National Curriculum Chart

Transcription

1 Schofield & Sims Year 1 programme of study number place value addition subtraction multiplication division Measurement count to across 100, forwards backwards, beginning with 0 or 1, or from any given number count, read write numbers to 100 in numerals; count in multiples of twos, fives tens given a number, identify one more one less identify represent numbers using objects pictorial representations including the number line, use the language of: equal to, more than, less than (fewer), most, least read write numbers from 1 to 20 in numerals words. read, write interpret mathematical statements involving addition (+), subtraction ( ) equals (=) signs represent use number bonds related subtraction facts within 20 add subtract one-digit two-digit numbers 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 [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 1 1

2 Schofield & Sims Year 1 programme of study Measurement properties of shapes position direction 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 3-D shapes, including: 2-D shapes [for example, rectangles (including squares), circles triangles] 3-D shapes [for example, cuboids (including cubes), pyramids spheres]. describe position, direction movement, including whole, half, quarter three-quarter turns

3 Schofield & Sims Year 2 programme of study number place value addition subtraction multiplication division count in steps of 2, 3, 5 from 0, in tens from any number, forward backward recognise the place value of each digit in a two-digit number (tens, ones) identify, represent estimate numbers using different representations, including the number line compare order numbers from 0 up to 100; use <, > = signs read write numbers to at least 100 in numerals in words use place value number facts to solve problems. solve problems with addition subtraction: using concrete objects pictorial representations, including those involving numbers, 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 numbers using concrete objects, pictorial representations, mentally, including: a two-digit number ones a two-digit number tens two two-digit numbers adding three one-digit numbers show that addition of two numbers 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 solve missing number problems. recall use multiplication division facts for the 2, 5 10 multiplication tables, including recognising odd even numbers calculate mathematical statements for multiplication division within the multiplication tables write them using the multiplication ( ), division ( ) equals (=) signs show that multiplication of two numbers can be done in any order (commutative) division of one number 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 1 3, 1 4, of a length, shape, set of objects or quantity write simple for example, 1 2 of 6 = 3 recognise the equivalence of

4 Schofield & Sims Year 2 programme of study Measurement properties of shapes position direction Statistics 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. identify describe the properties of 2-D shapes, including the number of sides line 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. 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 anti-clockwise). 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

5 Schofield & Sims Year 3 programme of study number place value addition subtraction multiplication division count from 0 in multiples of 4, 8, ; find 10 or 100 more or less than a given number recognise the place value of each digit in a three-digit number (hundreds, tens, ones) compare order numbers up to 1000 identify, represent estimate numbers using different representations read write numbers up to 1000 in numerals in words solve number problems practical problems involving these ideas. add subtract numbers mentally, including: a three-digit number ones a three-digit number tens a three-digit number hundreds add subtract numbers 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 number problems, using number facts, place value, more complex addition subtraction. recall use multiplication division facts for the 3, 4 8 multiplication tables write calculate mathematical statements for multiplication division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental progressing to formal written methods solve problems, including missing number 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 one-digit numbers or quantities by 10 recognise, find write of a discrete set of objects: unit non-unit with small denominators recognise use as numbers: unit non-unit with small denominators recognise show, using diagrams, equivalent with small denominators add subtract with the same denominator within one whole [for example, = 6 7 ]

6 Schofield & Sims Year 3 programme of study Measurement properties of shapes Statistics compare order unit, 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 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 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 halfturn, 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

7 Schofield & Sims Year 4 programme of study number place value addition subtraction multiplication division (including decimals) count in multiples of 6, 7, 9, find 1000 more or less than a given number count backwards through zero to include negative numbers recognise the place value of each digit in a four-digit number (thouss, hundreds, tens, ones) order compare numbers beyond 1000 identify, represent estimate numbers using different representations round any number to the nearest 10, 100 or 1000 solve number practical problems that involve all of the above with increasingly large positive numbers 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 numbers 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 use place value, known derived facts to multiply divide mentally, including: multiplying by 0 1; dividing by 1; multiplying together three numbers recognise use factor pairs commutativity in mental calculations multiply two-digit three-digit numbers by a one-digit number using formal written layout solve problems involving multiplying adding, including using the distributive law to multiply two digit numbers 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 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 to calculate quantities, to divide quantities, including non-unit where the answer is a whole number

8 Schofield & Sims Year 4 programme of study (including decimals) Measurement properties of shapes position direction Statistics add subtract with the same denominator recognise write decimal equivalents of any number of tenths or hundredths recognise write decimal equivalents to 1 4, 1 2, 3 4 find the effect of dividing a one- or two-digit number by , 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 numbers with the same number of decimal places up to two decimal places solve simple measure money problems involving 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 (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 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

9 Schofield & Sims Year 5 programme of study number place value addition subtraction multiplication division read, write, order compare numbers to at least determine the value of each digit count forwards or backwards in steps of powers of 10 for any given number up to interpret negative numbers in context, count forwards backwards with positive negative whole numbers, including through zero round any number up to to the nearest 10, 100, 1000, solve number problems practical problems that involve all of the above read Roman numerals to 1000 (M) recognise years written in Roman numerals. add subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition subtraction) add subtract numbers mentally with increasingly large numbers 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 numbers know use the vocabulary of prime numbers, prime factors composite (non-prime) numbers establish whether a number up to 100 is prime recall prime numbers up to 19 multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers multiply divide numbers mentally drawing upon known facts divide numbers up to 4 digits by a one-digit number using the formal written method of short division interpret remainders appropriately for the context multiply divide whole numbers those involving decimals by 10,

10 Schofield & Sims Year 5 programme of study multiplication division (including decimals percentages) recognise use square numbers cube numbers, the notation for squared ( 2 ) cubed ( 3 ) 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 problems involving simple rates. compare order whose denominators are all multiples of the same number identify, name write equivalent of a given fraction, represented visually, including tenths hundredths recognise mixed numbers improper convert from one form to the other write mathematical statements > 1 as a mixed number [for example, = 6 5 = 11 5 ] add subtract with the same denominator denominators that are multiples of the same number multiply proper mixed numbers by whole numbers, supported by materials diagrams read write decimal numbers as [for example, 0.71 = ] 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 numbers with up to three decimal places solve problems 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 100, as a decimal solve problems which require knowing percentage decimal equivalents of 1 2, 1 4, 1 5, 2 5, 4 5 those with a denominator of a multiple of 10 or

11 Schofield & Sims Year 5 programme of study Measurement properties of shapes position direction Statistics 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 (including squares), including using stard units, square centimetres (cm 2 ) square metres (m 2 ) estimate the area of irregular shapes estimate volume [for example, using 1cm 3 blocks to build cuboids (including 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. 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 ( ) identify: angles at a point one whole turn (total 360 ) angles at a point on a straight line 1 2 a turn (total 180 ) other multiples of 90 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

12 Schofield & Sims Year 6 programme of study number place value addition, subtraction, multiplication division (including decimals percentages) read, write, order compare numbers up to determine the value of each digit round any whole number to a required degree of accuracy use negative numbers in context, calculate intervals across zero solve number practical problems that involve all of the above. multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, interpret remainders as whole number remainders,, or by rounding, as appropriate for the context divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context perform mental calculations, including with mixed operations large numbers identify common factors, common multiples prime numbers 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 ; use common multiples to express in the same denomination compare order, including > 1 add subtract with different denominators mixed numbers, using the concept of equivalent multiply simple pairs of proper, writing the answer in its simplest form [for example, = 1 8 ] divide proper by whole numbers [for example, = 1 6 ] associate a fraction with division calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3 8 ] identify the value of each digit in numbers given to three decimal places multiply divide numbers by 10, giving answers up to three decimal places multiply one-digit numbers with up to two decimal places by whole numbers

13 Schofield & Sims Year 6 programme of study (including decimals percentages) Ratio proportion Algebra Measurement 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, decimals percentages, including in different contexts. 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 360] 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 multiples. use simple formulae generate describe linear number sequences express missing number problems algebraically find pairs of numbers that satisfy an equation with two unknowns enumerate possibilities of combinations of two variables. 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 3 ) cubic metres (m 3 ), extending to other units [for example, mm 3 km 3 ]

14 Schofield & Sims Year 6 programme of study properties of shapes position direction Statistics 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. interpret construct pie charts line graphs use these to solve problems calculate interpret the mean as an average

15 Schofield & Sims Year 7+ programme of study (selected objectives) Algebra underst use place value for decimals, measures, integers of any size order positive negative integers, decimals ; use the symbols =,, <, >,, use the concepts vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation the unique factorisation property use the four operations, including formal written methods, applied to integers, decimals, proper improper, mixed numbers, all both positive negative use conventional notation for the priority of operations, including brackets, powers, roots reciprocals recognise use relationships between operations including inverse operations use integer powers associated real roots (square, cube higher), work interchangeably with terminating decimals their corresponding define percentage as number of parts per hundred, interpret percentages percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, work with percentages greater than 100% interpret percentages as operators use stard units of mass, length, time, money other measures, including with decimal quantities round numbers measures to an appropriate degree of accuracy [for example, to a number of decimal places]. use interpret algebraic notation, including: ab in place of a b, 3y in place of y + y + y 3 y, a 2 in place of a a, a 3 in place of a a a, a/b in place of a b, coefficients written as rather than as decimal, brackets substitute numerical values into formulae expressions, including scientific formulae underst use the concepts vocabulary of expressions, equations, inequalities, terms factors underst use stard mathematical formulae work with coordinates in all four quadrants generate terms of a sequence from r a term-to-term or a positionto-term rule recognise arithmetic sequences find the nth term

16 Schofield & Sims Year 7+ programme of study (selected objectives) Ratio, proportion rates of change Ratio proportion use common factors to simplify ; use common multiples to express in the same denomination compare order, including > 1 add subtract with different denominators mixed numbers, using the concept of equivalent multiply simple pairs of proper, writing the answer in its simplest form [for example, = 1 8 ] divide proper by whole numbers [for example, = 1 6 ] associate a fraction with division calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3 8 ] identify the value of each digit in numbers given to three decimal places multiply divide numbers by 10, giving answers up to three decimal places multiply one-digit numbers with up to two decimal places by whole numbers use written division methods in cases where the answer has up to two decimal places solve problems which require answers to be rounded to specified degrees of accuracy recall use equivalences between simple, decimals percentages, including in different contexts. change freely between related stard units [for example time, length, area, volume/capacity, mass] use scale factors, scale diagrams maps express one quantity as a fraction of another, where the fraction is less than 1 greater than 1 use ratio notation, including reduction to simplest form divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio solve problems involving percentage change, including: percentage increase, decrease original value problems simple interest in financial mathematics solve problems involving direct proportion use compound units such as speed, unit pricing density to solve problems

17 Schofield & Sims Year 7+ programme of study (selected objectives) measures Probability Statistics derive apply formulae to calculate solve problems involving: perimeter area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) other prisms (including cylinders) calculate solve problems involving: perimeters of 2-D shapes (including circles), areas of circles composite shapes draw measure line segments angles in geometric figures, including interpreting scale drawings describe, sketch draw using conventional terms notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, other polygons that are reflectively rotationally symmetric derive illustrate properties of triangles, quadrilaterals, circles, other plane figures [for example, equal lengths angles] using appropriate language technologies identify properties of, describe the results of, translations, rotations reflections applied to given figures apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles underst use the relationship between parallel lines alternate corresponding angles derive use the sum of angles in a triangle use it to deduce the angle sum in any polygon, to derive properties of regular polygons apply angle facts, triangle congruence, similarity properties of quadrilaterals to derive results about angles sides use the properties of faces, surfaces, edges vertices of cubes, cuboids, prisms, cylinders, pyramids, cones spheres to solve problems in 3-D. record, describe analyse the frequency of outcomes of simple probability experiments involving romness, fairness, equally unequally likely outcomes, using appropriate language the 0-1 probability scale underst that the probabilities of all possible outcomes sum to 1 enumerate sets unions/intersections of sets systematically, using tables, grids Venn diagrams. construct interpret appropriate tables, charts, diagrams, including frequency tables, bar charts, pie charts, pictograms for categorical data, vertical line (or bar) charts for ungrouped grouped numerical data