Countupto100objectsbygroupingthemandcountingintens,fivesortwos;explainwhateachdigitinatwo-digitnumberrepresents,includingnumberswhere0isaplaceholder;partitiontwo-digitnumbersindifferentways,includingintomultiples of ten and one

“Countinstepsof2,3,and5from0”“Recognisetheplacevalueofeachdigitinatwo-digitnumber”“Useplacevalueandnumberfactstosolveproblems.”

© Pearson 2014. This work is credited to the author Michael Tidd


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Ordertwo-digitnumbersandpositionthemonanumberline;usethegreaterthan(>),lessthan(<)signs

Compareandordernumbersfrom0upto100;use<,>and = signs

Estimateanumberofobjectsandroundtwo-digitnumbersto the nearest 10

Notexplicitlymentioned

Findonehalf,onequarterandthreequartersofshapesandsetsofobjects

Recognise,find,nameandwritefractions1/3,1/4,2/4and3/4 of a length,shape,setofobjectsorquantity

Adds“writesimplefractionse.g.1/2of6=3andrecognisetheequivalenceof2/4and1/2.”

Number Facts


Deriveandrecallalladditionandsubtractionfactsforeachnumbertoatleast10,allpairswithtotalsto20andallpairsofmultiplesof10withtotalsupto100

Moves to Y1“recallanduseadditionandsubtractionfactsto20fluently,and derive and use related facts up to 100”

Understandthathalvingistheinverseofdoublingandderiveandrecalldoublesofallnumbersto20,andthecorresponding halves

• Notexplicitlymentioned

Deriveandrecallmultiplicationfactsforthe2,5and10times-tablesandtherelateddivisionfacts;recognisemultiplesof2,5and10

“Recallandusemultiplicationanddivisionfactsforthe2,5and10multiplicationtables”

Useknowledgeofnumberfactsandoperationstocheckanswerstocalculations

“Use…numberfactstosolveproblems”

Calculations


Addorsubtractmentallyasingle-digitnumberoramultipleof10toorfromanytwo-digitnumber;usepracticalandinformalwrittenmethodstosupportadditionandsubtractionoftwo-digitnumbers

Addandsubtractnumbersusingconcreteobjects,pictorialrepresentations,andmentally,including:atwo-digitnumberandones;atwo-digitnumberandtens;twotwo-digitnumbers;addingthreeone-digitnumbers

Understandthatsubtractionreversesadditionandviceversa and use this to derive and record related addition and subtractionnumbersentences

“Recogniseandusetheinverserelationshipbetweenadditionandsubtractionandusethistocheckcalculationsandmissingnumberproblems”

Representrepeatedadditionandarraysasmultiplication,andsharingandrepeatedsubtraction(grouping)asdivision;usepracticalandinformalwrittenmethodsandrelatedvocabularytosupportmultiplicationanddivisioncalculations,includingthosewithremainders

“Solveproblemsinvolvingmultiplicationanddivision,usingmaterials,arrays,repeatedaddition,mentalmethods,andmultiplicationanddivisionfacts,includingproblemsincontexts”

Usethesymbols+,–,×,÷and=torecordandinterpretnumbersentencesinvolvingallfouroperations;calculatethevalueofanunknowninanumbersentence,e.g.30–≤=24,≤÷2=6

“Calculate mathematical statements for multiplication and divisionwithinthemultiplicationtablesandwritethemusingthemultiplication(×),division(÷)andequals(=)signs”

Adds“showthatadditionoftwonumberscanbedoneinanyorder(commutative)andsubtractionofonenumberfromanothercannot”;and“showthatmultiplicationoftwonumberscanbedoneinanyorder(commutative)anddivisionofonenumberbyanother cannot”





Visualisecommon2-Dshapesand3-Dsolidsandidentifythem from pictures of them in different positions and orientations;sort,makeanddescribeshapes,referringtotheir properties

“Identify2-Dshapesonthesurfaceof3-Dshapes”“Compare and sort common 2-D and 3-D shapes and everydayobjects.”

Identifyreflectivesymmetryinpatternsand2-Dshapesanddrawlinesofsymmetryinshapes

“Describethepropertiesof2-Dshapes,including…symmetryinaverticalline”

Adds“describethepropertiesof2-Dshapes,includingthenumberofsides”;and“describethepropertiesof3-Dshapes,includingthenumberofedges,verticesandfaces”

Followandgiveinstructionsinvolvingposition,directionand movement

“Usemathematicalvocabularytodescribeposition,direction and movement”

Recogniseandusewhole,halfandquarterturns,bothclockwiseandanti-clockwise;knowthatarightanglerepresentsaquarterturn

“Distinguishingbetweenrotationasaturnandintermsofrightanglesforquarter,halfandthree-quarterturns (clockwiseandanti-clockwise)”

Measure


Estimate,compareandmeasurelengths,massesandcapacitiesusingstandardunits(m,cm,kg,litre)andsuitablemeasuring instruments

“Choose and use appropriate standard units to estimate andmeasurelength/heightinanydirection(m/cm);mass(kg/g);temperature (°C);capacity(litres/ml)”

Readthenumbereddivisionsonascale,andinterpretthedivisionsbetweenthem,e.g.onascalefrom0to25withintervalsof1shownbutonlythedivisions0,5,10,15and20numbered;usearulertodrawandmeasurelinestothenearestcentimetre

“Tothenearestappropriateunit,usingrulers,scales,thermometers and measuring vessels”

Useunitsoftime(seconds,minutes,hours,days)andknowtherelationshipsbetweenthem;readthetimetothequarterhourandidentifytimeintervals,includingthosethatcrossthehourboundary

“Compareandsequenceintervalsoftime““Tellandwritethetimetofiveminutes,includingquarterpast/tothehouranddrawthehandsonaclockfacetoshowthesetimes”

Adds“compareandorder[measurements]using>,<and=”;and“recogniseandusesymbolsforpounds(£)andpence(p);combineamountstomakeaparticularvalue”;and“solvesimpleproblemsinapracticalcontextinvolvingadditionandsubtractionofmoneyofthesameunit,including giving change”

Data handling


Answeraquestionbyrecordingdatainlistsandtables;representthedataasblockgraphsorpictogramstoshowresults;useICTtoorganiseandpresentdata

“interpretandconstructsimplepictograms,tallycharts,blockdiagramsandsimpletables”“askandanswersimplequestionsbycountingthenumberofobjectsineachcategoryandsortingthecategoriesbyquantity”

Uselists,tablesanddiagramstosortobjectsagainstoneortwocriteria;explainchoicesusingappropriatelanguage,including not

NotexplicitlyrequiredinProgrammeofStudy




What’s gone? What’s been added?• Specificdetailofproblem-solvingstrategies(although• therequirementtosolveproblemsremains)• Rounding to nearest 10/100 moves to Year 4• ReflectivesymmetrymovestoYear4• ConvertingbetweenmetricunitsmovestoYear4• NorequirementtouseCarroll/Venndiagrams

• Addingtensorhundredsto3-digitnumbers• Formalwrittenmethodsforaddition/subtraction• 8timestablereplaces6timestables(!)• Counting in tenths• Comparing,ordering,adding&subtractingfractionswith

common denominators• Indentifyingangleslargerthan/smallerthanrightangles• Indentifyhorizontal,vertical,parallelandperpendicularlines• Telltimetothenearestminute,including24-hourclockand

using Roman numerals• Knowthenumberofsecondsinaminuteandthenumberofdaysineachmonth,yearandleapyear


RedindicatesnolongerrequiredinYear3BluecontenthasbeenmovedtoYearKS1GreencontentisnewtoYear3



Solveone-andtwo-stepproblemsinvolvingnumbers,moneyormeasures,includingtime,choosingandcarryingout appropriate calculations

Becomes“solvenumberproblemsandpracticalproblems”

Representtheinformationinaproblemusingnumbersandimages;usethesetofindasolutionandpresentitincontext,whereappropriateusing£.pnotationorunitsofmeasure

NolongerexplicitintheProgrammeofStudy

Moved to Year 2

Followalineofenquirybydecidingwhatinformationisimportant;makeanduselists,tablesandgraphstoorganiseand interpret the information

Becomesbroader“interpret and present data using bar charts, pictograms and tables”

Lineofenquirynolongerrequired

Usepatterns,propertiesofandrelationshipsbetweennumbersorshapestoidentifysimilaritiesanddifferences,and to solve puzzles


Describeandexplainmethods,choicesandsolutionstoproblems,orallyandinwriting,usingpicturesanddiagrams




Orderwholenumberstoatleast1000andpositionthemonanumberline

Becomes “compare and order numbers up to 1000 “ and “read and write numbers up to 1000 in numerals and in words”

Becomes“countfrom0inmultiplesof4,8,50and100”Buildingoncountinginmultiplesof2,3,5&10inKS1.



Partitionthree-digitnumbersindifferentways,includingintomultiplesofonehundred,tenandone

Becomes “recognise the place value of each digit in a three-digit number (hundreds, tens, ones)”

Roundtwo-orthree-digitnumberstothenearest10or100andgiveestimatesandapproximationstotheirsumsand differences

Moves to Year 4

Readandwriteproperfractions,e.g.3/7,9/10,interpretingthedenominatorasthepartsofawholeandthenumeratorasthenumberofparts;identifyfractionsofshapesandusediagramstocomparefractionsandestablishequivalents

Childrenareexpectedto:•Understandandcountintenths•Recognise&findfractionsofsetsofobjects•Recognise&usefractions•Showequivalentfractionsusingdiagrams•Add&subtractfractionswithcommondenominators•Compare&orderunitfractions&thosewithcommon

denominators

Number Facts


Deriveandrecallalladditionandsubtractionfactsforeachnumberto20,sumsanddifferencesofmultiplesof10andnumberpairsthattotal100

Moves to Year 2

Deriveandrecallmultiplicationfactsforthe2,3,4,5,6and10times-tablesandthecorrespondingdivisionfacts

2,5and10times-tablesmovedtoYear23,4and8requiredinYear3

Useknowledgeofnumberoperationsandcorrespondinginverses to check calculations

Becomes “estimate the answer to a calculation and use inverse operations to check answers”

Calculations


Addorsubtractmentallycombinationsofone-digitandtwo-digitnumbers

Moves to Year 2Adds “add units, tens or hundreds to 3-digit numbers mentally”

Developandrefinewrittenmethodstosupport,recordorexplaintheadditionandsubtractionoftwo-digitandthree-digitnumbers

Becomesmoreexplicit“add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction”

Multiplyone-andtwo-digitnumbersby10or100,anddescribetheeffect

Multiplyingby10coveredinYear2;further scale left to upper KS2

Usepracticalandinformalwrittenmethodstosupportmultiplicationanddivisionoftwo-digitnumbers(e.g.13×3,30÷4);roundremaindersupordown,dependingonthecontext

Becomes “write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods”

Understand that division reverses multiplication and vice versa and use to derive and record related multiplication anddivisionnumbersentences

Narrowedto“write and calculate mathematical statements for multiplication and division using the multiplication tables that they know”

Findunitfractionsofnumbersandquantities,e.g.1/2,1/3,1/4and1/6of12litres

Begins in Y2 as “write simple fractions e.g. 1/2 of 6 = 3”





Relate2-Dshapesand3-Dsolidstodrawingsofthem,anddescribe,classify,drawandmaketheshapes

Becomes “draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them”

Drawandcompleteshapeswithreflectivesymmetryanddrawthereflectionofashapeinamirrorlinealongoneside

Moves to Year 4

Readandrecordthevocabularyofposition,directionandmovement,usingthefourcompassdirectionstodescribemovementaboutagrid

Moves to Year 4

Useaset-squaretodrawrightanglesandtoidentifyrightanglesin2-Dshapes;compareangleswitharightangle;recognisethattworightanglescanformastraightline

Becomes more detailed “identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle”

Adds “ identify horizontal and vertical lines and pairs of perpendicular and parallel lines”

Measure


Knowtherelationshipsbetweenkilometresandmetres,metresandcentimetres,kilogramsandgrams,litresandmillilitres;chooseanduseappropriateunitstoestimate,measure,andrecord measurements

Moves to Year 4

Moves to Year 2

Read,tothenearestdivisionandhalf-division,scalesthatarenumberedorpartiallynumbered;usetheinformationtomeasureanddrawtoasuitabledegreeofaccuracy

ReadingtonearestwholeunitmovestoYear2Studentsmeasure,compare,add&subtractusingcommon metric measures

Read the time on a 12-hour digital clock and to the nearest fiveminutesonananalogueclock;calculatetimeintervalsandfindstartorendtimesforagiventimeinterval

Movestoyear2; Y3 must tell time to nearest minute and usespecificvocab,inc.seconds,a.m.,p.m.,etc.StudentsmustalsouseRomannumeralsand24-hourclock.

Adds:“knowthenumberofsecondsinaminuteandthe numberofdaysineachmonth,yearandleapyear”

Data handling


Answeraquestionbyorganising,representingandinterpretingdata;usetallycharts,frequencytables,pictogramsandbarchartstohighlightresultsandobservations;useICTtocreateasimplebarchart

Becomesnarrower:“solve one-step and two-step using information presented in scaled bar charts and pictograms and tables”

Use Venn diagrams or Carroll diagrams to sort data and objectsusingmorethanonecriterion

NolongerexplicitinProgrammeofStudy




What’s gone? What’s been added?• Specificdetailonlinesofenquiry,representingproblemsandfindstrategiestosolveproblemsandexplainingmethods(i.e.largelyfromoldMa1)

• Usingmixednumbers(movedtoY5)• MostratioworkmovedtoY6• Written division methods (moved to Y5)• AllcalculatorskillsremovedfromKS2PoS• Measuring angles in degrees (moved to Y5)

• Solvingproblemswithfractionsanddecimalstotwo decimal places

• Roundingdecimalstowholenumbers• Roman numerals to 100• Recognisingequivalentfractions• Knowingequivalentdecimalstocommonfractions• Dividingby10and100(incl.withdecimalanswers)• Using factor pairs• Translation of shapes• Finding perimeter/area of compound shapes• Solvetimeconversionproblems





Solveone-andtwo-stepproblemsinvolvingnumbers,moneyormeasures,includingtime;chooseandcarryoutappropriatecalculations,usingcalculatormethodswhereappropriate

“Solve addition and subtraction two-step problems in contexts” and “solve problems involving multiplying and adding”

“Solve simple measure and money problems involving fractions and decimals to two decimal places”

Representaproblemusingnumbersentencesanddiagrams,usethesetofindastrategytosolvetheproblemandpresentthesolutioninthecontextoftheproblem

NolongerexplicitlyinProgrammeofStudy

Suggestalineofenquiryandthestrategyneededtopursueit;collect,organiseandinterpretselectedinformationtofindanswers


Useknowledgeofnumbersandshapestoidentifypatterns,propertiesandrelationships,andapplythemtounfamiliarsituations;investigateastatementinvolvingnumbersandtestitwithexamples


Reportsolutionstoproblems,explanationsandreasoningorallyandinwriting




Usepositiveandnegativenumbersincontext;positionthemonanumberlineandstateinequalitiesusingthesymbols<and>,e.g.–3>–5,–1>+1

“Count backwards through zero to include negative numbers”

(<>SymbolsareusedfromY2)



Usedecimalnotationfortenthsandhundredths,relatingthenotationtomoneyandmeasurement;positionone-andtwo-placedecimalsonanumberline

“Compare numbers with the same number of decimal places up to two decimal places”

Recognisetheequivalencebetweendecimalandfractionforms of tenths and hundredths

“Recognise and write decimal equivalents of any number of tenths or hundredths”

Usefractionstoidentifysubsetsofasetofobjectsusediagramstoidentifyequivalentfractions,e.g.6/8and3/4,or70/100and7/10;

interpretmixednumbersandpositionthemonanumberline,e.g.31/2

Becomes more challenging “solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number”

Moves to Year 5

Usethevocabularyofratioandproportiontodescribetherelationshipbetweentwoquantities,e.g.2toevery3,andbetweenpartandwhole,e.g.2inevery5;estimateproportion,e.g.‘forevery1redcarthereareabout4silvercars’,or‘I’masleepforabout1/3oftheday’

Solveproblemsrelatingto“hardercorrespondenceproblemssuchasnobjectsareconnectedtomobjects”MostratioworkmovestoYear6

Adds “round decimals with one decimal place to the nearest whole number”; and“read Roman numerals to 100”; “understand the introduction of zero”

Number Facts


Useknowledgeofadditionandsubtractionfactsandplacevalue to derive sums and differences of pairs of multiples of 10,100or1000

LargelymovedtoY2

Identifythedoublesoftwo-digitnumbers;usetocalculatedoublesofmultiplesof10and100andderivethecorresponding halves

DoublingisonlymentionedinY1;nototherwiserecordedexplicitlyinProgrammeofStudy

Deriveandrecallmultiplicationfactsupto10×10,thecorrespondingdivisionfactsandmultiplesofnumbersto10up to the tenth multiple

Recall multiplication and division facts for multiplication tablesupto12×12

Useknowledgeofrounding,numberoperationsandinverses to check calculations

“Round any number to the nearest 10, 100 or 1000” and “use inverse operations to check answers to a calculation”

Identifypairsoffractionsthattotal1 Adds “Recognise and show families of common equivalent fractions”; and“Recognise/write decimal equivalent to ¼, ½, & ¾. “

Calculations


Addorsubtractmentallypairsoftwo-digitwholenumbers,e.g.47+58,91–35

Moves to Year 2

Usethestandardwrittenmethodsforadditionandsubtractionoftwo-digitandthree-digitwholenumbersandcalculationswith£.p

Becomes “add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate" and “use the distributive law to multiply two digit numbers by one digit”

Multiplyordividenumbersto1000by10andthen100(wholenumberanswers),understandingtheeffect;relatetoscalingupordown

“find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as units, tenths and hundredths”



Developandrefinewrittenmethodsformultiplyinganddividingatwo-digitnumberbyaone-digitnumber,toincludedivisionwithremainders,e.g.15×9,98÷6

“Multiply two-digit and three-digit numbers by a one-digit number using formal written layout”

Written methods for division move to Y5

Findfractionsofnumbers,quantitiesorshapes,e.g.1/5of30plums,3/8ofa6by4rectangle

Moves to Year 3

Useacalculatortocarryoutone-andtwo-stepcalculationsinvolvingallfouroperations;recognisenegativenumbersinthedisplay,correctmistakenentriesandinterpretthedisplaycorrectlyinthecontextofmoney

AllcalculatorskillsmovetoKS3ProgrammeofStudy(guidance says some potential calculator use in upper KS2)

Adds “multiply & divide mentally, including multiplying by 0 and 1; dividing by 1; multiplying together three numbers”; and“ recognise and use factor pairs and commutativity in mental calculations”



Drawpolygonsandclassifythembyidentifyingtheirproperties

“Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes”

Visualise3-Dobjectsfrom2-Ddrawingsandmakenetsofcommon solids

NotexplicitlyrequiredinProgrammeofStudy

Recognisehorizontalandverticallines;usetheeightcompasspointstodescribedirection;describeandidentifythepositionofasquareonagridofsquares

Moves to Year 3RequiredinKS2Geography“Describe positions on a 2-D grid as coordinates in the first quadrant”

Knowthatanglesaremeasuredindegreesandthatonewholeturnis360ºcompareandorderangleslessthan180º

Moves to Year 5

“Identify acute and obtuse angles and compare and order angles up to two right angles by size”

Adds “describe movements as translations”; and “plot points and draw sides to complete a given polygon”

Measure


Usestandardmetricunitsandtheirabbreviationswhenestimating,measuringandrecordinglength,massandcapacity;knowthemeaningofkilo,centiandmilliand,whereappropriate,usedecimalnotationtorecordmeasurements,e.g.1.3mor0.6kg

Moves to Year 3“Estimate, compare and calculate different measures, including money in pounds and pence”

“Convert between different units of measure (e.g. kilometre to metre; hour to minute)”

Interpretintervalsanddivisionsonpartiallynumberedscalesandrecordreadingsaccurately,whereappropriatetothe nearest tenth of a unit

Scale-readingbeginsinY2;therearenofurtherspecificmentions

Drawrectanglesandmeasureandcalculatetheirperimeters,findtheareaofrectilinearshapesdrawnonasquaregridbycountingsquares

“Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres” and “find the area of rectilinear shapes by counting squares”

Readtimetothenearestminute;useam,pmand12-hourclocknotation;calculatetimeintervalsfromclocksandtimetables

Moves to Year 3Adds “read, write and convert time between analogue and digital 12 and 24-hour clocks”; and“solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days”



Data handling


Determinethedataneededtoansweraspecificquestion;organise,present,analyseandinterpretthedataintables,diagrams,tallycharts,pictogramsandbarcharts,usingICTwhereappropriate

“Interpret and present discrete and continuous data using appropriategraphicalmethods,includingbarchartsandtime graphs”Noneedforspecificquestions,presentation,etc.

Comparetheimpactofrepresentationswherescaleshaveintervals of differing step size

NolongermentionedinProgrammeofStudy




What’s gone? What’s been added?• Detailofproblem-solvingprocessanddatahandlingcyclenolongerrequired

• Calculator skills moved to KS3• ProbabilitymovestoKS3

SeveralelementsarenowexpectedtobecoveredinlowerKS2,e.g.decimals/fractionsknowledge,points inthefirstquadrant;parallel/perpendicularlines

• Understand & use decimals to 3dp• Solveproblemsusingupto3dp,andfractions• Write%agesasfractions;fractionsasdecimals• Usevocabularyofprimes,primefactors,compositenum-bers,etc.

• Knowprimenumbersto20• Understandsquareandcubenumbers• Use standard multiplication & division methods for up to 4

digits• Addandsubtractfractionswiththesamedenominator• Multiplyproperfractionsandmixednumbersbywholenumbers

• Deducefactsbasedonshapeknowledge• Distinguishregularandirregularpolygons• Calculate the mean average


RedindicatesnolongerrequiredinYear5BluecontenthasbeenmovedtolowerKS2GreencontentisnewtoYear5



Solveoneandtwo-stepproblemsinvolvingwholenumbersanddecimalsandallfouroperations,choosingandusingappropriatemethods,includingcalculatoruse

“Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why”; and“solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign”; and“solve problems involving number up to three decimal places”; and“solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those with a denominator of a multiple of 10 or 25”

Representaproblembyidentifyingandrecordingthecalculationsneededtosolveit;findpossiblesolutionsandconfirmtheminthecontextoftheproblem

NotexplicitlymentionedinProgrammeofStudy

Planandpursueanenquiry;presentevidencebycollecting,organisingandinterpretinginformation;suggestextensionstotheenquiry


Explorepatterns,propertiesandrelationshipsandproposeageneralstatementinvolvingnumbersorshapes;identifyexamplesforwhichthestatementistrueorfalse


Explainreasoningusingdiagrams,graphsandtext NotexplicitlymentionedinProgrammeofStudy





Countfromanygivennumberinwholenumberstepsanddecimalnumbersteps,extendingbeyondzerowhencountingbackwards;relatethenumberstotheirpositiononanumberline

“Count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000”

Explainwhateachdigitrepresentsinwholenumbersandnumberswithuptotwodecimalplaces,andpartitionthesenumbers

Decimals to 2dp covered in Year 4;Year 5 adds “recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents”;and“read, write, order and compare numbers with up to three decimal places”

Usesequencestoscalenumbersupordown;solveproblemsinvolvingproportionsofquantitiesandmeasurements,e.g.decreasequantitiesinarecipedesignedtofeedsixpeople

“scaling by simple fractions and problems involving simple rates”

Expressasmallerwholenumberasafractionofalargerone;findequivalentfractions,includingequivalentimproperfractionsandmixednumbers;relate fractions to their decimal representations

ExpectedinlowerKS2“ Recognise mixed numbers and improper fractions and convert from one form to the other”; and “identify, name and write equivalent fractions of a given fraction”

Becomes “read and write decimal numbers as fractions (e.g. 0.71 = 71/100)”

Understandpercentageasthenumberofpartsinevery100andexpresstenthsandhundredthsaspercentages

“Recognise the per cent symbol (%) and understand that per cent relates to “number of parts per hundred”, and write percentages as a fraction with denominator hundred, and as a decimal fraction”

Adds: “compare and order fractions whose denominators are all multiples of the same number”;and“know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers”;and“establish whether a number up to 100 is prime and recall prime numbers up to 19”

Number Facts


Useknowledgeofplacevalueandadditionandsubtractionoftwo-digitnumberstoderivesumsanddifferences,doublesandhalvesofdecimals,e.g.6.5±2.7,halve5.6,double0.34

MovestolowerKS2

Recallquicklymultiplicationfactsupto10×10,usetomultiplypairsofmultiplesof10and100andderivequicklycorrespondingdivisionfacts

TableknowledgeexpectedbyY4to12x12“Multiply and divide numbers mentally drawing upon known facts”

Identifypairsoffactorsoftwo-digitwholenumbersandfindcommonmultiples,e.g.for6and9

“Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.”

Useknowledgeofnumberfacts,placevalueandroundingto estimate and to check calculations

“Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy”; and“round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000”;and“round decimals with two decimal places to the nearest whole number and to one decimal place”

Adds: “ recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)”



Calculations


MultiplymentallyTU×U;usementalmethodsinspecialcases,e.g.tosubtract1995from6007,tomultiply18by25

“Multiply and divide numbers mentally drawing upon known facts”

Usethestandardwrittenmethodsforadditionandsubtractionofwholenumbersanddecimalswithoneortwoplaces

Moves to Year 4

Useunderstandingofplacevaluetomultiplyanddividewholenumbersanddecimalsby10,100or1000

“Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000”

UsethestandardwrittenmethodsformultiplicationanddivisioncalculationsofHTU×U,U.t×U,TU×TUandHTU÷U

“Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers”;and“divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context”

Findfractionsusingdivision,e.g.1/100of5kg,andpercentagesofnumbersandquantities,e.g.10%,5%and15% of £80

MovestolowerKS2; Year 5 adds:“add and subtract fractions with the same denominator and multiples of the same number”;and“multiplyproperfractionsandmixednumbersbywholenumbers”

Useacalculatortosolveproblems,includingthoseinvolvingdecimalsorfractions,e.g.tofind3/4of150g;interpretthedisplaycorrectlyinthecontextofmeasurement

CalculatorskillsareallmovedtoKS3ProgrammeofStudy

Adds: “solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors”



Identify,visualiseanddescribepropertiesofrectangles,triangles,regularpolygonsand3-Dsolids;useknowledgeofpropertiestodraw2-Dshapesandidentifyanddrawnetsof3-Dshapes

“Identify 3-D shapes, including cubes and other cuboids, from 2-D representations”

Readandplotco-ordinatesinthefirstquadrantandrecognise parallel and perpendicular lines in grids and shapes;useaset-squareandrulertodrawperpendicularandparallel lines

PlottingpointsmovestoYear4Parallel&PerpendicularlinesmovestoYear3

Completepatternswithuptotwolinesofsymmetryanddrawthepositionofashapeafterareflectionortranslation

TranslationmovedtoYear4;SymmetryintroducedinY4; “identify, describe and represent the position of a shape following a reflection or translation”

Estimate,drawandmeasureacuteandobtuseanglesusingananglemeasurerorprotractortoasuitabledegreeofaccuracy;calculateanglesinastraightline

“Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles”;

“draw given angles, and measure them in degrees (o)” &

“identify angles at a point on a straight line and ½ a turn (total 180o)”



Measure


Read,useandrecordstandardmetricunitstoestimateandmeasurelength,massandcapacity;convertlargertosmallerunitsusingdecimalstooneplace,e.g.change2.6kgto 2600g

“Convert between different units of metric measure”; and “estimate volume and capacity “

Estimatemeasurementsoflength,massandcapacitytoarequireddegreeofaccuracy,e.g.thenearestcentimetre;interpretareadingthatliesbetweentwounnumbereddivisions on a scale

“estimate volume and capacity “


Drawandmeasurelinestothenearestmillimetre;measureand calculate the perimeter of regular and irregular polygons;usetheformulafortheareaofarectangletocalculate its area

“Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres”; and “calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes”

Adds: “use the properties of rectangles to deduce related facts and find missing lengths and angles”;and“distinguish between regular and irregular polygons based on reasoning about equal sides and angles”

Readtimetablesandtimeusing24-hourclocknotation;use a calendar to calculate time intervals

24-hourclockusedinlowerKS2“Complete, read and interpret information in tables, including timetables“

“Solve problems involving converting between units of time”

Data handling


Describetheoccurrenceoffamiliareventsusingthelanguage of chance or likelihood

ProbabilitymovestoKS3ProgrammeofStudy

Determinethedataneededtoanswerasetofrelatedquestions;selectandorganiserelevantdatausingfrequencytables;constructpictogramsandbargraphs,andlinegraphsthatrepresentthefrequenciesofeventsandchangesovertime;useICTtopresentandhighlightfeaturesthatleadtofurtherquestions

Narrowsto“solve comparison, sum and difference problems using information presented in a line graph”

(i.e.removesneedforICT,dataprocess,selecting/organisingdata,etc.)

Find and interpret the mode of a set of data NotexplicitlymentionedinProgrammeofStudy




What’s gone? What’s been added?• Detailofproblem-solvingprocessesnolongerexplicit• Divisibilitytests• CalculatorskillsmovetoKS3PoS• Rotation moves to KS3• ProbabilitymovestoKS3• Median/Mode/Rangenolongerrequired

• Compare and ordering fractions greater than 1• Long division• 4operationswithfractions• Calculatedecimalequivalentoffractions• Understand & use order of operations• Plotpointsinall4quadrants• Convertbetweenmilesandkilometres• Nameradius/diameterandknowrelationship• Use formulae for area/volume of shapes• Calculate area of triangles & parallelograms• Calculate volume of 3-d shapes• Useletterstorepresentunknowns(algebra)• Generateanddescribelinearsequences• Findsolutionstounknownsinproblems





Solvemulti-stepproblems,andproblemsinvolvingfractions,decimalsandpercentages,choosingandusingappropriateandefficientmethodsateachstage,includingcalculatoruse

“Solve problems involving addition, subtraction, multiplication and division”; “solve problems which require answers to be rounded to specified degrees of accuracy”; and “solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate”

Representaproblembyidentifyingandrecordingthecalculationsneededtosolveit,usingsymbolsforunknownquantitieswhereappropriate;setsolutionsintheoriginalcontextandchecktheiraccuracy

“Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why”

“Use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy.”

(See also algebra notes at foot of page)

Suggest,plananddeveloplinesofenquiry;collect,organiseandrepresentinformation,interpretresultsandreviewmethods;identifyandanswerrelatedquestions

NotexplicitlyinProgrammeofStudy

Recogniseandusesequences,patternsandrelationshipsinvolvingnumbersandshapes;suggesthypothesesandtestthemsystematically


Explainreasoningandconclusions,usingsymbolswhereappropriate






Findthedifferencebetweenapositiveandanegativeinteger,ortwonegativeintegers,incontext

“use negative numbers in context, and calculate intervals across zero”

Usedecimalnotationfortenths,hundredthsandthousandths,partitionandordernumberswithuptothreedecimalplaces,andpositionthemonthenumberline

Moves to Year 5

Roundnumbers,includingthosewithuptothreedecimalplaces

Becomes “round any whole number to a required degree of accuracy” and “solve problems which require answers to be rounded to specified degrees of accuracy”

Usefractions,percentagesandthevocabularyofratioandproportiontodescribetherelationshipsbetweentwoquantitiesandsolveproblems,e.g.identifythequantitiesneededtomakeafruitdrinkbymixingwaterandjuiceinagiven ratio

“Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts”

Expressalargerwholenumberasafractionofasmallerone;simplifyfractions;orderasetoffractionsbyconvertingthemtofractionswithacommondenominator

ExpectedlowerinKS2

“Use common factors to simplify fractions; use common multiples to express fractions in the same denomination”

Expressonequantityasapercentageofanother,e.g.express£400asapercentageof£1000;findequivalentpercentages,decimalsandfractions

“Solve problems involving the calculation of percentages (e.g. of measures) such as 15% of 360 and the use of percentages for comparison”

Adds: “compare and order fractions, including fractions >1”

Number Facts


Useknowledgeofplacevalueandmultiplicationfactsto10×10toderiverelatedmultiplicationanddivisionfactsinvolvingdecimalnumbers,e.g.0.8×7,4.8÷6

“Multiply one-digit numbers with up to two decimal places by whole numbers”

Useknowledgeofmultiplicationfactstoderivequicklysquaresofnumbersto12×12Thecorrespondingsquaresofmultiplesof10

ExpectedfromlowerKS2


Recognisethatprimenumbershaveonlytwofactorsandidentifyprimenumberslessthan100;findtheprimefactorsoftwo-digitwholenumbers

Moves to Year 5“Identify common factors, common multiples and prime numbers”

Useapproximationsandapplytestsofdivisibilitytocheckresults


Calculations


Calculatementallywithwholenumbersanddecimals,e.g.U.t±U.t,TU×U,U.t×U,TU÷U,U.t÷U

“Perform mental calculations, including with mixed operations and large numbers”

Consolidatetheuseofstandardwrittenmethodstoadd,subtract,multiplyanddivideintegersanddecimalnumbers;calculatetheanswertoHTU÷UandU.t÷Utooneortwodecimalplaces

“Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication”

“Use written division methods in cases where the answer has up to two decimal places”

“Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context”



Findfractionsandpercentagesofwhole-numberquantities,e.g.5/8of96,65%of£260

ExpectedlowerinKS2

Useacalculatortosolveproblemsinvolvingmulti-stepcalculations;carryoutcalculationsinvolvingtimebyconverting hours and minutes to minutes

CalculatorskillsmovetoKS3ProgrammeofStudy

Adds: “use their knowledge of the order of operations to carry out calculations involving the four operations”

Adds: “add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions”;

“multiply simple pairs of proper fractions, writing the answer in its simplest form”;

“divide proper fractions by whole numbers (e.g. 1/3 ÷ 2 = 1/6 )”

“associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (eg. 3/8)”

Measure


Usestandardmetricunitsofmeasureandconvertbetweenunitsusingdecimalstotwoplacesnotation,e.g.change2.75litresto2750ml,orviceversa

“Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places”

Measureandcalculateusingimperialsunitsstillineverydayuse;knowtheirapproximateequivalentmetricvalues

Common conversions included in Year 5Adds “convert between miles and kilometres”

Readscalesandrecordresultstoarequireddegreeofaccuracy,recognisingthatthemeasurementmadeisapproximate

“Use, read, write and convert between standard units, […], using decimal notation to up to three decimal places”

Calculatetheperimeterandareaofrectilinearshapes;estimatetheareaofanirregularshapebycountingsquares

Moves to Year 4/5Adds:”recognise that shapes with the same areas can have different perimeters and vice versa”;“recognise when it is possible to use formulae for area and volume of shapes”;“calculate the area of parallelograms and triangles”;and“calculate, estimate and compare volume of cubes and cuboids using standard units”

Data handling


Describeandpredictoutcomesfromdatausingthelanguage of chance or likelihood

ProbabilitymovestoKS3ProgrammeofStudy

Solveproblemsinvolvingselecting,processing,presentingandinterpretingdata,usingICTwhereappropriate;constructandinterpretfrequencytables,barchartswithgroupeddiscretedata,andlinegraphs;interpretpiecharts;drawconclusionsandidentifyfurtherquestionstoask

“Interpret and construct pie charts and line graphs and use these to solve problems”

Nodetailaboutdatahandlingprocessisincluded

Describeandinterpretresultsandsolutionstoproblemsusingthemode,range,medianandmean

“calculate and interpret the mean as an average.”

(Otheraveragesarenotexplicitlymentioned)



Algebra


Usingsymbolsforunknownquantitieswhereappropriate •Expressmissingnumberproblemsalgebraically•Usesimpleformulaeexpressedinwords•Generateanddescribelinearnumbersequences•Findpairsofnumbersthatsatisfynumbersentences involvingtwounknowns•Enumerateallpossibilitiesofcombinationsoftwo variables.

Maths2014 Curriculum changes proof - Mathematics … · Changes to the Maths Curriculum: Year 1 ... 1999 curriculum, subjects are compared to the more detailed provisions that were

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