# Maths

We are determined to equip the pupils of St Thomas’ with a uniquely powerful set of tools to understand and change the world. These tools include logical reasoning, problem solving skills and the ability to think in abstract ways. We recognise that mathematics is integral to all aspects of life and with this in mind; we endeavour to ensure that our children develop a positive and enthusiastic attitude towards mathematics that will stay with them.

We use the National Curriculum for Mathematics as the basis of our mathematics programme. We are committed to ensuring that all pupils achieve mastery in the key concepts of mathematics, appropriate for their age group, in order that they make genuine progress and avoid gaps in their understanding that provide barriers to learning as they move through their education.

Research around metacognition underpins our mathematical teaching in school. Teachers use precise questioning in class to test conceptual and procedural knowledge and effective modelling of concepts allows our children to view the workings and thinking of the master at work. Children are then given adequate time to practice concepts with scaffolds and supports being withdrawn to ensure the children have opportunity to grapple with new learning in order for it to be committed to long term memory eventually.

A detailed, structured curriculum is mapped out across all phases, ensuring continuity and supporting transition. Effective mastery curricula in mathematics are designed in relatively small carefully sequenced steps, which must each be mastered before pupils move to the next stage. Fundamental skills and knowledge are secured first. This often entails focusing on curriculum content in considerable depth at early stages.

As a school, we are passionate about children acquiring the basic skills of mathematics that will be valuable to them as they move on to further education and beyond.

Reception

 Autumn Spring Summer In Number we will be learning:To use some number names and number language spontaneously.To use some number names accurately in play.To recite numbers in order to 10.To being to represent numbers using fingers, marks on the page or pictures. To sometimes match numeral and quantity correctly. To show an interest in representing numbers.To show an interest in numerals in the environment. In Shape, Space and Measure we will be learning:2D shape names and properties. We will look for shapes in our environment and show an interest in shapes by playing with them.To being to talk about the shapes of everyday objects e.g ‘round’ and ‘tall’.To make patterns. To measure using non-standard units To have a sense of time. To identify and write numbers up to 10.To add groups of objects.To find one more and one less than a given number.The names and properties of 3D shapes. Positional language. To understand, recognise and use money.To halve and double. To solve simple addition and subtraction sums using numbers to 20. To apply our knowledge to problem solving.

Year 1

 Autumn Spring Summer Counting and representing numbers to 20 and beyondAddition and subtraction using numbers to 20 and beyondDoubling numbersRecognising and naming some 2D shapesIdentifying one more and one less when given a number Knowing and using number bonds to 10 including subtraction factsUsing the language of, equal to, more than, less than etc.Counting on and back to 100Forming numbers correctlyCounting in 2s, 5s and 10sPosition and direction; lengthAddition and subtraction using moneyEstimationKnowing simple directions; right, left, forwards and backwardsShowing whole, ½, ¼ and ¾ turns.Measuring and beginning to record length and heightUsing objects to work out missing numbersPartitioning numbers into Tens and OnesFinding half of an amount and shapeComparing, describing and solving practical problems for measurements of length and time Saying the number one more or less and two more or less using a number line or a 100 grid, writing and saying 2-digit numbers and understanding them as some tens and some onesRecalling number facts and using these to solve simple word problemsUsing known number facts to add and subtractNaming and identifying 3D shapes and their propertiesCounting in 2s, 5s and 10s and identifying patternsTelling the time to the nearest half hourAddition and subtraction; counting on and back, sometimes crossing 10.Understanding place value in two digit numbers and then in relation to moneyForming numbers correctlyRehearsing the days of the week and months of the yearEstimating a number of objects within a range and counting by grouping into 10s or 5sFinding half, quarter and three quarters of shapesDeveloping an understanding of how long a minute, hour, day, week, etc. are Consolidating understanding of 2-digit numbers, representing these in different ways, and partitioning into 10s and 1sRevision of number facts and using these to solve additions and subtractions involving 1- and 2-digit numbers to 100Doubling and halving numbersRecognising halves and quarters of shapes. Rehearsing place value in 2-digit numbersIdentifying and exploring patterns in multiples of 2, 5 and 10.Relating counting in 2s to doubling and halvingRecognise, find and name ½, ¼ of shapes, objects or quantitiesTelling the time to the quarter hourComparing and using uniform non-standard units to measure weight and capacity; information is recorded in block graphs for ease and clarityMeasuring lengths and heights, mass/weight, capacity and volume.Recording information in pictograms and block graphsCreating repeating patterns using 2D shapesRecognising and using pounds and pence; solving money problems

Year 2

 Autumn Spring Summer Comparing and ordering numbers from 0-100.Using place value in a two-digit number to solve problems.Partitioning any two-digit number into different combinations of tens and ones, explaining their thinking verbally, in pictures or using apparatus.Adding and subtracting any 2 two-digit numbers using an efficient strategy, explaining methods verbally, in pictures or using apparatus (e.g. 48 + 35; 72 – 17).Recalling all number bonds to and within 10 and use these to reason with and calculate bonds to and within 20. Counting forwards and backwards in steps of 2, 3 and 5 from 0 and in 10s from any number. Recalling multiplication and division facts for 2, 5 and 10 and use them to solve simple problems, demonstrating an understanding of commutativity as necessary.Naming and describing properties of 2-D and 3-D shapes, including number of sides, vertices, edges, faces and lines of symmetry.Adding amounts of money and working out change. Numbers to 100 – reciting, reading, writing. Counting on/back in ones, twos and tens to 100.Recognising the place value of each digit in a 2 digit number.Appropriate standard units to measure length/ height (m/cm) in any direction; mass (kg/g); to the nearest appropriate unit, using rulers and scales.The terms clockwise and anti-clockwise. Reading scales in divisions of ones, twos, fives and tens. Adding and subtracting any 2 two-digit numbers using an efficient strategy and with greater confidence, explaining methods verbally, in pictures or using apparatus (e.g. 48 + 35; 72 – 17).Using all number bonds to and within 10 to reason with and calculate bonds to and within 20, recognising other associated additive relationships (e.g. If 7 + 3 = 10, then 17 + 3 = 20; if 7 – 3 = 4, then 17 – 3 = 14; leading to if 14 + 3 = 17, then 3 + 14 = 17, 17 – 14 = 3 and 17 – 3 = 14).Recalling multiplication and division facts for 2, 5 and 10 and use them to solve problems, demonstrating an understanding of commutativity as necessary.Identifying 1/4, 1/3, 1/2, 2/4, 3/4, of a number or shape and know that all parts must be equal parts of the whole.Using different coins to make the same amount.Reading the time on a clock to the nearest 15 minutes.Naming, describing and comparing the properties of 2-D and 3-D shapes, including number of sides, vertices, edges, faces and lines of symmetry.Working with numbers to 100 – reciting, reading and writing with greater accuracy. Counting on/back in ones, twos, threes, fives and tens and relating to times tables.Using < and >.Recalling and using addition and subtraction facts to 10, 20 and 100 fluently. Comparing, ordering, estimating and measuring volume, capacity and temperature.Combining amounts of money to make a particular value. (50p, £1.00, £2.00)Estimating and measuring length/ height (m/cm) in any direction, mass (kg/g) and capacity to the nearest appropriate unit, using rulers and scales. Comparing and sequencing intervals of time. Read scales in divisions of ones, twos, fives and tens. Partition any two-digit number into different combinations of tens and ones, explaining their thinking verbally, in pictures or using apparatus.Add and subtract any 2 two-digit numbers using an efficient strategy, explaining methods verbally, in pictures or using apparatus (e.g. 48 + 35; 72 – 17).Recall multiplication and division facts for 2, 5 and 10 and use them to solve simple problems, demonstrating an understanding of commutativity as necessary.Identify 1/4, 1/3, 1/2, 2/4, 3/4, of a number or shape and know that all parts must be equal parts of the whole.Use a variety of different coins to make the same amount.Read the time on a clock to the nearest 5 minutes.Name and describe properties of 2-D and 3-D shapes, including number of sides, vertices, edges, faces and lines of symmetry. Compare the similarities and differences of shapes.Identifying, representing and estimating numbers using different representations, including on an empty number line.Using place value and number facts to solve problems.Applying knowledge of mental and written methods through addition and subtraction problems involving numbers, quantities and measures by using objects and pictures.  Recognising the inverse relationship between addition and subtraction and using this to check calculations and solve missing number problems. Choosing and using appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/ g). Recognising the equivalence of 2/4 and 1/2.

Year 3

 Autumn Spring Summer Place ValueRepresent numbers to 1,000 and know the value of each digitCount in hundredsRecognise 100s, 10s and 1sFind 1, 10, 100 more or less than a given numberCompare, read and write numbers up to 1000 in numerals and wordsOrder numbers up to 1000Count in 50sNumber: Addition and SubtractionAdd and subtract numbers by a single digit, ten or hundredAdd and subtract numbers with up to 3-digits using the column methodEstimate and check using inverse Number: Multiplication and DivisionUse arrays to represent multiplication factsLearn 2, 5, 10 and 3 times-tableMake equal groups - sharingMake equal groups - groupingDivide by 2, 5, 10 and 3 Number: Multiplication and DivisionConsolidate 2-, 4- and 8-times tablesMultiply and divide 2-digits by 1-digitSolve multiplication, simple division and missing number problems. Measurement: MoneyCount money (pence)Count money (pounds)Convert pounds and penceAdd and subtract money, giving change in £ and pStatisticsMake tally chartsDraw and interpret pictograms (2, 5 and 10)Interpret and present data using bar charts and tablesSolve one and two step questions using information in scaled bar charts, pictograms and tablesMeasurement: Length and PerimeterMeasure lengthRecognise and find equivalent lengths (m & cm, mm & cm)Compare lengthsAdd and subtract lengthsMeasure perimeterCalculate perimeterNumber: FractionsMake equal partsRecognise, name, write and find a half, a quarter and a thirdRecognise unit fractions and non-unit fractionsRecognise and show equivalent fractions with the same denominator Number: FractionsMake a wholeRecognise tenths as decimalsFind fractions of a set of objects Compare and order fractions up to a wholeAdd and subtract fractions with the same denominatorMeasurement: TimeRecognise O’clock, half past, quarter past and quarter toKnow the number of seconds in a minute, and the number of days in each month, year and leap yearKnow how many hours are in a dayTell the time to 5 minutes and to the minuteTell the time using an analogue clock and 12-hour clockFind and compare durationsGeometry: Properties of ShapeIdentify right angles in shapes and those that are less than a right angleCompare anglesIdentify horizontal/ vertical lines and pairs of parallel and perpendicular linesRecognise and describe 2-D shapesRecognise, describe and make 3-D shapes Measurement: Mass and CapacityCompare and measure massAdd and subtract massCompare volumeMeasure and compare capacity Add and subtract capacity

Year 4

 Autumn Spring Summer Number: Place ValueRepresent numbers to 1,000Recognise place value in a 4-digit numberRecognise 1000s, 100s, 10s and 1sRound any number to the nearest 10 and 100Count in 1,000sPartition numbers up to 10,000Find 1, 10, 100, 1000 more or lessCompare 4-digit numbersNumber: Addition and SubtractionAdd and subtract 1s, 10s, 100s and 1,000sUse column method when adding and subtracting with up to 4 digitsRecognise and use efficient subtraction methodsEstimate answers and check using the inverseMeasurement: Length and PerimeterFind equivalent lengths - m and cmFind equivalent lengths - mm and cmAdd and subtract lengthsMeasure and calculate perimeters (on a grid, of a rectangle or of a rectilinear shape) in centimetres and metersNumber: Multiplication and DivisionMultiply by 10 and 100Divide by 10 and 100Multiply by 1 and 0Divide by 1 and itselfMultiply and divide by 3, 6, 9 and 7 Number: Multiplication and DivisionLearn 11 and 12 times-tableMultiply three single digits Using formal written methods, multiply and divide 2 or 3-digit numbers by 1-digit Measurement: AreaFind the area of straight-sided shapes by counting squaresComparing areaNumber: FractionsRecognise unit and non-unit fractionsCount in tenthsFind common equivalent fractions Recognise and find fractions greater than 1Add 2 or more fractionsNumber: DecimalsRecognise tenths and hundredths as decimalsDivide a 1-digit or 2-digit number by 10 or 100 to create a decimal numberIdentify the value of the digits in a decimal answer Number: DecimalsMake a wholeCompare and order decimalsRound decimalsRecognise and write decimal equivalents to ½ and ¼  Measurement: MoneyOrder and estimate moneyEstimate moneyConvert pounds and penceAdd and subtract money, giving change when necessaryMeasurement: TimeTelling the time to 5 minutes and to the minuteUse a.m. and p.m.Read, write and convert between analogue and digital clocks, including 24 hourSolve problems involving conversion between hours to minutes, minutes to seconds, years to months and weeks to daysStatisticsInterpret and present discrete and continuous data in various ways, including bar charts and time graphsSolve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphsBegin to interpret line graphsGeometry: Properties of ShapeIdentify right angles in shapesIdentify and compare the sizes of acute and obtuse angleCompare and order anglesRecognise and describe 2-D shapesCompare and classify geometric shapes, including quadrilaterals and triangles based on properties and sizesUnderstand horizontal and verticalIdentify lines of symmetry in 2D shapes in different orientations-complete drawingsComplete a symmetric figureGeometry: Position and DirectionDescribe positionDraw and move on a gridDescribe movement on a grid

Year 5

 Autumn Spring Summer Number: Place ValueRead, write and order numbers up to 1,000,000Round any number up to 1,000,000 to nearest 10, 100, 1,000, 10,000 and 100,000Count forwards and backwards in steps of 10s, 100s, 1,000s, 10,000s, and 100,000sCompare and order numbers to one millionCount forwards and backwards through zero and use negative numbers in simple calculationsDemonstrate knowledge of Roman Numerals to 1,000 and be able to read years written in this wayNumber: Addition and SubtractionUsing standard columns methods add two 4-digit numbers - one exchange and more than one exchangeAdd whole numbers with more than 4 digits (using column method)Subtract two 4-digit numbers - one exchange and more than one exchangeSubtract whole numbers with more than 4 digits (using column method)Round to estimate and approximateUse inverse operations (addition and subtraction)Solve multi-step addition and subtraction problemsStatisticsInterpret chartsCompare, sum and find the differenceRead and interpret line graphsDraw line graphs and use them to solve problems Read and interpret tables (including two-way tables and timetables)Number: Multiplication and DivisionUnderstand the terms: factor, factor pairs, composite numbers, prime and multipleRecognise and find common factors, prime numbers, square numbers and cube numbersMultiply by 10, 100 and 1000Divide by 10, 100 and 1000Recognise and find multiples of 10, 100 and 1,000Measurement: Perimeter and AreaMeasure perimeter on a grid, of rectangles and rectilinear shapesCalculate perimeterFind the area of shapes by counting squaresFind the areas of rectangles, compound shapes and irregular shapes Number: Multiplication and DivisionUsing formal written methods, multiply up to 4- digits by both one- and two-digit numbersUsing short division, divide up to four digits by one digitDivide with remainders and be able to explain remainders.Number: FractionsBe able to explain what a fraction isRecognise and find equivalent fractionsRecognise and find fractions greater than 1Recognise mixed numbers and improper fractions and be able to convert from one to the other. Compare and order fractions where denominators are multiples of the same number. Add and subtract fractions with a common denominatorMultiply proper fractions and mixed numbers by a whole numberNumber: Decimals and PercentagesSay, read and write decimals up to 2 d.p.Recognise and write decimals as fractions (1)Understand thousandthsRecognise and write thousandths as decimalsRound decimals with two decimal places to the nearest whole number and also to one decimal placeOrder and compare decimalsUnderstand percentagesRecognise and write percentages as fractions and decimalsFind equivalent fractions, decimals and percentages Number: DecimalsAdd and subtract decimals within 1Add decimals – crossing the wholeAdd decimals with the same/ different number of decimal placesSubtract decimals with the same/ different number of decimal placesAdd and subtract wholes and decimalsMultiply decimals by 10, 100 and 1,000Divide decimals by 10, 100 and 1,000Geometry: Properties of ShapeIdentify, compare and order anglesMeasure angles in degreesMeasure with a protractor Draw lines and angles accuratelyCalculating angles on a straight line and around a pointCalculating lengths and angles in shapesKnow 360 degrees is a whole turnMatch a net to its 3D shapeGeometry: Position and DirectionDescribe position following a reflection or translationFind and draw lines of symmetryComplete a symmetric figureMeasurement: Converting UnitsConvert between similar units of metric measureConvert from metric to imperial units (giving the rough equivalent)Measurement: VolumeCompare and estimate volumeEstimate capacity

Year 6

 Autumn Spring Summer Number: Place ValueRead, write, order and compare numbers up to ten million and know the value of each digitRound numbers to 10, 100 and 1,000Use negative numbers in context and calculate intervals across zeroNumber: Four OperationsUsing formal written methods, add and subtract whole numbers with more than 4 digitsRecognise and use inverse operations (addition and subtraction)Solve multi-step addition and subtraction problemsUse both long and short multiplication methods of multiplication with numbers up to 4-digitsUse long division to divide numbers with up to 4-digits by a 2-digit whole number and interpret any remainders appropriatelyNumber: FractionsFind equivalent fractionsSimplify, compare and order fractions (including fractions more than one)Recognise mixed numbers and improper fractions and be able to convert from one to the otherAdd and subtract fractions with different denominators and mixed numbersMultiply pairs of fractions and write the answer in its simplest formDivide fractions by integers Geometry: Position and DirectionTranslate and reflect shapes using all four quadrants Number: DecimalsMultiply and divide by 10, 100 and 1,000. Know the value of each digit to three decimal places.Multiply one-digit numbers with up to two decimals places by integersUse written division methods where the answer has two decimal placesRecognise and write decimals as fractionsConvert fractions to decimals Number: PercentagesUnderstand percentagesMatch fractions to decimals and percentagesOrder fractions, decimals and percentagesFind the percentage of an amountNumber: AlgebraExpress unknown numbers using symbols or lettersFind pairs of numbers that satisfy an equation with two unknownsUse simple formulae expressed in wordsKnow when to use the formulae for area and volume of shapesGenerate and describe linear number sequences Solve one-step and two-step equationsMeasurement: Converting unitsConvert between units of measure: weight, distance and time.Calculate with metric measuresImperial measuresMeasurement: Perimeter, Area & VolumeRecognise that shapes with the same area can have a different perimeter and vice versaCalculate the area of a triangle and a parallelogramEstimate, calculate and compare the volume of cubes and cuboids using standard units StatisticsRead, interpret and draw line graphsRead, interpret and draw pie chartsUse line graphs and pie charts to solve problemsKnow how and when to calculate the averages of a set of data. Geometry: Properties of ShapeRecognise angles around a point, on a straight line or are vertically oppositeFind missing angles of triangles, quadrilaterals and polygons Draw shapes accuratelyDraw nets of 3-D shapes Number: RatioCalculating ratioCalculate scale factorsReduce ratios to their simplest formsSolve ratio and proportion problems Revision:Calculate fractionsEstimate fractionsRecognise when to find the common denominatorCalculate decimals and use them to solve problems (money)Solve multi-step problems

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