📐 Mathematics – Key Stage 2

Years 3-6

Official GOV.UK source

Aims

The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the 4 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. 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 4 operations, including long multiplication and division, and in working with fractions, decimals and percentages. Pupils should read, spell and pronounce mathematical vocabulary correctly.

Year 3

Number - number and place value6 objectives + 3 guidance

Pupils should be taught to:

MA-KS2-Y3-NPV-01count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number
MA-KS2-Y3-NPV-02recognise the place value of each digit in a 3-digit number (100s, 10s, 1s)
MA-KS2-Y3-NPV-03compare and order numbers up to 1,000
MA-KS2-Y3-NPV-04identify, represent and estimate numbers using different representations
MA-KS2-Y3-NPV-05read and write numbers up to 1,000 in numerals and in words
MA-KS2-Y3-NPV-06solve number problems and practical problems involving these ideas

Teaching guidance (non-statutory)

MA-KS2-Y3-NPV-N01Pupils now use multiples of 2, 3, 4, 5, 8, 10, 50 and 100.
MA-KS2-Y3-NPV-N02They use larger numbers to at least 1,000, applying partitioning related to place value using varied and increasingly complex problems, building on work in year 2 (for example, 146 = 100 + 40 + 6, 146 = 130 +16).
MA-KS2-Y3-NPV-N03Using a variety of representations, including those related to measure, pupils continue to count in 1s, 10s and 100s, so that they become fluent in the order and place value of numbers to 1,000.

Number - addition and subtraction4 objectives + 2 guidance

Pupils should be taught to:

MA-KS2-Y3-AS-01add and subtract numbers mentally, including: a three-digit number and 1s; a three-digit number and 10s; a three-digit number and 100s
MA-KS2-Y3-AS-02add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction
MA-KS2-Y3-AS-03estimate the answer to a calculation and use inverse operations to check answers
MA-KS2-Y3-AS-04solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction

Teaching guidance (non-statutory)

MA-KS2-Y3-AS-N01Pupils practise solving varied addition and subtraction questions. For mental calculations with two-digit numbers, the answers could exceed 100.
MA-KS2-Y3-AS-N02Pupils use their understanding of place value and partitioning, and practise using columnar addition and subtraction with increasingly large numbers up to 3 digits to become fluent (see mathematics appendix 1 (PDF, 248KB)).

Number - multiplication and division3 objectives + 4 guidance

Pupils should be taught to:

MA-KS2-Y3-MD-01recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
MA-KS2-Y3-MD-02write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
MA-KS2-Y3-MD-03solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

Teaching guidance (non-statutory)

MA-KS2-Y3-MD-N01Pupils 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.
MA-KS2-Y3-MD-N02Pupils develop efficient mental methods, for example, using commutativity and associativity (for example, 4 × 12 × 5 = 4 × 5 × 12 = 20 × 12 = 240) and multiplication and division facts (for example, 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).
MA-KS2-Y3-MD-N03Pupils develop reliable written methods for multiplication and division, starting with calculations of two-digit numbers by one-digit numbers and progressing to the formal written methods of short multiplication and division.
MA-KS2-Y3-MD-N04Pupils solve simple problems in contexts, deciding which of the 4 operations to use and why. These include measuring and scaling contexts, (for example 4 times as high, 8 times as long etc) and correspondence problems in which m objects are connected to n objects (for example, 3 hats and 4 coats, how many different outfits?, 12 sweets shared equally between 4 children, 4 cakes shared equally between 8 children).

Number - fractions7 objectives + 5 guidance

Pupils should be taught to:

MA-KS2-Y3-FR-01count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10
MA-KS2-Y3-FR-02recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
MA-KS2-Y3-FR-03recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
MA-KS2-Y3-FR-04recognise and show, using diagrams, equivalent fractions with small denominators
MA-KS2-Y3-FR-05add and subtract fractions with the same denominator within one whole [for example, [Fraction:5/7]+[Fraction:1/7] = [Fraction:6/7]]
MA-KS2-Y3-FR-06compare and order unit fractions, and fractions with the same denominators
MA-KS2-Y3-FR-07solve problems that involve all of the above

Teaching guidance (non-statutory)

MA-KS2-Y3-FR-N01Pupils connect tenths to place value, decimal measures and to division by 10.
MA-KS2-Y3-FR-N02They begin to understand unit and non-unit 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, including relating this to measure.
MA-KS2-Y3-FR-N03Pupils understand the relation between unit fractions as operators (fractions of), and division by integers.
MA-KS2-Y3-FR-N04They continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, and unit fractions as a division of a quantity.
MA-KS2-Y3-FR-N05Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency.

Measurement7 objectives + 4 guidance

Pupils should be taught to:

MA-KS2-Y3-M-01measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
MA-KS2-Y3-M-02measure the perimeter of simple 2-D shapes
MA-KS2-Y3-M-03add and subtract amounts of money to give change, using both £ and p in practical contexts
MA-KS2-Y3-M-04tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks
MA-KS2-Y3-M-05estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o’clock, am/pm, morning, afternoon, noon and midnight
MA-KS2-Y3-M-06know the number of seconds in a minute and the number of days in each month, year and leap year
MA-KS2-Y3-M-07compare durations of events [for example, to calculate the time taken by particular events or tasks]

Teaching guidance (non-statutory)

MA-KS2-Y3-M-N01Pupils continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units (for example, 1 kg and 200g) and simple equivalents of mixed units (for example, 5m = 500cm).
MA-KS2-Y3-M-N02The comparison of measures includes simple scaling by integers (for example, a given quantity or measure is twice as long or 5 times as high) and this connects to multiplication.
MA-KS2-Y3-M-N03Pupils 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 record £ and p separately. The decimal recording of money is introduced formally in year 4.
MA-KS2-Y3-M-N04Pupils use both analogue and digital 12-hour clocks and record their times. In this way they become fluent in and prepared for using digital 24-hour clocks in year 4.

Geometry - properties of shapes4 objectives + 2 guidance

Pupils should be taught to:

MA-KS2-Y3-G-01draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
MA-KS2-Y3-G-02recognise angles as a property of shape or a description of a turn
MA-KS2-Y3-G-03identify right angles, recognise that 2 right angles make a half-turn, 3 make three-quarters of a turn and 4 a complete turn; identify whether angles are greater than or less than a right angle
MA-KS2-Y3-G-04identify horizontal and vertical lines and pairs of perpendicular and parallel lines

Teaching guidance (non-statutory)

MA-KS2-Y3-G-N01Pupils’ knowledge of the properties of shapes is extended at this stage to symmetrical and non-symmetrical polygons and polyhedra. Pupils extend their use of the properties of shapes. They should be able to describe the properties of 2-D and 3-D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle.
MA-KS2-Y3-G-N02Pupils connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts.

Statistics2 objectives + 2 guidance

Pupils should be taught to:

MA-KS2-Y3-S-01interpret and present data using bar charts, pictograms and tables
MA-KS2-Y3-S-02solve one-step and two-step questions [for example ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables

Teaching guidance (non-statutory)

MA-KS2-Y3-S-N01Pupils understand and use simple scales (for example, 2, 5, 10 units per cm) in pictograms and bar charts with increasing accuracy.
MA-KS2-Y3-S-N02They continue to interpret data presented in many contexts.

Year 4

Number - number and place value9 objectives + 3 guidance

Pupils should be taught to:

MA-KS2-Y4-NPV-01count in multiples of 6, 7, 9, 25 and 1,000
MA-KS2-Y4-NPV-02find 1,000 more or less than a given number
MA-KS2-Y4-NPV-03count backwards through 0 to include negative numbers
MA-KS2-Y4-NPV-04recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)
MA-KS2-Y4-NPV-05order and compare numbers beyond 1,000
MA-KS2-Y4-NPV-06identify, represent and estimate numbers using different representations
MA-KS2-Y4-NPV-07round any number to the nearest 10, 100 or 1,000
MA-KS2-Y4-NPV-08solve number and practical problems that involve all of the above and with increasingly large positive numbers
MA-KS2-Y4-NPV-09read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value

Teaching guidance (non-statutory)

MA-KS2-Y4-NPV-N01Using a variety of representations, including measures, pupils become fluent in the order and place value of numbers beyond 1,000, including counting in 10s and 100s, 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.
MA-KS2-Y4-NPV-N02They connect estimation and rounding numbers to the use of measuring instruments.
MA-KS2-Y4-NPV-N03Roman 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 0 and place value were introduced over a period of time.

Number - addition and subtraction3 objectives + 1 guidance

Pupils should be taught to:

MA-KS2-Y4-AS-01add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
MA-KS2-Y4-AS-02estimate and use inverse operations to check answers to a calculation
MA-KS2-Y4-AS-03solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

Teaching guidance (non-statutory)

MA-KS2-Y4-AS-N01Pupils continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency (see mathematics appendix 1 (PDF, 248KB)).

Number - multiplication and division5 objectives + 5 guidance

Pupils should be taught to:

MA-KS2-Y4-MD-01recall multiplication and division facts for multiplication tables up to 12 × 12
MA-KS2-Y4-MD-02use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers
MA-KS2-Y4-MD-03recognise and use factor pairs and commutativity in mental calculations
MA-KS2-Y4-MD-04multiply two-digit and three-digit numbers by a one-digit number using formal written layout
MA-KS2-Y4-MD-05solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

Teaching guidance (non-statutory)

MA-KS2-Y4-MD-N01Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency.
MA-KS2-Y4-MD-N02Pupils practise mental methods and extend this to 3-digit numbers to derive facts, (for example 600 ÷ 3 = 200 can be derived from 2 x 3 = 6).
MA-KS2-Y4-MD-N03Pupils practise to become fluent in the formal written method of short multiplication and short division with exact answers (see mathematics appendix 1 (PDF, 248KB)).
MA-KS2-Y4-MD-N04Pupils write statements about the equality of expressions (for example, use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4 = 2 × (3 × 4)). They combine their knowledge of number facts and rules of arithmetic to solve mental and written calculations for example, 2 x 6 x 5 = 10 x 6 = 60.
MA-KS2-Y4-MD-N05Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as the numbers of choices of a meal on a menu, or 3 cakes shared equally between 10 children.

Number - fractions (including decimals)10 objectives + 8 guidance

Pupils should be taught to:

MA-KS2-Y4-FR-01recognise and show, using diagrams, families of common equivalent fractions
MA-KS2-Y4-FR-02count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10
MA-KS2-Y4-FR-03solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
MA-KS2-Y4-FR-04add and subtract fractions with the same denominator
MA-KS2-Y4-FR-05recognise and write decimal equivalents of any number of tenths or hundreds
MA-KS2-Y4-FR-06recognise and write decimal equivalents to [Fraction:1/4], [Fraction:1/2], [Fraction:3/4]
MA-KS2-Y4-FR-07find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
MA-KS2-Y4-FR-08round decimals with 1 decimal place to the nearest whole number
MA-KS2-Y4-FR-09compare numbers with the same number of decimal places up to 2 decimal places
MA-KS2-Y4-FR-10solve simple measure and money problems involving fractions and decimals to 2 decimal places

Teaching guidance (non-statutory)

MA-KS2-Y4-FR-N01Pupils should connect hundredths to tenths and place value and decimal measure.
MA-KS2-Y4-FR-N02They extend the use of the number line to connect fractions, numbers and measures.
MA-KS2-Y4-FR-N03Pupils understand the relation between non-unit fractions and multiplication and division of quantities, with particular emphasis on tenths and hundredths. Pupils make connections between fractions of a length, of a shape and as a representation of one whole or set of quantities. Pupils use factors and multiples to recognise equivalent fractions and simplify where appropriate (for example, [Fraction:6/9] = [Fraction:2/3] or [Fraction:1/4] = [Fraction:2/8]).
MA-KS2-Y4-FR-N04Pupils continue to practise adding and subtracting fractions with the same denominator, to become fluent through a variety of increasingly complex problems beyond one whole.
MA-KS2-Y4-FR-N05Pupils are taught throughout that decimals and fractions are different ways of expressing numbers and proportions.
MA-KS2-Y4-FR-N06Pupils’ 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 number by 10 and later 100.
MA-KS2-Y4-FR-N07They practise counting using simple fractions and decimals, both forwards and backwards.
MA-KS2-Y4-FR-N08Pupils 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 1 or 2 decimal places in several ways, such as on number lines.

Measurement6 objectives + 4 guidance

Pupils should be taught to:

MA-KS2-Y4-M-01convert between different units of measure [for example, kilometre to metre; hour to minute]
MA-KS2-Y4-M-02measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
MA-KS2-Y4-M-03find the area of rectilinear shapes by counting squares
MA-KS2-Y4-M-04estimate, compare and calculate different measures, including money in pounds and pence
MA-KS2-Y4-M-05read, write and convert time between analogue and digital 12- and 24-hour clocks
MA-KS2-Y4-M-06solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days

Teaching guidance (non-statutory)

MA-KS2-Y4-M-N01Pupils build on their understanding of place value and decimal notation to record metric measures, including money.
MA-KS2-Y4-M-N02They use multiplication to convert from larger to smaller units.
MA-KS2-Y4-M-N03Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit.
MA-KS2-Y4-M-N04They relate area to arrays and multiplication.

Geometry - properties of shapes4 objectives + 3 guidance

Pupils should be taught to:

MA-KS2-Y4-G-01compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
MA-KS2-Y4-G-02identify acute and obtuse angles and compare and order angles up to 2 right angles by size
MA-KS2-Y4-G-03identify lines of symmetry in 2-D shapes presented in different orientations
MA-KS2-Y4-G-04complete a simple symmetric figure with respect to a specific line of symmetry

Teaching guidance (non-statutory)

MA-KS2-Y4-G-N01Pupils continue to classify shapes using geometrical properties, extending to classifying different triangles (for example, isosceles, equilateral, scalene) and quadrilaterals (for example, parallelogram, rhombus, trapezium).
MA-KS2-Y4-G-N02Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular.
MA-KS2-Y4-G-N03Pupils 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, including where the line of symmetry does not dissect the original shape.

Geometry - position and direction3 objectives + 1 guidance

Pupils should be taught to:

MA-KS2-Y4-GP-01describe positions on a 2-D grid as coordinates in the first quadrant
MA-KS2-Y4-GP-02describe movements between positions as translations of a given unit to the left/right and up/down
MA-KS2-Y4-GP-03plot specified points and draw sides to complete a given polygon

Teaching guidance (non-statutory)

MA-KS2-Y4-GP-N01Pupils draw a pair of axes in one quadrant, with equal scales and integer labels. They read, write and use pairs of co-ordinates, for example (2, 5), including using co-ordinate-plotting ICT tools.

Statistics2 objectives + 2 guidance

Pupils should be taught to:

MA-KS2-Y4-S-01interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs
MA-KS2-Y4-S-02solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

Teaching guidance (non-statutory)

MA-KS2-Y4-S-N01Pupils understand and use a greater range of scales in their representations.
MA-KS2-Y4-S-N02Pupils begin to relate the graphical representation of data to recording change over time.

Year 5

Number - number and place value6 objectives + 3 guidance

Pupils should be taught to:

MA-KS2-Y5-NPV-01read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit
MA-KS2-Y5-NPV-02count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
MA-KS2-Y5-NPV-03interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0
MA-KS2-Y5-NPV-04round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
MA-KS2-Y5-NPV-05solve number problems and practical problems that involve all of the above
MA-KS2-Y5-NPV-06read Roman numerals to 1,000 (M) and recognise years written in Roman numerals

Teaching guidance (non-statutory)

MA-KS2-Y5-NPV-N01Pupils identify the place value in large whole numbers.
MA-KS2-Y5-NPV-N02They 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.
MA-KS2-Y5-NPV-N03They should recognise and describe linear number sequences (for example, 3, 3[Fraction:1/2], 4, 4[Fraction:1/2] …), including those involving fractions and decimals, and find the term-to-term rule in words (for example, add [Fraction:1/2]).

Number - addition and subtraction4 objectives + 2 guidance

Pupils should be taught to:

MA-KS2-Y5-AS-01add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
MA-KS2-Y5-AS-02add and subtract numbers mentally with increasingly large numbers
MA-KS2-Y5-AS-03use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
MA-KS2-Y5-AS-04solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Teaching guidance (non-statutory)

MA-KS2-Y5-AS-N01Pupils practise using the formal written methods of columnar addition and subtraction with increasingly large numbers to aid fluency (see mathematics appendix 1 (PDF, 248KB)).
MA-KS2-Y5-AS-N02They practise mental calculations with increasingly large numbers to aid fluency (for example, 12,462 – 2,300 = 10,162).

Number - multiplication and division11 objectives + 7 guidance

Pupils should be taught to:

MA-KS2-Y5-MD-01identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
MA-KS2-Y5-MD-02know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
MA-KS2-Y5-MD-03establish whether a number up to 100 is prime and recall prime numbers up to 19
MA-KS2-Y5-MD-04multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
MA-KS2-Y5-MD-05multiply and divide numbers mentally, drawing upon known facts
MA-KS2-Y5-MD-06divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
MA-KS2-Y5-MD-07multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
MA-KS2-Y5-MD-08recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
MA-KS2-Y5-MD-09solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes
MA-KS2-Y5-MD-10solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
MA-KS2-Y5-MD-11solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

Teaching guidance (non-statutory)

MA-KS2-Y5-MD-N01Pupils practise and extend their use of the formal written methods of short multiplication and short division (see mathematics appendix 1 (PDF, 248KB)). They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations.
MA-KS2-Y5-MD-N02They use and understand the terms factor, multiple and prime, square and cube numbers.
MA-KS2-Y5-MD-N03Pupils interpret non-integer answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (for example, 98 ÷ 4 = [Fraction:98/4] = 24 r 2 = 24[Fraction:1/2] = 24.5 ≈ 25).
MA-KS2-Y5-MD-N04Pupils 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 1,000 in converting between units such as kilometres and metres.
MA-KS2-Y5-MD-N05Distributivity can be expressed as a(b + c) = ab + ac.
MA-KS2-Y5-MD-N06They understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 9² x 10).
MA-KS2-Y5-MD-N07Pupils use and explain the equals sign to indicate equivalence, including in missing number problems (for example 13 + 24 = 12 + 25; 33 = 5 x ?).

Number - fractions (including decimals and percentages)12 objectives + 13 guidance

Pupils should be taught to:

MA-KS2-Y5-FR-01compare and order fractions whose denominators are all multiples of the same number
MA-KS2-Y5-FR-02identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
MA-KS2-Y5-FR-03recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, [Fraction:2/5]+[Fraction:4/5] = [Fraction:6/5] = 1 [Fraction:1/5] ]
MA-KS2-Y5-FR-04add and subtract fractions with the same denominator, and denominators that are multiples of the same number
MA-KS2-Y5-FR-05multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
MA-KS2-Y5-FR-06read and write decimal numbers as fractions [for example, 0.71 = [Fraction:71/100] ]
MA-KS2-Y5-FR-07recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
MA-KS2-Y5-FR-08round decimals with 2 decimal places to the nearest whole number and to 1 decimal place
MA-KS2-Y5-FR-09read, write, order and compare numbers with up to 3 decimal places
MA-KS2-Y5-FR-10solve problems involving number up to 3 decimal places
MA-KS2-Y5-FR-11recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction
MA-KS2-Y5-FR-12solve problems which require knowing percentage and decimal equivalents of [Fraction:1/2], [Fraction:1/4], [Fraction:1/5], [Fraction:2/5], [Fraction:4/5] and those fractions with a denominator of a multiple of 10 or 25

Teaching guidance (non-statutory)

MA-KS2-Y5-FR-N01Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions.
MA-KS2-Y5-FR-N02They extend their knowledge of fractions to thousandths and connect to decimals and measures.
MA-KS2-Y5-FR-N03Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions.
MA-KS2-Y5-FR-N04Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions > 1.
MA-KS2-Y5-FR-N05Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number.
MA-KS2-Y5-FR-N06Pupils continue to practise counting forwards and backwards in simple fractions.
MA-KS2-Y5-FR-N07Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities.
MA-KS2-Y5-FR-N08Pupils extend counting from year 4, using decimals and fractions including bridging 0, for example on a number line.
MA-KS2-Y5-FR-N09Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems.
MA-KS2-Y5-FR-N10They mentally add and subtract tenths, and one-digit whole numbers and tenths.
MA-KS2-Y5-FR-N11They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (for example, 0.83 + 0.17 = 1).
MA-KS2-Y5-FR-N12Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals.
MA-KS2-Y5-FR-N13Pupils should make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is [Fraction:1/100], 50% is [Fraction:50/100], 25% is [Fraction:25/100]) and relate this to finding ‘fractions of’.

Measurement7 objectives + 4 guidance

Pupils should be taught to:

MA-KS2-Y5-M-01convert between different units of metric measure [for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]
MA-KS2-Y5-M-02understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
MA-KS2-Y5-M-03measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
MA-KS2-Y5-M-04calculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes
MA-KS2-Y5-M-05estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]
MA-KS2-Y5-M-06solve problems involving converting between units of time
MA-KS2-Y5-M-07use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling

Teaching guidance (non-statutory)

MA-KS2-Y5-M-N01Pupils use their knowledge of place value and multiplication and division to convert between standard units.
MA-KS2-Y5-M-N02Pupils calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically, for example 4 + 2b = 20 for a rectangle of sides 2 cm and b cm and perimeter of 20cm.
MA-KS2-Y5-M-N03Pupils calculate the area from scale drawings using given measurements.
MA-KS2-Y5-M-N04Pupils use all 4 operations in problems involving time and money, including conversions (for example, days to weeks, expressing the answer as weeks and days).

Geometry - properties of shapes4 objectives + 3 guidance

Pupils should be taught to:

MA-KS2-Y5-G-01identify 3-D shapes, including cubes and other cuboids, from 2-D representations
MA-KS2-Y5-G-02know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
MA-KS2-Y5-G-03draw given angles, and measure them in degrees (°)
MA-KS2-Y5-G-04identify: angles at a point and 1 whole turn (total 360°); angles at a point on a straight line and half a turn (total 180°); other multiples of 90°; use the properties of rectangles to deduce related facts and find missing lengths and angles; distinguish between regular and irregular polygons based on reasoning about equal sides and angles

Teaching guidance (non-statutory)

MA-KS2-Y5-G-N01Pupils 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.
MA-KS2-Y5-G-N02Pupils use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools.
MA-KS2-Y5-G-N03Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems.

Geometry - position and direction1 objective + 1 guidance

Pupils should be taught to:

MA-KS2-Y5-GP-01identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed

Teaching guidance (non-statutory)

MA-KS2-Y5-GP-N01Pupils recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes.

Statistics2 objectives + 2 guidance

Pupils should be taught to:

MA-KS2-Y5-S-01solve comparison, sum and difference problems using information presented in a line graph
MA-KS2-Y5-S-02complete, read and interpret information in tables, including timetables

Teaching guidance (non-statutory)

MA-KS2-Y5-S-N01Pupils connect their work on coordinates and scales to their interpretation of time graphs.
MA-KS2-Y5-S-N02They begin to decide which representations of data are most appropriate and why.

Year 6

Number - number and place value4 objectives + 1 guidance

Pupils should be taught to:

MA-KS2-Y6-NPV-01read, write, order and compare numbers up to 10,000,000 and determine the value of each digit
MA-KS2-Y6-NPV-02round any whole number to a required degree of accuracy
MA-KS2-Y6-NPV-03use negative numbers in context, and calculate intervals across 0
MA-KS2-Y6-NPV-04solve number and practical problems that involve all of the above

Teaching guidance (non-statutory)

MA-KS2-Y6-NPV-N01Pupils use the whole number system, including saying, reading and writing numbers accurately.

Number - addition, subtraction, multiplication and division9 objectives + 6 guidance

Pupils should be taught to:

MA-KS2-Y6-ASMD-01multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
MA-KS2-Y6-ASMD-02divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
MA-KS2-Y6-ASMD-03divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
MA-KS2-Y6-ASMD-04perform mental calculations, including with mixed operations and large numbers
MA-KS2-Y6-ASMD-05identify common factors, common multiples and prime numbers
MA-KS2-Y6-ASMD-06use their knowledge of the order of operations to carry out calculations involving the 4 operations
MA-KS2-Y6-ASMD-07solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
MA-KS2-Y6-ASMD-08solve problems involving addition, subtraction, multiplication and division
MA-KS2-Y6-ASMD-09use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Teaching guidance (non-statutory)

MA-KS2-Y6-ASMD-N01Pupils practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division (see mathematics appendix 1 (PDF, 248KB)).
MA-KS2-Y6-ASMD-N02They undertake mental calculations with increasingly large numbers and more complex calculations.
MA-KS2-Y6-ASMD-N03Pupils continue to use all the multiplication tables to calculate mathematical statements in order to maintain their fluency.
MA-KS2-Y6-ASMD-N04Pupils round answers to a specified degree of accuracy, for example, to the nearest 10, 20, 50, etc, but not to a specified number of significant figures.
MA-KS2-Y6-ASMD-N05Pupils explore the order of operations using brackets; for example, 2 + 1 x 3 = 5 and (2 + 1) x 3 = 9.
MA-KS2-Y6-ASMD-N06Common factors can be related to finding equivalent fractions.

Number - Fractions (including decimals and percentages)11 objectives + 6 guidance

Pupils should be taught to:

MA-KS2-Y6-FR-01use common factors to simplify fractions; use common multiples to express fractions in the same denomination
MA-KS2-Y6-FR-02compare and order fractions, including fractions >1
MA-KS2-Y6-FR-03add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
MA-KS2-Y6-FR-04multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, [Fraction:1/4] × [Fraction:1/2] = [Fraction:1/8]]
MA-KS2-Y6-FR-05divide proper fractions by whole numbers [for example, [Fraction:1/3] ÷ 2 = [Fraction:1/6]]
MA-KS2-Y6-FR-06associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, [Fraction:3/8]]
MA-KS2-Y6-FR-07identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places
MA-KS2-Y6-FR-08multiply one-digit numbers with up to 2 decimal places by whole numbers
MA-KS2-Y6-FR-09use written division methods in cases where the answer has up to 2 decimal places
MA-KS2-Y6-FR-10solve problems which require answers to be rounded to specified degrees of accuracy
MA-KS2-Y6-FR-11recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

Teaching guidance (non-statutory)

MA-KS2-Y6-FR-N01Pupils 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 (for example, [Fraction:1/2]+[Fraction:1/8] = [Fraction:5/8]] and progress to varied and increasingly complex problems.
MA-KS2-Y6-FR-N02Pupils should use a variety of images to support their understanding of multiplication with fractions. This follows earlier work about fractions as operators (fractions of), as numbers, and as equal parts of objects, for example as parts of a rectangle. Pupils 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 (for example, if quarter of a length is 36cm, then the whole length is 36 × 4 = 144cm).
MA-KS2-Y6-FR-N03They practise calculations with simple fractions and decimal fraction equivalents to aid fluency, including listing equivalent fractions to identify fractions with common denominators.
MA-KS2-Y6-FR-N04Pupils can explore and make conjectures about converting a simple fraction to a decimal fraction (for example, 3 ÷ 8 = 0.375). For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context. Pupils multiply and divide numbers with up to 2 decimal places by one-digit and two-digit 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.
MA-KS2-Y6-FR-N05Pupils are introduced to the division of decimal numbers by one-digit whole numbers, initially, in practical contexts involving measures and money. They recognise division calculations as the inverse of multiplication.
MA-KS2-Y6-FR-N06Pupils 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.

Ratio and proportion4 objectives + 4 guidance

Pupils should be taught to:

MA-KS2-Y6-R-01solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts
MA-KS2-Y6-R-02solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison
MA-KS2-Y6-R-03solve problems involving similar shapes where the scale factor is known or can be found
MA-KS2-Y6-R-04solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

Teaching guidance (non-statutory)

MA-KS2-Y6-R-N01Pupils recognise proportionality in contexts when the relations between quantities are in the same ratio (for example, similar shapes and recipes).
MA-KS2-Y6-R-N02Pupils link percentages or 360° to calculating angles of pie charts.
MA-KS2-Y6-R-N03Pupils should consolidate their understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. They might use the notation a:b to record their work.
MA-KS2-Y6-R-N04Pupils solve problems involving unequal quantities, for example, ’for every egg you need 3 spoonfuls of flour’, ‘[Fraction:3/5] of the class are boys’. These problems are the foundation for later formal approaches to ratio and proportion.

Algebra5 objectives + 6 guidance

Pupils should be taught to:

MA-KS2-Y6-A-01use simple formulae
MA-KS2-Y6-A-02generate and describe linear number sequences
MA-KS2-Y6-A-03express missing number problems algebraically
MA-KS2-Y6-A-04find pairs of numbers that satisfy an equation with 2 unknowns
MA-KS2-Y6-A-05enumerate possibilities of combinations of 2 variables

Teaching guidance (non-statutory)

MA-KS2-Y6-A-N01Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:
MA-KS2-Y6-A-N02missing numbers, lengths, coordinates and angles
MA-KS2-Y6-A-N03formulae in mathematics and science
MA-KS2-Y6-A-N04equivalent expressions (for example, a + b = b + a)
MA-KS2-Y6-A-N05generalisations of number patterns
MA-KS2-Y6-A-N06number puzzles (for example, what 2 numbers can add up to)

Measurement7 objectives + 5 guidance

Pupils should be taught to:

MA-KS2-Y6-M-01solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate
MA-KS2-Y6-M-02use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3 decimal places
MA-KS2-Y6-M-03convert between miles and kilometres
MA-KS2-Y6-M-04recognise that shapes with the same areas can have different perimeters and vice versa
MA-KS2-Y6-M-05recognise when it is possible to use formulae for area and volume of shapes
MA-KS2-Y6-M-06calculate the area of parallelograms and triangles
MA-KS2-Y6-M-07calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³]

Teaching guidance (non-statutory)

MA-KS2-Y6-M-N01Pupils connect conversion (for example, from kilometres to miles) to a graphical representation as preparation for understanding linear/proportional graphs.
MA-KS2-Y6-M-N02They know approximate conversions and are able to tell if an answer is sensible.
MA-KS2-Y6-M-N03Using the number line, pupils use, add and subtract positive and negative integers for measures such as temperature.
MA-KS2-Y6-M-N04They relate the area of rectangles to parallelograms and triangles, for example, by dissection, and calculate their areas, understanding and using the formulae (in words or symbols) to do this.
MA-KS2-Y6-M-N05Pupils could be introduced to compound units for speed, such as miles per hour, and apply their knowledge in science or other subjects as appropriate.

Geometry - properties of shapes5 objectives + 3 guidance

Pupils should be taught to:

MA-KS2-Y6-G-01draw 2-D shapes using given dimensions and angles
MA-KS2-Y6-G-02recognise, describe and build simple 3-D shapes, including making nets
MA-KS2-Y6-G-03compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
MA-KS2-Y6-G-04illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
MA-KS2-Y6-G-05recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles

Teaching guidance (non-statutory)

MA-KS2-Y6-G-N01Pupils draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles.
MA-KS2-Y6-G-N02Pupils describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements.
MA-KS2-Y6-G-N03These relationships might be expressed algebraically for example, d = 2 × r; a = 180 − (b + c).

Geometry - position and direction2 objectives + 2 guidance

Pupils should be taught to:

MA-KS2-Y6-GP-01describe positions on the full coordinate grid (all 4 quadrants)
MA-KS2-Y6-GP-02draw and translate simple shapes on the coordinate plane, and reflect them in the axes

Teaching guidance (non-statutory)

MA-KS2-Y6-GP-N01Pupils draw and label a pair of axes in all 4 quadrants with equal scaling. This extends their knowledge of one quadrant to all 4 quadrants, including the use of negative numbers.
MA-KS2-Y6-GP-N02Pupils draw and label rectangles (including squares), parallelograms and rhombuses, specified by coordinates in the four quadrants, predicting missing coordinates using the properties of shapes. These might be expressed algebraically for example, translating vertex (a, b) to (a − 2, b + 3); (a, b) and (a + d, b + d) being opposite vertices of a square of side d.

Statistics2 objectives + 4 guidance

Pupils should be taught to:

MA-KS2-Y6-S-01interpret and construct pie charts and line graphs and use these to solve problems
MA-KS2-Y6-S-02calculate and interpret the mean as an average

Teaching guidance (non-statutory)

MA-KS2-Y6-S-N01Pupils connect their work on angles, fractions and percentages to the interpretation of pie charts.
MA-KS2-Y6-S-N02Pupils both encounter and draw graphs relating 2 variables, arising from their own enquiry and in other subjects.
MA-KS2-Y6-S-N03They should connect conversion from kilometres to miles in measurement to its graphical representation.
MA-KS2-Y6-S-N04Pupils know when it is appropriate to find the mean of a data set.

Practise Mathematics with free games

These games are aligned to the Mathematics national curriculum objectives above.

Times Tables

Multiplication & Division

Maths Challenge

Number - Four Operations

Number Mage

Number

Fraction Pizza

Fractions

Coin Shop

Measurement - Money

Balance Lab

Number Bonds

Bubble Pop

Addition

Star Forge

Place Value

Clock Tower

Measurement - Time

Data Explorer

Statistics

Data Detective

Statistics

Decimal Diner

Decimals

Symmetry Mirror

Geometry - Symmetry

Algebra Arena

Algebra

Coordinate Raiders

Position & Direction

Content sourced from the Mathematics programmes of study, Department for Education, published September 2013. Crown copyright. Each objective carries a reference code (e.g. MA-KS2-...) for identification. Verify any objective by searching the GOV.UK source page linked above. Last verified against GOV.UK: April 2026. About this data