Year 2 Learning And Progression Steps For Mathematics
Year 2 Learning and Progression Steps for MathematicsWhat are Learning and Progression Steps (LAPS)?The Learning and Progression Steps are designed to scaffold the learning required in order to meet the expectations of the National Curriculum. Statements in the LancashireKey Learning for Mathematics document have been broken down into smaller steps to support teachers in planning appropriate learning opportunities. These key pieces oflearning will support pupils in becoming fluent in the knowledge and skills of the curriculum and ensure that the learning is effective and sustained.The number of steps is dependent on the learning and do not constitute expectations for the end of each term.The final step in the progression for each strand of learning is the end of year expectation.The steps are not of equal size and different amounts of time may be required for children to move between individual steps. For example,Progression is likely to bewithin the same lessonProgression is likely to beover a series of lessonsSome learning within the same end of year expectation has been split and designed to run concurrently alongside each other. For example,Some LAPS may need to be completed before another can be started.Where have they come from?The Learning and Progression Steps (LAPS) have been derived from the Lancashire Key Learning in Mathematics statements, identified primarily from the National Curriculum2014 programmes of study.How are they different from the Key Learning Statements?The Learning and Progression Steps (LAPS) are smaller, progressive steps which support learning towards the Key Learning in Mathematics expectations. Lancashire County Council 2016
How are they different from the Key Learning Indicators of Performance (KLIPs)?The Key Learning Indicators of Performance (KLIPs) document is an assessment tool. The Learning and Progression Steps (LAPS) document is a planning tool and is not intendedto be used for summative assessment purposes. However, they may support teachers in judging whether children are on track to meet the end of year expectations at differentpoints throughout the year.The terms ‘entering’, ‘developing’ and ‘secure’ are used in Lancashire’s assessment approach, KLIPs, as summative judgements in relation to age related expectations.Definitions for these terms can be found in the introduction to the KLIPs document.How might Learning and Progression Steps (LAPS) in Mathematics be useful?Learning and Progression Steps (LAPS) may be used in a number of ways. For whole class teaching, LAPS may be used to support differentiation. When planning, it may beappropriate to use LAPS statements to inform learning objectives for a session or number of sessions. Learning and Progression Steps (LAPS) in Mathematics should be selectedaccording to the learning needs of the individual or group. Emphasis however, should always be on developing breadth and depth of learning to ensure skills, knowledge andunderstanding are sufficiently embedded before moving on.The LAPS should not be used as an assessment tool, but they can inform teachers about children’s progress towards the end of year expectations at the end of each term.Are LAPS consistent with the other resources from the Lancashire Mathematics Team?Yes, the LAPS are related to the content of the Mathematics Planning Support Disc and also the Progression Towards Written Calculation Policies and the Progression in MentalCalculation Strategies.These can be found on the s Lancashire County Council 2016
These Learning and Progression Statements (LAPS) are designed to show the necessary steps in learning to make effective and sustainable progress within a single year.They begin with the ‘end of year’ expectation from the previous year and build up to the ‘end of year expectation’ of the current year.The number of steps is dependent on the learning and do not constitute expectations for the end of each term.The steps are not of equal size and different amounts of time may be required for children to move between individual steps.End of Year 1expectationCount to and across100, forwards andbackwards, beginningwith 0 or 1, or fromany given numberNumber and Place ValueCount in multiples oftwos, fives and tensRead and writenumbers to 100 innumeralsBegin to recognisethe place value ofnumbers beyond 20(tens and ones)Identify andrepresent numbersusing objects andpictorialrepresentationsincluding the numberlineNo equivalentobjective in Year 1 Lancashire County Council 2016End of Year 2expectationLearning and Progression StatementsCount in steps of 10forwards andbackwards from anynumber using base 10equipmentCount in steps of 10forwards andbackwards from anynumber using a 100squareIdentify and discusspatterns on a 100square when countingin steps of2 or 5 from 0 and tensfrom any numberCount in steps of 3from 0 using practicalequipment such ascounters / cubesarranged in an arrayCount in steps of 3using a fully labellednumber lineCount in steps of 3from 0Read numbers up to 100 in words using a word list (giving numbers up toRead numbers up to 100 in words20 and the words for the multiples of 10)Write numbers up to 100 in words using a word list (giving numbers up toWrite numbers up to 100 in words20 and the words for the multiples of 10)Make and identify a twoMake and identify a twoMake and identify a twoMake and identify a twodigit number up to 50 using digit number up to 50 usingdigit number up to 100digit number up to 100Say what each digitconcrete materials e.g.concrete materials such asusing concrete materialsusing concrete materialsrepresents in a two digitbundles of straws, base 10place value counters,such as place valuee.g. bundles of straws, basenumberapparatus and match theseabacus and match these tocounters, abacus and arrow10 apparatusto arrow cardsarrow cardscardsMake and identify aMake and identify aCorrectly place atwo digit number upMake and identify aMake and identify atwodigitnumberupnumberfrom 1 to 100to 50 using concretetwo digit number uptwo digit number upCorrectly place ato 100 usingon a number line withmaterials e.g.to 50 using concreteto 100 using concretenumber from 1 to 100equipment such asmultiples of 10 markedmaterials such as place materials e.g. base 10on a number line withbundles of straws,place value counters,but not labelled (withvalue counters, abacusapparatus, bundles ofmultiples of 10 labelledbase 10 apparatusabacus and arrowstart and end labelled 0and arrow cardsstrawsand arrow cardscardsand 100)Make a two-digit numberusing concrete materialse.g. base 10 apparatus,bundles of straws, placevalue countersPartition a two-digit number(represented using base 10apparatus) into tens andones e.g. 43 is 4 tens (40)and 3 ones (3)Partition a two-digit number(represented using base 10apparatus) into two groupsin different ways where onegroup is a multiple of 10Partition a two-digit number(represented using base 10apparatus) into two groupsin different wayse.g. 43 40 3 or 31 12Partition a two-digit number(represented using base 10apparatus) in different wayse.g. 43 40 3 or 20 23 or20 21 2Count in steps of 2, 3,and 5 from 0, and intens from anynumber, forward andbackwardRead and writenumbers to at least100 in numerals andin wordsRecognise the placevalue of each digit ina two-digit number(tens, ones)Identify, representand estimatenumbers usingdifferentrepresentations,including the numberlinePartition numbers indifferent ways (e.g.23 20 3 and 23 10 13)
Use the language of:equal to, more than,less than (fewer),most, leastGiven a number,identify one moreand one lessNo equivalentobjective in Year 1Recognise and createrepeating patternswith numbers, objectsand shapesIdentify odd and evennumbers linked tocounting in twos from0 and 1Solve problems andpractical problemsinvolving all of theabove Lancashire County Council 2016Compare three or more 2-digitamounts when represented usingOrder three or more 2-digitUse the , and signs whenthe same practical equipmentamounts when represented usingcomparing one and two-digitsaying which amounts havethe same practical equipmentnumbersmore/most and fewer/less/Pay particular attention to numbersPay particular attention to numbersfewest/leastthat have the same digits e.g. 34that have the same digits e.g. 34Pay particular attention to numbersand 43and 43that have the same digits e.g. 34and 43Identify the number 1 more and 1Identify the number 1 more and 1Identify what changes and whatIdentify the number 10 more andless than a given number, where the less than a given number where thestays the same when 10 is added orless than a given numbertens digit stays the sametens digit might changeremoved from a two-digit numberIdentify the multiples of 10 immediately beforeRecognise that if a number is exactly half wayIdentify the multiples of 10 immediately beforeand after a given number (not ending in 5), countbetween two multiples of 10, then the numberor after a given numberto each of these multiples of 10 and say whichrounds to the higher multiple of 10multiple of 10 is closestCompare two 2-digit amounts whenrepresented using the samepractical equipment saying whichamount has more and fewer/lessPay particular attention to numbersthat have the same digits e.g. 34and 43Know that our number system is organised using groups of 10 and whateach digit represents in a two-digit number,e.g. 46 is 4 groups of ten and 6 onesDescribe the rule in anumber sequencecounting on and backin twos from anynumberExtend numbersequences counting onand back in twos fromany numberDescribe the rule in anumber sequencecounting on and backin tens or twos fromany numberRecognise the correspondence between ones and tens, e.g.6 ones 66 tens 60Extend numbersequences counting onand back in tens ortwos from any numberDescribe the rule in anumber sequencecounting on and backin fives, tens or twosfrom any numberExtend numbersequences counting onand back in fives, tensor twos from anynumberChildren need frequent access to a range of contexts using the content from all of the above.See Using and Applying, Contextual Learning and Assessment sections from the Lancashire Mathematics Planning Disc.Compare and ordernumbers from 0 up to100; use , and signsFind 1 or 10 more orless than a givennumberRound numbers to atleast 100 to thenearest 10Understand theconnection betweenthe 10 multiplicationtable and place valueDescribe and extendsimple sequencesinvolving counting onor back in differentstepsUse place value andnumber facts to solveproblems
End of Year 1expectationNumber – Addition and SubtractionNo equivalentobjective in Year 1No equivalentobjective in Year 1Read, write andinterpretmathematicalstatementsinvolving addition( ), subtraction (-)and equals ( ) signsRead, write andinterpretmathematicalstatementsinvolving addition( ), subtraction (-)and equals ( ) signsLearning and Progression StatementsEnd of Year 2expectationChildren need frequent opportunities to select appropriate strategies from the range they have learnt.The most efficient strategy may differ between children as it will be based on their confidence and competence.Choose anappropriate strategyto solve a calculationbased upon thenumbers involved(recall a known fact,calculate mentally,use a jotting)These steps fit the Lancashire Progression Towards Written Calculation Policies and Progression in Mental Calculations PoliciesRecognise calculations that requireRecognise that theRecogniseRecognisecounting on or back mentally, bridgingnumbers in additioncalculations thatRecognisecalculations thatthrough a multiple of 10 efficiently e.g.calculations can berequire counting oncalculations thatrequire counting on48 6 becomes 48 2 4reordered to makeor back mentallyrequire mentalmentally to find theand use this strategy where appropriatecounting on moree.g. 47 - 20partitioning e.g. 23Recognise and solvedifference e.g. 73 –(This should be supported by concreteefficient e.g. 4 33(counting back in 34 and use thiscalculations that65 and use thismaterials, pictures or jottings)becomes 33 4 andtens) and use thisstrategy whereinvolve known factsstrategy whereuse this strategystrategy whereappropriateRecognise calculations that require ae.g. 6 12appropriatewhere appropriateappropriate(This should bemental compensation method e.g. 73 –(This should be(This should be(This should besupported by9 becomes 73 – 10 1supported bysupported bysupported byconcrete materials,and use this strategy where appropriateconcrete materials,concrete materials,concrete materials,pictures or jottings)(This should be supported by concretepictures or jottings)pictures or jottings)pictures or jottings)materials, pictures or jottings)Model addition numbersentences usingconcrete materialsRecognise that addition oftwo or more numbers canbe done in any orderKnow that ‘take away’ is removal ofan amount from withinanother amount.Identify subtraction as ‘take away’ indifferent contexts by understandingand interpreting the languageinvolvedRepresent and usenumber bonds andrelated subtractionfacts within 20 Lancashire County Council 2016Recall and use addition andsubtraction facts totalling 10for addition and subtractionUse the fact that addition oftwo or more numbers canbe done in any order toreorder calculations forefficiencyKnow that ‘difference’ is comparingtwo amounts and finding how manymore or how many less/fewerRecall and use addition andsubtraction facts of allnumbers up to 10 foraddition and subtractionRecall and use addition andsubtraction facts totalling 20for addition and subtractionRecognise that (in practicalsituations) the subtraction ofone number from anothercannot be done in any orderShow that addition oftwo numbers can bedone in any order(commutative) andsubtraction of onenumber from anothercannotRecognise subtraction as ‘difference’in different contexts byunderstanding and interpreting thelanguage involvedUnderstandsubtraction as takeaway and difference(how many more,how manyless/fewer)Model subtraction numbersentences usingconcrete materialsModel subtraction as ‘difference’number sentences usingconcrete materialsSelect a mentalstrategy appropriatefor the numbersinvolved in thecalculationDerive and use addition andsubtraction facts ofmultiples of 10 totalling 100Use ten frames to exploreaddition and subtractionfacts for all numbers up to20Recall and useaddition andsubtraction facts to20 fluently, andderive and userelated facts up to100
Represent and usenumber bonds andrelated subtractionfacts within 20Add and subtractone-digit and twodigit numbers to20, including zero(using concreteobjects andpictorialrepresentations)Derive and use addition and subtraction facts of multiples of 10 totalling 60Partition andcombinemultiples of tensand onesAdd andsubtract a onedigit numberto/from a twodigit number(not crossingtens boundary)Add three singledigit numbersincludingbridging through10 and/or 20(Practically thenpictorially thenmentally)(Practically thenpictorially thenmentally)(Practically thenpictorially thenmentally)Add andsubtract amultiple of 10to/from a twodigit number(not crossinghundredsboundary)(Practically thenpictorially thenmentally)Derive and use addition and subtraction facts of multiples of 5 totalling 60Add andsubtract a onedigit numberto/from a twodigit numberincludingcrossing a tensboundary(Practically thenpictorially thenmentally)Add andsubtract a twodigit numberto/from anothertwo-digitnumber (notcrossing anyboundaries)(Practically thenpictorially thenmentally)Add andsubtract a twodigit numberto/from anothertwo-digitnumberincludingcrossing a tensboundary(Practically thenpictorially)Add a two-digitnumber toanother twodigit numberincludingcrossing thehundredsboundary(Practically thenpictorially)Recall and usenumber bonds formultiples of 5totalling 60 (tosupport telling timeto nearest5 minutes)Add and subtractnumbers usingconcrete objects,pictorialrepresentations, andmentally, including:- a two-digit numberand ones- a two-digit numberand tens- two two-digitnumbers- adding three onedigit numbersThese steps fit the Lancashire Progression Towards Written Calculation Policies and Progression in Mental Calculations PoliciesSolve one-stepproblems thatinvolve additionand subtraction,using concreteobjects andpictorialrepresentations,and missingnumber problemssuch as 7 - 9Solve one-stepproblems thatinvolve additionand subtraction,using concreteobjects andpictorialrepresentations,and missingnumber problemssuch as7 -9 Lancashire County Council 2016Recognise and use theknowledge that4 5 9 can bechecked by using theinverse operation9 – 4 5 or9–5 4Recognise and use theknowledge that12 – 4 8 can bechecked by using theinverse operation8 4 12 or4 8 12Represent and solve a problem usingconcrete materialsRecognise that4 ? 9 can be solvedby calculating 9 – 4 ?because 9 is the wholewhich is made of twoparts one of which is 4Recognise that12 – ? 8 can be solvedby calculating 12 – 8 ?because 12 is the wholewhich is made of twoparts one of which is 8Represent and solve a problem using pictorialrepresentations of the items inthe contextRecognise that? – 5 9 can besolved by calculating9 5 ? becausetwo parts which are9 and 5 go togetherto create the wholeRecognise and usethe inverserelationship betweenaddition andsubtraction and usethis to checkcalculations and solvemissing numberproblemsRepresent and solve a problem using structuredpictorial representations such as the bar modelSolve problems withaddition andsubtraction includingwith missingnumbers:- using concreteobjects and pictorialrepresentations,including thoseinvolving numbers,quantities andmeasures- applying theirincreasing knowledgeof mental and writtenmethodsRecognise that? 3 11 can be solvedby calculating 11 – 3 ?because 11 is the wholewhich is made of twoparts one of which is 3
End of Year 1expectationNo equivalentobjective in Year 1Represent doubling usingconcrete materialsUnderstand that doubling is adding anumber to itself and multiplying by 2No equivalentobjective in Year 1Number – Multiplication and DivisionEnd of Year 2expectationLearning and Progression StatementsNo equivalentobjective in Year 1Count in multiplesof twos, fives andtensRecall and usedoubles of allnumbers to 10 andcorrespondinghalvesRecall and usedoubles of allnumbers to 10 andcorrespondinghalves Lancashire County Council 2016Write two different numbersentences to represent adoubling situation e.g.6 6 12 and6 x 2 12Represent adding the same numberthree or more times usingconcrete materials arranged ingroups and then in more structuredform as an array and link thisto multiplicationWrite two different numbersentences to represent repeatedaddition situations e.g.5 5 5 15 and5 x 3 15In real life contexts, share anMake equal sized groups from anamount equally across sets whereMake equal sized groups from anShare an amount equally across setsamount where there is a remainderthere is a remainder e.g. share 23amount where there is no remainderwhere there is no remainder e.g.e.g. give 3 buttons to eachpencils between 3 tables results in 7 e.g. make teams of 5 from a group ofshare 20 sweets between 5 childrengingerbread man when there are 23pencils on each table and 2 pencils30 children; 24 6buttons in total; 26 5that cannot be sharedUse the fact thatmultiplication of twoCreate an array and identifynumbers can be done in anyRecognise that (in practicalthe two multiplicationorder to derive onesituations) the division ofModel division numberModel multiplicationstatements that aremultiplication statementone number from anothersentencesusingnumber sentences usingrepresented to show thatfrom another e.g. ‘I don’tcannot be done in any orderconcrete materialsconcrete materialsmultiplication of twoknow what two lots of fourbecause they give differentnumbers can be done inare but I know four lots ofanswersany ordertwo are eight so it is thesame.’Recall
End of Year 1 expectation Learning and Progression Statements End of Year 2 expectation Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number Count in multiples of twos, fives and tens Count in steps of 10 forwards and backwards from any number using base 10 equipment Count in steps of 10 forwards and
Enlisted Career Progression Charts 10-1-1. General This chapter contains career progression charts for each enlisted career management field (CMF) and approved for enlisted classification. 10-1-2. Specifications for Enlisted Career Progression Charts This chapter contains career progression charts for each enlisted specialty. The chapter is
Student Progression Plan Table of Contents I. Student Progression Plan Overview A. Purpose of Student Progression Plan B. Mission, Vision, and Values of School District C. Nondiscrimination Statement II. Georgia Standards of Excellence A. Georgia Standards of Excellence Ge
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00_Crawford_Price_BAB1407B0153_Prelims.indd 1 11/11/2014 7:36:56 PM. 1 INTRODUCING GROUPWORK Chapter summary In this chapter you will learn about the overall purpose, aims, scope and features of this book how the book is structured and the brief contents of each chapter how the book is aligned with a range of national standards and requirements related to professional social work .
