Hampden Gurney School Mathematics Skills And Progression Map

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Hampden Gurney SchoolMathematics Skills and ProgressionMap1

Number: Number and Place ValueKey SkillsEYFSYear 1Year 2CountingCount reliably with numbers to 20and place them in order.Count an irregular amount of objects.Identify and represent numbers usingobjects and pictorial representationsincluding the number line, and usethe language of: equal to, more than,less than (fewer), most, least.Subitise up to 10 (recognisenumber patterns withoutcounting)Count to and across 100, forwards and backwards, beginning with 0 or 1, or from anygiven nt, read and write numbers to 100 in sharkNumbersDemo online/index.htmlCount in multiples of twos, fives and tens.www.ictgames.com/saucerSorter.htmlRepresent and use number bonds and related subtraction facts within 20.www.topmarks.co.uk/Flash.aspx?b maths/additionAdd and subtract one-digit and two-digit numbers to 20, including zero.Composition of numbers up to 10Lead and write numbers from 1 to 20in numerals and word.Count, recognise and order numbersto ering-andsequencingIdentify and represent numbers using objects and pictorial representations including thenumber line, and use the language of: equal to, more than, less than (fewer), most, least.Partition numbers into two or more parts.Add two or more of these parts in any order (commutativity).Add and subtract numbers using concrete objects, pictorial representations, andmentally, including: two two-digit numbers.Add or subtract by counting on or back in ones BUT knowing the order of sums can helpadd or subtract by calculation.Can say which number is one more orone less than a given number.Identify and represent numbers using objects and pictorial representations including thenumber line, and use the language of: equal to, more than, less than (fewer), most, least2Count from 0 in multiples of 4, 8, 50 and 100; finding10 or 100 more or less than a given number.Recognise the place value of each digit in a three-digitnumber (hundreds, tens, ones).Compare and order numbers up to 100.Identify, represent and estimate numbers usingdifferent representations.Read and write numbers to at least 100 in numeralsand in ictgames.com/arrowCards revised v6.htmlKnow the place value of a 2- digit number (tens ks.co.uk/place-value/place-value-chartsCount in steps of 2, 3, and 5 from 0 from anynumber, forward and backward.www.ictgames.com/fairyfog random.htmlRecall and use addition and subtraction facts to 20fluently, and derive and use related facts up to dd and subtract numbers using concrete objects,pictorial representations, and mentally, including: atwo-digit number and ones.Count in steps of 2, 3, and 5 from 0, and in tens fromany number, forward or backward.

Comparing NumbersIdentify and represent numbers usingobjects and pictorial representationsincluding the number line, and usethe language of: equal to, more than,less than (fewer), most, least. and – means ‘equivalent’, ‘the same as’ or ‘balances’.Understanding this before other symbols are introduced helps children make sense ofequations written with in different positions.We can compare numbers using or Select the correct numeral torepresent numbers to 20.Estimate how many objects they cansee and checks by counting.Identify and represent numbers using objects and pictorial representations including thenumber line.Read and write numbers from 1 to 20in numerals and words.Read and write numbers from 1 to 100 in numerals and words.Relating numbers to 5 and 10 canadd by calculating, using bonds.Form digit 0-9 correctly.Say one more and one less thannumbers to twenty.Add and subtract 2 single digitnumbers.Use a whole-part model (Dienes) to picture addition and subtraction.Relating numbers to 5 and 20 can help us to add by calculating, using bonds.Understand number system is base 10. The tens numbers must be seen as ten and one,ten and two and so on. The position (place) of a digit in a number determines its value.Partition numbers into two or more parts.Add two or more of these parts in any order (commutativity).Add or subtract by counting on or back in ones BUT knowing the order of sums can helpadd or subtract by calculation.Begin to identify own mathematicalproblems based on own interests andfascinations.Use drawings, diagrams, or symbols to represent numbers.Write numbers up to 100 using numerals and words, learning by playing matching games.Compare and order numbers, that one number is bigger or smaller than another:Use more than ( ) and less than ( ) symbols when comparing numbers e.g. can write 32 76 or 76 32.Estimate how many there are before counting.Partition numbers in different waysReinforce understanding of number, finding everyday opportunities to use knownnumber facts to solve problems.Compare and order numbers from 0 up to 100; useand signs.Compare and order numbers from 0 up to 100; use , and signsIdentify, represent and estimate numbers usingdifferent representations, including the number line.Compare and order numbers from 0 up to 100 useand signsIdentifying, representing and estimating numbersIdentify, represent and estimate numbers usingdifferent representations, including the number line.Reading and writing numbers (including Roman Numerals)Read and write numbers to at least 100 in numeralsand in words.Understanding Place ValueRecognise the place value of each digit in a two-digitnumber (tens, ones)Count in steps of 2, 3, and 5 from 0, and count in tensfrom any number, forward or backward.Recognise the place value of each digit 2-digit,10, 1s.Recognise the place value of each digit in a 2- digitnumber (tens, ones). Identify, represent and estimatenumbers using.Use a whole-part model (Dienes) to picture additionand subtraction. Relating numbers to 5 and 100 canhelp us to add by calculating, using bonds.Problem Solving3Use place value and number facts to solve problems.Use more than ( ) and less than ( ) symbols whencomparing numbers e.g. can write 32 76 or 76 32.Estimate how many there are before counting.Partition numbers in different waysReinforce understanding of number, finding everydayopportunities to use known number facts to solveproblems.

Greater depth-GLDEstimate a number of objects and check quantities by counting up to20.Solve practical problems that involve combining groups of 2, 5 or 10.Key vocabularyZero, number, one, two, three .to twenty and beyond, count, counton, count back, is the same as, more, less, pattern, digit, the samenumber as, more, larger, bigger, greater, fewer, smaller, less, fewest,smallest, least, most, biggest, largest, greatest, one more, one less,compare, order, size, first, second, third twentieth, last, before, after,next, between. Guess, estimate, nearly, close, about the same as, justover, just under, too many, too few, enough, not enough.Greater depthCount reliably well beyond 100.Count on and back in 3’s from any given numberto beyond 100.Say the number that is ten more or ten less than anumber to 100. Know the signs and .Key vocabularyNumeral, twenty one, twenty two one hundred,forwards, backwards, equal to, equivalent to,most, least, many, multiple of, half way between,above, below, roughly, equal to, more than, lessthan (fewer), most, least4Greater depthReason with numbers showing an understanding of placevalue.Read and write numbers to at least 100 in numerals and inwords. Use place value and number facts to solve problemsKey vocabularyTwo hundred .one thousand, threes, fours, tally, sequence,continue, predict, rule, greater than,

Number: Number and Place ValueKEY SKILLSYear 3Year 4Year 5Year 6Mental CalculationAdd and subtract numbers mentally, including:* a three-digit number and ones* a three-digit number and tens* a three-digit number and hundredsMultiply by 50 by multiplying by 100 andhalving e.g. 8 x 50 8 x 100 divided by 2.Children must rapidly recall the related divisionfacts as well. For example, for 4 x 6 24, childrenshould know 24 6 4 and 24 4 6.Read and write numbers up to 1000 in numeralsand in words.Solve number problems and practical problemsinvolving these ideas.Addition and subtraction of multiples of 10 wherethe answer is between 0 and 100 (e.g. 70 30 100,20 40 60);Know the value of digit and explore place valuethrough partitioning.Solve addition and subtraction two-step problemsin contexts.Count in multiples of 6, 7, 9, 25 and 1000. Countbackwards through zero to include negativenumbers and solve number and practical problemsthat involve all of the above and with increasinglylarge positive numbersAddition and subtraction of multiples of 10 (e.g. 70 30 100, 50 60 110, 20 40 60);Addition and subtraction of multiples of 100where the answer is 1,000 or less (e.g.300 400 700, 400 600 1,000);Double and halves of multiples of 10 100 (e.g.double 60 120, half 50 25);Multiplying two-digit numbers by 10 (e.g.24x10 240);halves of any even number to 100 (e.g. half of22 11);Multiplying any two and three-digit number by 10and 100 (e.g. 24x100 2400.Interpret negative numbers in context,count forwards and backwards withpositive and negative whole numberthrough zero.Understand place value and its overallvalue, as well as its position relative toother numbers, including tenths andhundredths.Add and subtract numbers mentallywith increasingly large numbers.Interpret negative numbers in context,count forwards and backwards withpositive and negative whole numbers.Addition and subtraction of multiples of10 (e.g.70 30 100, 50 60 110,20 40 60; Addition and subtraction ofmultiples of 100 (e.g.300 400 700,400 600 1,000, 800 500 1,300);Addition and subtraction of multiples of1000 (e.g. 3000 4000 7000).Multiply a 2-digit number by a single digit bypartitioning– e.g. 26 x 3 20 x 3 6 x 3.Multiply a decimal number with up to 2 decimalplaces by a single digit by partitioning– e.g. 3.42 x 4 3 x 4 0.4 x 4 0.02 x 4.Find the doubles and halves of any two-digitnumber and any multiple of 10 or 100– e.g. half680 or double 73.Round any number up to 1,000,000 tothe nearest 10, 100, 1000, 10,000 and100,000.Solve number problems and practicalproblems that involve all of the above.Add and subtract whole numbers withmore than 4 digits, including usingefficient written methods (columnaraddition and subtraction).5Use negative numbers in context,and calculate intervals across zeroUnderstand negative numbers aspositions on a number line.Use conventional notation for thepriority of operations, includingbrackets, powers, roots andreciprocals (reciprocals will bedescribed in the form 1 𝑥𝑥 and not𝑥𝑥-1.Counting on or back in tens fromany number– e.g. working out 27 60 ? by counting on in tens from27.Counting on or back in fives fromany multiple of 5– e.g. 35 15 ? bycounting on in steps of 5 from 35.Counting on or back in hundredsfrom any number e.g. 570 300 ?by counting on in hundreds from570.Counting on or back in tenthsand/or hundredths- e.g. 3.2 0.6 ? by counting on in tenths. 1.7 0.55 ? by counting on in tenths andhundredths.Use their knowledge of the order ofoperations to carry out calculationsinvolving the four operations.Calculations with whole numberswhich do not involve crossing placevalue boundaries- e.g. 23 45 ? by40 5 20 3 or 40 23 5.Calculations with whole numberswhich involves crossing place value

Double and halves of multiples of 10 to 100 (e.g.double 60 120);Multiplying two-digit number by 10 (e.g.24x10 240).Multiply and divide by 4 by doubling/halving twiceand 8 by doubling/halving again. – e.g. 34 x 4 34x 2 x 2.Find the doubles and halves of any number up to10,000 by partitioning – e.g. half of 32,202 byhalving 3,000, 2000, 200 and 2.Mentally find fractions of numbers in the 2,3,4,5and 10 times table using known multiplication anddivision facts– e.g. 3/5 of 45 by 45 5 x 3.Recall percentage equivalents to ½, 1/3, ⅕, ⅙, 1/10and 1/100 – e.g. ¼ 25%.Find 10% or multiples of 10% of whole numbersand quantities- e.g. 30% of 50 by 50 10 x 3.Mentally find 50% by halving and 25% by dividingby 4 or 2 of numbers and quantities- e.g. 25% of150 by 150 4.Year 4 mental maths with only 38 newmultiplications (and related division) facts left thatchildren need to develop the ability to rapidlyrecall.6Double and halves of multiples of 10 to100 (e.g. double 60 120, half 50 25);quadruples (x4) of all numbers to 10(e.g. 6x4 24);Multiplying two-digit number by 10(e.g. 24x10 240);Halves of any number to 100 (e.g. halfof 22 11, half of 51 25.5);Multiplying and dividing any number of10 and 100 (e.g. 24x100 24000, 45divided 100 0.45, 3.4x10 34);Squares of all number up to 12; andcubes of 2,3,4 and 5.Near doubles to numbers under20 e.g. 18 16 is double 18 andsubtract 2 or double 16 and add 2.Near doubles to multiples of 10 e.g. 60 70 is double 60 and add 10 or double70 and subtract 10 or 75 76 is double76 and subtract 1 or double 75 and add1.Decimal near doubles to wholenumbers e.g. 2.5 2.6 is double 2.5 add0.1 or double 2.6 subtract 0.1.Divide a multiple of 25 by 25 dividing by100 then multiplying by 4 (by doublingand doubling again) e.g. 350 25 350 100 x 2 x2.Divide a multiple of 50 by 50 by dividingby 100 then doubling- e.g. 450 50 450 10 x 2.boundaries e.g. 49 – 32 ? by 49 – 9– 23 or 57 34 ? by 57 3 31.Calculations with decimal numberswhich do not involve crossing placevalue boundaries 5.6 3.7 ? by 5.6 3 0.7 or 540 380 ? by 540 300 80 or 540 360 20.Calculations with decimal numberswhich involve crossing place valueboundaries e.g. 1.4 1.7 ? by 1.4 0.6 1.1 and 0.8 0.35 ? by 0.8 0.2 0.15.Compensating and adjusting to 10–e.g. 34 9 ? by 34 10 – 1 or 34 –11 ? by 34 – 100 – 1 ?.Compensating and adjustingmultiples of 10 e.g. 38 68 ? by 38 70 – 2 or 45 – 29 45 – 30 1.Compensating and adjustingmultiples of 10 or 100 e.g. 138 69 ? by 138 70 – 1 or 299 – 48 300– 48 – 1.Compensating and adjustingmultiples with decimals e.g2 ½ 1 ¾ by 2½ 2 – ¼ or 5.7 3.9by 5.7 4.0 – 0.1.

Written MethodsAdd and subtract numbers with up to three digits,using formal written methods of columnaraddition and subtraction.Solve problems involving all four operationsincluding missing number problems, using numberfacts and place value.Focus on calculations rather than counting on inones.Relate numbers to their parts (partitioning) and tomultiples of 10 to bridge multiples of ten.Understand the concept of ‘difference’ betweennumbers.Add and subtract numbers with up to 4 digits usingthe formal written methods of columnar additionand subtraction where appropriate.Solve addition and subtraction two-step problemsin contexts.Estimate the answer to a calculation and useinverse operations to check answers.Use inverse operations to estimate and checkanswers.Recall and use multiplication and division facts forthe 3, 4 and 8 multiplication tables.Estimate and use inverse operations to checkanswers to a calculationSolve problems, including missing numberproblems, using number facts, place value, andmore complex addition and subtractionSolve addition and subtraction twostep problemsin contexts, deciding which operations andmethods to use and whyAccurately use formal written methods:column addition, column subtraction,formal written multiplication, shortdivision, chunking, long division andapply this knowledge to solve problems.Add and subtract whole numbers withmore than 4 digits, including usingformal written methods (columnaraddition and subtraction).Solve addition and subtraction multistep problems in contexts, decidingwhich operations and methods to useand why. Use rounding to checkanswers to calculations and determine,in the context of a problem, levels ofaccuracy.Solve problems involving numbers up tothree decimal places.Number of digits in a number does notnecessarily make it larger or smaller e.g.0.35 0.5.Read, write, order and comparenumbers at least to 1,000,000 anddetermine the value of each digit.Order, add and subtract positiveand negative integers, decimals andfractions; use the number line as amodel for ordering of the realnumbers; use the symbols , , , .Use the 4 operations, includingformal written methods, applied tointegers, decimals, proper andimproper fractions, and mixednumbers, all both positive andnegative.Round numbers and measures to anappropriate degree of accuracy [forexample, to a number of decimalplaces or significant figures].Inverse operations, estimating and checking answersUse rounding to check answers tocalculations and determine, in thecontext of a problem, levels of accuracyUse estimation to check answers tocalculations and determine, in thecontext of a problem, levels ofaccuracy. Recognise and userelationships between operationsincluding inverse operations.Solve addition and subtractionmultistep problems in contexts,deciding which operations and methodsto use and whySolve addition and subtractionmultistep problems in contexts,deciding which operations andmethods to use and whySolve problems involving addition,subtraction, multiplication anddivision.Problem Solving7

Greater DepthAdd and subtract numbers with any number ofdigits using formal written methods.Solve integer scaling problems andcorrespondence problems in which n objects areconnected to m objectsKey vocabularyTens boundary, hundreds boundary, complex,operations.Greater DepthGreater DepthUse tenths, hundreds and thousandths whensolving addition and subtraction problems. Solvemulti-step problems involving more than one ofthe operations.Key vocabularyCalculate number problemsalgebraically for example 2x-3 5.Key vocabularytenths, hundredths, thousandths, partitioning,inverse operation, integer8Units boundary, tenths boundary,algebraic, significant figuresGreater DepthUse integer powers and associatedreal roots (square, cube and higher),recognise powers of 2, 3, 4, 5 anddistinguish between exactrepresentations of roots and theirdecimal approximations (Squareand cube roots and powers up to 5may be tested.Key vocabularyinteger powers, decimalapproximations

Number: Multiplication and DivisionKey SkillsYear 1Multiplication and division factsEYFSSolve one-step problems involving multiplicationand divisionAble to count in steps of 2, 5, and 10.Start linking this to the idea of multiplication as‘repeated addition’ e.g. they will know that 3 2 isthe same as 2 2 2.They will begin to understand the relationshipbetween multiplication and division, and willcalculate with concrete objects, pictorialrepresentations and arrays with support.Year 2Count in multiples of twos, fives and tens (copied fromNumber and Place Value).Expect to solve simple division problems throughsharing and grouping. For example:10 2 can be thought of as sharing 10 objects into 2equal groups. This gives us 5 in each group.10 2 can be thought of as finding how many groups of2 there are in 10. This gives us 5 groups of 2.Division can be explored as the inverse through‘grouping’, as well as ‘sharing’.Inverse relationship can also be explored through arraysCount in steps of 2, 3, and 5 from 0, and in tens from any number,forward or backward (copied from Number and Place Value).Recall and use multiplication and division facts for the 2, 5 and 10multiplication tables, including recognising odd and even numbersMental CalculationCount in multiples of twos, fives and tens –understanding that this is repeated addition.Doubling as ‘two groups of’ and counting in other‘groups of’ numbers.9Show that multiplication of two numbers can be done in any order(commutative) and division of one number by another cannot.Show that multiplication of two numbers can be done in any order(commutative) and division of one number by another cannot.By the end of Year 2, and by the time children reach KS2, they shouldhave developed rapid recall in mental maths for their basic additionand subtraction facts, including number bonds to 20, and doubles to20.

Written CalculationUnderstand adding objects that are grouped in 2s,5s, and 10s.Provide lots of opportunities to do this using thingsaround your home.Use pairs of shoes or socks to practise counting intwos, gloves to count in fives, and ice cube trays topractise counting in tens.Draw pictures of the items counted and use these topractise counting in steps of 2, 5, or 10 at any time.Solve problems using concrete objects or pictorials.Division can be seen as ‘how many groups of in ’.Use objects and drawings to help them understandmultiplication and division. They will make anduse arrays to solve problems.Arrays are sets of objects arranged in rows and columnsto make a rectangle e.g. egg boxes, muffin trays, icecube trays, and chocolate bars with rows of pieces areall arrays.Solve problems , including doubling, halving andsharing.Solve one-step problems involving multiplication anddivision, by calculating the answer using concreteobjects, pictorial representations and arrays.Calculate mathematical statements for multiplication and divisionwithin the multiplication tables and write them using the multiplication( ), division ( ) and equals ( ) signsProblem SolvingGreater depth-GLDSolve practical problems that involve combininggroups of 2, 5 or 10, or sharing into equal groups.Key vocabularySharing, doubling, halving, number patterns.Greater depthSolve problems involving multiplication and division, using materials,arrays, repeated addition, mental methods, and multiplication anddivision facts, including problems in contextsGreater depthApply knowledge of number to solve a one-stepproblem involving simple multiplication and division.Solve one-step problems that involve addition andsubtraction, using concrete objects and pictorialrepresentations, and missing number problems.Key vocabularyRecall and use multiplication and division facts for 2, 5 and 10, andmake deductions outside known multiplication facts.Solve unfamiliar word problems that involve more than one step.Key vocabularyMultiplication, multiply, multiplied by, multiple,division, dividing, grouping, array10Groups of, times, once, twice, three times ten times, repeatedaddition, divide, divided by, divided into, share, share equally, left over,one each, two each group in pairs, threes equal groups of, row,column, multiplication table, fact

Number: Multiplication and DivisionYear 3KEY SKILLSYear 5Year 4Year 6Multiplication and division factsCount from 0 in multiples of 4,8, 50 and 100.Recall and use multiplicationand division facts for the 3, 4and 8 multiplication tables.Solve number and practicalproblems that involve all of theabove and with increasinglylarger positive numbersCount in multiples of 6, 7, 9, 25 and1 000Recall multiplication facts formultiplication and division tables upto 12 12.Solve multiplication and division.Recognise and use factors.Multiply and divide two-digit andthree-digit numbers using formalwritten layout and solve problemsinvolving multiplying and adding andharder multiplication problem.Consolidate number and place valueRound any number to the nearest 10,100 or 1000.Solve number and practical problemsthat involve all of the above and withincreasingly large positive numbers.Read Roman numerals to 100 (I to C)and understand how, over time, thenumeral system changed to includethe concept of zero and place value.Count forwards or backwards in steps of powers of 10 for anygiven number up to 1 000 000 (copied from Number and PlaceValue)Interpret negative numbers in context, count forwards andbackwards with positive and negative whole numbers throughzero.Round any number up to 1,000,000 to the nearest 10, 100,1000, 10,000 and 100,000.Solve number problems and practical problems that involve allof the above.Read numerals to 1000 (M) and recognise years written inRoman numerals.Use rounding to check answers to calculations for accuracy.Solve problems involving numbers up to three decimal places.Recognise and use square numbers and cube numbers, and thenotation for squared and cubed.Calculate and compare the area of squares and rectanglesincluding using standard units, square.Multiply and divide numbers mentally using known facts.Multiply and divide whole numbers and those involving decimalsby 10, 100 and 1000.Solve problems involving multiplication and division, includingscaling by simple fractions and problems involving simple rates.Use Venn and Carroll diagrams e.g. sortingnumbers into multiples of 8 and multiples of6.Create and interpret line graphs where theintermediate values.Understand and use the mean of discretedata.Use the concepts of fractions, multiples,primes and special number patterns.Use the concepts and vocabulary of primenumbers, factors (or divisors), multiples,common factors, common multiples,highest common factor, lowest commonmultiple, prime factorisation, includingusing product notation and the uniquefactorisation property.Count forwards or backwards in steps ofpowers of 10 for any given number up to1,000,000Mental CalculationUse place value, known andderived facts to multiply anddivide mentally, including:multiplying by 0 and 1; dividingby 1; multiplying together threenumbersUse place value, known and derivedfacts to multiply and divide mentally,including: multiplying by 0 and 1;dividing by 1-2 digits; multiplyingtogether three numbers using longand short calculationMental methods to solve problems where appropriate,modelling mental partitioning.Rounding can help to get a sense of the size of the answer or tofind an equivalent calculation, then adjust.Numbers should be looked at before a method is chosen todecide which will be most efficient.Recognise and use factor pairsof number for mentalcalculationsRecognise and use factor pairs andcommutativity in mental calculations(in Properties of Nos)Multiply and divide whole numbers and those involving decimalsby 10, 100 and 100011Perform mental calculations, including withmixed operations and large numbers.Consolidate and extend mental methods ofcalculation to include decimals, fractionsand percentages, accompanied whereappropriate by suitable jottings; solvesimple word problems mentally.Associate a fraction with division andcalculate decimal fraction equivalents (e.g.0.375) for a simple fraction (e.g. 3 /8)

Written CalculationWrite and calculatemathematical statements formultiplication and divisionusing the multiplication tablesthat they know, including fortwo-digit numbers times onedigit numbersMultiply two-digit and three-digitnumbers by a one-digit number usingformal written layout.Ideas to be explored are partitioning,scaling and recombining formalmultiplication.Multiply numbers up to 4 digits by aone- or two-digit number using aformal written method, includinglong multiplication for two-digitnumber.Numbers should be looked at before a method is chosen todecide which will be most efficient.Accurately use formal written methods: column addition,column subtraction, formal written multiplication, short division,chunking, long division and apply this knowledge to solveproblemsMultiply multi-digit numbers up to 4 digitsby a two-digit whole number using theformal written method of longmultiplicationUse written division methods in cases wherethe answer has up to two decimal places(copied from Fractions (including decimals))Use a range of written and mental methodsusing the four operations applied tointegers, both positive and negative.Decide best method to be mostefficient to solve problems.Solve missing number problemsDivide numbers up to 4 digits by aone-digit number using the formalwritten method of short division andinterpret remainders appropriatelyfor the contextSolve problems involving addition, subtraction, multiplicationand division and a combination of these, includingunderstanding the meaning of the equals sign.Divide numbers up to 4-digits by a two-digitwhole number using the formal writtenmethod of short division where appropriatefor the context divide numbers up to 4digits by a two-digit whole number.Using the formal written method of longdivision, and interpret remainders as wholenumber remainders, fractions, or byrounding, as appropriate for the context.Recognise and use factor pairsand commutativity in mentalcalculations (repeated).Recognise and use factor pairs andcommutativity in mental calculationswith increasing difficulty (repeated).Identify multiples and factors,including finding all factor pairs of anumber, and common factors of twonumbersKnow and use the vocabulary of prime numbers, prime factorsand composite (non-prime) numbersEstablish whether a number up to 100 is prime and recall primenumbers up to 19Understand what are factors,multiples, composite and primenumbers.Solve simple problems using 12 digit numbers.Understand the links betweenfactors, multiples, composite andprime numbers.Solve and calculate factors and primenumbers using the four operations.Understand the links between factors, multiples, composite andprime numbers, rather than seeing these as separate facts to belearnt.Solve word problems using factors, multiples and primenumbers.Properties of numbers: Multiples, factors, primes, square and cube numbers12Identify common factors, commonmultiples and prime numbersUse common factors to simplify fractions;use common multiples to express fractionsin the same denomination (copied fromFractions).Recognise the symbol for square root andwork out square roots for numbers up to100.Calculate, estimate and compare volume ofcubes and cuboids using standard units,including centimetre cubed (cm 3 ) andcubic metres (m 3 ), and extending to otherunits such as mm 3 and km 3.

Order of operationsSolve two-step problems, deciding Rec BIDMAS rule, using only parentheses.which operations and methods to ·Carryout combined operations using BIDMAS rules.use and why.Use standard

Know the value of digit and explore place value through partitioning. Solve addition and subtraction two-step problems in contexts. Count in multiples of 6, 7, 9, 25 and 1000. Count backwards through zero to include negative numbers and solve number and practical problems that involve all of the above and with increasingly large positive numbers

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