Fractions. Pupils should be taught to:

Transcription

1 Year 1 programme of study (statutory requirements) Number place taught 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 objects pictorial the line, use the language of: equal to, more than, less than (fewer), most, least read write from 1 to 0 in numerals words Addition taught read, write statements addition (+), (-) equals (=) signs represent use bonds related facts within 0 add subtract onedigit two-digit to 0, zero one-step that involve addition, concrete objects pictorial, missing such as 7 = - 9 Multiplication taught one-step multiplication, by calculating the answer concrete objects, pictorial 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, practical for: - lengths heights (for longshort, longershorter, tallshort, doublehalf) - mass weight (for heavylight, heavier than, lighter than) - capacity volume (fullempty, more than, less than, half, half full, quarter) - time (quicker, slower, earlier, later) measure begin to record the following: - lengths heights - massweight - capacity volume - time (hours, minutes, seconds) recognise know the of denominations of coins notes sequence events in chronological order language (for before after, next, first, today, yesterday, tomorrow, morning, afternoon evening) recognise name common - D -D, : - -D [for rectangles ( squares), circles triangles - -D [for cuboids ( cubes), pyramids spheres position taught position, movement, whole, half, quarter three-quarter turns 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 Y1 notes Guidance (non-statutory) Number place practise counting (1,, ), ordering (for first, second, third ), or to indicate a quantity (for apples, centimetres), solving simple concrete, until they are fluent. begin to recognise place in beyond 0 by reading, writing, counting comparing up to 100, supported by objects pictorial. They practise counting as reciting counting as enumerating objects, counting in twos, fives tens from multiples to develop their recognition of patterns in the system (for odd even ), varied frequent practice through complex questions. Addition memorise reason with bonds to 10 0 in several forms (for = 16; 16-7 = 9; 7 = 16-9). They should realise the effect of adding or subtracting zero. This establishes addition as related operations. combine increase, counting forwards backwards. They discuss in familiar practical contexts, quantities. Problems should include the terms: put together, add, altogether, total, take away, distance between, difference between, more than less than, so that pupils develop the concept of addition are enabled to use these operations flexibly. Multiplication Through grouping sharing small quantities, pupils begin to underst: multiplication ; doubling quantities; finding simple fractions of objects, quantities. They make connections between arrays, patterns, counting in twos, fives tens. are taught half quarter as fractions of discrete continuous quantities by solving, objects quantities. For they could recognise find half a length, quantity, set of objects or shape. connect halves quarters to the equal sharing grouping of sets of objects to measures, as well as recognising combining halves quarters as parts of a whole. The pairs of terms: mass weight, volume capacity, are used interchangeably at this stage. move from comparing types of quantities measures non-stard units, discrete (for counting) continuous (for liquid) measurement, to manageable common stard units. In order to become familiar with stard measures, pupils begin to use measuring tools such as a ruler, weighing scales containers. use the language of time, telling the time throughout the day, first o clock then half past. hle common -D -D, naming these related everyday objects fluently. They recognise these in orientations sizes, know that rectangles, triangles, cuboids pyramids are not always similar to each other. position use the language of position, motion, : left right, top, middle bottom, on top of, in front of, above, between, around, near, close far, up down, forwards backwards, inside outside. make whole, half, quarter threequarter turns in both s connect turning clockwise with movement on a clock face. They recognise create repeating patterns with objects with.

2 Year programme of study (statutory requirements) Number place taught count in steps of,, from 0, in tens from any, forward or backward recognise the place of each digit in a two-digit (tens, ones) identify, represent estimate, the line order from 0 up to 100; use <, > = signs read write to at least 100 in numerals in words use place facts to Addition taught with addition : - concrete objects pictorial, those, quantities measures - applying their increasing knowledge of mental written methods recall use addition facts to 0 fluently, derive use related facts up to 100 add subtract concrete objects, pictorial, mentally, : - a two-digit ones - a two-digit tens - two two-digit - adding three onedigit show that addition of two can be done in any order (commutative) of one from another cannot recognise use the inverse relationship between addition use this to check calculations missing Multiplication taught recall use multiplication facts for the, 10 multiplication tables, recognising odd even statements for multiplication within the multiplication tables write them the multiplication ( ), ( ) equals (=) signs show that multiplication of two can be done in any order (commutative) of one by another cannot multiplication, materials, arrays, repeated addition, mental methods, multiplication facts, in contexts recognise, find, name write fractions 1, 1, of a length, shape, set of objects or quantity write simple fractions for 1 of 6 = recognise the equivalence of 1. taught choose use appropriate stard units to estimate measure lengthheight in any (mcm); mass (kgg); temperature ( C); capacity (litresml) to the nearest appropriate unit, rulers, scales, thermometers measuring vessels order lengths, mass, volumecapacity record the results >, < = recognise use symbols for pounds ( ) pence (p); combine amounts to make a particular find combinations of coins that equal the same amounts of money simple in a practical context addition of money of the same unit, giving change sequence intervals of time tell write the time to five minutes, quarter pastto 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 the -D, the of sides symmetry in a vertical line identify the -D, the of edges, vertices faces identify -D on the surface of -D [for example a circle on a cylinder a triangle on a pyramid sort common -D -D everyday objects position order arrange combinations of objects in patterns sequences use vocabulary to position, movement, movement in a straight line distinguishing between rotation as a turn in terms of right angles for quarter, half threequarter turns (clockwise anticlockwise) 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 Y notes guidance (non-statutory) Number place Using materials a range of, pupils practise counting, reading, writing comparing to at least 100 solving a variety of related to develop fluency. They count in multiples of three to support their later understing of a third. As they become more confident with up to 100, pupils are introduced to larger to develop further their recognition of patterns within the system represent them in ways, spatial. partition in ways (for = 0 + = 10+1) to support. They become fluent apply their knowledge of to reason with, discuss that emphasise the of each digit in two-digit. They begin to underst zero as a place holder. Addition extend their understing of the language of addition to include sum difference. practise addition to 0 to become fluent in deriving facts such as + 7 = 10, 10-7 = 7 = 10 - to = 100, = 0 70 = They check their calculations, by adding to check adding in a order to check addition (for = = ). This establishes commutativity associativity of addition. Recording addition in columns supports place prepares for formal written methods with larger. Multiplication use a variety of language to multiplication. are introduced to the multiplication tables. They practise to become fluent in the, 10 multiplication tables connect them to each other. They connect the 10 multiplication table to place, the multiplication table to the s on the clock face. They begin to use other multiplication tables recall multiplication facts, related facts to perform written mental calculations. work with a range of materials contexts in which multiplication relate to grouping sharing discrete continuous quantities, to arrays to repeated addition. They begin to relate these to fractions measures (for 0 = 0, 0 is a half of 0). They use commutativity inverse relations to develop multiplicative reasoning (for =0 0 =). use fractions as fractions of discrete continuous quantities by solving, objects quantities. They connect unit fractions to equal sharing grouping, to when they can be d, to measures, finding fractions of lengths, quantities, set of objects or. They meet as the first example of a nonunit fraction. count in fractions up to 10, starting from any the 1 equivalence on the line (for 1 1, 1 (or 1 1 ), 1, ). This reinforces the concept of fractions as that they can add up to more than one. use stard units of measurement with increasing accuracy, their knowledge of the system. They use the appropriate language record stard abbreviations. Comparing measures includes simple multiples such as half as high ; twice as wide. They become fluent in telling the time on analogue clocks recording it. become fluent in counting recognising coins. They read say amounts of money confidently use the symbols p accurately, recording pounds pence separately. hle name a wider variety of common -D -D : quadrilaterals polygons, cuboids, prisms cones, identify the each shape (for of sides, of faces). identify, sort on the basis of their properties use vocabulary precisely, such as sides, edges, vertices faces. read write names for that are appropriate for their word reading spelling. draw lines a straight edge. position work with patterns of, those in orientations. use the concept language of angles to turn by applying rotations, in practical contexts (for pupils themselves moving in turns, giving instructions to other pupils to do so, programming robots instructions given in right angles). record,, collate, organise (for many-to-one correspondence with simple ratios,, 10).

3 Year programme of study (statutory requirements) Number place taught count from 0 in multiples of, 8, 0 100; find 10 or 100 more or less than a given recognise the place of each digit in a three-digit (hundreds, tens, ones) order up to 1000 identify, represent estimate read write up to 1000 in numerals in words practical these ideas Addition add subtract mentally, : - a threedigit ones - a threedigit tens - a threedigit hundreds add subtract with up to three digits, formal written methods of columnar addition estimate the answer to a calculation use inverse operations to check answers Solve, missing, facts, place, more complex addition Multiplication recall use multiplication facts for the, 8 multiplication tables write statements for multiplication the multiplication tables that they know, for two-digit times onedigit, mental progressing to formal written methods, missing, multiplication, positive integer scaling correspondence in which n objects are connected to m objects taught count up down in tenths; recognise that tenths arise from dividing an object into 10 equal parts in dividing one-digit or quantities by 10 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, diagrams, equivalent fractions with small denominators add subtract fractions with the same denominator within one whole (for = 6 7 ) order unit fractions, fractions with the same denominators that involve all of the above measure,, add subtract: lengths (mcmmm); mass (kgg); volumecapacity (lml) measure the perimeter of simple -D add subtract amounts of money to give change, both p in practical contexts tell write the time from an analogue clock, Roman numerals from I to XII, 1-hour - hour clocks estimate read time with increasing accuracy to the nearest minute; record 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 durations of events [for example to the time taken by particular events or tasks properties of taught draw -D make -D modelling materials; recognise -D in orientations them recognise that angles are 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 present data bar charts, pictograms tables one-step two-step questions[ for How many more? How many fewer? presented in scaled bar charts pictograms tables Y notes guidance (non-statutory) Number place now use multiples of,,,, 8, 10, They use larger to at least 1000, applying partitioning related to place varied complex, building on work in year (for 16 = , 16 = 10 16). Using a variety of, those related to measure, pupils continue to count in ones, tens hundreds, so that they become fluent in the order place of to Addition practise solving varied addition questions. For mental calculations with twodigit, the answers could exceed 100. use their understing of place partitioning, practise columnar addition with large up to three digits to become fluent (see Appendix 1). Multiplication continue to practise their mental recall of multiplication tables when they are calculating statements in order to improve fluency. Through doubling, they connect the, 8 multiplication tables. develop efficient mental methods, for commutativity associativity (for 1 = 1 = 0 1 = 0) multiplication facts (for = 6, 6 = = 6 ) to derive related facts (0 = 60, 60 = 0 0 = 60 ). develop reliable written methods for multiplication, starting with calculations of two-digit by one-digit progressing to the formal written methods of short multiplication. simple in contexts, deciding which of the four operations to use why. These include measuring scaling contexts, (for four times as high, eight times as long etc.) correspondence in which m objects are connected to n objects (for hats coats, how many outfits?; 1 sweets shared equally between children; cakes shared equally between 8 children). connect tenths to place, decimal measures to by 10. They begin to underst unit non-unit fractions as on the line, deduce relations between them, such as size equivalence. They should go beyond the [0, 1 interval, relating this to measure. underst the relation between unit fractions as operators (fractions of), by integers. They continue to recognise fractions in the context of parts of a whole,, measurements, a shape, unit fractions as a of a quantity. practise adding subtracting fractions with the same denominator through a variety of complex to improve fluency. continue to measure the appropriate tools units, progressing to a wider range of measures, comparing mixed units (for 1 kg 00g) simple equivalents of mixed units (for m = 00cm). The comparison of measures should also include simple scaling by integers (for a given quantity or measure is twice as long or five times as high) this connects to multiplication. continue to become fluent in recognising the of coins, by adding subtracting amounts, mixed units, giving change manageable amounts. They record p separately. The decimal recording of money is introduced formally in year. use both analogue digital 1-hour clocks record their times. In this way they become fluent in prepared for digital -hour clocks in year. knowledge of the is extended at this stage to symmetrical nonsymmetrical polygons polyhedra. extend their use of the. They able to the -D -D accurate language, lengths of lines acute obtuse for angles greater or lesser than a right angle. connect decimals rounding to drawing measuring straight lines in centimetres, in a variety of contexts. underst use simple scales (for,, 10 units per cm) in pictograms bar charts with increasing accuracy. They continue to data presented in many contexts.

4 Year programme of study (statutory requirements) Number place count in multiples of 6, 7, 9, 1000 find 1000 more or less than a given count backwards through zero to include negative recognise the place of each digit in a four-digit (thouss, hundreds, tens, ones) order beyond 1000 identify, represent estimate round any to the nearest 10, 100 or 1000 practical that involve all of the above with 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 Addition be add subtract with up to digits the formal written methods of columnar addition where appropriate estimate use inverse operations to check answers to a calculation addition two-step in contexts, deciding which operations methods to use why Multiplication recall multiplication facts for multiplication tables up to 1 1 use place, known derived facts to multiply divide mentally, : 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 formal written layout multiplying adding, the distributive law to multiply two digit by one digit, integer scaling harder correspondence such as n objects are connected to m objects Y notes guidance (non-statutory) ( decimals) recognise show, 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. harder fractions to quantities, fractions to divide quantities, non-unit fractions where the answer is a whole add subtract fractions with the same denominator recognise write decimal equivalents of any of tenths or hundredths recognise write decimal equivalents to 1 ; 1 ; find the effect of dividing a one- or two-digit by , identifying the of the digits in the answer as ones, tenths hundredths round decimals with one decimal place to the nearest whole with the same of decimal places up to two decimal places simple measure money fractions decimals to two decimal places convert between units of measure [for kilometre to metre; hour to minute measure the perimeter of a rectilinear figure ( squares) in centimetres metres find the area of rectilinear by counting squares estimate, measures, money in pounds pence read, write convert time between analogue digital 1 -hour clocks converting from hours to minutes; minutes to seconds; years to months; weeks to days classify geometric, quadrilaterals triangles, based on their properties sizes identify acute obtuse angles order angles up to two right angles by size identify lines of symmetry in -D presented in orientations complete a simple symmetric figure with respect to a specific line of symmetry position be positions on a -D grid as s in the first quadrant movement s between positions as translation s of a given unit to the leftright updown plot specified points draw sides to complete a given polygon be present discrete continuous data appropriate graphical methods, bar charts time graphs comparison, sum difference presented in bar charts, pictograms, tables other graphs Number place Using a variety of, measures, pupils become fluent in the order place of beyond 1000, counting in tens hundreds, maintaining fluency in other multiples through varied frequent practice. They begin to extend their knowledge of the system to include the decimal fractions that they have met so far. They connect estimation rounding to the use of measuring instruments. Roman numerals put in their historical context so pupils underst that there have been ways to write whole that the important concepts of zero place were introduced over a period of time. Addition continue to practise both mental methods columnar addition with large to aid fluency (see Mathematics Appendix 1). Multiplication continue to practise recalling multiplication tables related facts to aid fluency. practise mental methods extend this to three-digit to derive facts (for example 600 = 00 can be derived from x = 6). practise to become fluent in the formal written method of short multiplication short with exact answers (see Mathematics Appendix 1). write statements about the equality of expressions (for use the distributive law 9 7 = associative law ( ) = ( )). They combine their knowledge of facts rules of arithmetic to mental written calculations for x 6 x = 10 x 6 = 60. two-step in contexts, choosing the appropriate operation, working with harder. This should include correspondence questions such as the of choices of a meal on a menu, or three cakes shared equally between 10 children. ( decimals) connect hundredths to tenths place decimal measure. They extend the use of the line to connect fractions, measures. underst the relation between nonunit fractions multiplication of quantities, with particular emphasis on tenths hundredths make connections between fractions of a length, of a shape as a representation of one whole or set of quantities. use factors multiples to recognise equivalent fractions simplify where appropriate (for 6 9 = or 1 = 8 ). continue to practice adding subtracting fractions with the same denominator, to become fluent through a variety of complex beyond one whole. are taught throughout that decimals fractions are ways of expressing proportions. understing of the system decimal place is extended at this stage to tenths then hundredths. This includes relating the decimal notation to of whole by 10 later 100. They practise counting simple fractions decimal fractions, both forwards backwards. learn decimal notation the language associated with it, in the context of measurements. They make comparisons order decimal amounts quantities that are expressed to the same of decimal places. They able to represent with one or two decimal places in several ways, such as on lines. build on their understing of place decimal notation to record metric measures, money. They use multiplication to convert from larger to smaller units. Perimeter can be expressed algebraically as (a + b) where a b are the dimensions in the same unit. They relate area to arrays multiplication. continue to classify geometrical properties, extending to classifying triangles (for isosceles, equilateral, scalene) quadrilaterals (for parallelogram, rhombus, trapezium). order angles in preparation for a protractor lengths angles to decide if a polygon is regular or irregular. draw symmetric patterns a variety of media to become familiar with orientations of lines of symmetry; recognise line symmetry in a variety of diagrams, where the line of symmetry does not dissect the original shape. position, draw a pair of axes in one quadrant, with equal scales integer labels. They read, write use pairs of s, for example (, ), plotting ICT tools. underst use a greater range of scales in their. begin to relate the graphical representation of data to recording change over time.

5 Year programme of study (statutory requirements) Number place read, write, order to at least determine the of each digit count forwards or backwards in steps of powers of 10 for any given up to negative in context, count forwards backwards with positive negative whole, through zero round any up to to the nearest 10, 100, 1000, practical that involve all of the above read Roman numerals to 1000 (M) recognise years written in Roman numerals Addition be add subtract whole with more than digits, formal written methods (columnar addition ) add subtract mentally with large use rounding to check answers to calculations determine, in the context of a problem, levels of accuracy addition multi-step in contexts, deciding which operations methods to use why Multiplication identify multiples factors, 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 digits by a one- or two-digit a formal written method, long multiplication for two-digit multiply divide mentally drawing upon known facts divide up to digits by a one-digit the formal written method of short remainders appropriately for the context multiply divide whole those decimals by 10, recognise use square cube, the notation for squared ( ) cubed ( ) multiplication their knowledge of factors multiples, squares cubes addition,, multiplication a combination of these, understing the meaning of the equals sign multiplication, scaling by simple fractions simple rates Y notes guidance (non-statutory) Number place identify the place in large whole. They continue to use in context, measurement. extend apply their understing of the system to the decimal fractions that they have met so far. They should recognise linear sequences (for, ½,, 1...), those fractions decimals, find the term-toterm rule in words (for add ½). Addition practise the formal written methods of columnar addition with large to aid fluency (see Mathematics Appendix 1). They practise mental calculations with large to aid fluency (for = 10 16). Multiplication practise extend their use of the formal written methods of short multiplication short (see Mathematics Appendix 1). They apply all the multiplication tables related facts frequently, commit them to memory use them confidently to make larger calculations. They use underst the terms factor, multiple prime, square cube. non-integer answers to by expressing results in ways according to the context, with remainders, as fractions, as decimals or by rounding (for 98 = 98 = r = 1 =. ). use multiplication as inverses to support the introduction of ratio in year 6, for by multiplying dividing by powers of 10 in scale drawings or by multiplying dividing by powers of a 1000 in converting between units such as kilometres metres. Distributivity can be expressed as a(b + c) = ab + ac. They underst the terms factor, multiple prime, square cube use them to construct equivalence statements (for x = x x ; x 70 = x x 9 x 10 = 9 x 10). use explain the equals sign to indicate equivalence, in missing (for 1 + = 1 + ; = x ). ( decimals 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 improper fractions convert from one form to the other write statements > 1 as a mixed [ for + = 6 = 1 1 add subtract fractions with the same denominator multiples of the same multiply proper fractions mixed by whole, supported by materials diagrams read write decimal as fractions [ for 0.71 = 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 with up to three decimal places 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 which require knowing percentage decimal equivalents of 1, 1, 1,, those with a denominator of a multiple of 10 or ( decimals taught throughout that percentages, decimals fractions are ways of expressing proportions. They extend their knowledge of fractions to thousths connect to decimals measures. connect equivalent fractions > 1 that simplify to integers with other fractions > 1 to with remainders, the line other models, hence move from these to improper mixed fractions. connect multiplication by a fraction to fractions as operators (fractions of), to, building on work from previous years. This relates to scaling by simple fractions, fractions > 1. practise adding subtracting fractions to become fluent through a variety of complex. They extend their understing of adding subtracting fractions to calculations that exceed 1 as a mixed. continue to practise counting forwards backwards in simple fractions. continue to develop their understing of fractions as, measures operators by finding fractions of quantities. extend counting from year, decimals fractions bridging zero, for example on a line. say, read write decimal fractions related tenths, hundredths thousths accurately are confident in checking the reasonableness of their answers to. They mentally add subtract tenths, onedigit whole tenths. They practise adding subtracting decimals, a mix of whole decimals, decimals with of decimal places, complements of 1 (for = 1). go beyond the measurement money models of decimals, for by solving puzzles decimals. make connections between percentages, fractions decimals (for 100% represents a whole quantity 1% is 1100, 0% is 0100, % is 100) relate this to finding fractions of. convert between units of metric measure (for 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 the perimeter of composite rectilinear in centimetres metres the area of rectangles ( squares) stard units, square centimetres (cm ) square metres (m ) estimate the area of irregular estimate volume [for 1 cm blocks to build cuboids( cubes) capacity[for water converting between units of time use all four operations to measure [for length, mass, volume, money decimal notation scaling use their knowledge of place multiplication to convert between stard units. the perimeter of rectangles related composite, the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically, for example + b = 0 for a rectangle of sides cm b cm perimeter of 0cm. the area from scale drawings given measurements. use all four operations in time money, conversions (for days to weeks, expressing the answer as weeks days). be identify -D, cubes other cuboids, from - D know angles are measured in degrees: estimate acute, obtuse reflex angles draw given angles, measure them in degrees ( o ) identify: - angles at a point one whole turn (total 60 o ) - angles at a point on a straight line ½ a turn (total 180 o ) - other multiples of 90 o use the rectangles to deduce related facts find missing lengths angles distinguish between regular irregular polygons based on reasoning about equal sides angles become accurate in drawing lines with a ruler to the nearest millimetre, measuring with a protractor. They use conventional markings for parallel lines right angles. use the term diagonal make conjectures about the angles formed between sides, between diagonals parallel sides, other quadrilaterals, for example dynamic geometry ICT tools. use angle sum facts other properties to make deductions about missing angles relate these to missing. Geometry : position identify, represent the position of a shape following a reflection or translation, the appropriat e language, know that the shape has not changed Geometry : position recognise use reflection translation in a variety of diagrams, continuing to use a - D grid s in the first quadrant. Reflection in lines that are parallel to the axes. compariso n, sum difference presented in a line graph comple te, read in tables, timetables connect their work on s scales to their ati on of time graphs. They begin to decide which representa tions of data are most appropriat e why.

6 Year 6 programme of study (statutory requirements) Number place read, write, order up to determine the of each digit round any whole to a required degree of accuracy use negative in context, intervals across zero practical that involve all of the above Addition,, multiplication taught multiply multi-digit up to digits by a two-digit whole the formal written method of long multiplication divide up to digits by a two-digit whole the formal written method of long, remainders as whole remainders, fractions, or by rounding, as appropriate for the context divide up to digits by a two-digit the formal written method of short where appropriate, ing remainders according to the context perform mental calculations, with mixed operations large. identify common factors, common multiples prime use their knowledge of the order of operations to carry out calculations the four operations addition multi-step in contexts, deciding which operations methods to use why addition,, multiplication use estimation to check answers to calculations determine, in the context of a problem, an appropriate degree of accuracy ( decimals use common factors to simplify fractions; use common multiples to express fractions in the same denomination order fractions, fractions >1 add subtract fractions with denominators mixed, the concept of equivalent fractions multiply simple pairs of proper fractions, writing the answer in its simplest form [ for 1 1 = 1 8 divide proper fractions by whole [for 1 = 1 6 associate a fraction with decimal fraction equivalents [for 0.7 for a simple fraction [for 8 identify the of each digit to three decimal places multiply divide by 10, giving answers up to three decimal places multiply one-digit with up to two decimal places by whole use written 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, in contexts Y6 notes guidance (non-statutory) Number place use the whole system, saying, reading writing accurately. Addition,, multiplication practise addition,, multiplication for larger, the formal written methods of columnar addition, short long multiplication, short long (see Mathematics Appendix 1). They undertake mental calculations with large more complex calculations. continue to use all the multiplication tables to statements in order to maintain their fluency. round answers to a specified degree of accuracy, for to the nearest 10, 0, 0 etc, but not to a specified of significant figures. explore the order of operations brackets; for + 1 x = ( + 1) x = 9. Common factors can be related to finding equivalent fractions. ( decimals practise, use underst the addition of fractions with denominators by identifying equivalent fractions with the same denominator. They should start with fractions where the denominator of one fraction is a multiple of the other (for ½ + 18 = 8) progress to varied complex. use a variety of images to support their understing of multiplication with fractions. This follows earlier work about fractions as operators (fractions of), as, as equal parts of objects, for example as parts of a rectangle. use their understing of the relationship between unit fractions to work backwards by multiplying a quantity that represents a unit fraction to find the whole quantity (for if ¼ of a length is 6cm, then the whole length is 6 = 1cm). They practise calculations with simple fractions decimal fraction equivalents to aid fluency, listing equivalent fractions to identify fractions with common denominators. can explore make conjectures about converting a simple fraction to a decimal fraction (for 8 = 0.7). For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context. multiply divide with up to two decimal places by one-digit two-digit whole. multiply decimals by whole, starting with the simplest cases, such as 0. = 0.8, in practical contexts, such as measures money. are introduced to the of decimal by one-digit whole, initially, in practical contexts measures money. They recognise calculations as the inverse of multiplication. also develop their skills of rounding estimating as a means of predicting checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy checking the reasonableness of their answers. Ratio proportion the relative sizes of two quantities where missing s can be found by integer multiplication facts the calculation of percentages [for of measures such as 1% of 60 the use of percentages for comparison similar where the scale factor is known or can be found unequal sharing grouping knowledge of fractions multiples Ratio proportion recognise proportionality in contexts when the relations between quantities are in the same ratio (for similar, recipes). link percentages or 60 to calculating angles of pie charts. consolidate their understing of ratio when comparing quantities, sizes scale drawings by solving a variety of. They might use the notation a:b to record their work. unequal quantities for for every egg you need three spoonfuls of flour, of the class are boys. These are the foundation for later formal approaches to ratio proportion. Algebra be use simple formulae generate linear sequences express missing algebraically find pairs of that satisfy an equation with two unknowns enumerate possibilities of combinations of two variables Algebra be introduced to the use of symbols letters to represent variables unknowns in situations that they already underst, such as: missing, lengths, s angles formulae in mathematics science equivalent expressions (for a + b = b + a) generalisatio ns of patterns puzzles (for what two can add up to). the calculation conversion of units of measure, 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, decimal notation to up to three decimal places convert between miles kilometres recognise that with the same areas can have perimeters vice versa recognise when it is possible to use formulae for area volume of the area of parallelograms triangles, estimate volume of cubes cuboids stard units, centimetre cubed (cm ) cubic metres (m ), extending to other units [for example mm km connect conversion (for from kilometres to miles) to a graphical representation as preparation for understing linearproportional graphs. They know approximate conversions are able to tell if an answer is sensible. Using the line, pupils use, add subtract positive negative integers for measures such as temperature. They relate the area of rectangles to parallelograms triangles, for by dissection, their areas, understing the formulae (in words or symbols) to do this. could be introduced to compound units for speed, such as miles per hour, apply their knowledge in science or other subjects as appropriate. be draw -D given dimensions angles recognise, build simple - D, making nets classify geometric 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, find missing angles draw nets accurately, measuring tools conventional markings labels for lines angles. the explain how unknown angles lengths can be derived from known measurements. These relationships might be expressed algebraically for d = r; a = (b + c). position, be positions on the full grid (all four quadrants) draw translate simple on the plane, reflect them in the axes position draw label a pair of axes in all four quadrants with equal scaling. This extends their knowledge of one quadrant to all four quadrants, the use of negative. draw label rectangles ( squares), parallelogram s rhombuses, specified by s in the four quadrants, predicting missing s the. These might be expressed algebraically for translating vertex (a, b) to (a-, b+); (a, b) (a+d, b+d) being opposite vertices of a square of side d. be construct pie charts line graphs use these to the mean as an average connect their work on angles, fractions percentages to the ation of pie charts. both encounter draw graphs relating two variables, arising from their own enquiry in other subjects. They should connect conversion from kilometres to miles in measurement to its graphical representation. know when it is appropriate to find the mean of a data set

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