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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