Skip to content ↓

Early Years Programme of Study

By the end of the Foundation Stage the children should have attained the expected level for a child over 60 months of age, which is the Early Learning Goal, in both Number and Shape, Space and Measures.

Number

Pupils will be taught to:

  • Count reliably with numbers from 1-20, place them in order and say which number is one more or one less than a given number.
  • Using quantities and objects, add and subtract two single-digit numbers and count on or back to find the answer.
  • Solve problems, including doubling, halving and sharing.

Shape, Space and Measure

Pupils will be taught to:

  • Use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems.
  • Recognise, create and describe patterns.
  • Explore characteristics of everyday objects and shapes and use mathematical language to describe them.

Year 1 Programme of Study 

Number – number and place value

Pupils will be taught to:

  • Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.
  • Count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens.
  • Given a number, identify one more and one less.
  • Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least.
  • Read and write numbers from 1 to 20 in numerals and words.

Number – addition and subtraction

Pupils will be taught to:

  • Read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs.
  • Represent and use number bonds and related subtraction facts within 20.
  • Add and subtract one-digit and two-digit numbers to 20, including zero.
  • Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = _– 9.

Number – multiplication and division

Pupils will be taught to:

  • Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Number – fractions

Pupils will be taught to:

  • Recognise, find and name a half as one of two equal parts of an object, shape or quantity.
  • Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

Measurement

Pupils will be taught to:

  • Compare, describe and solve practical problems for:
    • lengths and heights [for example, long/short, longer/shorter, tall/short, double/half] .
  • Mass/weight [for example, heavy/light, heavier than, lighter than].
  • Capacity and volume [for example, full/empty, more than, less than, half, half full, quarter].
  • Time [for example, quicker, slower, earlier, later].
  • Measure and begin to record the following:
    • Lengths and heights.
    • Mass/weight.
    • Capacity and volume.
    • Time (hours, minutes, seconds).
  • Recognise and know the value of different denominations of coins and notes.
  • Sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening].
  • Recognise and use language relating to dates, including days of the week, weeks, months and years.
  • Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

Geometry – properties of shapes

Pupils will be taught to:

  • Recognise and name common 2-D and 3-D shapes, including:
    • 2-D shapes [for example, rectangles (including squares), circles and triangles].
    • 3-D shapes [for example, cuboids (including cubes), pyramids and spheres].

Geometry – position and direction

Pupils will be taught to:

  • Describe position, direction and movement, including whole, half, quarter and three-quarter turns.

Year 2 Programme of Study

Number – number and place value

Pupils will be taught to:

  • count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
  • recognise the place value of each digit in a two-digit number (tens, ones)
  • identify, represent and estimate numbers using different representations, including the number line
  • compare and order numbers from 0 up to 100; use <, > and = signs
  • read and write numbers to at least 100 in numerals and in words
  • use place value and number facts to solve problems.

Number – addition and subtraction

Pupils will be taught to:

  • solve problems with addition and subtraction:
  • using concrete objects and pictorial representations, including those involving numbers, quantities and measures
  • applying their increasing knowledge of mental and written methods
  • recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
  • add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
  • a two-digit number and ones
  • a two-digit number and tens
  • two two-digit numbers
  • adding three one-digit numbers
  • show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
  • recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.

Number – multiplication and division

Pupils will be taught to:

  • recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
  • calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
  • show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
  • solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

Number – fractions

Pupils will be taught to:

  • recognise, find, name and write fractions 1/3, ¼, 2/4, and ¾ of a length, shape, set of objects or quantity
  • write simple fractions for example ½ of 6 = 3 and recognise the equivalence of 2/4 and ½

Measurement

Pupils will be taught to:

  • choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
  • compare and order lengths, mass, volume/capacity and record the results using >, < and =
  • recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value
  • find different combinations of coins that equal the same amounts of money
  • solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change
  • compare and sequence intervals of time
  • tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times
  • know the number of minutes in an hour and the number of hours in a day.

Geometry – properties of shapes

Pupils will be taught to:

  • identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line
  • identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
  • identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
  • compare and sort common 2-D and 3-D shapes and everyday objects.

Geometry – position and direction

Pupils will be taught to:

  • order and arrange combinations of mathematical objects in patterns and sequences
  • use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right

Statistics

Pupils will be taught to:

  • interpret and construct simple pictograms, tally charts, block diagrams and simple tables
  • ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity
  • ask and answer questions about totalling and comparing categorical data.

Year 3 Programme of Study

Number – number and place value

Pupils will be taught to:

  • count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number
  • recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
  • compare and order numbers up to 1000
  • identify, represent and estimate numbers using different representations
  • read and write numbers up to 1000 in numerals and in words
  • solve number problems and practical problems involving these ideas.

Number – addition and subtraction

Pupils will be taught to:

  • add and subtract numbers mentally, including:
  • a three-digit number and ones
  • a three-digit number and tens
  • a three-digit number and hundreds
  • add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction
  • estimate the answer to a calculation and use inverse operations to check answers
  • solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

Number – multiplication and division

Pupils will be taught to:

  • recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
  • write 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
  • solve 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.

Number – fractions

Pupils will be taught to:

  • count 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
  • recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
  • recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
  • recognise and show, using diagrams, equivalent fractions with small denominators
  • add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7]
  • compare and order unit fractions, and fractions with the same denominators
  • solve problems that involve all of the above.

Measurement

Pupils will be taught to:

  • measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
  • measure the perimeter of simple 2-D shapes
  • add and subtract amounts of money to give change, using both £ and p in practical contexts
  • tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks
  • estimate 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, a.m./p.m., morning, afternoon, noon and midnight
  • know the number of seconds in a minute and the number of days in each month, year and leap year
  • compare durations of events [for example to calculate the time taken by particular events or tasks].

Geometry – properties of shapes

Pupils will be taught to:

  • draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
  • recognise angles as a property of shape or a description of a turn
  • identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle
  • identify horizontal and vertical lines and pairs of perpendicular and parallel lines.

Statistics

Pupils will be taught to:

  • interpret and present data using bar charts, pictograms and tables
  • solve 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.

Year 4 Programme of Study

Number – number and place value

Pupils will be taught to:

  • count in multiples of 6, 7, 9, 25 and 1000
  • find 1000 more or less than a given number
  • count backwards through zero to include negative numbers
  • recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
  • order and compare numbers beyond 1000
  • identify, represent and estimate numbers using different representations
  • round any number to the nearest 10, 100 or 1000
  • solve number and practical problems that involve all of the above and with increasingly large positive numbers
  • read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.

Number – addition and subtraction

Pupils will be taught to:

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

Number – multiplication and division

Pupils will be taught to:

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

Number – fractions (including decimals)

Pupils will be taught to:

  • recognise and show, using diagrams, families of common equivalent fractions
  • count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
  • solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
  • add and subtract fractions with the same denominator
  • recognise and write decimal equivalents of any number of tenths or hundredths
  • recognise and write decimal equivalents to ¼, ½ and ¾
  • find 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
  • round decimals with one decimal place to the nearest whole number
  • compare numbers with the same number of decimal places up to two decimal places
  • solve simple measure and money problems involving fractions and decimals to two decimal places.

Measurement

Pupils will be taught to:

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

Geometry – properties of shapes

Pupils will be taught to:

  • compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
  • identify acute and obtuse angles and compare and order angles up to two right angles by size
  • identify lines of symmetry in 2-D shapes presented in different orientations
  • complete a simple symmetric figure with respect to a specific line of symmetry.

Geometry – position and direction

Pupils will be taught to:

  • describe positions on a 2-D grid as coordinates in the first quadrant
  • describe movements between positions as translations of a given unit to the left/right and up/down
  • plot specified points and draw sides to complete a given polygon.

Statistics

Pupils will be taught to:

  • interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.
  • solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

Year 5 Programme of Study

 Number – number and place value

Pupils will be taught to:

  • read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
  • count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
  • interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
  • round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
  • solve number problems and practical problems that involve all of the above
  • read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Number – addition and subtraction

Pupils will be taught to:

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

Number – multiplication and division

Pupils will be taught to:

  • identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
  • know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
  • establish whether a number up to 100 is prime and recall prime numbers up to 19
  • multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
  • multiply and divide numbers mentally drawing upon known facts
  • divide 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
  • multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
  • recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)
  • solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes
  • solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
  • solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Number – fractions (including decimals and percentages)

Pupils will be taught to:

  • compare and order fractions whose denominators are all multiples of the same number
  • identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
  • recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 1 1/5
  • add and subtract fractions with the same denominator and denominators that are multiples of the same number
  • multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
  • read and write decimal numbers as fractions [for example, 0.71 = 71/100]
  • recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
  • round decimals with two decimal places to the nearest whole number and to one decimal place
  • read, write, order and compare numbers with up to three decimal places
  • solve problems involving number up to three decimal places
  • recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal
  • solve problems which require knowing percentage and decimal equivalents of ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.

Measurement

Pupils will be taught to:

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

Geometry – properties of shapes

Pupils will be taught to:

  • identify 3-D shapes, including cubes and other cuboids, from 2-D representations
  • know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
  • draw given angles, and measure them in degrees (o)
  • identify:

- angles at a point and one whole turn (total 360o)

- angles at a point on a straight line and ½ a turn (total 180o)

- other multiples of 90o

  • 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.

Geometry – position and direction

Pupils will be taught to:

  • identify, 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.

Statistics

Pupils will be taught to:

  • solve comparison, sum and difference problems using information presented in a line graph
  • complete, read and interpret information in tables, including timetables.

Year 6 Programme of Study

Number – number and place value

Pupils will be taught to:

  • read, write, order and compare numbers up to 10 000 000 and determine the value of each digit
  • round any whole number to a required degree of accuracy
  • use negative numbers in context, and calculate intervals across zero
  • solve number and practical problems that involve all of the above.

Number – addition, subtraction multiplication and division

Pupils will be taught to:

  • multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
  • divide 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
  • divide 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
  • perform mental calculations, including with mixed operations and large numbers
  • identify common factors, common multiples and prime numbers
  • use their knowledge of the order of operations to carry out calculations involving the four operations
  • solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
  • solve problems involving addition, subtraction, multiplication and division
  • use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

Number – fractions (including decimals and percentages)

Pupils will be taught to:

  • use common factors to simplify fractions; use common multiples to express fractions in the same denomination
  • compare and order fractions, including fractions > 1
  • add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
  • multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ¼ x ½ = 1/8]
  • divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]
  • associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8]
  • identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places
  • multiply one-digit numbers with up to two decimal places by whole numbers
  • use written division methods in cases where the answer has up to two decimal places
  • solve problems which require answers to be rounded to specified degrees of accuracy
  • recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

Ratio and proportion

Pupils will be taught to:

  • solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
  • solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison
  • solve problems involving similar shapes where the scale factor is known or can be found
  • solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Algebra

Pupils will be taught to:

  • use simple formulae
  • generate and describe linear number sequences
  • express missing number problems algebraically
  • find pairs of numbers that satisfy an equation with two unknowns
  • enumerate possibilities of combinations of two variables.

Measurement

Pupils will be taught to:

  • solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
  • use, 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 three decimal places
  • convert between miles and kilometres
  • recognise that shapes with the same areas can have different perimeters and vice versa
  • recognise when it is possible to use formulae for area and volume of shapes
  • calculate the area of parallelograms and triangles
  • calculate, 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].

Geometry – properties of shapes

Pupils will be taught to:

  • draw 2-D shapes using given dimensions and angles
  • recognise, describe and build simple 3-D shapes, including making nets
  • compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
  • illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
  • recognise angles where they meet

Geometry – position and direction

Pupils will be taught to:

  • describe positions on the full coordinate grid (all four quadrants)
  • draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

Statistics

Pupils will be taught to:

  • interpret and construct pie charts and line graphs and use these to solve problems
  • calculate and interpret the mean as an average.