Year 1 count to across 100, forwards backwards, beginning with 0 or 1, or from any given count, read write to 100 in numerals; count in multiples of twos, fives tens given a, identify one more one less identify represent using objects pictorial representations including the line, use the language of: equal to, more than, less than (fewer), most, least read write from 1 to 20 in numerals words. read, write interpret mathematical statements involving addition (+), subtraction ( ) equals (=) signs represent use bonds related subtraction facts within 20 add subtract onedigit two-digit to 20, including zero solve one-step problems that involve addition subtraction, using concrete objects pictorial representations, missing problems such as 7 = 9. solve one-step problems involving multiplication division, by calculating the answer using concrete objects, pictorial representations arrays with the support of the teacher. recognise, find name a half as one of two equal parts of an object, shape or quantity recognise, find name a quarter as one of four equal parts of an object, shape or quantity. compare, describe solve practical problems for: lengths heights [for example, long/short, longer/shorter, tall/short, double/half] mass/weight [for example, heavy/light, heavier than, lighter than] capacity volume [for example, full/empty, more than, less than, half, half full, quarter] time [for example, quicker, slower, earlier, later] measure begin to record the following: lengths heights mass/weight capacity volume time (hours, minutes, seconds) recognise know the value of different denominations of coins notes sequence events in chronological order using language [for example, before after, next, first, today, yesterday, tomorrow, morning, afternoon evening] recognise use language relating to dates, including days of the week, weeks, months years tell the time to the hour half past the hour draw the hs on a clock face to show these times. recognise name common 2-D -D shapes, including: 2-D shapes [for example, rectangles squares), circles triangles] -D shapes [for example, cuboids cubes), pyramids spheres]. describe position, direction movement, including whole, half, quarter three-quarter turns.
Year 2 count in steps of 2,, 5 from 0, in tens from any, forward backward recognise the place value of each digit in a two-digit (tens, ones) identify, represent estimate using different representations, including the line compare order from 0 up to 100; use <, > = signs read write to at least 100 in numerals in words use place value facts to solve problems. solve problems with addition subtraction: using concrete objects pictorial representations, including those involving, quantities measures applying their increasing knowledge of mental written methods recall use addition subtraction facts to 20 fluently, derive use related facts up to 100 add subtract using concrete objects, pictorial representations, mentally, including: a two-digit ones a two-digit tens two two-digit adding three one-digit show that addition of two can be done in any order (commutative) subtraction of one from another cannot recognise use the inverse relationship between addition subtraction use this to check calculations solve missing problems. recall use multiplication division facts for the 2, 5 10 multiplication tables, including recognising odd even calculate mathematical statements for multiplication division within the multiplication tables write them using the multiplication ( ), division ( ) equals (=) signs show that multiplication of two can be done in any order (commutative) division of one by another cannot solve problems involving multiplication division, using materials, arrays, repeated addition, mental methods, multiplication division facts, including problems in contexts. recognise, find, name write fractions 1/, 1/4, 2/4 /4 of a length, shape, set of objects or quantity write simple fractions for example,1/2 of 6 = recognise the equivalence of 2/4 1/2. choose use appropriate stard units to estimate 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 measuring vessels compare order lengths, mass, volume/capacity record the results using >, < = recognise use symbols for pounds ( ) 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 subtraction of money of the same unit, including giving change compare sequence intervals of time tell write the time to five minutes, including quarter past/to the hour draw the hs on a clock face to show these times know the of minutes in an hour the of hours in a day. identify describe the properties of 2-D shapes, including the of sides line symmetry in a vertical line identify describe the properties of -D shapes, including the of edges, vertices faces identify 2-D shapes on the surface of -D shapes, [for example, a circle on a cylinder a triangle on a pyramid] compare sort common 2-D -D shapes everyday objects. order arrange combinations of mathematical objects in patterns sequences use mathematical vocabulary to describe position, direction movement, including movement in a straight line distinguishing between rotation as a turn in terms of right angles for quarter, half three-quarter turns (clockwise anticlockwise). interpret construct simple pictograms, tally charts, block diagrams simple tables ask answer simple questions by counting the of objects in each category sorting the categories by quantity ask answer questions about totalling comparing categorical data.
Year count from 0 in multiples of 4, 8, 50 100; find 10 or 100 more or less than a given recognise the place value of each digit in a three-digit (hundreds, tens, ones) compare order up to 1000 identify, represent estimate using different representations read write up to 1000 in numerals in words solve problems practical problems involving these ideas. add subtract mentally, including: a three-digit ones a three-digit tens a three-digit hundreds add subtract with up to three digits, using formal written methods of columnar addition subtraction estimate the answer to a calculation use inverse operations to check answers solve problems, including missing problems, using facts, place value, more complex addition subtraction. recall use multiplication division facts for the, 4 8 multiplication tables write calculate mathematical statements for multiplication division using the multiplication tables that they know, including for two-digit times one-digit, using mental progressing to formal written methods solve problems, including missing problems, involving multiplication division, including positive integer scaling problems correspondence problems in which n objects are connected to m objects. count up down in tenths; recognise that tenths arise from dividing an object into 10 equal parts in dividing onedigit or quantities by 10 recognise, find write fractions of a discrete set of objects: unit fractions nonunit fractions with small denominators recognise use fractions as : unit fractions nonunit fractions with small denominators recognise show, using diagrams, equivalent fractions with small denominators add subtract denominator within one whole [for example, 5/7 + 1/7 = 6/7] compare order unit fractions, denominators solve problems that involve all of the above. measure, compare, add subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml) measure the perimeter of simple 2-D shapes add subtract amounts of money to give change, using both p in practical contexts tell write the time from an analogue clock, including using Roman numerals from I to XII, 12-hour 24-hour clocks estimate read time with increasing accuracy to the nearest minute; record compare time in terms of seconds, minutes hours; use vocabulary such as o clock, a.m./p.m., morning, afternoon, noon midnight know the of seconds in a minute the of days in each month, year leap year compare durations of events [for example to calculate the time taken by particular events or tasks]. draw 2-D shapes make -D shapes using modelling materials; recognise -D shapes in different orientations 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 four a complete turn; identify whether angles are greater than or less than a right angle identify horizontal vertical lines pairs of perpendicular parallel lines. interpret present data using bar charts, pictograms tables solve one-step two-step questions [for example, How many more? How many fewer? ] using information presented in scaled bar charts pictograms tables.
Year 4 count in multiples of 6, 7, 9, 25 1000 find 1000 more or less than a given count backwards through zero to include negative recognise the place value of each digit in a four-digit (thouss, hundreds, tens, ones) order compare beyond 1000 identify, represent estimate using different representations round any to the nearest 10, 100 or 1000 solve practical problems that involve all of the above with increasingly large positive read Roman numerals to 100 (I to C) know that over time, the numeral system changed to include the concept of zero place value. add subtract with up to 4 digits using the formal written methods of columnar addition subtraction where appropriate estimate use inverse operations to check answers to a calculation solve addition subtraction two-step problems in contexts, deciding which operations methods to use why. recall multiplication division facts for multiplication tables up to 12 12 use place value, known derived facts to multiply divide mentally, including: multiplying by 0 1; dividing by 1; multiplying together three recognise use factor pairs commutativity in mental calculations multiply two-digit three-digit by a one-digit using formal written layout solve problems involving multiplying adding, including using the distributive law to multiply two digit by one digit, integer scaling problems harder correspondence problems such as n objects are connected to m objects. recognise show, using diagrams, families of common equivalent fractions count up down in hundredths; recognise that hundredths arise when dividing an object by one hundred dividing tenths by ten. solve problems involving increasingly harder fractions to calculate quantities, fractions to divide quantities, including nonunit fractions where the answer is a whole add subtract denominator recognise write decimal equivalents of any of tenths or hundredths recognise write decimal equivalents to 1/4,1/2, /4 find the effect of dividing a one- or twodigit by 10 100, identifying the value of the digits in the answer as ones, tenths hundredths round decimals with one decimal place to the nearest whole compare with the same of decimal places up to two decimal places solve simple measure money problems involving fractions decimals to two decimal places. Convert between different units of measure [for example, kilometre to metre; hour to minute] measure calculate the perimeter of a rectilinear figure squares) in centimetres metres find the area of rectilinear shapes by counting squares estimate, compare calculate different measures, including money in pounds pence read, write convert time between analogue digital 12-24-hour clocks solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days. compare classify geometric shapes, including quadrilaterals triangles, based on their properties sizes identify acute obtuse angles compare 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. 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 up/down plot specified points draw sides to complete a given polygon. interpret present discrete continuous data using appropriate graphical methods, including bar charts time graphs. solve comparison, sum difference problems using information presented in bar charts, pictograms, tables other graphs.
Year 5 read, write, order compare to at least 1 000 000 determine the value of each digit count forwards or backwards in steps of powers of 10 for any given up to 1 000 000 interpret negative in context, count forwards backwards with positive negative whole, including through zero round any up to 1 000 000 to the nearest 10, 100, 1000, 10 000 100 000 solve problems practical problems that involve all of the above read Roman numerals to 1000 (M) recognise years written in Roman numerals. add subtract whole with more than 4 digits, including using formal written methods (columnar addition subtraction) add subtract mentally with increasingly large use rounding to check answers to calculations determine, in the context of a problem, levels of accuracy solve addition subtraction multi-step problems in contexts, deciding which operations methods to use why. identify multiples factors, including finding all factor pairs of a, common factors of two know use the vocabulary of prime, prime factors composite (non-prime) establish whether a up to 100 is prime recall prime up to 19 multiply up to 4 digits by a one- or twodigit using a formal written method, including long multiplication for twodigit multiply divide mentally drawing upon known facts divide up to 4 digits by a one-digit using the formal written method of short division interpret remainders appropriately for the context multiply divide whole those involving decimals by 10, 100 1000 recognise use square cube, the notation for squared ( ) cubed 2 ( ) solve problems involving multiplication division including using their knowledge of factors multiples, squares cubes solve problems involving addition, subtraction, multiplication division a combination of these, including understing the meaning of the equals sign solve problems involving multiplication division, including scaling by simple fractions problems involving simple rates. & compare order fractions whose denominators are all multiples of the same identify, name write equivalent fractions of a given fraction, represented visually, including tenths hundredths recognise mixed improper fractions convert from one form to the other write mathematical statements > 1 as a mixed [for example, 2/5 + 4/5 = 6/5 = 1 1/5 ] add subtract denominator denominators that are multiples of the same multiply proper fractions mixed by whole, supported by materials diagrams read write decimal as fractions [for example, 0.71 = 71/100 ] recognise use thousths relate them to tenths, hundredths decimal equivalents round decimals with two decimal places to the nearest whole to one decimal place read, write, order compare with up to three decimal places solve problems involving up to three decimal places recognise the per cent symbol (%) underst that per cent relates to of parts per hundred, write percentages as a fraction with denominator 100, as a decimal solve problems which require knowing percentage decimal equivalents of 1/2, 1/4, 1/5,2/5, 4/5 those fractions with a denominator of a multiple of 10 or 25. convert between different units of metric measure (for example, kilometre metre; centimetre metre; centimetre millimetre; gram kilogram; litre millilitre) underst use approximate equivalences between metric units common imperial units such as inches, pounds pints measure calculate the perimeter of composite rectilinear shapes in centimetres metres calculate compare the area of rectangles squares), including using stard units, square centimetres (cm ) square metres (m ) estimate the area of irregular shapes estimate volume [for example, using 1 cm blocks to build cuboids cubes)] 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. 2 2 identify -D shapes, including cubes other cuboids, from 2-D representations know angles are measured in degrees: estimate compare acute, obtuse reflex angles draw given angles, measure them in degrees (o) identify: angles at a point one whole turn (total 60o) angles at a point on a straight line 2 1 a turn (total 180o) other multiples of 90o use the properties of rectangles to deduce related facts find missing lengths angles distinguish between regular irregular polygons based on reasoning about equal sides angles. identify, describe represent the position of a shape following a reflection or translation, using the appropriate language, know that the shape has not changed. solve comparison, sum difference problems using information presented in a line graph complete, read interpret information in tables, including timetables.
Year 6 read, write, order compare up to 10 000 000 determine the value of each digit round any whole to a required degree of accuracy use negative in context, calculate intervals across zero solve practical problems that involve all of the above. multiply multi-digit up to 4 digits by a twodigit whole using the formal written method of long multiplication divide up to 4 digits by a two-digit whole using the formal written method of long division, interpret remainders as whole remainders, fractions, or by rounding, as appropriate for the context divide up to 4 digits by a two-digit using the formal written method of short division where appropriate, interpreting remainders according to the context perform mental calculations, including with mixed operations large identify common factors, common multiples prime use their knowledge of the order of operations to carry out calculations involving the four operations solve addition subtraction multi-step problems in contexts, deciding which operations methods to use why solve problems involving addition, subtraction, multiplication division use estimation to check answers to calculations determine, in the context of a problem, an appropriate degree of accuracy. use common factors to simplify fractions; use common multiples to express fractions in the same denomination compare order fractions, including fractions > 1 add subtract fractions with different denominators mixed, using the concept of equivalent fractions multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 x 1/2 = 1/8] divide proper fractions by whole [for example, 1/ 2 = 1/6 ] associate a fraction with division calculate decimal fraction equivalents [for example, 0.75] for a simple fraction [for example, /8 ] identify the value of each digit in given to three decimal places multiply divide by 10, 100 1000 giving answers up to three decimal places multiply one-digit with up to two decimal places by whole 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 use equivalences between simple fractions, decimals percentages, including in different contexts. solve problems involving the calculation conversion of units of measure, using decimal notation up to three decimal places where appropriate use, read, write convert between stard units, converting measurements of length, mass, volume time from a smaller unit of measure to a larger unit, vice versa, using decimal notation to up to three decimal places convert between miles kilometres recognise that shapes with the same areas can have different perimeters vice versa recognise when it is possible to use formulae for area volume of shapes calculate the area of parallelograms triangles calculate, estimate compare volume of cubes cuboids using stard units, including cubic centimetres (cm ) cubic metres (m ), extending to other units [for example, mm km ]. draw 2-D shapes using given dimensions angles recognise, describe build simple -D shapes, including making nets compare classify geometric shapes based on their properties sizes find unknown angles in any triangles, quadrilaterals, regular polygons illustrate name parts of circles, including radius, diameter circumference 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, find missing angles. describe positions on the full coordinate grid (all four quadrants) draw translate simple shapes on the coordinate plane, reflect them in the axes. interpret construct pie charts line graphs use these to solve problems calculate interpret the mean as an average. solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication division facts solve problems involving the calculation of percentages [for example, of measures, such as 15% of 60] 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 grouping using knowledge of fractions multiples. Algebra use simple formulae generate describe linear sequences express missing problems algebraically find pairs of that satisfy an equation with two unknowns enumerate possibilities of combinations of two variables.