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