Mathematics
Mathematics is a key life skill. Through our work at Southfields Primary School in Mathematics, children will gain the knowledge and understanding to confidently use their skills to work within our world today.
Aims
 An enjoyment of Mathematics for all children whatever their needs, talents or cultural background via a positive attitude.
 Every individual’s potential is recognised in Mathematics by promoting independent learners, confident and logical thinkers with flexibility of mind.
 The importance of using mathematical language as a means of communicating ideas and concepts with understanding of the language.
 Mathematics skills and knowledge accompanied by the quick recall of basic skills.
 An awareness of the uses of Mathematics beyond the classroom with the ability to apply skills in a changing world.
Objectives
 Develop an understanding of numbers and the number system.
 Develop an ability to use and apply Mathematics skills in everyday situations.
 To understand and relate Mathematics sills using ICT effectively.
 Develop a positive attitude to Mathematics involving parents and guardians.
Planning
At Southfields Primary School we use the National Curriculum Programmes of Study (2014) as a basis to form the coverage needed to be taught in each year group. In addition to this, teachers have access to Abacus Evolve planning, with linked Interactive Teaching Programmes (ITP’s) and resources. This resource is a starting point, from which teachers create a short term plan from adding and changing some of the suggested activities and teaching. It outlines a suggested order in which to teach mathematics, which is in line with the 2014 National Curriculum.
Teachers are expected to produce medium term plans outlining the intended areas they propose to teach each term. These should include references to ICT links for resources the school have bought into (Mathletics and Mathswatch), links to everyday life and homework tasks.
Short Term Planning
Weekly plans are written by the class teacher ensuring the requirements of the key objectives from the National Curriculum (2014) Programmes of Study are covered.
Whilst the class teacher will refer to plans from Abacus Evolve, teachers will adapt the given key objectives to be taught to reflect the class, group and individual needs, these will be annotated on the weekly plans.
Weekly plans should indicate where mental maths, times tables, number bonds and problem solving skills are, as well as what the Mathematics lesson focus is. Plans should also show the key vocabulary to be used and taught for the day/week, they should highlight how other adults in the classroom will be used as well as highlighting key questions that are going to be asked during the lesson, including those which are metacognitive questions.
Teaching Aims
The emphasis in Mathematics is on group teaching, so all children have a proportion of dedicated teacher interactivity. The direct teaching is oral, interactive and lively. This ensures a twoway process in which pupils are expected to play an active role. Each daily lesson should have a clear lesson objective and a clear oral mental started objective.
Calculators
Calculator skills are no longer taught as part of the Primary Mathematics Curriculum (2014) however as a school we will use calculators as we feel appropriate.
Monitoring and Evaluation
The policy and practice will be monitored and evaluated by the mathematics coordinator and the Head Teacher. Teachers are observed as part of the School Development Plan to achieve high expectations in Mathematics teaching and learning. Feedback is given to the individual teacher orally by the observer and a written response will follow, targets are set to address areas of development with a measurable timescale.
What mathematics will my child be taught  Please see the coverage below it is divided into year groups
Key Stage 1 Overview see below for Coverage
The principal focus of mathematics teaching in Key Stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the four operations, including with practical resources (e.g. concrete objects and measuring tools).
At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.
By the end of Year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency.
Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at Key Stage 1.
Year 1
Year 1 programme of study (statutory requirements) 
Notes and Guidance (nonstatutory) 

Number and place value
Pupils should be taught to:

Number and place value
Pupils should practise counting (1, 2, 3), ordering (e.g. first, second, third), or to indicate a quantity (e.g. 3 apples, 2 centimetres), including solving simple concrete problems, until they are fluent. They should practise counting as reciting numbers and counting as enumerating objects, and counting in ones, twos, fives and tens from different multiples to develop their recognition of patterns in the number system (e.g. odd and even numbers). They connect these patterns with objects and with shapes, including through varied and frequent practice of increasingly complex questions. Pupils begin to recognise place value in numbers beyond 20 by reading, writing, counting and comparing numbers up to 100, supported by concrete objects and pictorial representations. 
Addition and subtraction
Pupils should be taught to:

Addition and subtraction
Pupils should memorise and reason with number bonds to 10 and 20 in several forms (e.g. 9 + 7 = 16; 16 – 7 = 9; 7 = 16  9). They should realise the effect of adding or subtracting zero. Pupils should combine and increase numbers, counting forwards and backwards. They should discuss and solve problems in familiar practical contexts, including using quantities. Problems should include the terms put together, add, altogether, total, take away, difference between, more than and less than so that pupils develop the concept of addition and subtraction and are enabled to use these operations flexibly. 
Multiplication and division
Pupils should be taught to:

Multiplication and division
Through grouping and sharing small quantities, pupils should begin to understand multiplication and division; doubling numbers and quantities, and finding simple fractions of objects, numbers and quantities. They should make connections between arrays, number patterns, and counting in twos, fives and tens.

Fractions
Pupils should be taught to:

Fractions
Pupils should be taught 1/2 and 1/4 as operators on discrete and continuous quantities by solving problems using shapes, objects and quantities. For example, they could recognise and find half a length, quantity, set of objects or shape. Pupils connect halves and quarters to the equal sharing and grouping of sets of objects and to measures, as well as recognising and combining halves and quarters as parts of a whole. 
Measures
Pupils should be taught to:

Measures
The terms mass and weight, volume and capacity are used interchangeably at this stage Pupils should move from using and comparing different types of quantities and measures using nonstandard units, including discrete (e.g. counting) and continuous (e.g. liquid) measures, to using manageable common standard units. They should understand the difference between nonstandard and standard units. In order to become familiar with standard measures, pupils begin to use measuring tools such as a ruler, weighing scales and containers. Pupils should use the language of time, including telling the time throughout the day, first using o’clock and then half past. 
Geometry: properties of shapes
Pupils should be taught to:

Geometry: properties of shapes
Pupils should handle common 2D and 3D shapes, naming these and related everyday objects fluently. They should recognise these shapes in different orientations and sizes, and know that rectangles, triangles, cuboids and pyramids can be different shapes. 
Geometry: position, direction, motion
Pupils should be taught to:

Geometry: position, direction, motion
Pupils should create, copy, describe and reorganise patterns. They should use the language of position, direction and motion, including: left and right, top, middle and bottom, on top of, in front of, above, between, around, near, close and far, up and down, forwards and backwards, inside and outside. Pupils should make turns to show they understand half, quarter and threequarter turns and routinely make these turns in a clockwise direction. 
Year 2
Year 2 programme of study (statutory requirements) 
Notes and Guidance (nonstatutory) 

Number and place value
Pupils should be taught to:

Number and place value
Using materials and a range of representations, pupils should practise counting, reading, writing and comparing numbers to at least 100 and solving a variety of related problems to develop fluency. They should count in multiples of three to support their later understanding of a third. As they become more confident with numbers up to 100, pupils should be introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations. Pupils should partition numbers in different ways (e.g. 23 = 20 + 3 and 23 = 10 + 13) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in twodigit numbers. They begin to understand zero as a place holder. 
Addition and subtraction
Pupils should be taught to:

Addition and subtraction
Pupils should extend their understanding of the language of addition and subtraction to include sum and difference. Pupils should practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 + 7 = 10, 10  7 = 3 and 7 = 10  3 to calculate 30 + 70 = 100, 100  70 = 30 and 70 = 100  30. They should check their calculations, including by adding to check subtraction and adding numbers in a different order to check addition (e.g. 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). Recording addition and subtraction in columns supports place value and prepares for efficient written methods with larger numbers. 
Multiplication and division
Pupils should be taught to:

Multiplication and division
Pupils should use a variety of language to describe multiplication and division. They are taught multiplication and division with larger numbers through equal grouping and sharing out quantities, relating multiplication tables to arrays and repeated addition and finding more complex fractions of objects, numbers and quantities. Pupils should be introduced to the multiplication tables. They should practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. They connect the 10 multiplication table to place value, and the 5 multiplication table to the divisions on the clock face. They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations. Pupils should work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, relating these to fractions and measures (e.g. 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (e.g. 4 × 5 = 20 and 20 ÷ 5 = 4). 
Fractions
Pupils should be taught to:

Fractions
Pupils should use additional fractions as operators on discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantity, a set of objects or shapes. They meet 3/4 as the first example of a nonunit fraction. Pupils should count in fractions up to 10, starting from any number and using the 1/2 and 2/4 equivalence on the number line (e.g. 11/4, 12/4 , (or 11/2), 13/4, 2). This reinforces the concept of fractions as numbers and that they can add up to more than one. 
Measures
Pupils should be taught to:

Measures
Pupils should use standard units of measurement with increasing accuracy, using their knowledge of the number system. They should use the appropriate language and record using standard abbreviations. They should become fluent in telling the time on analogue clocks and recording it. Pupils should also become fluent in counting and recognising coins. They should use the symbols £ and p accurately and say the amounts of money confidently. 
Geometry: properties of shapes
Pupils should be taught to:

Geometry: properties of shapes
Pupils should handle and name a wider variety of common 2D and 3D shapes including: quadrilaterals and cuboids, prisms, cones and polygons, and identify the properties of each shape (e.g. number of sides, number of faces). Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces. Pupils should read and write names for shapes that are appropriate for their word reading and spelling. Pupils should draw lines and shapes using a straight edge. 
Geometry: position, direction, motion Pupils should be taught to:

Geometry: position, direction, motion Pupils should work with patterns of shapes, including those in different orientations. Pupils should use the concept and language of angles to describe ‘turn’ by applying rotations, including in practical contexts (e.g. pupils themselves moving in turns, giving instructions to other pupils to do so, and programming robots using instructions given in right angles). 
Data Pupils should be taught to:

Data At this stage, pupils’ recording and interpretation become more sophisticated as they collate, organise and compare information (e.g. using manytoone correspondence in pictograms and using simple ratios 2, 5, 10). 
Lower Key Stage 2 – Years 34
The principal focus of mathematics teaching in lower Key Stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.
At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they can use measuring instruments with accuracy and make connections between measure and number.
By the end of Year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work.
Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.
Year 3
Year 3 programme of study (statutory requirements) 
Notes and guidance (nonstatutory) 

Number, place value and rounding
Pupils should be taught to:

Number, place value and rounding
Pupils should work with larger numbers, applying partitioning related to place value using varied and increasingly complex problems, building on work in Year 2 (e.g. 46 = 40 and 6, 46 = 30 and 16). Using a variety of representations, including those related to measure, pupils should continue to count in ones, tens and hundreds, so that they become fluent in the order and place value of numbers to 1000. 
Addition and subtraction Pupils should be taught to:

Addition and subtraction Pupils should practise solving varied addition and subtraction questions. For mental calculations with twodigit numbers, the answers could exceed 100. Pupils should use their understanding of place value and partitioning, and practise using columnar addition and subtraction with increasingly large numbers up to three digits to become fluent.

Multiplication and division Pupils should be taught to:

Multiplication and division Pupils should continue to practise their mental recall of multiplication tables when they are calculating mathematical statements in order to improve fluency. Through doubling, they connect the 2, 4 and 8 multiplication tables. Pupils should develop efficient mental methods, for example, using commutativity (e.g. 4 × 12 × 5 = 4 × 5 × 12 = 20 × 12 = 240) and multiplication and division facts (e.g. using 3 × 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3) to derive related facts (30 × 2 = 60, 60 ÷ 3 = 20 and 20 = 60 ÷ 3). Pupils should develop reliable written methods for multiplication and division, starting with calculations of twodigit numbers by onedigit numbers and progressing to the efficient written methods of short multiplication and division. Pupils should solve simple problems in contexts, deciding which of the four operations to use and why, including measuring and scaling contexts, and correspondence problems in which m objects are connected to n objects (e.g. 3 hats and 4 coats, how many different outfits; 12 sweets shared equally between 4 children; 4 cakes shared equally between 8 children). 
Fractions Pupils should be taught to:

Fractions Pupils should connect tenths to place value and decimal measures, not restricted to decimals between 0 and 1 inclusive and to division by 10. They should begin to understand unit and nonunit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval, and 1/4 + 3/4 = 1 for example, relating this to measure. Pupils should understand the relation between unit fractions as operators and division by integers. They should continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, or unit fractions as a division of a quantity. Pupils should practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency. 
Measures Pupils should be taught to:

Measures Pupils should continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units (e.g. 1 kg and 200g) and simple equivalents of mixed units (e.g. 5m = 500cm). The comparison of measures should also include simple scaling (e.g. a given quantity or measure is twice as long or five times as high) and connect this to multiplication. Pupils should continue to become fluent in recognising the value of coins, by adding and subtracting amounts, including mixed units, and giving change using manageable amounts. They should record £ and p separately. The decimal recording of money is introduced formally in Year 4. Pupils should use both analogue and digital 12hour clocks and record their times. In this way they become fluent in and prepared for using digital 24hour clocks in Year 4. 
Geometry: properties of shapes Pupils should be taught to:

Geometry: properties of shapes Pupils’ knowledge of the properties of shapes is extended at this stage to symmetrical and nonsymmetrical polygons and polyhedra. Pupils extend their use of the properties of shapes. They should be able to describe the properties of 2D and 3D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle. Pupils should draw and measure straight lines in centimetres. 
Data Pupils should be taught to:

Data Pupils should understand and use simple scales (e.g. 2, 5, 10 units per cm) in pictograms and bar charts with increasing accuracy. They should continue to interpret data presented in many contexts. 
Year 4
Year 4 programme of study (statutory requirements) 
Notes and guidance (nonstatutory) 

Number, place value and rounding Pupils should be taught to

Number, place value and rounding Using a variety of representations, including measures, pupils should become fluent in the order and place value of numbers beyond 1000, including counting in tens and hundreds, and maintaining fluency in other multiples through varied and frequent practice. They begin to extend their knowledge of the number system to include the decimal numbers and fractions that they have met so far. Roman numerals should be put in their historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of zero and place value were introduced over a period of time. 
Addition and subtraction Pupils should be taught to:

Addition and subtraction Pupils should continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency. 
Multiplication and division Pupils should be taught to:

Multiplication and division Pupils should continue to practise recalling and using multiplication tables and related division facts to aid fluency. Pupils should practise mental methods and extend this to threedigit numbers to derive facts, for example 200 × 3 = 600 into 600 ÷ 3 = 200, to become fluent. Pupils should practise to become fluent in the efficient written method of short multiplication for multiplying using multidigit numbers, and short division with exact answers when dividing by a onedigit number. Pupils should write statements about the equality of expressions (e.g. use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4 = 2 × (3 × 4)). Pupils should solve twostep problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as three cakes shared equally between 10 children. 
Fractions Pupils should be taught to:

Fractions Pupils should connect hundredths to tenths and place value and decimal measure. They should extend the use of the number line to connect fractions, numbers and measures. Pupils should understand the relation between nonunit fractions and multiplication and division of quantities, with particular emphasis on tenths and hundredths. Pupils should associate fractions of a length, of a shape and as a representation of one whole or set of quantities. Pupils should use factors and multiples to recognise equivalent fractions and simplify where appropriate (e.g. 6/9 = 2/3 or 1/4 = 2/8). Pupils should continue practice in adding and subtracting fractions with the same denominator, to become fluent through a variety of increasingly complex problems beyond one whole. They should practise counting using simple fractions and decimal fractions, both forwards and backwards. 
Decimals and fractions Pupils should be taught to:

Decimals and fractions Pupils should be taught throughout that decimals and fractions are different ways of expressing numbers. Pupils’ understanding of the number system and decimal place value is extended at this stage to tenths and then hundredths. This includes relating the decimal notation to division of whole numbers by 10 and later 100. Pupils should learn decimal notation and the language associated with it, including in the context of measurements. They make comparisons and order decimal amounts and quantities that are expressed to the same number of decimal places. They should be able to represent numbers with one or two decimal places in multiple ways, such as on number lines. 
Measures Pupils should be taught to:

Measures Pupils should use multiplication and their knowledge of place value to convert from larger to smaller units. They should relate area to arrays and multiplication. Pupils should build on their understanding of decimal notation to record measures. 
Geometry: properties of shapes Pupils should be taught to:

Geometry: properties of shapes Pupils should continue to classify shapes using geometrical properties, extending to classifying different triangles (e.g. isosceles, equilateral, scalene) and quadrilaterals (e.g. parallelogram, rhombus, trapezium). Pupils should compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular. Pupils should draw symmetric patterns using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams. 
Geometry: position, direction, motion Pupils should be taught to:

Geometry: position, direction, motion Pupils should draw a pair of axes in one quadrant, with equal scales and integer labels. They should read, write and use pairs of coordinates (2, 5), including using coordinateplotting ICT tools. 
Data Pupils should be taught to:

Data Pupils should understand and use a greater range of scales in their representations. Pupils should begin to relate the graphical representation of data to recording change over time. 
Upper Key Stage 2 – Years 56
The principal focus of mathematics teaching in upper Key Stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio.
At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems. Teaching in geometry and measures should consolidate and extend knowledge developed in number. Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them.
By the end of Year 6, pupils should be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.
Pupils should read, spell and pronounce mathematical vocabulary correctly.
Year 5
Year 5 programme of study (statutory requirements) 
Notes and guidance (nonstatutory) 

Number, place value, approximation and estimation Pupils should be taught to:

Number, place value, approximation and estimation Pupils should identify the place value in large whole numbers. They should continue to use number in context, including measurement. Pupils extend and apply their understanding of the number system to the decimal numbers and fractions that they have met so far. They should recognise and describe linear number sequences, including those involving fractions and decimals, and find the termtoterm rule. 
Addition and subtraction Pupils should be taught to:

Addition and subtraction Pupils should practise using the efficient written methods of columnar addition and subtraction with increasingly large numbers to aid fluency. They should practise mental calculations with increasingly large numbers to aid fluency (e.g. 12 462 – 2 300 = 10 162). 
Multiplication and division Pupils should be taught to:

Multiplication and division Pupils should practise and extend their use of the efficient written methods of short multiplication and short division. They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations. They should use and understand the terms factor, multiple and prime, square and cube numbers. Pupils should interpret noninteger answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (e.g. 98 ÷ 4 = 24 r 2 = 241/2 = 24.5 ≈ 25). Pupils use multiplication and division as inverses to support the introduction of ratio in Year 6, for example, by multiplying and dividing by powers of 10 in scale drawings or by multiplying and dividing by powers of a 1000 in converting between units such as kilometres and metres. 
Fractions Pupils should be taught to:

Fractions Pupils should connect equivalent fractions >1 that simplify to integers with division and fractions >1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions. Pupils should connect multiplication by a fraction to using fractions as operators, and to division, building on work from previous years. This relates to scaling by simple fractions. They should extend their knowledge of fractions to thousandths and connect to decimals and measures. Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities, writing remainders as a fraction. Pupils should practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They should extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number. Pupils should read and write proper fractions and mixed numbers accurately and continue to practise counting forwards and backwards with mixed fractions. 
Decimals and fractions Pupils should be taught to:

Decimals and fractions Pupils extend counting from Year 4, using decimals and fractions including bridging zero, for example on a number line. They should add and subtract decimals including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (e.g. 0.83 + 0.17 = 1). They should mentally add and subtract tenths, and onedigit whole numbers and tenths. Pupils should say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and be confident in checking the reasonableness of their answers to problems. Pupils should go beyond the measurement and money models of decimals, for example by solving puzzles involving decimals. 
Percentages, decimals and fractions Pupils should be taught to:

Percentages, decimals and fractions Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing numbers. Pupils should make connections between percentages, fractions and decimals (e.g. 100% represents a whole quantity and 1% is 1/100, 50% is 50/100, 25% is 25/100) and relate this to finding ‘fractions of’. They recognise that percentages are proportions of quantities as well as operators on quantities. 
Measures Pupils should be taught to:

Measures Pupils should use their knowledge of place value and multiplication and division to convert between standard units. Pupils should calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing number questions such as these are the beginning of algebraic understanding. They should also calculate the area of scale drawings using given measurements. Pupils should use all four operations in problems involving time and money, including conversions (e.g. days to weeks, leaving the answer as weeks and days). 
Geometry: properties of shapes Pupils should be taught to:

Geometry: properties of shapes Pupils should become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles. Pupils should use the term diagonal and make conjectures about the angles formed by diagonals and sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools. Pupils should use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems. 
Geometry: position, direction, motion Pupils should be taught to:

Geometry: position, direction, motion Pupils should recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes. 
Data Pupils should be taught to:

Data Pupils should connect their work on coordinates and scales to their interpretation of time graphs using ICT tools, except where data are easily calculable. They should begin to decide which representations of data are most appropriate and why. 
Year 6
Year 6 programme of study (statutory requirements) 
Notes and guidance (nonstatutory) 

Number, place value and rounding Pupils should be taught to:

Number, place value and rounding Pupils should use the whole number system, including saying, reading and writing numbers accurately. 
Addition, subtraction, multiplication and division Pupils should be taught to:

Addition, subtraction, multiplication and division Pupils should practise addition, subtraction, multiplication and division for larger numbers, using the efficient written methods of columnar addition and subtraction, short and long multiplication, and short and long division. They should undertake mental calculations with increasingly large numbers and more complex calculations. Pupils should continue to use all the multiplication tables to calculate mathematical statements in order to maintain their fluency. Pupils should round answers to a specified degree of accuracy. Pupils explore the order of operations using brackets; for example, 2 + 1 x 3 = 5 and (2 + 1) x 3 = 9. Common factors can be related to finding equivalent fractions. 
Fractions Pupils should be taught to:

Fractions Pupils should use their understanding of the relationship between unit fractions and division to work backwards by multiplying a quantity that represents a unit fraction to find the whole quantity (e.g. if ¼ of a length is 36cm, then the whole length is 36 × 4 = 144cm). They should practise with simple fractions and decimal fraction equivalents to aid fluency, including listing equivalent fractions to identify fractions with common denominators. Denominators of given fractions should not exceed 12, with the exception of 100 and 1000. Pupils can explore and make conjectures about converting a simple fraction to a decimal fraction (e.g. 3 ÷ 8 = 0.375). For simple fractions with recurring decimal equivalents, pupils should learn about rounding the decimal to three decimal places. Pupils should practise, use and understand the addition and subtraction of fractions with different denominators by identifying equivalent fractions with the same denominator. They should start with fractions where the denominator of one fraction is a multiple of the other (e.g. 1/2 + 1/8 = 5/8) and progress to varied and increasingly complex problems. Pupils should use a variety of images to support their understanding of multiplication with fractions. This follows earlier work about fractions as operators, as numbers, and as equal parts of objects, for example as parts of a rectangle. 
Decimals and fractions Pupils should be taught to:

Decimals and fractions Pupils should begin to multiply and divide numbers with up to two decimal places by onedigit and twodigit whole numbers. Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money. Pupils should also be introduced to the division of decimal numbers by onedigit whole numbers and, initially, in practical contexts involving measures and money. They should recognise division calculations as the inverse of multiplication. Pupils should also develop their skills of rounding and estimating as a means of predicting and checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy and checking the reasonableness of their answers. 
Percentages, decimals and fractions Pupils should be taught to:

Percentages, decimals and fractions Pupils should understand that calculating a percentage of a quantity is the same as calculating a fraction of a quantity. 
Ratio and proportion Pupils should be taught to:

Ratio and proportion Pupils should consolidate their understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. They may use the notation a:b to record their work. Pupils should recognise proportionality in contexts when the relations between quantities are in the same ratio (e.g. similar shapes, recipes). 
Algebra Pupils should be taught to:

Algebra Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:

Measures Pupils should be taught to:

Measures Using the number line, pupils should use, add and subtract positive and negative integers for measures such as temperature. They should know approximate conversions and be able to tell if an answer is sensible. They should relate the area of rectangles to parallelograms and triangles, and be able to calculate their areas, understanding and using the formula to do this. Pupils could be introduced to other compound units for speed, such as miles per hour, and apply their knowledge in science or other subjects as appropriate.

Geometry: properties of shapes Pupils should be taught to:

Geometry: properties of shapes Pupils should draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles. Pupils should describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements. 
Geometry: position, direction, motion Pupils should be taught to:

Geometry: position, direction, motion Pupils should draw and label a pair of axes in all four quadrants with equal scaling. This extends their knowledge of one quadrant to all four quadrants, including the use of negative numbers. Pupils should draw and label rectangles (including squares), parallelograms and rhombuses, specified by coordinates in the four quadrants, predicting missing coordinates using the properties of shapes. 
Data Pupils should be taught to:

Data Pupils should connect their work on angles, fractions and percentages to the interpretation of pie charts. Pupils should both encounter and draw graphs relating two variables, arising from their own enquiry and in other subjects. They should connect conversion from kilometres to miles in measure to its graphical representation. Pupils should know when it is appropriate to find the mean of a data set. 