Number place value Addition subtraction Multiplication division Fractions Measurement Properties of shapes Position direction YEAR count to across 00, forwards backwards, beginning with 0 or, or from any given number count, read write to 00 in numerals; count in multiples of twos, fives tens given a number, identify one more one less identify represent using objects pictorial representations including the number line, use the language of: equal to, more than, less than (fewer, most, least read write from to 20 in numerals words. read, write interpret mathematical statements involving addition (+, subtraction (- equals (= signs represent use number bonds related subtraction facts within 20 one-digit two-digit to 20, including zero solve one-step problems that involve addition subtraction, using concrete objects pictorial representations, missing number 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 (e.g. long/short, longer/shorter, tall/short, double/half mass or weight (e.g. heavy/light, heavier than, lighter than capacity/volume (full/empty, more than, less than, quarter time (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 such as: 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. taught recognise name common 2-D 3-D shapes, including: 2-D shapes (e.g. rectangles (including squares, circles triangles 3-D shapes (e.g. cuboids (including cubes, pyramids spheres. describe position, directions movements, including half, quarter threequarter turns.
Number place value Addition subtraction Multiplication division Fractions Measurement Properties of shapes Position direction YEAR 2 count in steps of 2, 3, 5 from 0, in tens from any number, forward or backward recognise the place value of each digit in a two-digit number (tens, ones identify, represent estimate using different representations, including the number line compare order from 0 up to 00; use <, > = signs read write to at least 00 in numerals in words use place value number facts to solve problems. taught 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 00 using concrete objects, pictorial representations, mentally, including: a two-digit number ones a two-digit number tens two two-digit adding three one-digit show that addition of two can be done in any order (commutative subtraction of one number from another cannot recognise use the inverse relationship between addition subtraction use this to check calculations missing number problems. taught recall use facts for the 2, 5 0 multiplication tables, including recognising odd even calculate mathematical statements for 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 number by another cannot involving multiplication division, using materials, arrays, repeated addition, mental methods, facts, including problems in contexts. recognise, find, name write fractions / 3, / 4, 2 / 4 3 /4 of a length, shape, set of objects or quantity write simple fractions e.g. / 2 of 6 = 3 recognise the equivalence of 2 / 4 /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 number of minutes in an hour the number of hours in a day taught identify describe the properties of 2-D shapes, including the number of sides symmetry in a vertical line identify describe the properties of 3-D shapes, including the number of edges, vertices faces identify 2-D shapes on the surface of 3-D shapes, for example a circle on a cylinder a triangle on a pyramid compare sort common 2-D 3-D shapes everyday objects. taught order arrange combinations of mathematical objects in patterns 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. taught interpret construct simple pictograms, tally charts, block diagrams simple tables ask answer simple questions by counting the number of objects in each category sorting the categories by quantity ask answer questions about totalling comparing categorical data. 2
Number place value Addition subtraction Multiplication division Fractions Measurement : Properties of shapes YEAR 3 count from 0 in multiples of 4, 8, 50 00; find 0 or 00 more or less than a given number recognise the place value of each digit in a three-digit number (hundreds, tens, ones compare order up to 000 identify, represent estimate using different representations read write up to 000 in numerals in words solve number problems practical problems involving these ideas. mentally, including: a three-digit number ones a three-digit number tens a three-digit number hundreds 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, including missing number problems, using number facts, place value, more complex addition subtraction. recall use facts for the 3, 4 8 multiplication tables write calculate mathematical statements for using the multiplication tables that they know, including for two-digit times one-digit, using mental progressing to formal written methods, including missing number problems, involving multiplication division, including 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 0 equal parts in dividing one-digit or quantities by 0 recognise, find write fractions of a discrete set of objects: unit fractions non-unit fractions with small denominators recognise use fractions as : unit fractions non-unit fractions with small denominators recognise show, using diagrams, equivalent fractions with small denominators fractions with the same denominator within one whole (e.g. 5 / 7 + / 7 = 6 / 7 compare order unit fractions, fractions with the same denominators 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 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, 2-hour 24-hour clocks estimate read time with increasing accuracy to the nearest minute; record compare time in terms of seconds, minutes, hours o clock; use vocabulary such as a.m./p.m., morning, afternoon, noon midnight know the number of seconds in a minute the number 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 3-D shapes using modelling materials; recognise 3-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 twostep questions such as How many more? How many fewer? using information presented in scaled bar charts pictograms tables. 3
Number place value Addition subtraction Multiplication division Fractions Measurement Properties of shape Position direction YEAR 4 taught to count in multiples of 6, 7, 9, 25 000 find 000 more or less than a given number count backwards through zero to include negative recognise the place value of each digit in a four-digit number (thouss, hundreds, tens, ones order compare beyond 000 identify, represent estimate using different representations round any number to the nearest 0, 00 or 000 solve number practical problems that involve all of the above with increasingly large positive read Roman numerals to 00 (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 2 2 use place value, known derived facts to multiply divide mentally, including: multiplying by 0 ; dividing by ; multiplying together three recognise use factor pairs commutativity in mental calculations multiply twodigit three-digit by a onedigit number using formal written layout 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 a hundred dividing tenths by ten. involving increasingly harder fractions to calculate quantities, fractions to divide quantities, including nonunit fractions where the answer is a whole number fractions with the same denominator recognise write decimal equivalents of any number of tenths or hundredths recognise write decimal equivalents to / 4 ; /2 ; 3 / 4 find the effect of dividing a one- or two-digit number by 0 00, identifying the value of the digits in the answer as ones, tenths hundredths round decimals with one decimal place to the nearest whole number compare with the same number 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 (e.g. kilometre to metre; hour to minute measure calculate the perimeter of a rectilinear figure (including 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 2 24-hour clocks 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. 4
Number place value Addition subtraction Multiplication division Fractions Measurement Properties of shape Position direction YEAR 5 read, write, order compare to at least 000 000 determine the value of each digit count forwards or backwards in steps of powers of 0 for any given number up to 000 000 interpret negative in context, count forwards backwards with positive negative whole through zero round any number up to 000 000 to the nearest 0, 00, 000, 0 000 00 000 solve number problems practical problems that involve all of the above read Roman numerals to 000 (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 number, common factors of two. know use the vocabulary of prime, prime factors composite (non-prime establish whether a number up to 00 is prime recall prime up to 9 multiply up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit multiply divide mentally drawing upon known facts divide up to 4 digits by a one-digit number using the formal written method of short division interpret remainders appropriately for the context multiply divide whole those involving decimals by 0, 00 000 recognise use square cube, the notation for squared ( 2 cubed ( 3 Solve problems involving addition, subtraction, multiplication division including using their knowledge of factors multiples, squares cubes involving addition, subtraction, multiplication division a combination of these, including understing the meaning of the equals sign involving, including scaling by simple fractions problems involving simple rates. compare order fractions whose denominators are all multiples of the same number 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 > as a mixed number (e.g. 2 /5 + 4 / 5 = 6 / 5 = / 5 fractions with the same denominator multiples of the same number multiply proper fractions mixed by whole, supported by materials diagrams read write decimal as fractions (e.g. 0.7 = 7 / 00 recognise use thousths relate them to tenths, hundredths decimal equivalents round decimals with two decimal places to the nearest whole number to one decimal place read, write, order compare with up to three decimal places involving number up to three decimal places recognise the per cent symbol (% underst that per cent relates to number of parts per hundred, write percentages as a fraction with denominator hundred, as a decimal fraction which require knowing percentage decimal equivalents of / 2, / 4, / 5, 2 / 5, 4 / 5 those with a denominator of a multiple of 0 or 25. taught convert between different units of metric measure (e.g. kilometre metre; centimetre metre; centimetre millimetre; gram kilogram; litre millilitre underst use 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 (including squares including using stard units, square centimetres (cm 2 square metres (m 2 estimate the area of irregular shapes estimate volume (e.g. using cm 3 blocks to build cubes cuboids capacity (e.g. using water involving converting between units of time use all four operations to solve problems involving measure (e.g. length, mass, volume, money using decimal notation including scaling. taught identify 3-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 360 o angles at a point on a straight line ½ a turn (total 80 o other multiples of 90 o 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. Pupils should be 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. 5
Number place value Addition, subtraction, algebra Fractions Ratio proportion Measurement Properties of shape Position direction YEAR 6 Pupils should be read, write, order compare up to 0 000 000 determine the value of each digit round any whole number to a required degree of accuracy use negative in context, calculate intervals across zero solve number practical problems that involve all of the above. multiply multi-digit up to 4 digits by a two-digit whole number using the formal written method of long multiplication divide up to 4 digits by a two-digit whole number using the formal written method of long division, interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for 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 involving addition, subtraction, use estimation to check answers to calculations determine, in the context of a problem, levels of accuracy. Algebra use simple formulae generate describe linear number sequences express missing number problems algebraically find pairs of that satisfy number sentences involving two unknowns enumerate all possibilities of combinations of two variables. use common factors to simplify fractions; use common multiples to express fractions in the same denomination compare order fractions, including fractions > fractions with different denominators mixed, using the concept of equivalent fractions multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. /4 / 2 = / 8 divide proper fractions by whole (e.g. / 3 2 = / 6 associate a fraction with division calculate decimal fraction equivalents (e.g. 0.375 for a simple fraction (e.g. 3 / 8 identify the value of each digit to three decimal places multiply divide by 0, 00 000 where the answers are 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 which require answers to be rounded to specified degrees of accuracy recall use equivalences between simple fractions, decimals percentages, including in different contexts. involving the relative sizes of two quantities where missing values can be found by using integer multiplication division facts involving the calculation of percentages (e.g. of measures such as 5% of 360 the use of percentages for comparison involving similar shapes where the scale factor is known or can be found involving unequal sharing grouping using knowledge of fractions multiples. 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 centimetre cubed (cm 3 cubic metres (m 3, extending to other units such as mm 3 km 3. taught draw 2-D shapes using given dimensions angles recognise, describe build simple 3-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. Pupils should be interpret construct pie charts line graphs use these to solve problems calculate interpret the mean as an average. 6