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Overcoming barriers in mathematics - helping children move from ...

The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3Overcoming barriers in mathematics –helping children move fromlevel 2 to level 33Contents■ ■ Introduction4■■What mathematics appears on the CD?4■■How were the areas of mathematics identified?4■■How do I access the materials?4■■Who are these materials aimed at?4■■How do the materials link to the Primary Framework?5■■How are the CD materials structured?5■■How should I use the materials on the CD?6■■Contents of the CD7■■What is available to help me build the materials into my planning?9■■Links between objectives and Units20First published in 2008Ref: 00099-2008BKT-EN© Crown copyright 200800099-2008BKT-EN


4 The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3IntroductionWelcome to this CD-based resource. The materials are designed to help you ensure that, in mathematics,Year 3 and Year 4 children progress from level 2 to level 3 by the end of Year 4. Increasing numbers of childrenare achieving level 3, but some children still meet barriers in their learning that slow or block their progress. Thematerials on the CD provide teaching resources and ideas upon which you can draw when planning additionalsupport for those children. This CD is one of a set of focused intervention materials that are being developedfor mathematics. Materials to support moving children from level 3 to level 4 are already available (Ref: 00695-2007PCK-EN). We hope that you will find these materials useful when planning your teaching to help childrenworking around the level 2 to level 3 border make good progress.What mathematics appears on the CD?The materials address key areas of mathematics that Year 3 and Year 4 children working at level 2 oftenfind challenging – the areas of mathematics in which children need additional support to help them maintainprogress over Key Stage 2. While the CD includes all the Year 3 and Year 4 learning objectives for mathematics,not all these objectives have materials to support them, only those that have been identified as commonbarriers to progress.How were the areas of mathematics identified?The decision as to which areas of mathematics to include on the CD was informed by a scrutiny of optionalQCA test scripts of children whose attainment fell below, but was close to, the level 2 to 3 boundary. Thisanalysis was supported by evidence from other sources. It drew on QCA reports, research evidenceand feedback from teachers and consultants. This evidence pointed to a number of common barriers inmathematics that often prevent children from making progress. These are the areas of mathematics thatappear on the CD – the bits of mathematics children find difficult to learn, which are often the bits that are moredifficult to teach.How do I access the materials?The materials on the CD are accessed through the learning objectives for mathematics as set out in thePrimary Framework. The objectives are organised into the seven strands of the Framework to help you matchthem to the Unit of work you might be teaching. At the back of this booklet there is a sequence of charts. Thecharts make links between level descriptions, common barriers to progress, the associated Year 3 and Year 4objectives, and materials on the CD, with reference to the Blocks and Units in the Primary Framework. Thisprovides a see-at-a-glance guide to support you in identifying key barriers in moving children from level 2 tolevel 3 and pinpointing where children are having difficulties and how to move them on.The CD draws on existing materials, some of which can be found in the Primary Framework, and provides extrasupport and guidance on teaching approaches designed to support children in overcoming identified barriersto progress.Who are these materials aimed at?The materials are designed to be used flexibly and as appropriate for your planning and teaching context.There are aspects that require intervention by you, as the teacher, drawing on your knowledge of children’sprogress in mathematics, for example, when using the ‘Can I…?’ prompts and review questions to pinpointbarriers to progress. After the barriers to learning have been identified, other elements might be used by00099-2008BKT-EN© Crown copyright 2008


The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 37Contents of the CDFrom your tracking of children’s progress andongoing assessment you will have identifiedpotential barriers to learning. The Example reviewquestions provide support for confirming thatthis area is a barrier to learning for children andidentifying any specific misconceptions.The questions might be used as starting points fordiscussion with small groups or individuals.Depending upon the area of mathematics, thequestions include suggestions for closed and openendedquestions, and questions requiring reasoningand discussion.Can I make, name and describe 2-D and 3-D shapes?Teaching guidanceKey vocabularytriangle, square, rectangle, oblong, quadrilateral, pentagon, hexagon, octagon, circle,semicircle, cube, cuboid, pyramid, cone, cylinder, prism, sphere, hemisphere, face, edge,vertex/vertices, surface, solid, side, straight, curved, diagram, right-angled, symmetrical,2-D shape, two-dimensional, 3-D shape, three-dimensional, describe, propertyModels and imagesPractical resources to make shapesPinboards andSticks orelastic bands Shape tiles geostrips Art straws orconstructionkitsSets of plastic/wooden shapes and sets of 2-D shapes on cardComputer programsFixpoints ITPIsometric grids ITPThe Teaching guidance provides backgroundinformation about appropriate vocabulary, modelsand images, and teaching approaches. The listof vocabulary is a useful reference point for keyvocabulary that children need to be able to use andexplain. The models and images are drawn froma variety of sources, including the former modelsand images charts, intervention materials andinteractive teaching programs, and often includesome suggestions for their use. The Teaching tipssection provides a few starting points for tackling thearea of mathematics with children, ways of linkingconcepts with other areas of the curriculum, or waysof overcoming misconceptions.Teaching tips• Ensure that children meet shapes in different orientations.– For example, some children do not appreciate that this is a square:– Use computer programs that allow children to move and manipulateshapes, for example stretching one vertex. Ask them to describewhat has changed and what has stayed the same.• Ensure that the shape resources you use include irregular shapes.Children need to realise that any shape with three straight sides isa triangle, any shape with five straight sides is a pentagon, and so on.• Plan regular opportunities for children to build and create shapes using a range ofresources, including ICT programs. This helps them to secure their understanding ofthe properties of shapes.• Make sure that discussion is a key element of shape activities. Children needopportunities to describe shapes using appropriate mathematical language and toexplore their properties. Ask questions such as:– How do you know that this shape is a square but that one is an oblong?– Look at these two shapes. What is the same about them? What is different?– What can you say about the faces of a cylinder? What else?• Display the range of shape vocabulary that you want children to learn and use. Ifpossible, ask children to provide an illustration for each word. Refer to the display andstructure activities so that children use the vocabulary, for example:– ask a child to repeat his or her explanation but using a particular word from thedisplay;– ask children to work in pairs; each secretly chooses a shape from a set and usesthe vocabulary on the display to describe the shape to their partner.• Plan activities that involve solving problems and talking about shapes rather thansimply naming or colouring them. For example:– Place two identical right-angled triangles together.Ask: What different shapes is it possible to make?Explain how you recognise each shape.– Ask: How many different squares can you see in this pattern?• Children may find it hard to understand that one shape can be described using variousshape words, all of which would be correct. For example, a square is also aquadrilateral. Help children to establish questions that identify particular shapes, forexample to identify squares: Does the shape have four equal, straight sides? Does ithave four right angles?© Crown copyright 200800099-2008BKT-EN


The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 311Counting and understanding number strandYear 3 objectives Year 4 objectives Overcoming barriers sequences… count on from and back to zero in single-digitsteps or multiples of 10Recognise and continue number sequencesformed by counting on or back in steps of constantsizeRound two-digit or three-digit numbers to thenearest 10 or 100 and give estimates for their sumsand differencesRead, write and order whole numbers to at least1000 and position them on a number line…Partition three-digit numbers into multiples of 100,10 and 1 in different waysPartition, round and order four-digit wholenumbers; use positive and negative numbersin context and position them on a number line;state inequalities using the symbols < and > (e.g.–3 > –5, –1 < +1)■■■■■■Can I read, write and partition whole numbersto 1000?Can I order two-digit and three-digit numbersand position these on a number line?Can I round whole numbers to 1000 to thenearest 10 or 100?Use decimal notation for tenths and hundredthsand partition decimals; relate the notation to moneyand measurement; position one-place and twoplacedecimals on a number line■■Can I use and explain decimal notation fortenths and hundredths?Recognise the equivalence between decimal andfraction forms of one half, quarters, tenths andhundredthsRead and write proper fractions (e.g. 3 ⁄7, 9 ⁄10)interpreting the denominator as the parts of awhole and the numerator as the number of parts;identify and estimate fractions of shapes; usediagrams to compare fractions and establishequivalentsUse diagrams to identify equivalent fractions (e.g.6 ⁄8 and3 ⁄4, or70 ⁄100 and7 ⁄10); interpret mixed numbersand position them on a number line (e.g. 3 1 ⁄2)■■Can I read and write fractions and explain theirmeaning?Use the vocabulary of ratio and proportion todescribe the relationship between two quantities(e.g. 'There are 2 red beads to every 3 blue beads,or 2 beads in every 5 beads are red'); estimate aproportion (e.g. ‘About one quarter of the apples inthe box are green’)© Crown copyright 200800099-2008BKT-EN


12 The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3Knowing and using number facts strandYear 3 objectives Year 4 objectives Overcoming barriers sequencesDerive and recall all addition and subtraction factsfor each number to 20, sums and differences ofmultiples of 10 and number pairs that total 100Use knowledge of addition and subtraction factsand place value to derive sums and differences ofpairs of multiples of 10, 100 or 1000■■■■Can I recall and use addition and subtractionfacts to 20?Can I find pairs of numbers that total 100?Identify the doubles of two-digit numbers; usethese to calculate doubles of multiples of 10 and100 and derive the corresponding halvesDerive and recall multiplication facts for the 2, 3,4, 5, 6 and 10 times-tables and the correspondingdivision facts; recognise multiples of 2, 5 or 10 upto 1000Derive and recall multiplication facts up to 10 × 10,the corresponding division facts and multiples ofnumbers to 10 up to the tenth multiple■■■■Can I recall multiplication and division facts forthe 2, 3, 4, 5 and 10 times-tables?Can I use understanding of multiplication anddivision to solve problems?Use knowledge of number operations andcorresponding inverses, including doubling andhalving, to estimate and check calculationsUse knowledge of rounding, number operationsand inverses to estimate and check calculationsIdentify pairs of fractions that total 100099-2008BKT-EN© Crown copyright 2008


The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 313Calculating strandYear 3 objectives Year 4 objectives Overcoming barriers sequencesAdd or subtract mentally combinations of one-digitand two-digit numbersAdd or subtract mentally pairs of two-digit wholenumbers (e.g. 47 + 58, 91 – 35)■■Can I subtract mentally combinations of onedigitand two-digit numbers?■■Can I say a subtraction fact that is the inverse ofan addition fact, and vice versa?Develop and use written methods to record,support or explain addition and subtraction of twodigitand three-digit numbersRefine and use efficient written methods to addand subtract two-digit and three-digit wholenumbers and £.pMultiply one-digit and two-digit numbers by 10 or100, and describe the effectMultiply and divide numbers to 1000 by 10 andthen 100 (whole-number answers), understandingthe effect; relate to scaling up or down■■Can I multiply one-digit and two-digit numbersby 10 and 100?Use practical and informal written methods tomultiply and divide two-digit numbers (e.g. 13 × 3,50 ÷ 4); round remainders up or down, dependingon the contextDevelop and use written methods to record,support and explain multiplication and division oftwo-digit numbers by a one-digit number, includingdivision with remainders (e.g. 15 × 9, 98 ÷ 6)■■■■Can I multiply a two-digit number by a one-digitnumber?Can I divide a two-digit number by a one-digitnumber and explain any remainders?Understand that division is the inverse ofmultiplication and vice versa; use this to derive andrecord related multiplication and division numbersentencesFind unit fractions of numbers and quantities (e.g. Find fractions of numbers, quantities or shapes1 ⁄2,1 ⁄3,1 ⁄4 and1 ⁄6 of 12 litres) (e.g. 1 ⁄5 of 30 plums, 3 ⁄8 of a 6 by 4 rectangle)■■Can I find a unit fraction of a shape, number orquantity by splitting it into the correct number ofequal parts?Use a calculator to carry out one-step and twostepcalculations involving all four operations;recognise negative numbers in the display, correctmistaken entries and interpret the display correctlyin the context of money■■■■Can I identify the calculation needed to solve aword problem?Can I identify the stages involved in a two-stepproblem?■■Can I explain and record my methods andsolutions?© Crown copyright 200800099-2008BKT-EN


14 The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3Shape, space and measuresAttainment target 3: Shape, space and measuresLevel 2 Level 3 Commonly encountered difficultiesPupils use mathematical names for common 3-Dand 2-D shapes and describe their properties,including numbers of sides and corners.They distinguish between straight and turningmovements, understand angle as a measurementof turn, and recognise right angles in turns. Theybegin to use everyday non-standard and standardunits to measure length and mass.Pupils classify 3-D and 2-D shapes in various waysusing mathematical properties such as reflectivesymmetry for 2-D shapes. They use non-standardunits, standard metric units of length, capacity andmass, and standard units of time, in a range ofcontexts.■■■■■■Using mathematical vocabulary to name anddescribe 3-D and 2-D shapesClassifying 3-D and 2-D shapes according totheir propertiesExplaining relationships between standard unitsof length, mass and capacity■■Reading and interpreting numbered and partlynumbered scales■■Reading analogue clocks to the nearest5 minutes and using the vocabulary of time■■Converting analogue times to digital times, andvice versa■■Calculating time intervals00099-2008BKT-EN© Crown copyright 2008


The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 315Understanding shape strandYear 3 objectives Year 4 objectives Overcoming barriers sequencesRelate 2-D shapes and 3-D solids to drawings ofthem; describe, visualise, classify, draw and makethe shapesDraw polygons and classify them by identifyingtheir properties, including their line symmetryVisualise 3-D objects from 2-D drawings; makenets of common solids■■■■Can I make, name and describe 2-D and 3-Dshapes?Can I sort shapes choosing my own criteria?Draw and complete shapes with reflectivesymmetry; draw the reflection of a shape in a mirrorline along one sideRead and record the vocabulary of position,direction and movement, using the four compassdirections to describe movement about a gridRecognise horizontal and vertical lines; use theeight compass points to describe direction;describe and identify the position of a square on agrid of squaresUse a set-square to draw right angles and toidentify right angles in 2-D shapes; compare angleswith a right angle; recognise that a straight line isequivalent to two right anglesKnow that angles are measured in degrees andthat one whole turn is 360°; compare and orderangles less than 180°© Crown copyright 200800099-2008BKT-EN


16 The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3Measuring strandYear 3 objectives Year 4 objectives Overcoming barriers sequencesKnow the relationships between kilometresand metres, metres and centimetres, kilogramsand grams, litres and millilitres; choose and useappropriate units to estimate, measure and recordmeasurementsChoose and use standard metric units and theirabbreviations when estimating, measuring andrecording length, weight and capacity; know themeaning of ‘kilo’, ‘centi’ and ‘milli’ and, whereappropriate, use decimal notation to recordmeasurements (e.g. 1.3 m or 0.6 kg)■■Can I explain the relationships betweenkilometres and metres, metres and centimetres,kilograms and grams, litres and millilitres?Read, to the nearest division and half-division,scales that are numbered or partially numbered;use the information to measure and draw to asuitable degree of accuracyInterpret intervals and divisions on partiallynumbered scales and record readings accurately,where appropriate to the nearest tenth of a unit■■Can I explain what each division means on anumbered or partly numbered line and usethis information to read a scale to the nearestdivision or half-division?Draw rectangles and measure and calculate theirperimeters; find the area of rectilinear shapesdrawn on a square grid by counting squaresRead the time on a 12-hour digital clock and to thenearest 5 minutes on an analogue clock; calculatetime intervals and find start or end times for a giventime intervalRead time to the nearest minute; use am, pm and12-hour clock notation; choose units of time tomeasure time intervals; calculate time intervalsfrom clocks and timetables■■■■Can I read the time to the nearest 5 minuteson an analogue clock using the correctvocabulary?Can I show on a digital clock a time given tome on an analogue clock, and the other wayround?■■Can I work out how long it is between twotimes?00099-2008BKT-EN© Crown copyright 2008


The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 317© Crown copyright 200800099-2008BKT-EN


18 The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3Handling dataAttainment target 4: Handling dataLevel 2 Level 3 Commonly encountered difficultiesPupils sort objects and classify them using morethan one criterion. When they have gatheredinformation, pupils record results in simple lists,tables and block graphs, in order to communicatetheir findings.Pupils extract and interpret information presentedin simple tables and lists. They construct bar chartsand pictograms, where the symbol represents agroup of units, to communicate information theyhave gathered, and they interpret informationpresented to them in these forms.■■■■■■Creating and interpreting pictograms where thesymbols represent more than one objectCreating and interpreting the informationdisplayed in a bar chartUsing tables and lists to help solve a problem■■Answering a question by analysing andinterpreting data00099-2008BKT-EN© Crown copyright 2008


The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 319Handling data strandYear 3 objectives Year 4 objectives Overcoming barriers sequencesAnswer a question by collecting, organising andinterpreting data; use tally charts, frequency tables,pictograms and bar charts to represent results andillustrate observations; use ICT to create a simplebar chartAnswer a question by identifying what data tocollect; organise, present, analyse and interpret thedata in tables, diagrams, tally charts, pictogramsand bar charts, using ICT where appropriate■■■■■■Can I create and interpret a pictogram wherethe symbols represent more than one object?Can I create and interpret bar charts?Can I make and use lists and tables to organiseand interpret information to solve a problem?■■Can I use data to answer a question?Use Venn diagrams or Carroll diagrams to sort dataand objects using more than one criterionCompare the impact of representations wherescales have intervals of differing step size© Crown copyright 200800099-2008BKT-EN


20 The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3Links between objectives and UnitsUsing and applying mathematics strandYear 3 objectives Units Year 4 objectives UnitsSolve one-step and two-step problems involvingnumbers, money or measures, including time,choosing and carrying out appropriate calculations3D1, 3B2, 3E2, 3A3,3B3, 3D3, 3E3Solve one-step and two-step problems involvingnumbers, money or measures, including time;choose and carry out appropriate calculations, usingcalculator methods where appropriate4B1, 4D1, 4D2, 4A3,4B3, 4D3Represent the information in a puzzle or problemusing numbers, images or diagrams; use these to finda solution and present it in context, where appropriateusing £.p notation or units of measure3B1, 3B2, 3D2, 3B3 Represent a puzzle or problem using numbersentences, statements or diagrams; use these tosolve the problem; present and interpret the solutionin the context of the problem4E1, 4E2, 4E3Follow a line of enquiry by deciding what informationis important; make and use lists, tables and graphs toorganise and interpret the information3C1, 3E1, 3C2, 3C3,3E3Suggest a line of enquiry and the strategy neededto follow it; collect, organise and interpret selectedinformation to find answers4C1, 4C2, 4C3Identify patterns and relationships involving numbersor shapes, and use these to solve problems3B1, 3E1, 3B2, 3B3,3E3Identify and use patterns, relationships and propertiesof numbers or shapes; investigate a statementinvolving numbers and test it with examples4B1, 4B2, 4B3Describe and explain methods, choices and solutionsto puzzles and problems, orally and in writing, usingpictures and diagrams3A1, 3A2, 3C3 Report solutions to puzzles and problems, givingexplanations and reasoning orally and in writing, usingdiagrams and symbols4A1, 4B1, 4C1, 4A2,4B2, 4C2, 4B3, 4C300099-2008BKT-EN© Crown copyright 2008


The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 321Bold text signifies end-of-year (EOY) objectivesCounting and understanding number strandYear 3 objectives Units Year 4 objectives Units… count on from and back to zero in single-digitsteps or multiples of 103A1 Recognise and continue number sequences formedby counting on or back in steps of constant size4A1, 4A2, 4A3Round two-digit or three-digit numbers to the nearest10 or 100 and give estimates for their sums anddifferencesRead, write and order whole numbers to at least 1000and position them on a number line…3A2, 3A3 Partition, round and order four-digit whole numbers;use positive and negative numbers in context andposition them on a number line; state inequalitiesusing the symbols < and > (e.g. –3 > –5, –1 < +1)3A14A1, 4A3Partition three-digit numbers into multiples of100, 10 and 1 in different ways3A1, 3A2, 3E3 Use decimal notation for tenths and hundredths andpartition decimals; relate the notation to money andmeasurement; position one-place and two-placedecimals on a number line4A2, 4D2, 4A3, 4D3Recognise the equivalence between decimal andfraction forms of one half, quarters, tenths andhundredths4E1, 4E2, 4E3Read and write proper fractions (e.g. 3 ⁄7, 9 ⁄10)interpreting the denominator as the parts of a wholeand the numerator as the number of parts; identifyand estimate fractions of shapes; use diagrams tocompare fractions and establish equivalents3B2, 3E2, 3B3, 3E3 Use diagrams to identify equivalent fractions(e.g. 6 ⁄8 and 3 ⁄4, or 70 ⁄100 and 7 ⁄10); interpret mixednumbers and position them on a number line(e.g. 3 1 ⁄2)4E1, 4E2, 4E3Use the vocabulary of ratio and proportion to describethe relationship between two quantities (e.g. 'Thereare 2 red beads to every 3 blue beads, or 2 beads inevery 5 beads are red'); estimate a proportion (e.g.‘About one quarter of the apples in the box are green’)4E3© Crown copyright 200800099-2008BKT-EN


22 The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3Knowing and using number facts strandYear 3 objectives Units Year 4 objectives UnitsDerive and recall all addition and subtractionfacts for each number to 20, sums anddifferences of multiples of 10 and number pairsthat total 1003A1, 3B1, 3E1, 3A2,3B2, 3B3Use knowledge of addition and subtraction facts andplace value to derive sums and differences of pairs ofmultiples of 10, 100 or 10004A1, 4B1, 4B3Identify the doubles of two-digit numbers; use theseto calculate doubles of multiples of 10 and 100 andderive the corresponding halves4A1, 4B2, 4B3Derive and recall multiplication facts for the 2, 3, 4, 5,6 and 10 times-tables and the corresponding divisionfacts; recognise multiples of 2, 5 or 10 up to 10003B1, 3E1, 3A2, 3B2,3E2, 3A3, 3B3, 3E3Derive and recall multiplication facts up to10 × 10, the corresponding division facts andmultiples of numbers to 10 up to the tenthmultiple4A1, 4B1, 4E1, 4A2,4B2, 4D2, 4E2, 4A3,4B3, 4E3Use knowledge of number operations andcorresponding inverses, including doubling andhalving, to estimate and check calculations3B1, 3B3, 3D3 Use knowledge of rounding, number operations andinverses to estimate and check calculations4A1, 4B1, 4A2, 4B2,4A3, 4B3Identify pairs of fractions that total 1 4E1, 4E200099-2008BKT-EN© Crown copyright 2008


The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 323Calculating strandYear 3 objectives Units Year 4 objectives UnitsAdd or subtract mentally combinations of onedigitand two-digit numbers3A1, 3D1, 3A2, 3D2,3A3Add or subtract mentally pairs of two-digitwhole numbers (e.g. 47 + 58, 91 – 35)4A1, 4D1, 4A2, 4A3Develop and use written methods to record, supportor explain addition and subtraction of two-digit andthree-digit numbers3D2, 3A3, 3D3, 3E3 Refine and use efficient written methods to add andsubtract two-digit and three-digit whole numbers and£.p4A2, 4D2, 4A3, 4D3Multiply one-digit and two-digit numbers by 10 or100, and describe the effect3A2, 3E2 Multiply and divide numbers to 1000 by 10 and then100 (whole number answers), understanding theeffect; relate to scaling up or down4A1, 4A2Use practical and informal written methods to multiplyand divide two-digit numbers (e.g. 13 × 3, 50 ÷ 4);round remainders up or down, depending on thecontext3E1, 3D2, 3E2, 3A3,3D3, 3E3Develop and use written methods to record,support and explain multiplication and divisionof two-digit numbers by a one-digit number,including division with remainders(e.g. 15 × 9, 98 ÷ 6)4A2, 4D2, 4A3, 4E3Understand that division is the inverse of multiplicationand vice versa; use this to derive and record relatedmultiplication and division number sentences3E2, 3D3Find unit fractions of numbers and quantities (e.g. 1 ⁄2, 3D1, 3E1, 3D2, 3E2,1 ⁄3,1 ⁄4 and1 ⁄6 of 12 litres) 3E3Find fractions of numbers, quantities or shapes (e.g.1 ⁄5 of 30 plums,3 ⁄8 of a 6 by 4 rectangle)4E1, 4E2, 4E3Use a calculator to carry out one-step and two-stepcalculations involving all four operations; recognisenegative numbers in the display, correct mistakenentries and interpret the display correctly in thecontext of money4A1, 4A3© Crown copyright 200800099-2008BKT-EN


24 The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3Understanding shape strandYear 3 objectives Units Year 4 objectives UnitsRelate 2-D shapes and 3-D solids to drawings ofthem; describe, visualise, classify, draw and make theshapes3B1, 3B2, 3B3 Draw polygons and classify them by identifying theirproperties, including their line symmetryVisualise 3-D objects from 2-D drawings; make netsof common solids4B1, 4B2, 4B3Draw and complete shapes with reflectivesymmetry and draw the reflection of a shape ina mirror line along one side3B2, 3D2Read and record the vocabulary of position, directionand movement, using the four compass directions todescribe movement about a grid3D1, 3D2 Recognise horizontal and vertical lines; use the eightcompass points to describe direction; describe andidentify the position of a square on a grid of squares4D1, 4D2Use a set-square to draw right angles and to identifyright angles in 2-D shapes; compare angles with aright angle; recognise that a straight line is equivalentto two right angles3D2, 3B3, 3D3 Know that angles are measured in degrees andthat one whole turn is 360°; compare and orderangles less than 180°4D2, 4D300099-2008BKT-EN© Crown copyright 2008


The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 325Measuring strandYear 3 objectives Units Year 4 objectives UnitsKnow the relationships between kilometresand metres, metres and centimetres, kilogramsand grams, litres and millilitres; choose and useappropriate units to estimate, measure, and recordmeasurements3C1, 3D1, 3C2, 3D2,3C3Choose and use standard metric units and theirabbreviations when estimating, measuring andrecording length, weight and capacity; know themeaning of ‘kilo’, ‘centi’ and ‘milli’ and, whereappropriate, use decimal notation to recordmeasurements (e.g. 1.3 m or 0.6 kg)4C1, 4D1, 4C2, 4D2,4C3, 4D3Read, to the nearest division and half-division,scales that are numbered or partially numbered;use the information to measure and draw to asuitable degree of accuracy3C1, 3D1, 3C2, 3C3,3D3Interpret intervals and divisions on partially numberedscales and record readings accurately, whereappropriate to the nearest tenth of a unit4C1, 4D1, 4C2, 4D2,4C3, 4D3Draw rectangles and measure and calculate theirperimeters; find the area of rectilinear shapes drawnon a square grid by counting squares4D2, 4D3Read the time on a 12-hour digital clock and to thenearest 5 minutes on an analogue clock; calculatetime intervals and find start or end times for a giventime interval3D1, 3C2, 3D3 Read time to the nearest minute; use am, pm and12-hour clock notation; choose units of time tomeasure time intervals; calculate time intervals fromclocks and timetables4D1, 4D3© Crown copyright 200800099-2008BKT-EN


26 The National Strategies | PrimaryOvercoming barriers in mathematics –helping children move from level 2 to level 3Handling data strandYear 3 objectives Units Year 4 objectives UnitsAnswer a question by collecting, organising andinterpreting data; use tally charts, frequency tables,pictograms and bar charts to represent results andillustrate observations; use ICT to create a simple barchart3C1, 3C2, 3C3 Answer a question by identifying what data tocollect; organise, present, analyse and interpretthe data in tables, diagrams, tally charts,pictograms and bar charts, using ICT whereappropriate4C1, 4C2, 4C3Use Venn diagrams or Carroll diagrams to sortdata and objects using more than one criterion3C1, 3C2Compare the impact of representations where scaleshave intervals of differing step size4C2, 4C300099-2008BKT-EN© Crown copyright 2008


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