Maths Year 1 Programme of Study. Fractions Measurement Geometry properties of shape. Number Place Value and Rounding. Statistics


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1 Maths Year 1 Programme of Study Value count to across 100, forwards backwards, beginning with 0 or 1, or from any given count, read write s to 100 in numerals; count in multiples of 2s, 5s 10s given a, identify 1 more 1 less identify represent s using objects pictorial representations the line, use the language of: equal to, more than, less than (fewer), most, least read write s from 1 to 20 in numerals words Addition read, write interpret statements involving addition (+), subtraction ( ) equals (=) signs represent use bonds related subtraction facts within 20 add subtract onedigit twodigit s to 20, 0 solve onestep problems that involve addition subtraction, using concrete objects pictorial representations, missing problems such as 7 =? 9 Multiplication solve onestep problems involving multiplication division, by calculating the answer using concrete objects, pictorial representations arrays with the support of the teacher Fractions Measurement Geometry properties of shape recognise, find name a half as 1 of 2 equal parts of an object, shape or quantity recognise, find name a quarter as 1 of 4 equal parts of an object, shape or quantity compare, describe solve practical problems for: o lengths heights [for example, long/short, longer/shorter, tall/short, double/half] o mass/weight [for example, heavy/light, heavier than, lighter than] o capacity volume [for example, full/empty, more than, less than, half, half full, quarter] o time [for example, quicker, slower, earlier, later] measure begin to record the following: o lengths heights o mass/weight o capacity volume o time (hours, minutes, seconds) o recognise know the value of denominations of coins notes o 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, 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 2D 3D shapes, : o 2D shapes [for example, rectangles ( squares), circles triangles] o 3D shapes [for example, cuboids ( cubes), pyramids spheres] describe position,, whole, half, quarter threequarter turns N/A
2 Maths Year 2 Programme of Study Value Addition count in steps of 2, 3, 5 from solve problems with addition subtraction: 0, in 10s from o using concrete any, forward backward recognise the objects pictorial representations, those involving s, quantities measures place value of o applying their each digit in a twodigit increasing knowledge of mental written methods (10s, 1s) identify, represent estimate recall use addition subtraction facts to 20 fluently, derive use related facts up to 100 s using representations, the add subtract s using concrete objects, pictorial representations, mentally, : line compare o a twodigit 1s order s from 0 up to 100; o a twodigit 10s use <, > = o 2 twodigit s signs read write o adding 3 onedigit s s to at least 100 in numerals in words use place value show that addition of 2 s can be done in any order (commutative) subtraction of 1 from another cannot facts recognise use the inverse to solve problems relationship between addition subtraction use this to check calculations solve missing problems Multiplication recall use multiplication division facts for the 2, 5 10 multiplication tables, recognising odd even s calculate statements for multiplication division within the multiplication tables write them using the multiplication ( ), division ( ) equals (=) signs show that multiplication of 2 s can be done in any order (commutative) division of 1 by another cannot involving multiplication division, using materials, arrays, repeated addition, mental methods, multiplication division facts, problems in contexts Fractions Measurement Geometry properties of shape recognise, find, name write fractions,, of a length, shape, set of objects or quantity write fractions, for example of 6 = 3 recognise the equivalence of choose use appropriate stard units to estimate measure length/height in any (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 combinations of coins that equal the same amounts of money solve problems in a practical context involving addition subtraction of money of the same unit, giving change compare sequence intervals of time tell write the time to five minutes, 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, the of sides, line symmetry in a vertical line identify describe the properties of 3 D shapes, the of edges, vertices faces identify 2D shapes on the surface of 3D shapes, [for example, a circle on a cylinder a triangle on a pyramid] compare sort common 2 D 3D shapes everyday objects order arrange combinations of objects in patterns sequences use vocabulary to describe position,, in a straight line distinguishing between rotation as a turn in terms of right angles for quarter, half threequarter turns (clockwise anticlockwise) interpret construct pictograms, tally charts, block diagrams tables ask answer questions by counting the of objects in each category sorting the categories by quantity askanswer questions about totalling comparing categorical data
3 Maths Year 3 Programme of Study Value count from 0 in multiples of 4, 8, ; find 10 or 100 more or less than a given recognise the place value of each digit in a 3digit (100s, 10s, 1s) compare order s up to 1,000 identify, represent estimate s using representations read write s up to 1,000 in numerals in words solve problems practical problems involving these ideas Addition add subtract s mentally, : o a threedigit 1s o a threedigit 10s o a threedigit 100s add subtract s with up to 3 digits, using formal written methods of columnar addition subtraction estimate the answer to a calculation use inverse operations to check answers solve problems, missing problems, using facts, place value, more complex addition subtraction Multiplication recall use multiplication division facts for the 3, 4 8 multiplication tables write calculate statements for multiplication division using the multiplication tables that they know, for twodigit s times onedigit s, using mental progressing to formal written methods, missing problems, involving multiplication division, positive integer scaling problems correspondence problems in which n objects are connected to m objects Fractions Measurement Geometry properties of shape count up down in tenths; recognise that tenths arise from dividing an object into 10 equal parts in dividing onedigit s 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 s: unit fractions nonunit fractions with small denominators recognise show, using diagrams, equivalent fractions with small denominators add subtract fractions with the same denominator within one whole [for example, + = ] compare order unit fractions, fractions with the same 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 2D shapes add subtract amounts of money to give change, using both p in practical contexts tell write the time from an analogue clock, using Roman numerals from I to XII, 12hour 24hour 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, am/pm, 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 2D shapes make 3D shapes using modelling materials; recognise 3D shapes in orientations describe them recognise angles as a property of shape or a description of a turn identify right angles, recognise that 2 right angles make a halfturn, 3 make threequarters of a turn 4 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 onestep twostep questions [for example How many more? How many fewer? ] using information presented in scaled bar charts pictograms tables St
4 Maths Year 4 Programme of Study Value count in multiples of 6, 7, 9, 25 1,000 find 1,000 more or less than a given count backwards through 0 to include negative s recognise the place value of each digit in a fourdigit (1,000s, 100s, 10s, 1s) order compare s beyond 1,000 identify, represent estimate s using representations round any to the nearest 10, 100 or 1,000 solve practical problems that involve all of the above with increasingly large positive s read Roman numerals to 100 (I to C) know that over time, the numeral system changed to include the concept of 0 place value Addition add subtract s 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 twostep problems in contexts, deciding which operations methods to use why Multiplication recall multiplication division facts for multiplication tables up to use place value, known derived facts to multiply divide mentally, : multiplying by 0 1; dividing by 1; multiplying together 3 s recognise use factor pairs commutativity in mental calculations multiply twodigit threedigit s by a onedigit using formal written layout involving multiplying adding, using the distributive law to multiply twodigit s by 1 digit, integer scaling problems harder correspondence problems such as n objects are connected to m objects Fractions ( decimals, percentages ratio, proportion probability in years 4,5 6) recognise show, using diagrams, families of common equivalent fractions count up down in hundredths; recognise that hundredths arise when dividing an object by 100 dividing tenths by 10 solve problems involving increasingly harder fractions to calculate quantities, fractions to divide quantities, nonunit fractions where the answer is a whole add subtract fractions with the same denominator recognise write decimal equivalents of any of tenths or hundreds recognise write decimal equivalents to,, find the effect of dividing a one or twodigit by , identifying the value of the digits in the answer as ones, tenths hundredths round decimals with 1 decimal place to the nearest whole compare s with the same of decimal places up to 2 decimal places solve measure money problems involving fractions decimals to 2 decimal places Measurement Geometry properties of shape convert between 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 measures, money in pounds pence read, write convert time between analogue digital hour clocks involving converting from hours to minutes, minutes to seconds, years to months, weeks to days compare classify geometric shapes, quadrilaterals triangles, based on their properties sizes identify acute obtuse angles compare order angles up to 2 right angles by size identify lines of symmetry in 2D shapes presented in orientations complete a symmetric figure with respect to a specific line of symmetry describe positions on a 2D grid as coordinates in the first quadrant describe s 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, bar charts time graphs solve comparison, sum difference problems using information presented in bar charts, pictograms, tables other graphs
5 Maths Year 5 Programme of Study Value read, write, order compare s 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 s in context, count forwards backwards with positive negative whole s, through 0 round any up to 1,000,000 to the nearest 10, 100, 1,000, 10, ,000 solve problems practical problems that involve all of the above read Roman numerals to 1,000 (M) recognise years written in Roman numerals Addition add subtract whole s with more than 4 digits, using formal written methods (columnar addition subtraction) add subtract s mentally with increasingly large s use rounding to check answers to calculations determine, in the context of a problem, levels of accuracy solve addition subtraction multistep problems in contexts, deciding which operations methods to use why Multiplication identify multiples factors, finding all factor pairs of a, common factors of 2 s know use the vocabulary of prime s, prime factors composite (nonprime) s establish whether a up to 100 is prime recall prime s up to 19 multiply s up to 4 digits by a one or twodigit using a formal written method, long multiplication for twodigit s multiply divide s mentally, drawing upon known facts divide s up to 4 digits by a onedigit using the formal written method of short division interpret remainders appropriately for the context Fractions ( decimals, percentages ratio, proportion probability in years 4,5 6) compare order fractions whose denominators are all multiples of the same identify, name write equivalent fractions of a given fraction, represented visually, tenths hundredths recognise mixed s improper fractions convert from one form to the other write statements > 1 as a mixed [for example, + = = 1 ] add subtract fractions with the same denominator, denominators that are multiples of the same multiply proper fractions mixed s by whole s, supported by materials diagrams read write decimal s as Measurement convert between 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), using stard units, square centimetres (cm²) square metres (m²), estimate the area of irregular shapes estimate volume [for example, using 1 cm³ blocks to build cuboids ( cubes)] capacity [for example, using water] Geometry properties of shape identify 3D shapes, cubes other cuboids, from 2D representations know angles are measured in degrees: estimate compare acute, obtuse reflex angles draw given angles, measure them in degrees ( ) identify: o angles at a point 1 whole turn (total 360 ) o angles at a point on a straight line half a turn (total 180 ) o other multiples of 90 o use the properties of rectangles to deduce related facts find missing lengths angles o distinguish between regular irregular polygons based on reasoning 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, timetables
6 multiply divide whole s those involving decimals by 10, 100 1,000 recognise use square s cube s, the notation for squared (²) cubed (³) involving multiplication division, using their knowledge of factors multiples, squares cubes involving addition, subtraction, multiplication division a combination of these, understing the meaning of the equals sign involving multiplication division, scaling by fractions problems involving rates fractions [for example, 0.71 = ] recognise use thousths relate them to tenths, hundredths decimal equivalents round decimals with 2 decimal places to the nearest whole to 1 decimal place read, write, order compare s with up to 3 decimal places solve problems involving up to 3 decimal places recognise the per cent symbol (%) underst that per cent relates to of parts per 100, write percentages as a fraction with denominator 100, as a decimal fraction solve problems which require knowing percentage decimal equivalents of,,,, those fractions with a denominator of a multiple of 10 or 25 involving converting between units of time use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, scaling about equal sides angles
7 Maths Year 6 Programme of Study Value read, write, order compare s up to 10,000,000 determine the value of each digit round any whole to a required degree of accuracy use negative s in context, calculate intervals across 0 solve practical problems that involve all of the above Addition Multiplication multiply multidigit s up to 4 digits by a twodigit whole using the formal written method of long multiplication divide s up to 4 digits by a twodigit whole using the formal written method of long division, interpret remainders as whole remainders, fractions, or by rounding, as appropriate for the context divide s up to 4 digits by a twodigit using the formal written method of short division where appropriate, interpreting remainders according to the context perform mental calculations, with mixed operations large s identify common factors, common multiples prime s use their knowledge of the order of operations to carry out calculations involving the 4 operations solve addition subtraction multistep problems in contexts, Fractions ( decimals, percentages ratio, proportion probability in years 4,5 6) use common factors to simplify fractions; use common multiples to express fractions in the same denomination compare order fractions, fractions >1 add subtract fractions with denominators mixed s, using the concept of equivalent fractions multiply pairs of proper fractions, writing the answer in its st form [for example, = ] divide proper fractions by whole s [for example, 2 = ] associate a fraction with division calculate decimal fraction equivalents [for example, 0.375] for a fraction [for example, ] identify the value of each digit in s given to 3 decimal places multiply Measurement Geometry properties of shape solve problems involving the calculation conversion of units of measure, using decimal notation up to 3 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 3 decimal places draw 2D shapes using given dimensions angles recognise, describe build 3D shapes, 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, 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, describe positions on the full coordinate grid (all 4 quadrants) draw translate 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 Algebra use formulae generate describe linear sequences express missing problems algebraically find pairs of s that satisfy an equation with 2 unknowns enumerate possibilities of combinations of 2 variables
8 deciding which operations methods to use why involving addition, subtraction, multiplication division use estimation to check answers to calculations determine, in the context of a problem, an appropriate degree of accuracy divide s by 10, 100 1,000 giving answers up to 3 decimal places multiply onedigit s with up to 2 decimal places by whole s use written division methods in cases where the answer has up to 2 decimal places solve problems which require answers to be rounded to specified degrees of accuracy recall use equivalences between fractions, decimals percentages, in contexts Ratio Proportion involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication division facts involving the calculation of percentages [for example, of measures such as 15% 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 convert between miles kilometres recognise that shapes with the same areas can have 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, cubic centimetres (cm³) cubic metres (m³), extending to other units [for example, mm³ km³] find missing angles
9
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