Level descriptions for new KS3 Maths curriculum
Level descriptions
For new KS3 Maths curriculum – Free resource to help you Plan for the new 2008 changes. Provided by Collins Education.
Strand 1: Mathematical processes and applications
|Level |Current level description |Modified level description for 2008 change |
|4 |Pupils are developing their own strategies for |Pupils are developing their own strategies for solving |
| |solving problems and are using these strategies |problems and are using these strategies both in working |
| |both in working within mathematics and in applying|within mathematics and in applying mathematics to |
| |mathematics to practical contexts. They present |practical contexts. In solving problems with or without a |
| |information and results in a clear and organised |calculator, pupils check their results are reasonable by |
| |way. They search for a solution by trying out |considering the context or the size of the numbers. Pupils|
| |ideas of their own. |look for patterns and relationships, presenting |
| | |information and results in a clear and organised way. They|
| | |search for a solution by trying out ideas of their own. |
|5 |In order to carry through tasks and solve |In order to explore mathematical situations, carry through|
| |mathematical problems, pupils identify and obtain |tasks or tackle problems, pupils identify the mathematical|
| |necessary information. They check their results, |aspects and obtain necessary information. They calculate |
| |considering whether these are sensible. Pupils |accurately, using ICT when appropriate. Pupils check their|
| |show understanding of situations by describing |working and results, considering whether these are |
| |them mathematically using symbols, words and |sensible. They show understanding of situations by |
| |diagrams. They draw simple conclusions of their |describing them mathematically using symbols, words and |
| |own and give an explanation of their reasoning. |diagrams. They draw simple conclusions of their own and |
| | |give an explanation of their reasoning. |
|6 |Pupils carry through substantial tasks and solve |Pupils carry through substantial tasks and solve quite |
| |quite complex problems by independently breaking |complex problems by independently and systematically |
| |them down into smaller, more manageable tasks. |breaking them down into smaller, more manageable tasks. |
| |They interpret, discuss and synthesise information|They interpret, discuss and synthesise information |
| |presented in a variety of mathematical forms. |presented in a variety of mathematical forms, relating |
| |Pupils' writing explains and informs their use of |findings to the original context. Pupils written and |
| |diagrams. Pupils are beginning to give |spoken language explains and informs their use of |
| |mathematical justifications. |diagrams. Pupils are beginning to give mathematical |
| | |justifications, making connections between the current |
| | |situation and ones they have met before. |
|7 |Starting from problems or contexts that have been |Starting from problems or contexts that have been |
| |presented to them, pupils progressively refine or |presented to them, pupils explore the effects of varying |
| |extend the mathematics used to generate fuller |values and look for invariance in models and |
| |solutions. They give a reason for their choice of |representations working with and without ICT. They |
| |mathematical presentation, explaining features |progressively refine or extend the mathematics used, |
| |they have selected. Pupils justify their |giving a reason for their choice of mathematical |
| |generalisations, arguments or solutions, showing |presentation and explaining features they have selected. |
| |some insight into the mathematical structure of |Pupils justify their generalisations, arguments or |
| |the problem. They appreciate the difference |solutions, looking for equivalence to different problems |
| |between mathematical explanation and experimental |with similar structures. They appreciate the difference |
| |evidence. |between mathematical explanation and experimental |
| | |evidence. |
|8 |Pupils develop and follow alternative approaches. |Pupils develop and follow alternative approaches. They |
| |They reflect on their own lines of enquiry when |compare and evaluate representations of a situation, |
| |exploring mathematical tasks; in doing so they |introducing and using a range of mathematical techniques. |
| |introduce and use a range of mathematical |They reflect on their own lines of enquiry when exploring |
| |techniques. Pupils convey mathematical or |mathematical tasks. Pupils communicate mathematical or |
| |statistical meaning through precise and consistent|statistical meaning to different audiences through precise|
| |use of symbols that is sustained throughout the |and consistent use of symbols that is sustained throughout|
| |work. They examine generalisations or solutions |the work. They examine generalisations or solutions |
| |reached in an activity, commenting constructively |reached in an activity, commenting constructively on the |
| |on the reasoning and logic or the process |reasoning and logic or the process employed, or the |
| |employed, or the results obtained, and make |results obtained, and make further progress in the |
| |further progress in the activity as a result. |activity as a result. |
|EP |Pupils give reasons for the choices they make when|Pupils critically examine the strategies adopted when |
| |investigating within mathematics itself or when |investigating within mathematics itself or when using |
| |using mathematics to analyse tasks; these reasons |mathematics to analyse tasks. They explain why different |
| |explain why particular lines of enquiry or |strategies were used, considering the elegance and |
| |procedures are followed and others rejected. |efficiency of alternative lines of enquiry or procedures. |
| |Pupils apply the mathematics they know in familiar|Pupils apply the mathematics they know in a wide range of |
| |and unfamiliar contexts. Pupils use mathematical |familiar and unfamiliar contexts. They use mathematical |
| |language and symbols effectively in presenting a |language and symbols effectively in presenting a |
| |convincing reasoned argument. Their reports |convincing reasoned argument. Their reports include |
| |include mathematical justifications, explaining |mathematical justifications, distinguishing between |
| |their solutions to problems involving a number of |evidence and proof and explaining their solutions to |
| |features or variables. |problems involving a number of features or variables. |
Strand 2: number and algebra
|Level |Current level description |Modified level description |
|4 |Pupils use their understanding of place value to |Pupils use their understanding of place value to multiply |
| |multiply and divide whole numbers by 10 or 100. In|and divide whole numbers by 10 or 100. In solving number |
| |solving number problems, pupils use a range of |problems, pupils use a range of mental methods of |
| |mental methods of computation with the four |computation with the four operations, including mental |
| |operations, including mental recall of |recall of multiplication facts up to 10 X 10 and quick |
| |multiplication facts up to 10 x 10 and quick |derivation of corresponding division facts. They use |
| |derivation of corresponding division facts. They |efficient written methods of addition and subtraction and |
| |use efficient written methods of addition and |of short multiplication and division. They recognise |
| |subtraction and of short multiplication and |approximate proportions of a whole and use simple |
| |division. They add and subtract decimals to two |fractions and percentages to describe these. They begin to|
| |places and order decimals to three places. In |use simple formulae expressed in words. |
| |solving problems with or without a calculator, | |
| |pupils check the reasonableness of their results | |
| |by reference to their knowledge of the context or | |
| |to the size of the numbers. They recognise | |
| |approximate proportions of a whole and use simple | |
| |fractions and percentages to describe these. | |
| |Pupils recognise and describe number patterns, and| |
| |relationships including multiple, factor and | |
| |square. They begin to use simple formulae | |
| |expressed in words. Pupils use and interpret | |
| |coordinates in the first quadrant. | |
|5 |Pupils use their understanding of place value to |Pupils use their understanding of place value to multiply |
| |multiply and divide whole numbers and decimals by |and divide whole numbers and decimals. They order, add and|
| |10, 100 and 1000. They order, add and subtract |subtract negative numbers in context. They use all four |
| |negative numbers in context. They use all four |operations with decimals to two places. They solve simple |
| |operations with decimals to two places. They |problems involving ratio and direct proportion. They |
| |reduce a fraction to its simplest form by |calculate fractional or percentage parts of quantities and|
| |cancelling common factors and solve simple |measurements, using a calculator where appropriate. They |
| |problems involving ratio and direct proportion. |construct, express in symbolic form, and use simple |
| |They calculate fractional or percentage parts of |formulae involving one or two operations. They use |
| |quantities and measurements, using a calculator |brackets appropriately. Pupils use and interpret |
| |where appropriate. Pupils understand and use an |coordinates in all four quadrants. |
| |appropriate non-calculator method for solving | |
| |problems that involve multiplying and dividing any| |
| |three-digit number by any two-digit number. They | |
| |check their solutions by applying inverse | |
| |operations or estimating using approximations. | |
| |They construct, express in symbolic form, and use | |
| |simple formulae involving one or two operations. | |
| |They use brackets appropriately. Pupils use and | |
| |interpret coordinates in all four quadrants. | |
|6 |Pupils order and approximate decimals when solving|Pupils order and approximate decimals when solving |
| |numerical problems and equations [for example, x 3|numerical problems and equations, using |
| |+ x = 20], using trial and improvement methods. |trial-and-improvement methods. Pupils evaluate one number |
| |Pupils are aware of which number to consider as |as a fraction or percentage of another. They understand |
| |100 per cent, or a whole, in problems involving |and use the equivalences between fractions, decimals and |
| |comparisons, and use this to evaluate one number |percentages, and calculate using ratios in appropriate |
| |as a fraction or percentage of another. They |situations. They add and subtract fractions by writing |
| |understand and use the equivalences between |them with a common denominator. Pupils find and describe |
| |fractions, decimals and percentages, and calculate|in words the rule for the next term or nth term of a |
| |using ratios in appropriate situations. They add |sequence where the rule is linear. They formulate and |
| |and subtract fractions by writing them with a |solve linear equations with whole-number coefficients. |
| |common denominator. When exploring number |They represent mappings expressed algebraically, and use |
| |sequences, pupils find and describe in words the |Cartesian coordinates for graphical representation |
| |rule for the next term or nth term of a sequence |interpreting general features. |
| |where the rule is linear. They formulate and solve| |
| |linear equations with whole number coefficients. | |
| |They represent mappings expressed algebraically, | |
| |and use Cartesian coordinates for graphical | |
| |representation interpreting general features. | |
|7 |In making estimates, pupils round to one |In making estimates, pupils round to one significant |
| |significant figure and multiply and divide |figure and multiply and divide mentally. They understand |
| |mentally. They understand the effects of |the effects of multiplying and dividing by numbers between|
| |multiplying and dividing by numbers between 0 and |0 and 1. Pupils solve numerical problems involving |
| |1. Pupils solve numerical problems involving |multiplication and division with numbers of any size, |
| |multiplication and division with numbers of any |using a calculator efficiently and appropriately. They |
| |size, using a calculator efficiently and |understand and use proportional changes, calculating the |
| |appropriately. They understand and use |result of any proportional change using only |
| |proportional changes, calculating the result of |multiplicative methods. Pupils find and describe in |
| |any proportional change using only multiplicative |symbols the next term or nth term of a sequence where the |
| |methods. Pupils find and describe in symbols the |rule is quadratic. Pupils use algebraic and graphical |
| |next term or nth term of a sequence where the rule|methods to solve simultaneous linear equations in two |
| |is quadratic; they multiply two expressions of the|variables. |
| |form (x + n); they simplify the corresponding | |
| |quadratic expressions. Pupils use algebraic and | |
| |graphical methods to solve simultaneous linear | |
| |equations in two variables. They solve simple | |
| |inequalities. | |
|8 |Pupils solve problems involving calculating with |Pupils solve problems involving calculating with powers, |
| |powers, roots and numbers expressed in standard |roots and numbers expressed in standard form. They choose |
| |form, checking for correct order of magnitude. |to use fractions or percentages to solve problems |
| |They choose to use fractions or percentages to |involving repeated proportional changes or the calculation|
| |solve problems involving repeated proportional |of the original quantity given the result of a |
| |changes or the calculation of the original |proportional change. They evaluate algebraic formulae or |
| |quantity given the result of a proportional |calculate one variable, given the others, substituting |
| |change. They evaluate algebraic formulae, |fractions, decimals and negative numbers. Pupils |
| |substituting fractions, decimals and negative |manipulate algebraic formulae, equations and expressions, |
| |numbers. They calculate one variable, given the |finding common factors and multiplying two linear |
| |others, in formulae such as V = Yr2h. Pupils |expressions. They solve inequalities in two variables. |
| |manipulate algebraic formulae, equations and |Pupils sketch and interpret graphs of linear, quadratic, |
| |expressions, finding common factors and |cubic and reciprocal functions, and graphs that model real|
| |multiplying two linear expressions. They know that|situations. |
| |a 2 -b 2= (a+b)(a - b). They solve inequalities in| |
| |two variables. Pupils sketch and interpret graphs | |
| |of linear, quadratic, cubic and reciprocal | |
| |functions, and graphs that model real situations. | |
|EP |Pupils understand and use rational and irrational |Pupils understand and use rational and irrational numbers.|
| |numbers. They determine the bounds of intervals. |They determine the bounds of intervals. Pupils understand |
| |Pupils understand and use direct and inverse |and use direct and inverse proportion. In simplifying |
| |proportion. In simplifying algebraic expressions, |algebraic expressions, they use rules of indices for |
| |they use rules of indices for negative and |negative and fractional values. In finding formulae that |
| |fractional values. In finding formulae that |approximately connect data, pupils express general laws in|
| |approximately connect data, pupils express general|symbolic form. They solve simultaneous equations in two |
| |laws in symbolic form. They solve simultaneous |variables where one equation is linear and the other is |
| |equations in two variables where one equation is |quadratic. They solve problems using intersections and |
| |linear and the other is quadratic. They solve |gradients of graphs. |
| |problems using intersections and gradients of | |
| |graphs. | |
Strand 3: Geometry and measures
|Level |Current level description |Modified level description |
|4 |Pupils make 3D mathematical models by linking |Pupils make 3-D mathematical models by linking given faces|
| |given faces or edges, draw common 2D shapes in |or edges, draw common 2-D shapes in different orientations|
| |different orientations on grids. They reflect |on grids. They reflect simple shapes in a mirror line. |
| |simple shapes in a mirror line. They choose and |They choose and use appropriate units and tools, |
| |use appropriate units and instruments, |interpreting, with appropriate accuracy, numbers on a |
| |interpreting, with appropriate accuracy, numbers |range of measuring instruments. They find perimeters of |
| |on a range of measuring instruments. They find |simple shapes and find areas by counting squares. |
| |perimeters of simple shapes and find areas by | |
| |counting squares. | |
|5 |When constructing models and when drawing or using|When constructing models and when drawing or using shapes,|
| |shapes, pupils measure and draw angles to the |pupils measure and draw angles to the nearest degree, and |
| |nearest degree, and use language associated with |use language associated with angle. Pupils know the angle |
| |angle. Pupils know the angle sum of a triangle and|sum of a triangle and that of angles at a point. They |
| |that of angles at a point. They identify all the |identify all the symmetries of 2-D shapes. They convert |
| |symmetries of 2D shapes. They know the rough |one metric unit to another. They make sensible estimates |
| |metric equivalents of imperial units still in |of a range of measures in relation to everyday situations.|
| |daily use and convert one metric unit to another. |Pupils understand and use the formula for the area of a |
| |They make sensible estimates of a range of |rectangle. |
| |measures in relation to everyday situations. | |
| |Pupils understand and use the formula for the area| |
| |of a rectangle. | |
|6 |Pupils recognise and use common 2D representations|Pupils recognise and use common 2-D representations of 3-D|
| |of 3D objects. They know and use the properties of|objects. They know and use the properties of |
| |quadrilaterals in classifying different types of |quadrilaterals. They solve problems using angle and |
| |quadrilateral. They solve problems using angle and|symmetry properties of polygons and angle properties of |
| |symmetry properties of polygons and angle |intersecting and parallel lines, and explain these |
| |properties of intersecting and parallel lines, and|properties. They devise instructions for a computer to |
| |explain these properties. They devise instructions|generate and transform shapes and paths. They understand |
| |for a computer to generate and transform shapes |and use appropriate formulae for finding circumferences |
| |and paths. They understand and use appropriate |and areas of circles, areas of plane rectilinear figures |
| |formulae for finding circumferences and areas of |and volumes of cuboids when solving problems. |
| |circles, areas of plane rectilinear figures and | |
| |volumes of cuboids when solving problems. They | |
| |enlarge shapes by a positive whole-number scale | |
| |factor. | |
|7 |Pupils understand and apply Pythagoras' theorem |Pupils understand and apply Pythagoras' theorem when |
| |when solving problems in two dimensions. They |solving problems in two dimensions. They calculate |
| |calculate lengths, areas and volumes in plane |lengths, areas and volumes in plane shapes and right |
| |shapes and right prisms. Pupils enlarge shapes by |prisms. Pupils enlarge shapes by a fractional scale |
| |a fractional scale factor, and appreciate the |factor, and appreciate the similarity of the resulting |
| |similarity of the resulting shapes. They determine|shapes. They determine the locus of an object moving |
| |the locus of an object moving according to a rule.|according to a rule. Pupils appreciate the imprecision of |
| |Pupils appreciate the imprecision of measurement |measurement and recognise that a measurement given to the |
| |and recognise that a measurement given to the |nearest whole number may be inaccurate by up to one half |
| |nearest whole number may be inaccurate by up to |in either direction. They understand and use compound |
| |one half in either direction. They understand and |measures, such as speed. |
| |use compound measures, such as speed. | |
|8 |Pupils understand and use congruence and |Pupils understand and use congruence and mathematical |
| |mathematical similarity. They use sine, cosine and|similarity. They use sine, cosine and tangent in |
| |tangent in right-angled triangles when solving |right-angled triangles when solving problems in two |
| |problems in two dimensions. They distinguish |dimensions. |
| |between formulae for perimeter, area and volume, | |
| |by considering dimensions. | |
|EP |Pupils sketch the graphs of sine, cosine and |Pupils sketch the graphs of sine, cosine and tangent |
| |tangent functions for any angle, and generate and |functions for any angle, and generate and interpret graphs|
| |interpret graphs based on these functions. Pupils |based on these functions. Pupils use sine, cosine and |
| |use sine, cosine and tangent of angles of any |tangent of angles of any size, and Pythagoras' theorem |
| |size, and Pythagoras' theorem when solving |when solving problems in two and three dimensions. They |
| |problems in two and three dimensions. They use the|use the conditions for congruent triangles in formal |
| |conditions for congruent triangles in formal |geometric proofs [for example, to prove that the base |
| |geometric proofs [for example, to prove that the |angles of an isosceles triangle are equal]. They calculate|
| |base angles of an isosceles triangle are equal]. |lengths of circular arcs and areas of sectors, and |
| |They calculate lengths of circular arcs and areas |calculate the surface area of cylinders and volumes of |
| |of sectors, and calculate the surface area of |cones and spheres. Pupils appreciate the continuous nature|
| |cylinders and volumes of cones and spheres. Pupils|of scales that are used to make measurements. |
| |appreciate the continuous nature of scales that | |
| |are used to make measurements. | |
Strand 4: Statistics
|Level |Current level description |Modified level description |
|4 |Pupils collect discrete data and record them using|Pupils collect discrete data and record them using a |
| |a frequency table. They understand and use the |frequency table. They understand and use the mode and |
| |mode and range to describe sets of data. They |range to describe sets of data. They group data, where |
| |group data, where appropriate, in equal class |appropriate, in equal class intervals, represent collected|
| |intervals, represent collected data in frequency |data in frequency diagrams and interpret such diagrams. |
| |diagrams and interpret such diagrams. They |They construct and interpret simple line graphs. |
| |construct and interpret simple line graphs. | |
|5 |Pupils understand and use the mean of discrete |Pupils understand and use the mean of discrete data. They |
| |data. They compare two simple distributions, using|compare two simple distributions, using the range and one |
| |the range and one of the mode, median or mean. |of the mode, median or mean. They interpret graphs and |
| |They interpret graphs and diagrams, including pie |diagrams, including pie charts, and draw conclusions. They|
| |charts, and draw conclusions. They understand and |understand and use the probability scale from 0 to 1. |
| |use the probability scale from 0 to 1. Pupils find|Pupils find and justify probabilities, and approximations |
| |and justify probabilities, and approximations to |to these, by selecting and using methods based on equally |
| |these, by selecting and using methods based on |likely outcomes and experimental evidence, as appropriate.|
| |equally likely outcomes and experimental evidence,|They understand that different outcomes may result from |
| |as appropriate. They understand that different |repeating an experiment. |
| |outcomes may result from repeating an experiment. | |
|6 |Pupils collect and record continuous data, |Pupils collect and record continuous data, choosing |
| |choosing appropriate equal class intervals over a |appropriate equal class intervals over a sensible range to|
| |sensible range to create frequency tables. They |create frequency tables. They construct and interpret |
| |construct and interpret frequency diagrams. They |frequency diagrams. They construct pie charts. Pupils draw|
| |construct pie charts. Pupils draw conclusions from|conclusions from scatter diagrams, and have a basic |
| |scatter diagrams, and have a basic understanding |understanding of correlation. When dealing with a |
| |of correlation. When dealing with a combination of|combination of two experiments, pupils identify all the |
| |two experiments, pupils identify all the outcomes,|outcomes. In solving problems, they use their knowledge |
| |using diagrammatic, tabular or other forms of |that the total probability of all the mutually exclusive |
| |communication. In solving problems, they use their|outcomes of an experiment is 1. |
| |knowledge that the total probability of all the | |
| |mutually exclusive outcomes of an experiment is 1.| |
|7 |Pupils specify hypotheses and test them by |Pupils specify hypotheses and test them by designing and |
| |designing and using appropriate methods that take |using appropriate methods that take account of variability|
| |account of variability or bias. They determine the|or bias. They determine the modal class and estimate the |
| |modal class and estimate the mean, median and |mean, median and range of sets of grouped data, selecting |
| |range of sets of grouped data, selecting the |the statistic most appropriate to their line of enquiry. |
| |statistic most appropriate to their line of |They use measures of average and range, with associated |
| |enquiry. They use measures of average and range, |frequency polygons, as appropriate, to compare |
| |with associated frequency polygons, as |distributions and make inferences. Pupils understand |
| |appropriate, to compare distributions and make |relative frequency as an estimate of probability and use |
| |inferences. They draw a line of best fit on a |this to compare outcomes of experiments. |
| |scatter diagram, by inspection. Pupils understand | |
| |relative frequency as an estimate of probability | |
| |and use this to compare outcomes of experiments. | |
|8 |Pupils interpret and construct cumulative |Pupils interpret and construct cumulative frequency tables|
| |frequency tables and diagrams, using the upper |and diagrams, They estimate the median and interquartile |
| |boundary of the class interval. They estimate the |range and use these to compare distributions and make |
| |median and interquartile range and use these to |inferences. They understand how to calculate the |
| |compare distributions and make inferences. They |probability of a compound event and use this in solving |
| |understand how to calculate the probability of a |problems. |
| |compound event and use this in solving problems. | |
|EP |Pupils interpret and construct histograms. They |Pupils interpret and construct histograms. They understand|
| |understand how different methods of sampling and |how different methods of sampling and different sample |
| |different sample sizes may affect the reliability |sizes may affect the reliability of conclusions drawn. |
| |of conclusions drawn. They select and justify a |They select and justify a sample and method to investigate|
| |sample and method to investigate a population. |a population. They recognise when and how to work with |
| |They recognise when and how to work with |probabilities associated with independent mutually |
| |probabilities associated with independent mutually|exclusive events. |
| |exclusive events. | |
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