### Mathematics — Year 1

Number and Place Value

• 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

• 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

Multiplication and Division

• 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

Fractions

• 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

• 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 a Shape

• 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]

Gemoetry — Position and Direction

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

### Mathematics — Year 2

Number and Place Value

• 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

• 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
• 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

Multiplication and Division

• 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.

Fractions

• Recognise, find, name and write fractions 1/3, ¼, 2/4 and 3/4 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 1/2

Measurement

• 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 ℗; 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 a Shape

• 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

• 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 angles for quarter, half and three-quarter turns (clockwise and anti-clockwise).

Statistics

• 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

### Mathematics — Year 3

Number and Place Value

• 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

• 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

Multiplication and Division

• 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.

Fractions

• 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

• 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 a Shape

• 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

• 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

### Mathematics — Year 4

Number and Place Value

• 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

• 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.

Multiplication and Division

• 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.

Fractions and Decimals

• 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, 1/3
• 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

• 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 a Shape

• 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

• 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

• 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

### Mathematics — Year 5

Number and Place Value

• 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.

• 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

Multiplication and Division

• 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

Fractions, Decimals, and Percentages

• 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

• 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 a Shape

• 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

• 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

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

### Mathematics — Year 6

Number and Place Value

• 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.

Four Operations

• 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

Ratio and Proportion

• 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

• 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.

Fractions, Decimals, and Percentages

• 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 1/2 = 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.

Measurement

• 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 a Shape

• 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 at a point, are on a straight line, or are vertically opposite, and find missing angles.

Geometry — Position and Direction

• 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

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