KS3 maths curriculum review | 1
KS3 maths curriculum review
Content correlation between final (September 2013) and previous NC
Schoolzone September 2013
01242 262906 philip@schoolzone.co.uk
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Introduction
This correlation table is based on the September 2013 final version of the curriculum.
Correlations to the previous standards were carried out by maths teachers.
Items in red text are new to the maths curriculum while those in green are largely
unchanged from the previous standards.
Note that this correlation relates only to the learning objectives, not to any changes in
pedagogy, assessment or emphasis.
Code numbers prefixing each learning objective have been introduced by Schoolzone
for referencing purposes.
This document is protected by copyright and may not be shared via TES or other
websites. If you wish to share it, please use the link below, where updates will also be
posted.
Further support documents for the introduction of the new
curriculum can be found at:
http://www.schoolzone.co.uk/schools/NewCurriculum.asp
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Contents
Introduction
2
Purpose of study
4
Aims
5
Attainment targets
8
Introduction
9
Develop fluency
9
Reason mathematically
11
Solve problems
12
Number
15
Algebra
18
Ratio, proportion and rates of change
21
Geometry and measures
22
Probability
24
Statistics
25
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Purpose of study
Mathematics is a creative and highly
inter-connected discipline that has been
developed over centuries, providing the
solution to some of history’s most
intriguing problems. It is essential to
everyday life, critical to science,
technology and engineering, and
necessary in most forms of employment.
A high-quality mathematics education
therefore provides a foundation for
understanding the world, the ability to
reason mathematically, and a sense of
enjoyment and curiosity about the
subject.
The basic principles of this section are
unchanged. This is a more concise section
than the 2007 ‘The importance of
mathematics’ equivalent; however there are
no longer references to ‘personal decisionmaking’, being ‘financially capable’ and to
the subject ‘transcending cultural
boundaries’ and being fundamental to
‘national prosperity’.
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Statutory requirements
Correlation
Aims
The 2007 National Curriculum had 3 overarching aims, for all young people to
become:
 successful learners who enjoy
learning, make progress and achieve
 confident individuals who are able to
live safe, healthy and fulfilling lives
 responsible citizens who make a
positive contribution to society.
These aims were followed by four ‘Key
Concepts’ said to underpin the study of
mathematics. The four Key Concepts were:
1.1 Competence, 1.2 Creativity, 1.3
Applications and implications of
mathematics and 1.4 Critical
Understanding. These concepts are not
split out in the curriculum as they were
previously – some now appear under the
new ‘Aims’ section, whereas others have
been moved to form part of the Subject
Content.
The National Curriculum for mathematics
aims to ensure that all pupils:

become fluent in the fundamentals of
mathematics, including through varied
and frequent practice with
increasingly complex problems over
time, so that pupils develop
conceptual understanding and the
ability to recall and apply knowledge
rapidly and accurately.
1.1a Key Concepts, Competence –
‘applying suitable mathematics…’ The
Explanatory Notes state this requires
‘fluency and confidence in a range of
mathematical techniques and processes’.
1.2a, b Key Concepts, Creativity –
‘Combining understanding, experiences,
imagination and reasoning to construct new
knowledge’; Using existing mathematical
knowledge to create solutions to unfamiliar
problems’. 4b Curriculum opportunities –
‘work on sequences of tasks that involve
using the same mathematics in increasingly
difficult or unfamiliar contexts, or
increasingly demanding mathematics in
similar contexts’. This is perhaps the first
time that a key document has recognised
the need for learners to repeatedly practice
problems.
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 reason mathematically by
following a line of enquiry,
conjecturing relationships and
generalisations, and developing an
argument, justification or proof using
mathematical language.
 can solve problems by applying
their mathematics to a variety of
routine and non-routine problems with
increasing sophistication, including
breaking down problems into a series
of simpler steps and persevering in
seeking solutions.
2.2e, i, j Key Processes, Analysing, Use
mathematical reasoning – ‘make and
being to justify conjectures and
generalisations…’;‘appreciate that there
are a number of different techniques that
can be used to analyse a situation’;
‘reason inductively and deduce’. The
Explanatory Notes state ‘analyse a
situation: this includes using mathematical
reasoning to explain and justify inferences
when analysing data’ and ‘deduce: this
involves using reasoned arguments to
derive or draw a conclusion from
something already known’.1.1b Key
Concepts, Competence – ‘Communicating
mathematics effectively’. The Explanatory
Notes state that ‘pupils should be familiar
with and confident about mathematical
notation and conventions and be able to
select the most appropriate way to
communicate mathematics, both orally
and in writing’. 1.2c Key Processes,
Creativity – ‘Posing questions and
developing convincing arguments’. 2.3a
Key Processes, Interpreting and
evaluating – ‘form convincing arguments
based on findings and make general
statements’.
1.1a Key concepts, Competence –
‘applying suitable mathematics
accurately…’ 2.3 Key Processes,
Analysing, Use appropriate mathematical
procedures – ‘manipulate numbers,
algebraic expressions and equations and
apply routine algorithms’. 2.1a, c
Representing – ‘identify the mathematical
aspects of a situation
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Mathematics is an interconnected subject in
which pupils need to be able to move fluently
between representations of mathematical
ideas. The programme of study for key stage
3 is organised into apparently distinct
domains, but pupils should build on key
stage 2 and connections across
mathematical ideas to develop fluency,
mathematical reasoning and competence in
solving increasingly sophisticated problems.
They should also apply their mathematical
knowledge in science, geography, computing
and other subjects.
Decisions about progression should be based on
the security of pupils’ understanding and their
readiness to progress to the next stage. Pupils
who grasp concepts rapidly should be
challenged through being offered rich and
sophisticated problems before any acceleration
through new content in preparation for key
stage 4. Those who are not sufficiently fluent
should consolidate their understanding,
including through additional practice, before
moving on
or problem’; ‘simplify the situation or
problem in order to represent it
mathematically, using appropriate
variables, symbols, diagrams and
models’. The work on problem solving
was a key component of the 2007
document. The change here is the move
towards problems which require
perseverance and for pupils to apply
increasingly sophisticated mathematics.
2.2a Key Processes, Analysing, Use
mathematical reasoning – ‘make
connections within mathematics’.
4d Curriculum opportunities – ‘work on
problems that arise in other subjects and
in contexts beyond the school’. The
Explanatory Notes state that this could
include using formulas and relationships
in science.
.
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Attainment targets
By the end of each key stage, pupils are
expected to know, apply and understand
the matters, skills and processes
specified in the relevant programme of
study.
This makes no reference to differentiated
levels.
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Introduction
Through the mathematics content, pupils
should be taught to:
Develop fluency
Fl1: consolidate their numerical and
mathematical capability from Key Stage 2
and extend their understanding of the
number system and place value to include
decimals, fractions, powers and roots

This was previously ‘pupils should be able
to’
No reference to KS2 learning in 2007
PoS.
2.2l Key Processes, Analysing, Use
appropriate mathematical procedures ‘calculate accurately, selecting mental
methods or calculating devices as
Fl2: select and use appropriate calculation appropriate’. The reference to using
strategies to solve increasingly complex
‘calculating devices’ has been removed
problems
from the new PoS. 3.1d Range and
content, Number and algebra – ‘the study
of mathematics should include accuracy
and rounding’.
Fl3: Use algebra to generalise arithmetic
and to formulate mathematical
relationships
Fl4: substitute values in expressions;
rearrange and simplify expressions, and
solve equations
In the 2007 PoS there was no explicit
reference to fractions. The only mention
came under 3.1a Range and content,
Number and algebra – ‘The study of
mathematics should include rational
numbers, their properties and their
different representations’. No previous
mention of surds – the only mention of
irrational numbers was under ‘exceptional
performance’ for Attainment Target 2:
Number and algebra.
3.1 Range and content, Number and
algebra – ‘The study of mathematics
should include linear equations, formulae,
expressions and identities’; 2.2m Key
processes, Analysing, Use appropriate
mathematical procedures – ‘manipulate
numbers, algebraic expressions and
equations and apply routine algorithms’.
Attainment Target 2: Number and Algebra.
No previous explicit mention of
substituting values or rearranging and
simplifying expressions in the 2007 PoS –
the only mentions of ‘substituting…
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…fractions, decimals and negative
numbers’ and ‘simplifying algebraic
expressions’ was under Level 8 and
‘exceptional performance’ for Attainment
Target 2: Number and algebra.
Fl5: move freely between different
numerical, algebraic, graphical and
diagrammatic representations
Fl6: develop algebraic and graphical
fluency and understand linear and
quadratic functions
Fl7: use language and properties of 2-D
and 3-D shapes algebraic expressions,
probability and statistics
2.1 b Key Processes, Representing –
‘choose between representations’. 2.2a,
Key processes, Analysing, Use
mathematical reasoning – ‘make
connections within mathematics’ – the
explanatory notes state that an example of
this is realising that an equation, a table of
values and a line on a graph can all
represent the same thing. 2.2o Key
processes, Analysing, Using appropriate
mathematical procedures - ‘Record
methods, solutions and conclusions’ – the
explanatory notes state that recording
methods includes representing the results
of analyses in various ways e.g. tables,
diagrams and symbolic representation.
3.1e, f, g, h Range and content, Number
and algebra – ‘The study of mathematics
should include algebra as generalised
arithmetic; linear equations, formulae,
expressions and identities; analytical,
graphical and numerical methods for
solving equations’; polynomial graphs,
sequences and functions’. Reference to
fluency is new.
3.2a Range and Content, Geometry and
Measures – ‘The study of mathematics
should include properties of 2-D and 3-D
shapes’. ‘Precise language’ not previously
stipulated. 3.3 a, b, c, d Range and
Content, Statistics – ‘the study of
mathematics should include the handling
data cycle; presentation and analysis of
grouped and ungrouped data; measures
of central tendency and spread;
experimental and theoretical probabilities,
including those based on equally likely
outcomes’.
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Reason mathematically
Rm1: extend their understanding of the
number system, make connections
between number relationships, and
algebraic and graphical representations
2.2a Key Processes, Analysing, Use
mathematical reasoning – ‘make
connections within mathematics’.
Rm2: extend and formalise their
knowledge of ratio and proportion in
working with measures and geometry,
and in formulating proportional relations
algebraically
3.1c Range and Content, Number and
algebra – ‘The study of mathematics
should include applications of ratio and
proportion’. The Explanatory Notes state
that this includes contexts such as value
for money, scales, plans and maps,
statistical information, cooking etc. 3.2e, g
Range and Content, Geometry and
measures – ‘The study of mathematics
should include similarity, including the use
of scale; units, compounds measures and
conversions’.
Rm3: identify variables and express
relations between them algebraically and
graphically
Rm4: make and test conjectures about
patterns and relationships; look for
proofs or counter- examples
2.1b, c Key Processes, Representing –
‘choose between representations’;
‘simplify the situation or problem in order
to represent it mathematically, using
appropriate variables, symbols, diagrams
and models’. 3.1e, g Range and Content,
Number and algebra – ‘algebra as
generalised arithmetic’; analytical,
graphical and numerical methods for
solving equations’.
1.1c Key Concepts, Competence –
‘Selecting appropriate mathematical tools
and methods…’ The accompanying
Explanatory Notes state: ‘Mathematical
methods: At the heart of mathematics are
the concepts of equivalence, proportional
thinking, algebraic structure, relationships,
axiomatic systems, symbolic
representation, proof, operations and their
inverses’. The reference to the underlying
structure of a problem is new.
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Rm5: begin to reason deductively in
geometry, number and algebra,
including using geometrical
constructions
Rm6: interpret when the structure of a
numerical problem requires additive,
multiplicative or proportional reasoning
Rm7: explore what can and cannot be
inferred in statistical and probabilistic
settings and begin to express their
arguments formally.
Solve problems
Sp1: develop their mathematical
knowledge, in part through solving
problems and evaluating the outcomes,
including multi-step problems
Sp2: develop their use of formal
mathematical knowledge to interpret and
solve problems, including financial
mathematics
2.2j Key processes, Analysing, Use
mathematical reasoning – ‘reason
inductively and deduce’. Not previously
specified only in relation to geometry.
2.2 Key processes, Analysing, Use
mathematical reasoning. 1.2c Key
concepts, Creativity – ‘Posing questions
and developing convincing arguments’.
2.3 Key processes, Interpreting and
evaluating– ‘form convincing arguments
based on findings and make general
statements’. 2.4 Key processes,
Communicating and reflecting –
‘communicate findings effectively’.
‘Formally’ is a new inclusion.
1.2b Key Concepts, Creativity – ‘using
existing mathematical knowledge to create
solutions to unfamiliar problems’. 1.1a Key
Concepts, Competence – ‘applying
suitable mathematics accurately within the
classroom and beyond’. 1.3b Key
concepts, Applications and implications of
mathematics – ‘understanding that
mathematics is used as a tool in a wide
range of contexts’. The Explanatory Notes
accompanying this state that this includes
‘using mathematics as a tool for making
financial decisions in personal life…’ 4d
Curriculum opportunities – ‘work on
problems that arise in other subjects and
in contexts beyond the school’. The
Explanatory Notes state: ‘For
example…managing money in economic
wellbeing and financial capability’.
Devising problems is an addition, as is
inclusion of ‘formal’.
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Sp3: begin to model situations
mathematically and express the results
using a range of formal mathematical
representations
1.4a, b Key Concepts, Critical
Understanding – ‘Knowing that
mathematics is essentially abstract and
can be used to model, interpret or
represent situations; ‘recognising the
limitations and scope of a model or
representation’. 2.1a, b, c Key Processes,
Representing – ‘identify the mathematical
aspects of a problem’; ‘choose between
representations’; ‘simplify the situation or
problem in order to represent it
mathematically, using appropriate
variables, symbols, diagrams and models’.
2.2o Analysing, Use appropriate
mathematical procedures – ‘record
methods, solutions and conclusions’. The
Explanatory Notes state: ‘This includes
representing the results of analyses in
various ways (e.g. tables, diagrams and
symbolic representation).
1.2b Key Concepts, Creativity – ‘using
existing mathematical knowledge to create
solutions to unfamiliar problems’. 2.2b Key
processes, Analysing – ‘use knowledge of
related problems’. Addition of ‘multi-step’
(as in new primary PoS) and ‘increasingly
sophisticated’.
Sp4: Select appropriate concepts,
methods and techniques to apply to
unfamiliar and non-routine problems.
1.1c Key Concepts, Competence –
‘selecting appropriate mathematical tools
and methods, including ICT.’ 1.2b Key
concepts, Creativity – ‘using existing
mathematical knowledge to create
solutions to unfamiliar problems’. 2.1a, d
Key processes, Representing – ‘identify
the mathematical aspects of a situation or
problem; select mathematical information,
methods and tools to use’. 2.2i Key
processes, Analysing – ‘appreciate that
there are a number of different techniques
that can be used to analyse a situation.’
2.2l Key processes, Use appropriate
mathematical procedures – ‘calculate…
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…accurately, selecting mental
methods or calculating devices as
appropriate’. 4c Curriculum
opportunities – ‘develop confidence
in an increasing rang of methods
and techniques’.
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Number
Pupils should be taught to:
N1: understand and use place value, for
decimals, measures and integers of any
size
N2: order positive and negative integers,
decimals and fractions; use the number
line as a model for ordering of the real
numbers; use the symbols =, ≠, <, >, ≤,
≥
N3: use the concepts and vocabulary of
prime numbers, factors (or divisors),
multiples, common factors, common
multiples, highest common factor,
lowest common multiple, prime
factorisation, including using product
notation and the unique factorisation
property
N4: use the four operations, including
formal written methods, applied to
integers, decimals, proper and improper
fractions and mixed numbers, all both
positive and negative
N4: Understand the relation between
operations and their inverses and
identify the inverse of a given
operation where this exists
Place value and ordering numbers not
explicitly mentioned in the 2007 PoS;
previously came under Attainment Target
2: Number and algebra.
3.1a, b Range and content, Number and
algebra – ‘rational numbers, their
properties and different representations;
‘rules of arithmetic applied to calculations
and manipulations with rational numbers’.
The Explanatory Notes state: ‘This
includes using mental and written
methods’. Reference to ‘formal’ written
methods is new.
Recognising prime numbers was
previously a Year 6 objective; recognising
common factors, common multiples,
highest common factors and lowest
common factors was previously a Year 6
progression to Year 7 objective (in the
2007 Primary Framework for
Mathematics). Not necessarily new
content, but a change to the language
used.
1.1b, c Key Concepts, Competence –
‘communicating mathematics effectively;
selecting appropriate tools and methods’.
The Explanatory Notes state ‘ Pupils
should be familiar with and confident
about mathematical notation and
conventions and be able to select the
most appropriate way to communicate
mathematics, both orally and in writing’
and ‘at the heart of mathematics are the
concepts of equivalence, proportional
thinking, algebraic structure, relationships,
axiomatic systems, symbolic
representation, proof, operations and their
inverses’.
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N5: use conventional notation for the priority of
operations, including brackets, powers, roots and
reciprocals
N6: recognise and use relationships between
operations including inverse operations
N7: use integer powers and associated real
roots (square, cube and higher), recognise
powers of 2, 3, 4, 5 and distinguish between
exact representations of roots and their decimal
approximations
N8: interpret and compare numbers in standard
form A x10n 1≤A<10 where n is a positive or
negative integer or zero
N9: work interchangeably with terminating
decimals and their corresponding fractions (such
as 3.5 and 7/2 or 0.375 and 3/8)
N10:define percentage as ‘number of parts per
hundred’, interpret percentages and percentage
changes as a fraction or a decimal, interpret these
multiplicatively, express one quantity as a
percentage of another, compare two quantities
using percentages, and work with percentages
greater than 100%
3.1b Range and content,
Number and algebra – ‘rules of
arithmetic applied to
calculations and manipulations’
although this previously only
applied to rational numbers.
References to brackets,
powers, roots and reciprocals
previously came under
Attainment Target 2: Number
and algebra. Explanatory notes
state that ‘rules of arithmetic’
includes knowledge of
operations and inverse
operations and how calculators
use precedence.
Calculating with powers and
roots was not previously
explicitly identified within the
2007 PoS, but it was referred to
in Attainment Target 2: Number
and algebra under Level 8 and
exceptional performance
criteria.
Previously Level 8 under
Attainment Target 2:
Number and algebra.
Previously Level 6 under
Attainment Target 2: Number
and Algebra.
3.1c Range and Content,
Number and algebra –
‘applications of ratio and
proportion’.
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N11: interpret fractions and percentages as
operators
N12: use standard units of mass, length, time,
money and other measures, including with decimal
quantities
N13: round numbers and measures to an
appropriate degree of accuracy [e.g. to a
specified number of decimal places or significant
figures]
N14: use approximation through rounding to
estimate answers and calculate possible resulting
errors expressed using inequality notation a<x≤b
N15: use a calculator and other technologies to
calculate results accurately and then interpret
them appropriately
3.2g, h Range and content,
Geometry and measures – ‘The
study of mathematics should
include units, compound
measures and conversions;
perimeters, areas, surface
areas and volumes’
2.2l Key Processes, Analysing,
Use appropriate mathematical
procedures – ‘calculate
accurately, selecting mental
methods or calculating devices
as appropriate’. 2.3 Key
processes, Interpreting and
evaluating.
2.2 Key Processes,
Analysing, Use appropriate
mathematical procedures –
‘estimate, approximate and
check working’.
N16: appreciate the infinite nature of the sets of
integers, real and rational numbers
3.1d Range and content,
Number and algebra –
‘accuracy and rounding’.
New emphasis on simple
error intervals, using
standard interval and
inequality notation.
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Algebra
Pupils should be taught to:
A1: use algebraic notation, including:
 ab in place of a × b
 3y in place of y + y + y and 3 × y
2
3
 a in place of a × a, a in place of
a × a × a; a2b in place of a × a × b
 a/b in place of a b
 coefficients written as fractions rather than as
decimals
 brackets
A2: substitute numerical values into formulae and
expressions, including scientific formulae
A3: understand and use the concepts and
vocabulary of expressions, equations,
inequalities, terms, and factors
A4: simplify and manipulate algebraic expressions to
maintain equivalence by:
 collecting like terms
 multiplying a single term over a bracket
 taking out common factors
 expanding products of two or more binomials
Although not previously
referred to in as much detail,
reading and interpreting
algebraic notation and
expressing known relations
algebraically could come under
3.1b Range and content,
Number and algebra – ‘algebra
as generalised arithmetic.
Understanding and using the
concepts of terms and
expressions is inferred in 3.1f, h
Range and content, Number
and Algebra ‘linear equations,
formulae, expressions and
identities; polynomial graphs,
sequences and functions’,
however explicit reference is
only made to factors and terms
in Attainment target 2: Number
and Algebra.
2.2n Key Processes, Analysing,
Use appropriate mathematical
procedures – ‘use accurate
notation…’ 3.1 e Range and
content, Number and algebra –
‘rules of arithmetic applied to
calculations and manipulations
with rational numbers’.
2.2m Key processes, Analysing,
Use appropriate mathematical
procedures – ‘manipulate
numbers, algebraic expressions
and equations and apply routine
algorithms’. No previous mention
of factorising in the 2007 PoS,
although common factors are
referred to in Attainment target 2:
Number and Algebra.
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A5: understand and use standard mathematical
formulae; rearrange formulae to change the
subject
A6: model situations or procedures by
translating them into algebraic expressions or
formulae and by using graphs
A7: recognise, sketch and produce graphs of
linear and quadratic functions of one variable with
appropriate scaling, using equations in x and y
and the cartesian plane
A8: interpret mathematical relationships both
algebraically and graphically
2.1 Key processes,
Representing – ‘simplify the
situation or problem in order to
represent it mathematically,
using appropriate variables,
symbols, diagrams and models.
Solving problems involving
calculating with powers
previously came under Level 8
criteria for Attainment Target 2:
Number
3.1h Range and content,
Number and algebra –
‘polynomial graphs, sequences
and functions’. Not new
content, but a change to the
language used.
2.2e Key Processes,
Analysing, Use
mathematical reasoning –
‘make and begin to justify
conjectures and
generalisations, considering
special cases and counterexamples’. 3.1h Range and
content, Number and
algebra – ‘polynomial
graphs, sequences and
functions’. This section has
been massively expanded
and is potentially very
complex.
2.2k Key processes,
Analysing, Use
mathematical reasoning –
‘make accurate
mathematical diagrams,
graphs and constructions…’
3.1g Range and content,
Number and algebra –
‘analytical, graphical and
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numerical methods
for
solving equations’.
‘Cartesian plane’ = new
KS3 maths curriculum review | 20
A9: reduce a given linear equation in two variables
to the standard form y = mx + c; calculate and
interpret gradients and intercepts of graphs of such
linear equations numerically, graphically and
algebraically
A10: use linear and quadratic graphs to estimate
values of y for given values of x and vice versa and
to find approximate solutions of simultaneous linear
equations
A11: find approximate solutions to contextual
problems from given graphs of a variety of
functions, including piece-wise linear, exponential
and reciprocal graphs
A12: generate terms of a sequence from either a
term-to-term or a position-to-term rule
A13: recognise arithmetic sequences and find the
nth term
A14: recognise geometric sequences and appreciate
other sequences that arise.
2.1c Key processes,
Representing – ‘simplify the
situation of problem in order to
represent it mathematically,
using appropriate variables,
symbols, diagrams and
models’.
3.1 Range and content,
Number and algebra – ‘linear
equations, formulae,
expressions and identities’.
Inferred in the Explanatory
Notes for 2.2a Key processes,
Analysing, Use mathematical
reasoning – ‘make connections
within mathematics’: ‘For
example, realising that an
equation, a table of values and
a line on a graph can all
represent the same thing, or
understanding that an
intersection between two lines
on a graph can represent the
solution to a problem.’
3.1g Range and content,
Number and algebra –
‘analytical, graphical and
numerical methods for solving
equations’. 2.2p Key
processes, Analysing, Use
appropriate mathematical
procedures – ‘estimate,
approximate and check
working’.
3.1h Range and content,
Number and algebra –
‘polynomial graphs sequences
and functions’. Explicit
reference to exponential graphs
is new. ‘Piece-wise linear’ is
new terminology.
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Ratio, proportion and rates of change
Pupils should be taught to:
Ra1: change
freely between related
standard units
Ra2: use
scale factors, scale diagrams and maps
Ra3: express
one quantity as a fraction of
another, where the fraction is less than 1 and
greater than 1
ratio notation, including reduction to
simplest form
3.1c Range and Content,
Number and Algebra –
‘applications of ratio and
proportion’. 3.2e, g Range
and content, Geometry and
measures – ‘similarity,
including the use of scale;
units, compound measures
and conversions’.
Ra4: use
Ra5: divide
a given quantity into two parts in a given
part:part or part:whole ratio; express the division of
a quantity into two parts as a ratio
Ra6: understand
that a multiplicative relationship
between two quantities can be expressed as a ratio
or a fraction
3.1c Range and Content,
Number and algebra –
‘applications of ratio and
proportion’. The Explanatory
Notes state: ‘This includes
percentages and applying
concepts of ratio and
proportion to contexts such as
value for money, scales, plans
and maps, cooking and
statistical information’.
use compound units such as speed, unit
pricing and density to solve problems
Ra7:
No previous reference to
‘multiplicative reasoning’.
3.2g Range and Content,
Geometry and measures –
‘units, compound measures
and conversions’. The
Explanatory Notes state:
‘This includes making sense
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of information
compound measures, for
example fuel consumption,
KS3 maths curriculum review | 22
Geometry and measures
Pupils should be taught to:
Ge1: derive and apply formulae to calculate and
solve problems involving: perimeter and area of
triangles, parallelograms, trapezia, volume of
cuboids (including cubes) and other prisms
(including cylinders)
and solve problems involving:
perimeters of 2-D shapes (including circles),
areas of circles and composite shapes
3.2h Range and content,
Geometry and measures –
‘perimeters, areas, surface
areas and volumes’. The
Explanatory Notes state that
‘this includes 3D shapes based
on prisms’.
Ge2: calculate
Ge3: draw and measure line segments
and angles in geometric figures,
including interpreting scale drawings
Ge4: derive and use the standard ruler and compass
constructions (perpendicular bisector of a line
segment, constructing a perpendicular to a given
line from/at a given point, bisecting a given angle);
recognise and use the perpendicular distance from a
point to a line as the shortest distance to the line
Ge5: describe, sketch and draw using
conventional terms and notations: points, lines,
parallel lines, perpendicular lines, right angles,
regular polygons, and other polygons that are
reflectively and rotationally symmetric
Ge6:
use the standard conventions for labelling
the sides and angles of triangle ABC, and know
and use the criteria for congruence of triangles
3.2a, b, e Range and content,
Geometry and measures –
‘properties of 2D and 3D
shapes; constructions, loci and
bearing; similarity, including the
use of scale’. Reference to
‘digital instruments’ – 2007 PoS
stated ‘ICT’. The focus in the
previous PoS was on
‘constructing’ rather than
‘measuring’ geometrical figures.
3.2 b, d, f Range and content,
Geometry and measures –
‘constructions, loci and
bearings’ – the Explanatory
Notes state that this includes
constructing mathematical
figures using both straight
edge, compasses and ICT.
Also ‘points, lines and shapes
in 2D coordinate systems;
transformations’.
3.2 a, b, c Range and content,
Geometry and measures –
‘properties of 2D and 3D
shapes; constructions, loci and
bearings; Pythagoras’ theorem’.
3.2b, e, f Range and content,
Geometry and measures –
‘constructions, loci and
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bearings; similarity,
including
the use of scale; points, lines
and shapes in 2D coordinate
KS3 maths curriculum review | 23
Ge7: derive and illustrate properties of triangles,
quadrilaterals, circles, and other plane figures
using appropriate language and technologies
identify properties of, and describe the
results of, translations, rotations and reflections
applied to given figures
3.2f Range and content,
Geometry and measures –
‘points, lines and shapes in
2D coordinate systems’.
Ge8:
Ge9: identify and construct congruent triangles,
and construct similar shapes by enlargement,
including on coordinate grid
Ge10: apply
the properties of angles at a point,
angles at a point on a straight line, vertically
opposite angles
Ge11: understand
and use the relationship between
parallel lines and alternate and corresponding
angles
Ge12: derive
and use the sum of angles in a triangle
and use it to deduce the angle sum in any polygon,
and to derive properties of regular polygons
Not explicitly referred to in the
2007 PoS. Came under Level
6 criteria for Attainment target
3: Geometry and measures.
3.2a, d, e Range and content,
Geometry and measures –
‘properties of 2D and 3D
shapes; transformations;
similarity, including the use of
scale’. 1.1c – Key concepts,
Competence – ‘selecting
appropriate mathematical
tools and methods…’ The
Explanatory Notes states: ‘At
the heart of mathematics are
the concepts
of…relationships, axiomatic
systems, symbolic
representation…’.
Ge13: apply
angle facts, triangle congruence,
similarity and properties of quadrilaterals to derive
results about angles and sides, including
Pythagoras’ Theorem, and use known results to
obtain simple proofs
3.2c Range and content,
Geometry and measures –
‘Pythagoras’ theorem’.
use Pythagoras’ Theorem and trigonometric
ratios in similar triangles to solve problems
involving right-angled triangles
3.2a Range and content,
Geometry and measures –
‘Properties of 2D and 3D
shapes’.
Ge14:
Ge15:use
the properties of faces, surfaces, edges
and vertices of cubes, cuboids, prisms, cylinders,
pyramids, cones and spheres to solve problems in
3-D
Loci and bearings no longer
mentioned.
interpret mathematical relationships both
algebraically and geometrically.
Ge16:
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KS3 maths curriculum review | 24
Probability
Pupils should be taught to:
Pr1: record, describe and analyse the frequency
of outcomes of simple probability experiments
involving randomness, fairness, equally and
unequally likely outcomes, using appropriate
language and the 0-1 probability scale
Pr2: understand that the probabilities of all possible
outcomes sum to 1
Pr3: enumerate sets and combinations of sets
systematically, using tables, grids and Venn
diagrams
This section has been greatly
expanded. Probability was
previously only one objective,
under 3.3 Statistics.
3.3d Range and content,
Statistics – ‘experimental and
theoretical probabilities,
including those based on
equally likely outcomes’. 2.2
Key processes, Analysing, Use
appropriate mathematical
procedures – ‘record methods,
solutions and conclusions’.
2.1d Key processes,
Representing – ‘select
mathematical information,
methods and tools to use’. The
Explanatory Notes state: ‘This
involves using systematic
methods to explore a
situation…’Previously no
specific mention of using sets
or tabular, grid and Venn
diagrams.
Pr4: generate theoretical sample spaces for single
and combined events with equally likely, mutually
exclusive outcomes; use these to calculate
theoretical probabilities.
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KS3 maths curriculum review | 25
Statistics
Pupils should be taught to:
St1: describe, interpret and compare observed
distributions of a single variable through:
appropriate graphical representation involving
discrete, continuous and grouped data; and
appropriate measures of central tendency (mean,
mode, median) and spread (range, consideration
of outliers)
St2: construct and interpret appropriate tables,
charts, and diagrams, including frequency tables,
bar charts, pie charts, and pictograms for
categorical data, and vertical line (or bar) charts
for ungrouped and grouped numerical data
3.3d Range and content,
Statistics – ‘experimental
and theoretical probabilities,
including those based on
equally likely outcomes’.
Incorporates criteria from
Attainment Target 4:
Handling Data.
3.3b, c Range and content,
Statistics – ‘presentation
and analysis of grouped and
ungrouped data, including
time series and lines of best
fit; measures of central
tendency and spread’.
The specific reference to
‘graphical representation’ is
new; previously it only
specified ‘presentation and
analysis’.
St3: describe simple mathematical relationships
between two variables (bivariate data) in
observational and experimental contexts and
illustrate using scatter graphs.
This is a completely new
objective.
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Schoolzone
Formal House
60 St Georges Place
Cheltenham
GL50 3PN
01242 262906
research@schoolzone.co.uk
Further support documents for the introduction of the new
curriculum can be found at:
http://www.schoolzone.co.uk/schools/NewCurriculum.asp