VIEWS: 5 PAGES: 120 POSTED ON: 9/29/2012 Public Domain
Open the assessment criteria using the tab at the bottom of this page. This will list all the assessment criteria at all the levels. Enter names for your class in rows 1 and 2, column G onwards. (Up to column BZ) When you are assessing, enter R, A or G (for red, amber, green) to show pupils' achievement for that assessment criterion. The cells will be coloured If you want to limit the number of cells you see at any time you can use the autofilter. This is the down arrow at the top of the column. Pick the category you want. By putting a unit code in the "unit" column you can select the Assessment Criteria relevant to a particular unit. Each statement is linked to the relevant progression maps. The hyperlink in column A (map) will take you to the approximate position in the progression map. Hyperlinks from the progression map will take you to more detailed explanations, probing questions and resources that could be used. (On the National Strategies website). To graph pupil achievement for a limited number of assessment criteria, use the filter on the AT column, and/or insert a number in the "select" column, and filter by that. This will be useful when sharing achievement with a class and prioritising topics for revision and intervention. Open the chart using the tab at the bottom of the page map AF G Level rade Algebra 8 B equations, formulae and identities Algebra 8 B equations, formulae and identities Algebra 8 B equations, formulae and identities Algebra 8 B equations, formulae and identities Algebra 8 B equations, formulae and identities Using and applying Reasoning 8 B Algebra sequences, functions8 B and graphs FDPRP Calculating 8 B and powers IntegersCalculating 8 B 8 Handling Data B Handling data 8 Handling Data B Handling data Probability 8 Handling Data B Probability 8 Handling Data B Solving 8 B ProblemUsing and applying Using and applying Reasoning 8 B Using and applying Reasoning 8 B Using and applying communicating 8 B B FDPRP Numbers and8the number system Using and applying Reasoning 8 B Algebra sequences, functions8 B and graphs Shape and Space B Measures 8 Shape and Space B Measures 8 Shape 8 Shape & spaceand Space B Algebra 7 C equations, formulae and identities Algebra 7 C equations, formulae and identities Algebra 7 C equations, formulae and identities Algebra 7 C equations, formulae and identities Algebra sequences, functions7 C and graphs FDPRP Calculating 7 C FDPRP Calculating 7 C FDPRP Calculating 7 C Calculating 7 Place value C Calculating Written calculations 7 C 7 Handling Data C Handling data 7 Handling Data C Handling data 7 Handling Data C Handling data 7 Handling Data C Handling data 7 Handling Data C Handling data 7 Handling Data C Probability Using and applying communicating 7 C Solving 7 ProblemUsing and applyingC Using and applying Reasoning 7 C C FDPRP Numbers and7the number system Algebra sequences, functions7 C and graphs Solving 7 C ProblemUsing and applying Shape and Space C Measures 7 Shape and Space C Measures 7 Shape and Space C Measures 7 Shape and Space C Measures 7 Shape 7 Shape & spaceand Space C Shape 7 Shape & spaceand Space C Algebra 6 C equations, formulae and identities Algebra sequences, functions6 C and graphs Algebra 6 D equations, formulae and identities Solving 6 C ProblemUsing and applying Using and applying communicating 6 D Using and applying Reasoning 6 D FDPRP Calculating 6 C FDPRP Calculating 6 C 6 Handling Data C Handling data FDPRP Calculating 6 D FDPRP Calculating 6 D 6 Handling Data D Handling data 6 Handling Data D Handling data 6 Handling Data D Probability 6 Handling Data D Probability Algebra sequences, functions6 D and graphs FDPRP Numbers and6the number system Algebra sequences, functions6 D and graphs Shape 6 Shape & spaceand Space C Shape and Space D Measures 6 Shape and Space D Measures 6 Shape 6 Shape & spaceand Space C Shape 6 Shape & spaceand Space D Shape 6 Shape & spaceand Space D Shape 6 Shape & spaceand Space D Shape 6 Shape & spaceand Space D Shape 6 Shape & spaceand Space D Using and applying Reasoning 6 D Shape 6 Shape & spaceand Space D Using and applying Reasoning 5 E Algebra 5 E equations, formulae and identities Using and applying communicating 5 E Calculating Written calculations 5 D FDPRP Calculating 5 E Calculating Written calculations 5 E Calculating Written calculations 5 E Handling data Handling Data5 E Handling data Handling Data5 E 5 Handling Data E Probability Probability 5 Handling Data E Probability 5 Handling Data E Shape and Space E Measures 5 Shape and Space E Measures 5 Shape and Space E Measures 5 Shape 5 Shape & spaceand Space E Shape 5 Shape & spaceand Space E Algebra sequences, functions5 F and graphs Solving 5 ProblemUsing and applyingE Solving 5 ProblemUsing and applyingE Solving 5 ProblemUsing and applyingE and powers E IntegersNumbers and5the number system Numbers and5the number system Place value E Numbers and and Egraphs sequences, functions5the number system and powers IntegersCalculating 5 F Calculating Written calculations 5 F 5 Handling Data F Handling data Handling data 5 Handling Data F Shape 5 Shape & spaceand Space F Shape 5 Shape & spaceand Space F FDPRP Numbers and5the number system FDPRP Numbers and5the number system FDPRP Numbers and5the number system Using and applying Reasoning 4 F Shape and Space F Measures 4 Shape and Space F Measures 4 Shape 4 Shape & spaceand Space F Shape 4 Shape & spaceand Space F Shape and Space G Measures 4 Shape 4 Shape & spaceand Space G Algebra 4 F equations, formulae and identities Algebra sequences, functions4 G and graphs Using and applying communicating 4 E Calculating Mental Calculations 4 F Handling data Handling Data4 F Handling data Handling Data4 F Solving 4 ProblemUsing and applying F Solving 4 ProblemUsing and applying F Numbers and4the number system Place value F Calculating Mental Calculations 4 G Calculating Written calculations 4 G Calculating Written calculations 4 G Calculating Written calculations 4 G Calculating Written calculations 4 G Handling data Handling Data4 G Handling data Handling Data4 G Handling data Handling Data4 G FDPRP Numbers and4the number system FDPRP Numbers and4the number system FDPRP Numbers and4the number system and powers IntegersNumbers and4the number system Numbers and and graphs sequences, functions4the number system Shape 3 Shape & spaceand Space F Shape 3 Shape & spaceand Space G Shape and Space Measures 3 Shape and Space Measures 3 Shape 3 Shape & spaceand Space Shape 3 Shape & spaceand Space Algebra 3 equations, formulae and identities Solving 3 ProblemUsing and applying F Calculating Mental Calculations 3 G Using and applying communicating 3 G Using and applying communicating 3 G Solving 3 ProblemUsing and applyingG Using and applying Reasoning 3 G Algebra sequences, functions3and graphs Calculating Mental Calculations 3 Calculating Mental Calculations 3 Calculating Written calculations 3 Calculating Written calculations 3 Calculating Written calculations 3 Handling data Handling Data3 Handling data Handling Data3 Handling data Handling Data3 Handling data Handling Data3 FDPRP Numbers and3the number system FDPRP Numbers and3the number system and powers IntegersNumbers and3the number system Numbers and3the number system Place value Numbers and3the number system Place value Using and applying Reasoning 3 Shape and Space Measures 2 Shape and Space Measures 2 Shape 2 Shape & spaceand Space Shape 2 Shape & spaceand Space Shape 2 Shape & spaceand Space Shape 2 Shape & spaceand Space Algebra sequences, functions2and graphs Calculating Mental Calculations 2 Calculating Mental Calculations 2 Calculating Mental Calculations 2 Calculating Mental Calculations 2 Calculating Written calculations 2 Handling data Handling Data2 Handling data Handling Data2 Handling data Handling Data2 Handling data Handling Data2 2 Handling Data Handling data FDPRP Numbers and2the number system and powers IntegersNumbers and2the number system Numbers and2the number system Place value Using and applying communicating 2 Using and applying communicating 2 Using and applying communicating 2 Solving 2 ProblemUsing and applying Using and applying Reasoning 2 algebra graphs sequences, functions and *A Shape and Space*A Measures Shape and Space*A Measures Shape Shape & spaceand Space*A Shape Shape & spaceand Space*A algebra A equations, formulae and identities algebra A equations, formulae and identities algebra A equations, formulae and identities algebra A sequences, functions and graphs algebra A sequences, functions and graphs algebra A sequences, functions and graphs FDPRP calculating A and powers Integerscalculating A and powers Integerscalculating A calculating Place value A handling data A Handling data handling data A Handling data Handling data data handling A Handling data data handling A handling data A Probability and powers A IntegersNumbers and the number system Numbers and the number system Place value A MeasuresShape and Space A MeasuresShape and Space A Shape and Space A Measures Shape Shape & spaceand Space A Shape Shape & spaceand Space A Shape Shape & spaceand Space A Shape Shape & spaceand Space A Shape Shape & spaceand Space A Solving A ProblemUsing and applying Solving A ProblemUsing and applying Using and applying Reasoning A Using and applying Reasoning A TA level sing and applying U TA level umbers and the number system N TA level alculating c TA level lgebra a TA level hape and Space S TA level andling Data H Overall 7A17A2 Asessment criteria unit factorise quadratic expressions including the difference of two squares, e.g. x2 manipulate algebraic formulae, equations and expressions, finding common factors and multiplying two linear expressions derive and use more complex formulae and change the subject of a formula evaluate algebraic formulae, substituting fractions, decimals and negative numbers solve inequalities in two variables and find the solution set reflect on lines of enquiry when exploring mathematical tasks understand the effect on a graph of addition of (or multiplication by) a constant use fractions or percentages to solve problems involving repeated proportional changes or the calculation of the original quantity given the result of a proportional change solve problems involving calculating with powers, roots and numbers expressed in standard form, checking for correct order of magnitude and using a calculator as appropriate estimate and find the median, quartiles and interquartile range for large data sets, including using a cumulative frequency diagram compare two or more distributions and make inferences, using the shape of the distributions and measures of average and spread including median and quartiles know when to add or multiply two probabilities use tree diagrams to calculate probabilities of combinations of independent events develop and follow alternative methods and approaches select and combine known facts and problem solving strategies to solve problems of increasing complexity distinguish between practical demonstration and proof; know underlying assumptions, recognising their importance and limitations, and the effect of varying them convey mathematical meaning through precise and consistent use of symbols understand the equivalence between recurring decimals and fractions examine generalisations or solutions reached in an activity, commenting constructively on the reasoning and logic or the process employed, or the results obtained sketch, interpret and identify graphs of linear, quadratic, cubic and reciprocal functions, and graphs that model real situations understand and use trigonometrical relationships in right-angled triangles, and use these to solve problems, including those involving bearings understand the difference between formulae for perimeter, area and volume in simple contexts by considering dimensions understand and use congruence and mathematical similarity square a linear expression, and expand and simplify the product of two linear expressions of the form (x ± n) and simplify the corresponding quadratic expression use formulae from mathematics and other subjects; substitute numbers into expressions and formulae; derive a formula and, in simple cases, change its subject use algebraic and graphical methods to solve simultaneous linear equations in two variables solve inequalities in one variable and represent the solution set on a number line find the next term and nth term of quadratic sequences and functions and explore their properties 7A1 7A3 calculate the result of any proportional change using multiplicative methods understand the effects of multiplying and dividing by numbers between 0 and 1 add, subtract, multiply and divide fractions make and justify estimates and approximations of calculations; estimate calculations by rounding numbers to one significant figure and multiplying and dividing mentally use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to round during intermediate steps of a calculation suggest a problem to explore using statistical methods, frame questions and raise conjectures; identify possible sources of bias and plan how to minimise it select, construct and modify, on paper and using ICT suitable graphical representation to progress an enquiry including frequency polygons and lines of best fit on scatter graphs estimate the mean, median and range of a set of grouped data and determine the modal class, selecting the statistic most appropriate to the line of enquiry compare two or more distributions and make inferences, using the shape of the distributions and measures of average and range examine critically the results of a statistical enquiry, and justify the choice of statistical representation in written presentation understand relative frequency as an estimate of probability and use this to compare outcomes of an experiment give reasons for choice of presentation, explaining selected features and showing insight into the problems structure appreciate the difference between mathematical explanation and experimental evidence justify generalisations, arguments or solutions 7A2 7A1 understand and use proportionality 2 2 3 plot graphs of simple quadratic and cubic functions, e.g. y = x , y = 3x + 4, y = x solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a range of contexts: number, algebra, shape, space and measures, and handling data; refine or extend the mathematics used to generate fuller solutions calculate lengths, areas and volumes in plane shapes and right prisms recognise that measurements given to the nearest whole unit may be inaccurate by up to one half of the unit in either direction understand and use measures of speed (and other compound measures such as density or pressure) to solve problems enlarge 2-D shapes, given a centre of enlargement and a fractional scale factor, on paper and using ICT; recognise the similarity of the resulting shapes find the locus of a point that moves according to a given rule, both by reasoning and using ICT use systematic trial and improvement methods and ICT tools to find approximate solutions to equations such as x3 + x = 20 generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on paper and using ICT; write an expression to describe the nth term of an arithmetic sequence 7A1 7A3 construct and solve linear equations with integer coefficients, using an appropriate method 7A2 solve problems and carry through substantial tasks by breaking them into smaller, more manageable tasks, using a range of efficient techniques, methods and resources, including ICT; give solutions to an appropriate degree of accuracy present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory texts interpret, discuss and synthesise information presented in a variety of mathematical forms 7A3 divide a quantity into two or more parts in a given ratio and solve problems involving ratio and direct proportion use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole design a survey or experiment to capture the necessary data from one or more sources; design, trial and, if necessary, refine data collection sheets; construct tables for large discrete and continuous sets of raw data, choosing suitable class intervals; design and use two-way tables calculate percentages and find the outcome of a given percentage increase or decrease add and subtract fractions by writing them with a common denominator, calculate fractions of quantities (fraction answers), multiply and divide an integer by a fraction select, construct and modify, on paper and using ICT: pie charts for categorical data bar charts and frequency diagrams for discrete and continuous data simple time graphs for time series scatter graphs and identify which are most useful in the context of the problem communicate interpretations and results of a statistical survey using selected tables, graphs and diagrams in support find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y = mx + c correspond to straight-line graphs 7A3 use the equivalence of fractions, decimals and percentages to compare proportions construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations 7A3 solve geometrical problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons deduce and use formulae for the area of a triangle and parallelogram, and the volume of a cuboid; calculate volumes and surface areas of cuboids know and use the formulae for the circumference and area of a circle use straight edge and compasses to do standard constructions classify quadrilaterals by their geometric properties identify alternate and corresponding angles: understand a proof that the sum of the angles of a triangle is 180° and of a quadrilateral is 360° visualise and use 2-D representations of 3-D objects enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor know that translations, rotations and reflections preserve length and angle and map objects onto congruent images use logical argument to establish the truth of a statement 7A2 7A1 devise instructions for a computer to generate and transform shapes and paths draw simple conclusions of their own and give an explanation of their reasoning 7A2 7A1 construct, express in symbolic form, and use simple formulae involving one or two operations 7A2 7A1 show understanding of situations by describing them mathematically using symbols, words and diagrams 7A1 7A3 use known facts, place value, knowledge of operations and brackets to calculate including using all four operations with decimals to two places solve simple problems involving ratio and direct proportion use a calculator where appropriate to calculate fractions/percentages of quantities/measurements understand and use an appropriate non-calculator method for solving problems that involve multiplying and dividing any three digit number by any two digit number ask questions, plan how to answer them and collect the data required create and interpret line graphs where the intermediate values have meaning in probability, select methods based on equally likely outcomes and experimental evidence, as appropriate understand and use the probability scale from 0 to 1 understand that different outcomes may result from repeating an experiment read and interpret scales on a range of measuring instruments, explaining what each labelled division represents solve problems involving the conversion of units and make sensible estimates of a range of measures in relation to everyday situations understand and use the formula for the area of a rectangle and distinguish area from perimeter reason about position and movement and transform shapes use a wider range of properties of 2-D and 3-D shapes and identify all the symmetries of 2-D shapes use and interpret coordinates in all four quadrants 7A3 identify and obtain necessary information to carry through a task and solve mathematical problems check results, considering whether these are reasonable solve word problems and investigations from a range of contexts round decimals to the nearest decimal place and order negative numbers in context use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 and 1000 and explain the effect recognise and use number patterns and relationships 7A3 solve simple problems involving ordering, adding, subtracting negative numbers in context apply inverse operations and approximate to check answers to problems are of the correct magnitude understand and use the mean of discrete data and compare two simple distributions, using the range and one of mode, median or mean interpret graphs and diagrams, including pie charts, and draw conclusions use language associated with angle and know and use the angle sum of a triangle and that of angles at a point measure and draw angles to the nearest degree, when constructing models and drawing or using shapes use equivalence between fractions and order fractions and decimals reduce a fraction to its simplest form by cancelling common factors understand simple ratio use their own strategies within mathematics and in applying mathematics to practical contexts 7A2 choose and use appropriate units and instruments interpret, with appropriate accuracy, numbers on a range of measuring instruments use the properties of 2-D and 3-D shapes make 3-D models by linking given faces or edges and draw common 2-D shapes in different orientations on grids find perimeters of simple shapes and find areas by counting squares reflect simple shapes in a mirror line, translate shapes horizontally or vertically and begin to rotate a simple shape or object about its centre or a vertex begin to use simple formulae expressed in words 7A2 7A1 use and interpret coordinates in the first quadrant 7A3 present information and results in a clear and organised way 7A2 use a range of mental methods of computation with all operations group data, where appropriate, in equal class intervals understand and use the mode and range to describe sets of data develop own strategies for solving problems 7A2 7A1 search for a solution by trying out ideas of their own 7A2 use place value to multiply and divide whole numbers by 10 or 100 recall multiplication facts up to 10 × 10 and quickly derive corresponding division facts 7A3 use efficient written methods of addition and subtraction and of short multiplication and division multiply a simple decimal by a single digit solve problems with or without a calculator check the reasonableness of results with reference to the context or size of numbers collect and record discrete data continue to use Venn and Carroll diagrams to record their sorting and classifying of information construct and interpret frequency diagrams and simple line graphs recognise approximate proportions of a whole and use simple fractions and percentages to describe these order decimals to three decimal places begin to understand simple ratio recognise and describe number relationships including multiple, factor and square 7A3 recognise and describe number patterns 7A3 classify 3-D and 2-D shapes in various ways using mathematical properties such as reflective symmetry for 2-D shapes begin to recognise nets of familiar 3-D shapes, e.g. cube, cuboid, triangular prism, square-based pyramid use a wider range of measures including non-standard units and standard metric units of length, capacity and mass in a range of contexts use standard units of time recognise shapes in different orientations and reflect shapes, presented on a grid, in a vertical or horizontal mirror line describe position and movement 7A2 7A1 select the mathematics they use in a wider range of classroom activities derive associated division facts from known multiplication facts begin to organise their work and check results 7A2 use and interpret mathematical symbols and diagrams 7A2 7A1 try different approaches and find ways of overcoming difficulties that arise when they are solving problems 7A2 understand a general statement by finding particular examples that match it 7A1 recognise a wider range of sequences 7A1 7A3 add and subtract two digit numbers mentally use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers add and subtract three digit numbers using written method multiply and divide two digit numbers by 2, 3, 4 or 5 as well as 10 with whole number answers and remainders solve whole number problems including those involving multiplication or division that may give rise to remainders gather information construct bar charts and pictograms, where the symbol represents a group of units use Venn and Carroll diagrams to record their sorting and classifying of information extract and interpret information presented in simple tables, lists, bar charts and pictograms use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent begin to use decimal notation in contexts such as money recognise negative numbers in contexts such as temperature understand place value in numbers to 1000 use place value to make approximations review their work and reasoning begin to use a wider range of measures including to use everyday non-standard and standard units to measure length and mass begin to understand that numbers can be used not only to count discrete objects but also to describe continuous measures use mathematical names for common 3-D and 2-D shapes describe their properties, including numbers of sides and corners describe the position of objects distinguish between straight and turning movements, recognise right angles in turns and understand angle as a measurement of turn recognise sequences of numbers, including odd and even numbers 7A1 7A3 use the knowledge that subtraction is the inverse of addition and understand halving as a way of use mental recall of addition and subtraction facts to 10 use mental calculation strategies to solve number problems including those involving money and measures choose the appropriate operation when solving addition and subtraction problems record their work in writing sort objects and classify them using more than one criterion understand vocabulary relating to handling data collect and sort data to test a simple hypothesis record results in simple lists, tables, pictograms and block graphs communicate their findings, using the simple lists, tables, pictograms and block graphs they have recorded begin to use halves and quarters and relate the concept of half of a small quantity to the concept of half of a shape count sets of objects reliably begin to understand the place value of each digit; use this to order numbers up to 100 discuss their work using mathematical language 7A2 begin to represent their work using symbols and simple diagrams explain why an answer is correct select the mathematics they use in some classroom activities predict what comes next in a simple number, shape or spatial pattern or sequence and give reasons for their opinions 7A1 apply to the graph y = f(x ) the transformations y = f(x ) + a , y = f(ax ), y = f(x +a ) and y = a f(x ) for linear, quadratic, sine and cosine functions recognise limitations in the accuracy of measurements and judge the proportional effect on solutions solve problems involving more complex shapes and solids, including segments of circles and frustums of cones prove and use the alternate segment theorem prove the congruence of triangles and verify standard ruler and compass constructions using formal arguments solve exactly, by elimination of an unknown, two simultaneous equations in two unknowns, where one is linear in each unknown and the other is linear in one unknown and quadratic in the other or of the form x 2 + y 2 = r 2 solve quadratic equations by factorisation, completing the square and using the quadratic formula, including those in which the coefficient of the quadratic term is greater than 1 derive relationships between different formulae that produce equal or related results know and understand that the intersection points of the graphs of a linear and quadratic function are the approximate solutions to the corresponding simultaneous equations construct the graphs of simple loci, including the circle x 2 + y 2 = r 2; find graphically the intersection points of a given straight line with this circle and know this represents the solution to the corresponding two simultaneous equations plot and recognise the characteristic shapes of graphs of simple cubic functions (e.g. y = x 3), reciprocal functions (e.g. y = , x ≠ 0), exponential functions (y = k to the power x for integer values of x and simple positive values of k) and trigonometric functions, on paper and using ICT understand and use direct and inverse proportion; solve problems involving inverse proportion (including inverse squares) using algebraic methods use surds and π in exact calculations, without a calculator; rationalise a denominator such as one over square root of three = square root of three over three check results using appropriate methods use calculators, or written methods, to calculate the upper and lower bounds of calculations in a range of contexts, particularly when working with measurements select and justify a sampling scheme and a method to investigate a population, including random and stratified sampling understand how different methods of sampling and different sample sizes may affect the reliability of conclusions drawn construct histograms, including those with unequal class intervals use, interpret and compare histograms, including those with unequal class intervals recognise when and how to work with probabilities associated with independent and mutually exclusive events when interpreting data understand and use rational and irrational numbers understand upper and lower bounds use the sine and cosine rules to solve 2-D and 3-D problems calculate the area of a triangle using the formula ab sin C understand the difference between formulae for perimeter, area and volume by considering dimensions understand the necessary and sufficient conditions under which generalisations, inferences and solutions to geometrical problems remain valid draw, sketch and describe the graphs of trigonometric functions for angles of any size, including transformations involving scalings in either or both of the x and y directions calculate and represent graphically the sum of two vectors, the difference of two vectors and a scalar multiple of a vector; calculate the resultant of two vectors understand and use the commutative and associative properties of vector addition solve simple geometrical problems in 2-D using vectors systematically model contexts or problems through precise and consistent use of symbols and representations, and sustain this throughout the work use mathematical language and symbols effectively in presenting convincing conclusions or findings; critically reflect on own lines of enquiry when exploring; search for and appreciate more elegant forms of communicating approaches and solutions; consider the efficiency of alternative lines of enquiry or procedures present rigorous and sustained arguments; reason inductively, deduce and prove; explain and justify assumptions and constraints justify and explain solutions to problems involving an unfamiliar context or a number of features or variables; comment constructively on reasoning, logic, process, results and conclusions Using and applying Numbers and the number system 7GM3 N1 N2 N4 8GM1 8NA1NA1NA1 7A37A47GM1 7GM4GM4 NM3 S1 S2 8A28A3 8A4A4 8N2 8N3 8S1 8S2 8A2 8A2 8A2 8A4 8A2 8A3 8N3 8S2S2 8S2S2 8GM1 8A28A3 8NA1 8A28A3 8GM1 8A3 7GM4 7A4 8A2 8A2 8A4 8A4 7A3 8NA1 N2 N1 8N3 N2 8N2 N1 8N3 8N3 8S2S2 8S2S2 8S2S2 8S2S2 8S2S2 S2 8GM1 S1 8GM1 7A2 7GM3 8A28A3 8NA1 N4 8N2 8A3 7A4 N4 8A2 7GM1 7GM4 8GM1 7A3 8NA1 7A2 7A4 8A4 S2 8GM1 S2 8A3 7 7GM3 7A37A4GM1 N2NM3 8A3 N4 N4 S1 S2 8S2S2 N2 N2 8N2 S2 8S2S2 S2 8S2S2 S1 S1 7A3 8A3 N2 N4 8N2 7A3 8A3 7GM3 8GM1 7GM1 7GM3 7GM1 8GM1 7GM4 7GM3 8GM1 7GM3 8GM1 7GM3 7GM4 7GM4 7A2 7A4 8A2 8NA1 7GM4 8GM1 7A37A4 S1 S2 8A3 8GM1 8NA1 7A37A4 8A2 8A4 7 7A37A4GM1 N2NM3N4 S2 8A3 NM3 8N3 N4 8NA1 8N2 N2NM3N4 N1 NM3 8N2 8N3 S2 8S2S2 S2 S1 S1 S1 7GM1 NM3 NM3 7GM1 7GM4 7GM1 7GM4 8GM1 7A3 8A3 8NA1 7GM3 N2 N4 S2 N1 N4 N1 N2NM3N4 S2 N1 8N3 N1 8N2 8N3 7A3 N1 N1 NM3 8N3 S2 8S2S2 S2 8S2S2 7GM3 8GM1 7GM3 7GM1 8GM1 N4 N2 8N2 N4 N2 8N2 N4 8N2 7A2 N1 N2NM3N4 8GM1 8NA1 NM3 7GM1 NM3 7GM3 7GM1 7GM4 8GM1 7GM3 7GM1 7GM1 7GM4 7A37A4 8A28A3 8A4 7A3 8NA1 7A3 7GM3 S1 S2 N1 NM3 S2 8S2S2 S2 8S2S2 7A3 7GM1 N1 N2NM3N4 S2 7A3 S1 N1 8N2 8N3 7A3 N1 8N2 N1 NM3 8N3 N1 NM3 8N3 N1 NM3 8N3 N1 NM3 8N3 S1 S2 8S2S2 S2 8S2S2 N2 N4 N1 8N2 8N3 N4 8N2 7A3 8NA1 7A3 7GM1 7GM4 8GM1 7GM1 NM3 7GM4 7GM4 7A37A4 8A2 8A4 7GM3 N2 S2 N1 N4 7A2 S1 S2 7A2 7A4 7GM3 N1 NM3 S1 S2 7A2 N4 S2 7A4 8A2 7A3 8NA1 N1 8N2 8N3 N1 8N2 8N3 N1 8N3 N1 N1 S2 8S2S2 S2 8S2S2 S2 8S2S2 N2 N4 8N2 N1 8N2 8N3 N1 8NA1 N1 8N3 N1 8N3 N1 N2 NM3 7GM1 7GM4 7GM1 7GM4 7GM4 7GM4 7GM3 7A3 8A3 8NA1 S1 8S2 8S2 8S2 N2 N1 7A2 7A4 S2 7A4 88 GM3M3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 8 GM3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 equations, formulae and identities Algebra 8 B derive sequences, powers B use FDPRP Calculatingexpressions equationsfractions, Integers algebraic factorise more complex formulae and solveandthe of manipulateformulae 8Calculating 8AlgebratheBlines identities reflect 8 and use andfunctions formulae, 8 BAlgebraon B solve applying including problems equations, Using and and graphs B or percentages evaluate quadratic formulae,fractions change or Reasoning algebraicandData substituting 8 Handling Handling data two involvinggraphfindaddition of (or the inequalities the effect onData 8 B of theandtwo find involvingproblems variables and estimate numbers understand infinding common 8 B compare and set to solveofcalculating with a repeated and multiplying Handling andtwo squares, decimals data Handling mathematical solution enquiry offormula subject when exploringnumbers treetasks expressions, negative makeB factors proportional difference aHandling Datapowers, rootsdiagrams to Reasoning Using and two x2of Solving the + Data 8 use more distributionsand applying 8 B distinguish or changes quartiles aandinterquartile range using the data Probability in standard form,Bthe original for largeorder Probability = by) 3)constant inferences, and median, orHandling (x – 3) ofchecking for correct expressedexpressionsapplying 8 B selectdevelop multiplication(x calculation8 applyingwhenquantity and Reasoning UsingUsing and know 8 B of average e.g. linearthe distributions and measures to add between FDPRP sequences, result facts a Problem 9 Using and and applyingfrequency diagram probabilities cumulative 8 proof; calculate practical and the graphs Algebra shape –two functionsproportional B examine B sketch, Reasoning probabilities calculator B appropriate givenincluding using aofa numberchange 8 know communicating of using combinations of sets, theknown Using applying 8 andas convey multiply Numbers and and problem systemindependent of magnitude andmethods and B understand and use follow combine Shape demonstration quartiles strategies and solving Measures including median 8 approaches consistent meaning through and spreadassumptions, identities Algebra activity, eventsalternative andgraphsreached in an importance generalisations equivalence 8 linear, quadratic, Measures Shape solutions between recurring use mathematicalidentify Space of B understand C cubic underlying formulae and recognising their 7 C square equations, to solve and or Space complexity understandformulae increasingright-angled the equations, the relationships in precise and interpret problems of and identities Algebra 7triangles, trigonometrical Shape formulae from mathematics and and understand use of symbolsfunctions, expand other that model and a linear& space and the effect of varying themthe commenting constructively ongraphsB subjects;useand Shape expression, and and the 8 simplify equations, formulae and identities Algebra area and limitations,to solve and Spaceincluding 7thoselogic decimalsthesefractions problems, reasoning and real use and and reciprocal difference between formulae for perimeter, 7 C solve equations, formulae and identitiesAlgebra 7 C find the employed, sequences, functionsmathematicalAlgebra dimensions use congruence and expressions tosimilarity C ± n) or the processgraphical expressionssolve formulae; substitutebearings into methodsresultsjustify (x situations numbersvariablegraphs theand form any of two linear C calculate and volume in simple 7 and bytherepresent of product calculations Calculating 7 C the calculator algebraic and Handling 7 or makeof useobtained Calculating Data consideringconstruct Place value in nthcontexts Cand C select, a the solution involving data one term of quadratic sequences of and Written Calculating inequalities Handling understand the effects and Handling and FDPRP Calculating 7 C simple cases, change its Handlingformula and, in Data subtract,result problem next simplify the corresponding quadratic expression derive a Calculating 7 C add, 7in two variables and FDPRP datalinear equations7 C suggest a FDPRP number line simultaneous Handling Data 7performmultiply and term data appropriately to of calculations; mean, modify, estimatesdata Handling Data 7 C estimate the or Handling proportional change using properties complex Handling and approximations C compare two and 1 efficiently and multiplying paper and their ICT suitable graphical set on aonand explore usingnumbers frame questions functions and statistical multiplicative methods to explore usingdividing by methods, between 0 divide fractions subject calculations by rounding numbers to one of C examine and median and range and make any size, includingnot more distributionsprogress estimate data Handlingset7angrouped data critically to calculations with numbers ofC7possibleknowingthe the HandlingSolving Usingidentify enquiry Csources of Probability Handling Data applying 7 C give reasons Problem conjectures;and of inferences, solve representation Usinga Data understand relative and raiseSolving Using and applying 7 C using communicatingtoand class, selecting 7 statistic most increasingly and statistical Problem the distributions steps ofjustify theaveragea significantafigure estimate and of best the of scatter of the modal enquiry, and anddividing mentally determine polygons and problemsand calculation round duringdemandingand applying fitevaluate this to results of as an to minimisemeasureson choice shape of planintermediate of probability and use frequency offunctions multiplying C justifyappreciate sequences, presentation, graphs lines it Algebra 7 C plot mathematical explanation for choice Using and and number system 7 C features biasdifference betweenthe explaining selected Reasoning to howand applying 7 presentation and appropriate theand Space 7 C understand and FDPRP Numbers line of enquiry recognise that the rangerepresentation statistical outcomes of an in writtenmathematics across Measures Shape connections and compare explorequadratic or solutions graphs of simpleargumentsandin and showing insight into the problems structuree.g. y graphs experiment functions, solutions;space Shape and Space 7 C enlarge 2-D generalisations, and Space 7 C understand and cubic Shape & Solvinguse proportionality 6 C solve use experimental evidence and when calculate6 C mayin sequences, functions and graphs Algebra 6 C use Measures andgiven to identitiesAlgebra lengths, understandformulae andthe applying equations, contexts: number, algebra, find the apply Pythagoras’ theorem Spacesolving problems be measurements Shape = x2, centre Shapeand volumes in plane shapes and right prisms 7 Problemof ShapeUsing and nearest whole unit locus of a range=given+a4, y = x3 enlargementshape, fractional space measuresterms shapes, 3x2 speed (and other using C and a by and generate and problems trial areasy & space and oneofidentitiesmethodsmeasures systematic by carry through substantial tasksD ICT the 2-D measures, of a improvement Algebra and andhalf to a term-to-term inaccurateof up toaccording data;givenin or6extendby equations, formulae handlingof compoundeither the and factor,moves sequence the unit rule, both a point that on Using and applyingrefine a survey or communicatinginto smaller,using sequence, scale density or pressure) 6 C D interpret, ontasks, recognise tools approximate direction data Handling equations6 D present Handling themsolve linearsolutionsmanageable paper breaking and definitions of the design such as findUsing and applying 6 ICT;with integera or position-to-term paper C Data toa quantity into discuss mat...to Calculating 6ICTdivide solve problems such Reasoningand FDPRP Calculating 6 C usemore to equations construct of theusing reasoning to capture the necessary two similarityreasoned argument, using todata fractions by FDPRP range of efficientadd proportional reasoningnth information presented describe in FDPRP concise,x = 20 resultingDataand select, a from the or experiment using anan calculate method variety coefficients, FDPRP Calculating 6 ratio and solve problems one and usingdataa write6 appropriatesubtractconstructofto Handling in using partsICT;Handling expression symbols, and and more + a Calculating D techniques, methods synthesise given D shapes percentages 6D as x3 a problem, choosing the correct numbers to take related trial solveof them with a ICT; give6solutions to calculate find writing on paper andsequenceexplanatory texts diagrams,data formscommonpercentagerecord all or resources, arithmetic Data 6and,D communicate more sources; Handling Datadenominator, 6 D refine sequences, functions using termthe an graphsofdirect proportion mathematical andandgiven ICT:if Algebra an plot the Handling ratio design,and graphs and increase Probability includingaData D know that the sum of modify, outcome whole 6 D findnecessary, involving or as a Probability Handling (fraction answers), 6 D as 100%,of Handling and numberAlgebra multiply and Shape functions andof sequences,quantities construct systemsingle possible mutually and data collection and results graphstablessolveexplicitly appropria... categorical where y is given D use pie charts linear Shape for large interpretations sheets; thedata D deduce and use the fractionsNumbers and Space a statistical survey using FDPRPof Shape Measures mutually outcomes decreasespaceall exclusiveexclusiveC for 6 graphs & forof functions, Space 6 outcomes is 1 probabilities continuous sets 6 raw data, ... of construct functions arising diagrams systematic way discrete ofinteger by a using properties of the form y = divide antables, graphs adecimals in a percentages selected andproblemsof andeventsand inproblems of to geometrical thesuccessivefrom real-lifeofsupport and equivalencetwofractions,thatSpace and parallelogram, angles, Shape and x; of Shape fraction in use for recognise ... terms this when solving triangleknow identify the events & space area Spaceequations and use formulae Shape and plot 6D 6 and their space Shape andproblems D usegraphs Measures proportions graphs; interpret and intersecting Shape & space Shape and Space graphs straight compare and corresponding calculatetriangles and alternate Shape corresponda cuboid;Space 6 D classify 2-D parallel& corresponding lines, and 6 Cvolumes and mx + c & space Shape and Space 6area of a circle ofunderstand a and the& space Shape and Space D visualise Shape volume formulae for realof to straight-line 6 D enlarge and and angles: Shape from the circumference and constructions arisingpolygons situations standard know that edge andspace Shapeto do Space 6 D devise other that compasses geometric of a quadrilaterals bycentre and of Shape areas of cuboids anglesobjects and a positive surface&givensumandthe ofreflectionstriangle is length shapes, the a their andenlargement logical Reasoning formulae and 3-D 5 DAlgebra equations, use 2-D representations identities Ddraw known facts, Written Using of applying 5E use simple proof calculations Calculating6 properties5 E 180° translations, rotations and applying use show preserve E instructions for a computer Using 360° communicatingscale factor to generate and transform argumentquadrilateral the truth ofcongruent images and of acalculations own and give a statementsimple knowledge Written and map Calculating E and calculator whole-number theirin symbolic form,5anda brackets to conclusions establish isof onto5 anuse use Written calculations Calculating 5 E understand and angle to of of situationsoperationsexplanation of understanding construct, express objects bysimple problems and FDPRP and Calculating place value, paths 5 E solve describing them shapes appropriate non-calculatorcreate and interpret where data Handling Data in probability, with theiranappropriate one orall E5 fractions/percentages use reasoningHandling 5 four operationsdiagrams formulae involving toData two 5 words questions, plan Probability Handling symbols, E method Handling data using calculate E ask and select mathematically Handling including using proportion calculate ratio and directData operations for solving involving Shape and Space 5 E solve problems Measuresthat involve Space E and and have decimals where the intermediate data interpret how to answer on equally problemsbasedthem Datacollect thevalues and any the ProbabilityShape and multiplying readdividing different line graphs Handling Data 5likely outcomesthat use MeasurestoHandling and 5 E5understandrequired Probability two places of quantities/measurements E5understand and use methods Shape and Space E understand and of Measures number by any 1units and make sensible involving scale from 0 as three digit a range of from two digit E use a scales onspaceresult measuring instruments, wider meaning the conversionto appropriate reason probability may Shape and Space 5 E experiment Shape & space Shape andrepeatingnumber about Shape & Solving Using rectangle outcomes for the area of aapplying 5 and distinguish experimental evidence, and Space 5 anE identify and the formula a range and graphs in relation to sequences, functionsof measures Algebra 5 F use and Problem what each explaining properties of and and 3-D shapes and E estimates of Numbers labelled division represents use range value movementand applying 5 shapes 5system position and 2-D the and the system Place of and powers Numbersnumberthrough a identify information Problem Solving Using and transform E solve area from situations in and applying 5 E checkword Integers coordinates obtain necessaryUsing all graphs Numbers and task Problem perimeter and four carry number the everydaySolving place value toquadrants sequences, functionsCalculatingmultiply and divide interpret and powers 2-D shapes5 F solve simple use allE round decimals whether toF decimal place 5 the symmetries of understanding Handling DatatheseFare reasonable Written Integerscalculations to the nearestunderstandcontexts results, considering Calculating 5 apply of and Handling data investigations from a range inverseand problems mathematical problems and solve and of E recognise5and use number of number system Shape and Space10,F useand 1000 in whole numbersnumbers Datatoby interpret graphs and Shape & data 5 problemsspace approximate adding, Fanswers to the meanspace andordering, checksubtractingand Shape & involving data Space 5 measure order negative Handlingand contextsystem 5 simple operations and Shapethe and5compare two F use Handlinganddiscrete decimals F 5 100 language patterns FDPRP Numbers and the numberone of mode, angle of the context FDPRP numbers incorrectknow and use conclusions distributions, relationships degree, when constructing and explainwiththeand and number systemtheF reduce using pie charts, 4 negativeNumbers and applying and use their own associated Using the range andF draw Reasoning between problems areto effect fractions andsystemfractions and diagrams, includingnearestnumber order 5 F draw anglesthe angle the magnitude equivalence its simplest form 4 Fcancelling5 Measuresto mean FDPRPaNumbersand that of angles at a point a fractiontriangle and Space F choose and or Shape and Measures Shape and median and drawing or using 4and in applyinguse sum of & space ShapeSpace by interpret, with common Shape strategies within mathematicsshapesF use thesimple decimals simple ratioand Space 4 G reflect models& space Shape and Space 4 F make 3-D Shape factors understand accuracy, numbers on a range of appropriate appropriate units and instrumentsfind perimeters of Measures a mirrorand Space 4or edges and draw models in Shape given translate shapes horizontally shapes by of to practicalfaces G mathematics 2-D and 3-D contexts Algebra 4 F begin equations, instruments shapes and properties linking line, identitiesAlgebra 4 G use measuring formulaefind areas by counting squares and sequences, functions and graphs 4 E communicating Usingin different 4simplepresent grids simple shapes and Calculatingaorientations onor Mental Calculations rotate F common 2-D shapes and applying use data, where or use simple formulaetoData 4 F group a range of to vertically and begin expressedunderstand and use Handling data Handling the 4 quadrantshape Data interpret coordinates in in a first F andwords Handling data Handlingand clear in 4 system 4 F use information and centreand the numberorganised for a Problem Solving Using and applying Problem Solvingresultsor a vertex G recallapplying Place value Numbersclass intervals allF develop own object about in equalCalculating with 4 F search way mental methods of computation 4 G useoperations Mental Calculations Calculating sets of data appropriate, its Using describe 4 efficient range Written calculations problems the mode andsolving to and divide whole numbers by by to multiplication multiply strategies for facts up to 10 × theirG multiply derive place valuetrying out ideas of 104and quickly a simple solutioncalculations Calculating 4 G checkproblems Written calculations Calculating subtraction and Written written methods of addition andG continue the of ownsolve to use Data 4 Handling data Handlingfacts 4 G collect and record 10 or 100 a singleresults with reasonableness of digit Handling data divisionthe number system 4 the FDPRP by with multiplication and corresponding Handling divisionreference to and decimal Numbers and Data shortor without Handling Data 4 G construct G Handling data a calculator to record their sorting and Venn and Carroll diagrams size Integers data powers the proportions discreteor approximatethe number system 4 G and use FDPRP Numbers andand graphs the numberorder to context&Numbers numbersnumberNumbers andsystem FDPRP spaceof and and Space 3of a wider begin interpret andfunctions Space and simple line graphs recognise Shape andNumbers andsystem 4 Grange of sequences, information Shape & frequency diagrams 3 G use abegin to3-D and whole the Measuresto three decimal places 3 relationships classifying of and describe number G decimals space Shape and Shape Shape fractions Shape and Space to F classify these understand simple ratio 4 G recognise 4 G recognise and3 G number space andnon-standard mathematical simple &system ShapewaysSpace unitsrecognise describe number including Measures nets of familiar percentages describe standard 2-D shapes in various Spaceusinguse standard units of measuresmultiple,and and 3shapes, e.g. cube, recognise different factor 3-D square and shapes& Shape orientations G includingSolving Using and Space 3reflect shapes, and 3 for Problem such as reflective symmetry F selectshapes Shape units of length, and applying G describebegin patternsinspace Shapecapacity andAlgebra 2-D range of equations, metric triangular prism, identities mass in3aG properties formulae and square-based pyramid the time cuboid, Calculations Calculating 3 Ghorizontal mirror position Mental and they use and wider or derive associated presented onmovementa a applying 33 G try different contexts Solving Usingof ‘=’ applying Gofsign) to to understand the mathematics a grid, inand applying understand a communicating Using and (the G 3 G classroom communicating Using applying 3 ‘equals’begin Problem Using and in vertical range use and line Reasoning from role facts approaches functionsways graphs Algebra difficulties divisionCalculationsand check results factsG recall organise their workknown multiplicationexamples that activities mathematical symbols and diagramssubtract Mental Calculations Calculating 3 G use mental sequences, and findCalculating 3 G solve 3 Written interpretstatement by finding particular andand general calculations Calculating 3 G multiply Mental calculations and of overcoming whole add G add Written calculations Calculating 3problems subtract Written when they are of sequences and of addition and subtraction it that digitproblems includingfacts to 20 in solvingcharts recognisedata Handling Data 3 G construct bar match two a wider mentally those4use5 as well as 10 number digit numbers solving or Venn two arisenumbers rangeData 33, involving and Handling numbers using written dividedigitdata Handling Data 3 G method and interpret Handling data Handling by 2, G extract Handling Handling 3 problems involving larger numbergather information three Numbers and the numberssystem FDPRP Handling dataor division Datamay give rise 3 G use and pictograms, where the their Gremainders symbol the multiplication powers Numbers and represents asystem to group Carroll diagrams and in that lists, simple sorting and bar charts with whole number recordnumber system 3classifying Integers Numbersto answers andtables, numberbegin to FDPRP and information presented Space 2 Gparts of a use a wider Measures Shape and the unitsfractions that are several begin to whole and simplevalue of information remainders Numbers and the number system 3 G as ofG recognise negative numbers in contexts G 3 G use Place value Numbers and the number system Place 3 decimal notation in contexts such as moneywork recognise when two simple fractions are equivalent use pictograms and Space to G G reviewunderstand ReasoningShape including 2 3 begin to their and of measures applying use range Measures Using value in numbers everydaysuch understand place approximationsto 1000 non- Shape & space Shape andnot only2 Gcount discrete temperaturetocan be used Space 2 G distinguish Shape & space Shape & space Shape and Space 2 use the place value make Calculating 2 G G use that numbers standard units and reasoning Shape and Space 2 G describe their Mental Calculations and graphs to describe and sequences, functions Shape & space Shape and SpaceAlgebra recognise standard straight and turning to measure length the between and names for common 3-D and 2 G shapes 2-D mathematical subtraction ismovements,ofcorners knowledge also Mental position of that to numbers thesides properties,sequences of numbers,G use measures objects Calculations Calculating 2 inversemental recall Mental Calculations Calculating 2 G choose addition mass but including and understand use mental of including odd recognise objects describe continuousand as a and right angles in turns angle the of addition appropriate operation when number and understandsubtraction asolving10 objects doubling Written calculations CalculatingG sort problems even numbers turn solve2 to record and strategies to Data way G ‘undoing’ and calculation andofhalving as facts 2 of additiontheir work Handling data Handling measurement Handling Data 2 G understand sort data Handling versaHandling Data 2 G collect and their Handling data Handling those and the numbercommunicate including data Handling Data 2one system 2 G in in writing data involving than G record results and vicethem using more money and measuresbegin to classify FDPRP Numbers to handling data subtraction relating and the number system 2 G criterion Numbers Place a using hypothesis vocabulary problems Numbers and to test valueandthe simple lists, and thepictograms and Integers andtables, pictograms tables,Gconcept of half findings, simple Using and applying the number system communicating Using and relate 2 discuss use halves powers applying 2 G 2 G begin to simple lists,Using and and applying predict what their communicating quartersrecorded algebra graphs use Reasoningsets of objects reliably block 2 *A apply begin to understand the place value2 G explain why and applying communicating Using and graphs andeach shape sequences, functions the symbols 2 G count their work usingconcept of of G of adigit; block graphs they have and applying half select the a represent quantity to Space 2 *A recognise limitations of a small ShapeUsing number, shape or spatial Problem Solvingsimpleupidentities algebra 2 A solve work using formulae the transformations simple + to to nextmathematical to 2 comesgraph in = f(x) and identities algebra = f(x) equations, formulae and language 2 y 2 A solve equations, Measures correct Measures isnumbers thisanswer Shape and Space100 solve problems a, anthe order ytheyand in some *A 2 *A prove the diagramsspace of useandanSpacealgebra 2 A and use mathematics Shape of give reasonsjudge the exactly, f(x+a) graphs Shapeaccuracy Shape and af(x) for linear,activities sequences,=functions and = unknown, two their in the & more measurements 2 completing pattern &bysequence by and Spacealgebra 2quadratic, quadratic Shape or equations andshapesclassroom A plot and y = f(ax), spacecomplexfactorisation, *A for 2 including sequences,eliminationand graphs and prove the involving y formulaeand yidentitiesalgebra 2A know sequences, functions and verify algebra ruler triangles equations, functions solutions and solids, of the and congruence effect 2and in graphs opinionscalculatingonof understandstandard direct and and understand thatand intersection cones where points derive the alternateofequations frustums ofand use the one FDPRP of graphs theorem proportionalusing thethesimple loci, including A of circle constructcosine functions two 2 A of graphs sine and and circles A simultaneouspowers calculatingformula, including π segmentsthe segmentquadraticunknowns, produce square and between different formulae that and relationships the characteristic shapes arguments recogniseconstructions using formal use surds Integers a linear and quadratic function are the graphs = compass r2;calculating 2 problemsother is linear in one solve and intersection Place in in find graphically of calculators, inverse is linearof each unknown A usecalculator; rationalise a inversecubic functions (e.g. y athe quadraticpoints of x2exact proportion;coefficientthex3),involvingorterm is those or calculations, calculating the reciprocal written simplevalue powers without 2=A 2 A check results a in + y2 which handling data corresponding justify equal andcalculate thethe 2 Aand lower bounds of Integersstraightthe withdata other or of the how and approximate solutions to this circle andusing algebraic Handlingrelated line inverse squares) know form... (including methods, (e.g. y results unknown data handling inupper selectroot of this = Handling and = as proportionto such , one the understand and a given data handling xover squareinterpretthree greater than 1quadratic data 0),A exponential functions functions data handling data 2 A to investigateand how denominator equations method use, when a Handling data a range a 2≠ 2 construct histograms, using appropriate of samplingrecognisenumber when samplingmethods methods A and particularly system Probability handling Numbers simultaneouspowersdata contexts,different sample Handlingand Integers scheme and to calculations in solution of the correspo... different the of threexoverintegerand the represents power including those with methods histograms, three justify square rootthe with forand applying with use explain (y = k towithincludingunequal classstratifiedunequal Place valueUsing compare space Using and Space 2 2 understand Shape & Shape measurements toA understand and reliability 2 A intervalssampling includingSolving the use rationalvalues... sinedrawn probabilities associated the and population,affectShapeand theanduseA system and the ProblemwithNumbersrandom 2of conclusions sketch ReasoningShape and Space number draw, theA working space Shapeapplying A understand 2 sizes may Shape and and Space 2 A A independent Measuresthose ShapeSpace 2 A andA calculate andof 2 work& space and and Space 2 irrational area Problem Shape & Solving and involving 2 calculate the MeasurestoUsingUsing and applying interpreting data mathematicalexclusivelower bounds 2 A rigorous class intervalslanguageevents whenunder which in and mutuallyto solve 2-D conditions present area and solutions problems applying perimeter, Reasoning uppergraphs of foran problems context and describe A effectively understandand sufficientandtrigonometric functions and necessary between formulaesymbolsA understand for difference graphically and and Space unfamiliar numbers space Shape and of two C cosine & using the the sum ab sin Shape rules the formula 3-D 2 vectors, the represent ofarguments; reason inductively, deduce a triangle convincingcontexts or problems through or a number and sustained model or and solutions to generalisations,Shapeconclusions 2 Afindings; critically presenting considering andvariables; solve involving systematicallysize, including transformationssimple Shape & spacefeaturesdimensions or comment of volumeof anytwoinferences Space angles by of associative use the commutative andand a scalar properties a difference consistent use of symbolsmultiple precise andexplain andenquiryvalid process, andsearch reflect on own on vectors 2-D logic, vectors results constructively lines of remainusing y and geometrical problems in of assumptions and prove; either reasoning,thewhen exploring; of scalings in or justify x and directions vector calculate theboth vector;addition and resultantthistwo vectors the work constraints representations, more elegant forms of commun... for and appreciate sustain of throughout and conclusions level 3 3 4 5 5 5 6 6 6 6 6 6 7 7 6 Progression maps: Shape and space Step 1 Identify lines of symmetry in simple shapes and recognise shapes with no lines of symmetry. View step Step 2 Classify polygons, using criteria such as number of right angles, whether or not they are regular, and symmetry properties. Step 3 Recognise perpendicular and parallel lines, and properties of rectangles. View step Step 4 Recognise and visualise the transformation and symmetry of 2-D shapes, including reflection in given mirror lines Construct 3-D models by linking given faces or edges. View step Step 5 Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle and recognise Use a ruler and protractor to measure and draw lines to the nearest millimetre and angles, including reflex angles, to the ne Recognise and visualise the transformation and symmetry of a 2-D shape: reflection in given mirror lines and line symmetry; rotation about a given point and rotational symmetry. View step Step 6 Transform 2-D shapes by simple combinations of rotations, reflections and translations, on paper and using ICT; identify all Step 7 Use a straight edge and compasses to construct: the midpoint and perpendicular bisector of a line segment; the bisector of an angle; the perpendicular from a point to a line; the perpendicular from a point on a line. Construct a triangle, given three sides (SSS); use ICT to explore these constructions. View step Identify alternate and corresponding angles; understand a proof that the sum of the angles of a triangle is 180° and of a qua Classify quadrilaterals by their geometric properties. View step Enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor. View step Step 8 Know that translations, rotations and reflections preserve length and angle, and map objects on to congruent images. View Visualise and use 2-D representations of 3-D objects; analyse 3-D shapes through 2-D projections, including plans and elev Step 9 Explain how to find, calculate and use the interior and exterior angles of regular polygons. View step Enlarge 2-D shapes by a positive whole-number or fractional scale factor. View step Find the locus of a point that moves according to a given rule, both by reasoning and by using ICT. View step Step 10 Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying i nd symmetry properties. View step on in given mirror lines and line symmetry. n a triangle and recognise vertically opposite angles. View step ng reflex angles, to the nearest degree. View step and using ICT; identify all the symmetries of 2-D shapes. View step angle is 180° and of a quadrilateral is 360°. View step congruent images. View step s, including plans and elevations. View step other polygons, justifying inferences and explaining reasoning with diagrams and text. View step Progression Maps: Handling data Step 1 3 Solve a given problem by organising and interpreting numerical data in simple lists, tables and graphs; for exampl simple frequency tables; pictograms – symbol representing two units; bar charts – intervals labelled in ones and then twos; Venn and Carroll diagrams (one criterion). Step 2 4 Solve a problem by collecting, organising, representing and interpreting data in tables, charts, graphs and diagram tally charts and frequency tables; pictograms – symbol representing two, five, ten or twenty units; bar charts – intervals labelled in twos, fives, tens or twenties; Venn and Carroll diagrams (two criteria). Step 3 4 Find the mode and range of a set of data. Step 4 Solve a problem by representing, extracting and interpreting data in tables, graphs and charts. Calculate statistics fo 4 find the mode, median and range;calculate the mean in simple cases. Step 5 5 Understand the effect on the mean and median of altering the data. Interpret diagrams and graphs (including pie c Step 6 5 Compare two simple distributions using the range and one of the mode, median or mean. Step 7 6 Construct, on paper and using ICT: pie charts for categorical data; bar charts and frequency diagrams for discrete and continuous data; simple line graphs for time series; simple scatter graphs. Identify which are most useful in the context of the problem. Step 8 6 Design a survey or experiment to capture the necessary data from one or more sources; determine the sample si Communicate interpretations and results of a statistical enquiry using selected tables, graphs and diagrams in sup Step 9 7 Select, construct and modify, on paper and using ICT, suitable graphical representations to progress an enquiry, i Examine critically the results of a statistical enquiry, and justify the choice of statistical representation in written pre Step 10 7 Identify possible sources of bias and plan how to minimise it e lists, tables and graphs; for example: in tables, charts, graphs and diagrams, including those generated by a computer; for example: phs and charts. Calculate statistics for small sets of discrete data: diagrams and graphs (including pie charts) and draw simple conclusions based on the shape of graphs and simple statistics for a single dist re sources; determine the sample size and degree of accuracy needed; design, trial and, if necessary, refine data collection sheets; design a d tables, graphs and diagrams in support, using ICT as appropriate; construct tables for large, discrete and continuous sets of raw data, cho esentations to progress an enquiry, including scatter graphs to develop further understanding of correlation. statistical representation in written presentations. and simple statistics for a single distribution. efine data collection sheets; design and use two-way tables. and continuous sets of raw data, choosing suitable class intervals. Progression Maps: Probability Step 1 Step 2 Step 3 Step 4 Discuss the chance or likelihood of particular events. Use the language associated with probability to discuss events, including those with equally likely outcomes. Step 5 5 Understand and use the probability scale from 0 to 1. Find and justify probabilities based on equally likely outcomes in simple contexts. Step 6 6 Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p. 6 Estimate probabilities from experimental data; understand that: if an experiment is repeated, there will be different outcomes; increasing the number of times an experiment is repeated generally leads to better estimates of probability. Step 7 6 Find and record all possible mutually exclusive outcomes for single events and two successive events in a syste Step 8 6 Know that the sum of probabilities of all mutually exclusive outcomes is 1, and use this when solving problems. Use a single probability to find an estimate of frequency. Find an estimate of the frequency for up to two events. Step 9 7 Understand relative frequency as an estimate of probability and use this to compare outcomes of experiments. Step 10 8 Find the probability of two or more mutually exclusive events occurring. 8 Find the probability of two independent events occurring ose with equally likely outcomes. it not occurring is 1 – p. s to better estimates of probability. and two successive events in a systematic way. and use this when solving problems. compare outcomes of experiments. 3 4 5 5 6 6 6 7 7 7 Progression maps: Algebra - Sequences, Functions and Graphs Step 1 Describe and extend number sequences: count on or back in tens or hundreds, starting from any two- or three-digit numbe Step 2 Investigate a general statement about familiar numbers by finding examples that satisfy it. View step Step 3 Recognise and extend number sequences formed from counting from any number in steps of constant size, extending beyo Read and plot coordinates in the first quadrant. View step Step 4 Recognise and extend number sequences, such as the sequence of square numbers, or the sequence of triangular numbe Step 5 Read and plot coordinates in all four quadrants. View step Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions. View step Step 6 Begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the acti Express simple functions in symbols; represent mappings expressed algebraically. View step Step 7 Plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y = mx + c c Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on paper and using ICT Step 8 Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real sit Given values for m and c, find the gradient of lines given by equations of the form y = mx + c. View step Step 9 Find the next term and the nth term of quadratic sequences and explore their properties. View step Know simple properties of quadratic functions. View step Step 10 Plot the graphs of simple quadratic and cubic functions, e.g. y = x², y = 3x², y = x³. View step two- or three-digit number. View step stant size, extending beyond zero when counting back. View step ence of triangular numbers. View step rm by referring to the activity or practical context from which it was generated. View step s of the form y = mx + c correspond to straight-line graphs. View step e, on paper and using ICT. View step raphs arising from real situations. View step Progression maps: Number – FDPRP 2 Step 1 Recognise unit fractions such as , , , , ... and use them to find fractions of shapes and numbers. View step Step 2 3 Recognise simple fractions that are several parts of a whole, such as or , and mixed numbers, such as ; recognise the equivalence of simple fractions (e.g. fractions equivalent to , or ). View step Step 3 Relate fractions to division and to their decimal representations. View step Order a set of fractions such as 2, 2 ,1 ,2 ,1 and position them on a number line. View step 3/4 Use decimal notation for tenths and hundredths. View step Step 4 5 Reduce a fraction to its simplest form by cancelling common factors. View step Use a fraction as an 'operator' to find fractions of numbers or quantities (e.g. of 32, of 40, of 400 cm). View step 4 Understand percentage as the number of parts in every 100 and find simple percentages of small whole-numbe Step 5 5 Solve simple problems involving ratio and proportion. View step Begin to add and subtract simple fractions and those with common denominators. View step 5 Simplify fractions by cancelling all common factors and identify equivalent fractions. View step Step 6 5 Recognise the equivalence of percentages, fractions and decimals; calculate simple percentages and use perce Multiply and divide a fraction by an integer. View step Step 7 6 Use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and Order fractions by writing them with a common denominator or by converting them into decimals. View step Divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems in Step 8 6 Add and subtract fractions by writing them with a common denominator. View step 6 Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole. V Step 9 7 Use efficient methods to add, subtract, multiply and divide fractions. View step Step 10 7 Understand and use proportionality and calculate the result of any proportional change using multiplicative meth e percentages of small whole-number quantities. View step nators. View step ractions. View step te simple percentages and use percentages to compare simple proportions. View step oportions; calculate percentages and find the outcome of a given percentage increase or decrease. View step g them into decimals. View step hod to solve simple word problems involving ratio and direct proportion. View step ers to take as 100%, or as a whole. View step nal change using multiplicative methods. View step Progression maps: Number – Written calculation Step 1 Step 2 2 Use informal pencil and paper methods to support, record or explain HTU ± TU, HTU ± HTU. View step Develop and refine written methods for column addition and subtraction for two whole numbers less then 1000, and for Step 3 Extend efficient written methods to: 3 column addition/subtraction of two integers less than 10000; View step 3 short multiplication of HTU or TU by U; View step long multiplication of TU by TU; View step short division of HTU by U (with integer remainder). View step 3 Use all four operations to solve simple word problems involving numbers and quantities including time, explaining meth 4 Step 4 Extend written methods to: column addition and subtraction of numbers involving decimals; View step 5 long multiplication of a three-digit by a two-digit integer; View step short division of TU by U (mixed-number answer); View step division of HTU by TU (long division, whole-number answer); View step 5 short division of numbers involving decimals. View step 4 Identify and use the appropriate operations (including combinations of operations) to solve word problems involving nu Step 5 Know and use the order of operations including brackets. View step 4 Check a result by considering whether it is of the right order of magnitude and by working the problem backwards. View Step 6 5 Use standard column procedures for multiplication and division of integers and decimals, including by decimals such a 5 Enter numbers in a calculator and interpret the display in different contexts. View step Step 7 7 Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to Step 8 Use a calculator efficiently and appropriately, including using the reciprocal key. View step Step 9 Step 10 ± HTU. View step numbers less then 1000, and for addition of more than two such numbers. View step s including time, explaining methods and reasoning. View step olve word problems involving numbers and quantities, and explain methods and reasoning. View step ng the problem backwards. View step ls, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations. View ste bers of any size, knowing not to round during intermediate steps of a calculation. View step ring equivalent calculations. View step Progression maps: Number – Place value Step 1 2 Read, write and order whole numbers to at least 1000; know what each digit represents. View step Step 2 3 Read and write the vocabulary of comparing and ordering numbers. Use symbols correctly, including less than ( 3 Round any positive integer less than 1000 to the nearest 10 or 100. View step Step 3 4 Multiply and divide any positive integer up to 10000 by 10 or 100 and understand the effect. View step Round a number with one or two decimal places to the nearest integer. View step Step 4 Understand and use decimal notation and place value. View step Order a given set of positive and negative integers. View step Compare and order a mixed set of numbers or measurements with up to three decimal places. View step Step 5 5 Multiply and divide decimals mentally by 10 or 100, and integers by 1000, and explain the effect. View step Round positive whole numbers to the nearest 10, 100 or 1000 and decimals to the nearest whole number or one Find the difference between a positive and negative integer, or between two negative integers, in a context such Step 6 Round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two Multiply and divide integers and decimals by 0.1, 0.01. View step Step 7 Use rounding to make estimates; round numbers to the nearest whole number or to one or two decimal places. Step 8 Begin to write numbers in standard form. View step 7 Round numbers to a given number of significant figures. View step Step 9 Understand upper and lower bounds. View step Step 10 Estimate calculations by rounding numbers to one significant figure and multiplying or dividing mentally. View ste it represents. View step mbols correctly, including less than (<), greater than (>), equals (=). View step stand the effect. View step ree decimal places. View step nd explain the effect. View step s to the nearest whole number or one decimal place. View step o negative integers, in a context such as temperature or the number line. View step earest whole number or to one or two decimal places. View step ber or to one or two decimal places. View step ltiplying or dividing mentally. View step Progression maps: Number – Mental calculation Step 1 Know by heart all addition and subtraction facts for each number to 20. View step Add and subtract mentally a 'near multiple of 10' to or from a two-digit number. View step 3 Understand division as grouping or sharing and recognise that division is the inverse of multiplication. View step Know by heart facts for the 2, 5 and 10 multiplication tables. View step Step 2 3 Use known number facts and place value to add or subtract mentally, including any pair of two-digit whole numb Know by heart multiplication facts for the 2, 3, 4, 5 and 10 times tables. View step Derive quickly division facts corresponding to the 2, 3, 4, 5 and 10 multiplication tables. View step Find remainders after division. View step Step 3 4 Know by heart all multiplication facts up to 10 × 10. View step Find differences by counting up through next multiple of 10, 100 or 1000, e.g. calculate mentally a difference su Use known number facts and place value to consolidate mental addition and subtraction. View step Step 4 Derive quickly division facts corresponding to multiplication tables up to 10 × 10. View step Step 5 4 Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompa Step 6 Consolidate and extend mental methods of calculation, working with decimals, fractions and percentages, squa Step 7 Make and justify estimates and approximations of calculations. View step Step 8 Step 9 Step 10 ber. View step e inverse of multiplication. View step ding any pair of two-digit whole numbers. View step ation tables. View step g. calculate mentally a difference such as 8006 – 2993. View step d subtraction. View step × 10. View step fractions and percentages, accompanied where appropriate by suitable jottings; solve simple word problems mentally. View step als, fractions and percentages, squares and square roots, cubes and cube roots; solve word problems mentally. View step lems mentally. View step mentally. View step Progression maps: Using and applying mathematics – Communica Step 1 2 Discuss work, using mathematical language. Represent work, using symbols and simple diagrams. View step Step 2 2 Begin to organise work. Use and interpret mathematical symbols and diagrams. View step Step 3 3 Begin to refine ways of recording and use appropriate mathematical symbols correctly. View step Step 4 4 Present information and results in a clear and organised way. Present solutions/findings in the context of the pro Step 5 Present and interpret solutions/findings in the context of the problem/task. Begin to develop correct and consiste Step 6 5 Show understanding of situations by describing them mathematically, making correct use of symbols, words, dia Step 7 6 Choose and use correctly symbols, diagrams and graphs. Present and interpret solutions/findings in the context Step 8 7 Interpret, discuss and synthesise information presented in a variety of mathematical forms. Begin to explain rea Step 9 8 Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form Step 10 Examine critically, improve and justify the choice of mathematical presentation, explaining features selected. Vie ematics – Communicating ls and simple diagrams. View step ams. View step ls correctly. View step ions/findings in the context of the problem/task. View step Begin to develop correct and consistent use of notation, symbols and diagrams. View step ng correct use of symbols, words, diagrams, tables and graphs. View step rpret solutions/findings in the context of the original problem/task. View step ematical forms. Begin to explain reasons for selection and use of diagrams. View step graphical form; move from one form of presentation to another to gain a different perspective on the problem/task. View step ion, explaining features selected. View step blem/task. View step Progression maps: Using and applying mathematics – Problem so Step 1 3 Try different approaches to solve a problem. View step Step 2 3 Try different approaches and find ways of overcoming difficulties that arise when solving problems. View step Step 3 Use a range of strategies when solving problems. View step Step 4 4 Develop strategies for solving problems and use these strategies both in working within mathematics and in app Step 5 Begin to structure an approach when exploring a simple task or solving a problem. Generate and check the nec Step 6 5 Identify the necessary information to carry through tasks and solve mathematical problems. Check results and c Step 7 Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techni Step 8 6 Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques, methods Step 9 Starting from given problems or contexts, progressively refine or extend the mathematics used to generate fulle Step 10 7 Solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a ra ematics – Problem solving when solving problems. View step orking within mathematics and in applying mathematics to practical contexts. View step roblem. Generate and check the necessary information. View step atical problems. Check results and consider whether they are sensible. View step s, choosing and using efficient techniques for calculation, algebraic manipulation and graphical representation, and resources, including ICT. nge of efficient techniques, methods and resources, including ICT. View step e mathematics used to generate fuller solutions. View step nnections in mathematics across a range of contexts: number, algebra, shape, space and measures, and handling data. View step tation, and resources, including ICT. View step nd handling data. View step Progression maps: Using and applying mathematics – Reasoning Step 1 Explain why an answer is correct. View step Step 2 3 Understand a general statement by finding particular examples that match it. View step Step 3 Try out ideas to find a pattern or solution. View step Step 4 5 Make general statements, based on evidence produced, and explain reasoning. View step Step 5 6 Solve problems and investigate in a range of contexts, explaining and justifying methods and conclusions; begin Step 6 Draw simple conclusions and explain reasoning; suggest extensions to problems; conjecture and generalise. Vi Step 7 6 Use logical argument to establish the truth of a statement; begin to give mathematical justifications and test by c Step 8 Present a concise reasoned argument, using symbols, diagrams, graphs and related explanatory texts. View ste Step 9 7 Show some insight into mathematical structure by using pattern and symmetry to justify generalisations, argume Step 10 Appreciate the difference between mathematical explanation and experimental evidence. View step ematics – Reasoning ning. View step ying methods and conclusions; begin to generalise and to understand the significance of a counter-example. View step blems; conjecture and generalise. View step thematical justifications and test by checking particular cases. View step nd related explanatory texts. View step etry to justify generalisations, arguments or solutions. View step ntal evidence. View step mple. View step Progression maps: Measures Step 1 3 Use units of time and know the relationships between them (second, minute, hour, day, week, month, year). Vie Step 2 4 Know and use the relationship between familiar units of length, mass and capacity. View step Step 3 4 Understand an area measured in square centimetres (cm²). View step Step 4 5 Understand and use the formula in words 'length × breadth' for the area of a rectangle. View step Step 5 Calculate the perimeter and area of simple compound shapes that can be split into rectangles. View step 5 Convert one metric unit to another (e.g. grams to kilograms); read and interpret scales on a range of measuring Step 6 Use units of measure to estimate, calculate and solve problems in everyday contexts involving length, area, volu Step 7 6 Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shap 6 Deduce and use formulae for the area of a triangle, a parallelogram and a trapezium; calculate areas of compou Step 8 6 Know and use the formulae for the area and circumference of a circle. View step Step 9 7 Recognise that measurements given to the nearest whole unit may be inaccurate by up to one half of the unit in 7 Calculate the surface areas and volumes of right prisms; calculate lengths, areas and volumes in right prisms, in Step 10 7 Understand and use measures of speed (and other compound measures such as density or pressure) to solve 7 Understand and apply Pythagoras' theorem when solving problems in two dimensions. View step e, hour, day, week, month, year). View step apacity. View step a rectangle. View step split into rectangles. View step pret scales on a range of measuring instruments. View step y contexts involving length, area, volume, capacity, mass, time, angle and bearings; know rough metric equivalents of imperial measures in d nd surface areas of cuboids and shapes made from cuboids. View step rapezium; calculate areas of compound shapes made from rectangles and triangles. View step curate by up to one half of the unit in either direction. View step areas and volumes in right prisms, including cylinders. View step uch as density or pressure) to solve problems. View step dimensions. View step equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons). View step Progression maps: Number – Integers and powers Step 1 Recognise odd and even numbers up to 1000, and some of their properties, including the outcomes of sums or Describe and extend number sequences: count on or back in tens or hundreds, starting from any two- or three-d Step 2 3 Recognise negative numbers in contexts (e.g. on a number line, on a temperature scale). View step Recognise multiples of 2, 3, 4, 5 and 10, up to the tenth multiple. View step Step 3 Recognise and extend number sequences formed by counting from any number in steps of constant size. (See Recognise multiples of 6, 7, 8 and 9 up to the tenth multiple. View step 4 Know the squares of numbers up to 10 × 10. View step Know all the pairs of factors of any number up to 100. View step Know and apply tests of divisibility by 2, 4, 5, 10 or 100. View step Step 4 Factorise numbers to 100 into prime factors. View step Recognise and use multiples, factors and primes (less than 100). View step Know and apply simple tests of divisibility. View step Step 5 Recognise the first few triangular numbers, squares of numbers to at least 12 × 12 and the corresponding roots 5 Add and subtract positive and negative numbers in context. View step Step 6 Add, subtract, multiply and divide integers. View step Step 7 Use index notation for integer powers and simple instances of the index laws. View step Step 8 Know and use the index laws for multiplication and division of positive integer powers. View step Step 9 Step 10 , including the outcomes of sums or differences of pairs of odd/even numbers. View step eds, starting from any two- or three-digit number. View step erature scale). View step mber in steps of constant size. (See progression map for Sequences, Functions and Graphs.) View step 12 × 12 and the corresponding roots. View step ws. View step er powers. View step 3 4 5 6 6 6 7 7 Algebra - Equations, Formulae and Identities Step 1 Understand division and recognise that division is the inverse of multiplication. View step Step 2 Use symbols correctly including less than (<), greater than (>) and equals (=). View step Understand the principles of the commutative, associative and distributive laws as they apply to multiplication. View step Step 3 Make general statements about odd and even numbers. View step Explain a generalised relationship (formula) in words. View step Step 4 Understand and use the relationships between the four operations, and principles of the arithmetic laws. Use brackets. View ste Step 5 Use letter symbols to represent unknown numbers or variables. View step Know and use the order of operations and understand that algebraic operations follow the same conventions and order as arith Construct and solve linear equations with positive integer coefficients (unknown on one side only) using appropriate methods. V Step 6 Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket. View step Substitute integers into simple formulae. View step Step 7 Construct and solve linear equations with integer coefficients (with and without brackets, with negative signs anywhere in the eq Step 8 Use systematic trial and improvement methods and ICT tools to find approximate solutions to equations such as x³ + x = 20. Vie Transform algebraic expressions by factorising to produce a single term multiplied by terms in a bracket. View step Step 9 Square a linear expression, expand the product of two linear expressions of the form x ± n and simplify the corresponding quad Step 10 Solve a pair of simultaneous linear equations by eliminating one variable; link a graphical representation of an equation or pair o y to multiplication. View step hmetic laws. Use brackets. View step ame conventions and order as arithmetical operations. View step 6 6 6 6 6 6 n a bracket. View step nd simplify the corresponding quadratic expression. View step presentation of an equation or pair of equations to the algebraic solution. View step Progression maps: Algebra - Sequences, Functions and Graphs Step 1 Describe and extend number sequences: count on or back in tens or hundreds, starting from any two- or three-d Step 2 Investigate a general statement about familiar numbers by finding examples that satisfy it. View step Step 3 Recognise and extend number sequences formed from counting from any number in steps of constant size, ext Read and plot coordinates in the first quadrant. View step Step 4 Recognise and extend number sequences, such as the sequence of square numbers, or the sequence of triang Step 5 Read and plot coordinates in all four quadrants. View step Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions. View step Step 6 Begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referrin Express simple functions in symbols; represent mappings expressed algebraically. View step Step 7 Plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on paper an Step 8 Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising Given values for m and c, find the gradient of lines given by equations of the form y = mx + c. View step Step 9 Find the next term and the nth term of quadratic sequences and explore their properties. View step Know simple properties of quadratic functions. View step Step 10 Plot the graphs of simple quadratic and cubic functions, e.g. y = x², y = 3x², y = x³. View step nctions and Graphs eds, starting from any two- or three-digit number. View step s that satisfy it. View step number in steps of constant size, extending beyond zero when counting back. View step e numbers, or the sequence of triangular numbers. View step f simple linear functions. View step quence, justifying its form by referring to the activity or practical context from which it was generated. View step raically. View step ecognise that equations of the form y = mx + c correspond to straight-line graphs. View step nitions of the sequence, on paper and using ICT. View step ding graphs; interpret graphs arising from real situations. View step e form y = mx + c. View step eir properties. View step y = x³. View step