APP assessment criteria KS3 sow by YH95e8

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									Open the assessment criteria using the tab at the bottom of this page. This will list all the assessment criteria at all
the levels.



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Assessment Criteria relevant to a particular unit.


Each statement is linked to the relevant progression maps. The hyperlink in column A (map) will take you to the
approximate position in the progression map. Hyperlinks from the progression map will take you to more detailed
explanations, probing questions and resources that could be used. (On the National Strategies website).


To graph pupil achievement for a limited number of assessment criteria, use the filter on the AT column, and/or insert
a number in the "select" column, and filter by that. This will be useful when sharing achievement with a class and
prioritising topics for revision and intervention. Open the chart using the tab at the bottom of the page
map     AF             G
                   Level rade

       Algebra       8    B
equations, formulae and identities

       Algebra       8    B
equations, formulae and identities
       Algebra       8    B
equations, formulae and identities
       Algebra       8    B
equations, formulae and identities
       Algebra       8    B
equations, formulae and identities
       Using and applying
Reasoning            8    B
       Algebra
sequences, functions8     B
                      and graphs

FDPRP Calculating 8       B

        and powers
IntegersCalculating 8     B
                   8
       Handling Data      B
Handling data
                   8
       Handling Data    B
Handling data
Probability        8
       Handling Data    B
Probability        8
       Handling Data    B
         Solving   8    B
ProblemUsing and applying

      Using and applying
Reasoning         8    B

      Using and applying
Reasoning         8    B
      Using and applying
communicating     8    B
                       B
FDPRP Numbers and8the number system

      Using and applying
Reasoning         8    B

       Algebra
sequences, functions8    B
                     and graphs

      Shape and Space B
Measures         8

       Shape and Space B
Measures          8
       Shape      8
Shape & spaceand Space B

       Algebra       7    C
equations, formulae and identities

       Algebra       7    C
equations, formulae and identities
       Algebra       7    C
equations, formulae and identities
       Algebra       7    C
equations, formulae and identities

       Algebra
sequences, functions7    C
                     and graphs
FDPRP Calculating 7      C
FDPRP Calculating 7      C
FDPRP Calculating 7      C

       Calculating 7
Place value               C

        Calculating
Written calculations 7    C
                   7
       Handling Data      C
Handling data
                   7
       Handling Data      C
Handling data
                   7
       Handling Data      C
Handling data
                   7
       Handling Data      C
Handling data
                   7
       Handling Data      C
Handling data
                   7
       Handling Data      C
Probability

       Using and applying
communicating       7    C
        Solving     7
ProblemUsing and applyingC
       Using and applying
Reasoning           7    C
                         C
FDPRP Numbers and7the number system
       Algebra
sequences, functions7    C
                     and graphs


        Solving    7    C
ProblemUsing and applying
       Shape and Space C
Measures           7
       Shape and Space C
Measures           7

      Shape and Space C
Measures         7

      Shape and Space C
Measures         7

       Shape      7
Shape & spaceand Space C
       Shape      7
Shape & spaceand Space C

       Algebra       6    C
equations, formulae and identities

       Algebra
sequences, functions6     C
                      and graphs
       Algebra       6    D
equations, formulae and identities


        Solving    6    C
ProblemUsing and applying

      Using and applying
communicating     6    D
      Using and applying
Reasoning         6    D

FDPRP Calculating 6       C

FDPRP Calculating 6       C

                   6
       Handling Data      C
Handling data
FDPRP Calculating 6       D

FDPRP Calculating 6       D


                    6
        Handling Data     D

Handling data
                   6
       Handling Data      D
Handling data
                   6
       Handling Data      D
Probability
                   6
       Handling Data      D
Probability

       Algebra
sequences, functions6    D
                     and graphs
FDPRP Numbers and6the number system

       Algebra
sequences, functions6    D
                     and graphs

       Shape      6
Shape & spaceand Space C

       Shape and Space D
Measures          6
       Shape and Space D
Measures          6
       Shape      6
Shape & spaceand Space C
       Shape      6
Shape & spaceand Space D

       Shape      6
Shape & spaceand Space D
       Shape      6
Shape & spaceand Space D
       Shape      6
Shape & spaceand Space D

       Shape         6
Shape & spaceand Space D
       Using and applying
Reasoning            6    D
       Shape         6
Shape & spaceand Space D
       Using and applying
Reasoning            5    E
       Algebra       5    E
equations, formulae and identities

     Using and applying
communicating    5    E

        Calculating
Written calculations 5    D
FDPRP Calculating 5       E
        Calculating
Written calculations 5    E

        Calculating
Written calculations 5    E
Handling data
        Handling Data5    E
Handling data
        Handling Data5    E
                   5
       Handling Data      E
Probability
Probability        5
       Handling Data      E
Probability        5
       Handling Data      E

      Shape and Space E
Measures         5

       Shape and Space E
Measures          5
       Shape and Space E
Measures          5
       Shape      5
Shape & spaceand Space E

        Shape       5
Shape & spaceand Space E
        Algebra
sequences, functions5    F
                     and graphs
         Solving    5
ProblemUsing and applyingE
         Solving    5
ProblemUsing and applyingE
         Solving    5
ProblemUsing and applyingE
        and powers       E
IntegersNumbers and5the number system

        Numbers and5the number system
Place value              E
        Numbers and and Egraphs
sequences, functions5the number system
        and powers
IntegersCalculating 5    F
        Calculating
Written calculations 5    F
                   5
       Handling Data      F
Handling data
Handling data      5
       Handling Data      F

       Shape      5
Shape & spaceand Space F

       Shape       5
Shape & spaceand Space F
FDPRP Numbers and5the number system
FDPRP Numbers and5the number system
FDPRP Numbers and5the number system
       Using and applying
Reasoning          4    F
       Shape and Space F
Measures           4
       Shape and Space F
Measures           4
       Shape       4
Shape & spaceand Space F

       Shape      4
Shape & spaceand Space F
       Shape and Space G
Measures          4

        Shape        4
Shape & spaceand Space G
        Algebra      4    F
equations, formulae and identities
        Algebra
sequences, functions4     G
                      and graphs
        Using and applying
communicating        4    E
        Calculating
Mental Calculations 4     F
Handling data
        Handling Data4    F
Handling data
        Handling Data4    F
         Solving     4
ProblemUsing and applying F
         Solving     4
ProblemUsing and applying F
        Numbers and4the number system
Place value               F
        Calculating
Mental Calculations 4     G
        Calculating
Written calculations 4    G
        Calculating
Written calculations 4    G
        Calculating
Written calculations 4    G
        Calculating
Written calculations 4    G
Handling data
        Handling Data4    G
Handling data
        Handling Data4    G
Handling data
        Handling Data4    G

FDPRP Numbers and4the number system
FDPRP Numbers and4the number system
FDPRP Numbers and4the number system
        and powers
IntegersNumbers and4the number system
        Numbers and and graphs
sequences, functions4the number system

       Shape      3
Shape & spaceand Space F

       Shape      3
Shape & spaceand Space G

      Shape and Space
Measures         3
      Shape and Space
Measures         3

       Shape         3
Shape & spaceand Space
       Shape         3
Shape & spaceand Space
       Algebra       3
equations, formulae and identities
        Solving      3
ProblemUsing and applying F
       Calculating
Mental Calculations 3   G
       Using and applying
communicating       3   G
       Using and applying
communicating       3   G

        Solving     3
ProblemUsing and applyingG
       Using and applying
Reasoning           3    G
       Algebra
sequences, functions3and graphs
       Calculating
Mental Calculations 3

        Calculating
Mental Calculations 3
        Calculating
Written calculations 3

        Calculating
Written calculations 3

        Calculating
Written calculations 3
Handling data
        Handling Data3
Handling data
        Handling Data3
Handling data
        Handling Data3
Handling data
        Handling Data3

FDPRP Numbers and3the number system
FDPRP Numbers and3the number system
        and powers
IntegersNumbers and3the number system
        Numbers and3the number system
Place value
        Numbers and3the number system
Place value
        Using and applying
Reasoning           3

      Shape and Space
Measures         2

       Shape and Space
Measures          2
       Shape      2
Shape & spaceand Space
       Shape      2
Shape & spaceand Space
       Shape      2
Shape & spaceand Space

       Shape        2
Shape & spaceand Space
       Algebra
sequences, functions2and graphs

       Calculating
Mental Calculations 2
       Calculating
Mental Calculations 2

        Calculating
Mental Calculations 2
        Calculating
Mental Calculations 2
        Calculating
Written calculations 2
Handling data
        Handling Data2
Handling data
        Handling Data2
Handling data
        Handling Data2
Handling data
        Handling Data2
                   2
       Handling Data
Handling data

FDPRP Numbers and2the number system
        and powers
IntegersNumbers and2the number system
        Numbers and2the number system
Place value
        Using and applying
communicating       2
        Using and applying
communicating       2
        Using and applying
communicating       2
        Solving    2
ProblemUsing and applying

      Using and applying
Reasoning         2

       algebra           graphs
sequences, functions and *A

      Shape and Space*A
Measures

       Shape and Space*A
Measures
       Shape
Shape & spaceand Space*A

       Shape
Shape & spaceand Space*A


       algebra            A
equations, formulae and identities

       algebra            A
equations, formulae and identities
       algebra            A
equations, formulae and identities

       algebra           A
sequences, functions and graphs


       algebra           A
sequences, functions and graphs



       algebra           A
sequences, functions and graphs

FDPRP calculating         A

         and powers
Integerscalculating       A
         and powers
Integerscalculating       A

       calculating
Place value               A
       handling data      A
Handling data
       handling data      A
Handling data
Handling data data
       handling           A
Handling data data
       handling           A
        handling data   A
Probability
         and powers     A
IntegersNumbers and the number system
        Numbers and the number system
Place value             A
MeasuresShape and Space A
MeasuresShape and Space A

      Shape and Space A
Measures

       Shape
Shape & spaceand Space A

       Shape
Shape & spaceand Space A

       Shape
Shape & spaceand Space A
       Shape
Shape & spaceand Space A
       Shape
Shape & spaceand Space A
        Solving         A
ProblemUsing and applying



        Solving         A
ProblemUsing and applying

      Using and applying
Reasoning              A


      Using and applying
Reasoning              A


TA level sing and applying
        U
TA level umbers and the number system
        N
TA level alculating
        c
TA level lgebra
        a
TA level hape and Space
        S
TA level andling Data
        H
Overall
                                                                                                              7A17A2
Asessment criteria                                                                                            unit
factorise quadratic expressions including the difference of two squares,                    e.g. x2

manipulate algebraic formulae, equations and expressions, finding common factors and multiplying two
linear expressions
derive and use more complex formulae and change the subject of a formula
evaluate algebraic formulae, substituting fractions, decimals and negative numbers
solve inequalities in two variables and find the solution set
reflect on lines of enquiry when exploring mathematical tasks
understand the effect on a graph of addition of (or multiplication by) a constant
use fractions or percentages to solve problems involving repeated proportional changes or the
calculation of the original quantity given the result of a proportional change
solve problems involving calculating with powers, roots and numbers expressed in standard form,
checking for correct order of magnitude and using a calculator as appropriate
estimate and find the median, quartiles and interquartile range for large data sets, including using a
cumulative frequency diagram
compare two or more distributions and make inferences, using the shape of the distributions and
measures of average and spread including median and quartiles
know when to add or multiply two probabilities
use tree diagrams to calculate probabilities of combinations of independent events
develop and follow alternative methods and approaches
select and combine known facts and problem solving strategies to solve problems of increasing
complexity
distinguish between practical demonstration and proof; know underlying assumptions, recognising their
importance and limitations, and the effect of varying them
convey mathematical meaning through precise and consistent use of symbols
understand the equivalence between recurring decimals and fractions
examine generalisations or solutions reached in an activity, commenting constructively on the reasoning
and logic or the process employed, or the results obtained
sketch, interpret and identify graphs of linear, quadratic, cubic and reciprocal functions, and graphs that
model real situations
understand and use trigonometrical relationships in right-angled triangles, and use these to solve
problems, including those involving bearings
understand the difference between formulae for perimeter, area and volume in simple contexts by
considering dimensions
understand and use congruence and mathematical similarity
square a linear expression, and expand and simplify the product of two linear expressions of the
form (x ± n) and simplify the corresponding quadratic expression
use formulae from mathematics and other subjects; substitute numbers into expressions and
formulae; derive a formula and, in simple cases, change its subject
use algebraic and graphical methods to solve simultaneous linear equations in two variables
solve inequalities in one variable and represent the solution set on a number line
find the next term and nth term of quadratic sequences and functions and explore their properties
                                                                                                              7A1   7A3
calculate the result of any proportional change using multiplicative methods
understand the effects of multiplying and dividing by numbers between 0 and 1
add, subtract, multiply and divide fractions
make and justify estimates and approximations of calculations; estimate calculations by rounding
numbers to one significant figure and multiplying and dividing mentally
use a calculator efficiently and appropriately to perform complex calculations with numbers of any size,
knowing not to round during intermediate steps of a calculation
suggest a problem to explore using statistical methods, frame questions and raise conjectures; identify
possible sources of bias and plan how to minimise it
select, construct and modify, on paper and using ICT suitable graphical representation to progress an
enquiry including frequency polygons and lines of best fit on scatter graphs
estimate the mean, median and range of a set of grouped data and determine the modal class, selecting
the statistic most appropriate to the line of enquiry
compare two or more distributions and make inferences, using the shape of the distributions and
measures of average and range
examine critically the results of a statistical enquiry, and justify the choice of statistical representation in
written presentation
understand relative frequency as an estimate of probability and use this to compare outcomes of an
experiment
give reasons for choice of presentation, explaining selected features and showing insight into the
problems structure
appreciate the difference between mathematical explanation and experimental evidence
justify generalisations, arguments or solutions                                                                    7A2
                                                                                                                 7A1
understand and use proportionality
                                                                        2        2            3
plot graphs of simple quadratic and cubic functions, e.g. y = x , y = 3x + 4, y = x
solve increasingly demanding problems and evaluate solutions; explore connections in mathematics
across a range of contexts: number, algebra, shape, space and measures, and handling data; refine or
extend the mathematics used to generate fuller solutions

calculate lengths, areas and volumes in plane shapes and right prisms
recognise that measurements given to the nearest whole unit may be inaccurate by up to one half of the
unit in either direction
understand and use measures of speed (and other compound measures such as density or pressure) to
solve problems
enlarge 2-D shapes, given a centre of enlargement and a fractional scale factor, on paper and using ICT;
recognise the similarity of the resulting shapes
find the locus of a point that moves according to a given rule, both by reasoning and using ICT
use systematic trial and improvement methods and ICT tools to find approximate solutions to equations
such as x3 + x = 20
generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on
paper and using ICT; write an expression to describe the nth term of an arithmetic sequence              7A1 7A3
construct and solve linear equations with integer coefficients, using an appropriate method                7A2
solve problems and carry through substantial tasks by breaking them into smaller, more manageable
tasks, using a range of efficient techniques, methods and resources, including ICT; give solutions to an
appropriate degree of accuracy
present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory texts
interpret, discuss and synthesise information presented in a variety of mathematical forms                           7A3
divide a quantity into two or more parts in a given ratio and solve problems involving ratio and direct
proportion
use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a
whole
design a survey or experiment to capture the necessary data from one or more sources; design, trial and,
if necessary, refine data collection sheets; construct tables for large discrete and continuous sets of raw
data, choosing suitable class intervals; design and use two-way tables
calculate percentages and find the outcome of a given percentage increase or decrease
add and subtract fractions by writing them with a common denominator, calculate fractions of quantities
(fraction answers), multiply and divide an integer by a fraction
select, construct and modify, on paper and using ICT:                                   pie charts for
categorical data                                                     bar charts and frequency diagrams for
discrete and continuous data                       simple time graphs for time series
scatter graphs                                                               and identify which are most
useful in the context of the problem
communicate interpretations and results of a statistical survey using selected tables, graphs and
diagrams in support
find and record all possible mutually exclusive outcomes for single events and two successive events in a
systematic way
know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving
problems
plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of
the form y = mx + c correspond to straight-line graphs                                                              7A3
use the equivalence of fractions, decimals and percentages to compare proportions
construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs
arising from real situations                                                                                        7A3
solve geometrical problems using properties of angles, of parallel and intersecting lines, and of triangles
and other polygons
deduce and use formulae for the area of a triangle and parallelogram, and the volume of a cuboid;
calculate volumes and surface areas of cuboids
know and use the formulae for the circumference and area of a circle
use straight edge and compasses to do standard constructions
classify quadrilaterals by their geometric properties
identify alternate and corresponding angles: understand a proof that the sum of the angles of a triangle
is 180° and of a quadrilateral is 360°
visualise and use 2-D representations of 3-D objects
enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor
know that translations, rotations and reflections preserve length and angle and map objects onto
congruent images
use logical argument to establish the truth of a statement                                                      7A2
                                                                                                              7A1
devise instructions for a computer to generate and transform shapes and paths
draw simple conclusions of their own and give an explanation of their reasoning                                 7A2
                                                                                                              7A1
construct, express in symbolic form, and use simple formulae involving one or two operations                    7A2
                                                                                                              7A1
show understanding of situations by describing them mathematically using symbols, words and
diagrams                                                                                                      7A1   7A3
use known facts, place value, knowledge of operations and brackets to calculate including using all four
operations with decimals to two places
solve simple problems involving ratio and direct proportion
use a calculator where appropriate to calculate fractions/percentages of quantities/measurements
understand and use an appropriate non-calculator method for solving problems that involve multiplying
and dividing any three digit number by any two digit number
ask questions, plan how to answer them and collect the data required
create and interpret line graphs where the intermediate values have meaning
in probability, select methods based on equally likely outcomes and experimental evidence, as
appropriate
understand and use the probability scale from 0 to 1
understand that different outcomes may result from repeating an experiment
read and interpret scales on a range of measuring instruments, explaining what each labelled division
represents
solve problems involving the conversion of units and make sensible estimates of a range of measures in
relation to everyday situations
understand and use the formula for the area of a rectangle and distinguish area from perimeter
reason about position and movement and transform shapes
use a wider range of properties of 2-D and 3-D shapes and identify all the symmetries of 2-D shapes
use and interpret coordinates in all four quadrants                                                                 7A3
identify and obtain necessary information to carry through a task and solve mathematical problems
check results, considering whether these are reasonable
solve word problems and investigations from a range of contexts
round decimals to the nearest decimal place and order negative numbers in context
use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 and
1000 and explain the effect
recognise and use number patterns and relationships                                                                 7A3
solve simple problems involving ordering, adding, subtracting negative numbers in context
apply inverse operations and approximate to check answers to problems are of the correct magnitude
understand and use the mean of discrete data and compare two simple distributions, using the range
and one of mode, median or mean
interpret graphs and diagrams, including pie charts, and draw conclusions
use language associated with angle and know and use the angle sum of a triangle and that of angles at a
point
measure and draw angles to the nearest degree, when constructing models and drawing or using shapes
use equivalence between fractions and order fractions and decimals
reduce a fraction to its simplest form by cancelling common factors
understand simple ratio
use their own strategies within mathematics and in applying mathematics to practical contexts               7A2
choose and use appropriate units and instruments
interpret, with appropriate accuracy, numbers on a range of measuring instruments
use the properties of 2-D and 3-D shapes
make 3-D models by linking given faces or edges and draw common 2-D shapes in different orientations
on grids
find perimeters of simple shapes and find areas by counting squares
reflect simple shapes in a mirror line, translate shapes horizontally or vertically and begin to rotate a
simple shape or object about its centre or a vertex
begin to use simple formulae expressed in words                                                             7A2
                                                                                                          7A1
use and interpret coordinates in the first quadrant                                                            7A3
present information and results in a clear and organised way                                                7A2
use a range of mental methods of computation with all operations
group data, where appropriate, in equal class intervals
understand and use the mode and range to describe sets of data
develop own strategies for solving problems                                                                 7A2
                                                                                                          7A1
search for a solution by trying out ideas of their own                                                      7A2
use place value to multiply and divide whole numbers by 10 or 100
recall multiplication facts up to 10 × 10 and quickly derive corresponding division facts                      7A3
use efficient written methods of addition and subtraction and of short multiplication and division
multiply a simple decimal by a single digit
solve problems with or without a calculator
check the reasonableness of results with reference to the context or size of numbers
collect and record discrete data
continue to use Venn and Carroll diagrams to record their sorting and classifying of information
construct and interpret frequency diagrams and simple line graphs
recognise approximate proportions of a whole and use simple fractions and percentages to describe
these
order decimals to three decimal places
begin to understand simple ratio
recognise and describe number relationships including multiple, factor and square                              7A3
recognise and describe number patterns                                                                         7A3
classify 3-D and 2-D shapes in various ways using mathematical properties such as reflective symmetry
for 2-D shapes
begin to recognise nets of familiar 3-D shapes, e.g. cube, cuboid, triangular prism, square-based pyramid
use a wider range of measures including non-standard units and standard metric units of length, capacity
and mass in a range of contexts
use standard units of time
recognise shapes in different orientations and reflect shapes, presented on a grid, in a vertical or
horizontal mirror line
describe position and movement
                                                                                                              7A2
                                                                                                            7A1
select the mathematics they use in a wider range of classroom activities
derive associated division facts from known multiplication facts
begin to organise their work and check results                                                                 7A2
use and interpret mathematical symbols and diagrams                                                            7A2
                                                                                                             7A1
try different approaches and find ways of overcoming difficulties that arise when they are solving
problems                                                                                                       7A2
understand a general statement by finding particular examples that match it                                  7A1
recognise a wider range of sequences                                                                         7A1 7A3
add and subtract two digit numbers mentally
use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers
add and subtract three digit numbers using written method
multiply and divide two digit numbers by 2, 3, 4 or 5 as well as 10 with whole number answers and
remainders
solve whole number problems including those involving multiplication or division that may give rise to
remainders
gather information
construct bar charts and pictograms, where the symbol represents a group of units
use Venn and Carroll diagrams to record their sorting and classifying of information
extract and interpret information presented in simple tables, lists, bar charts and pictograms
use simple fractions that are several parts of a whole and recognise when two simple fractions are
equivalent
begin to use decimal notation in contexts such as money
recognise negative numbers in contexts such as temperature
understand place value in numbers to 1000
use place value to make approximations
review their work and reasoning
begin to use a wider range of measures including to use everyday non-standard and standard units to
measure length and mass
begin to understand that numbers can be used not only to count discrete objects but also to describe
continuous measures
use mathematical names for common 3-D and 2-D shapes
describe their properties, including numbers of sides and corners
describe the position of objects
distinguish between straight and turning movements, recognise right angles in turns and understand
angle as a measurement of turn
recognise sequences of numbers, including odd and even numbers                                               7A1   7A3
use the knowledge that subtraction is the inverse of addition and understand halving as a way of

use mental recall of addition and subtraction facts to 10
use mental calculation strategies to solve number problems including those involving money and
measures
choose the appropriate operation when solving addition and subtraction problems
record their work in writing
sort objects and classify them using more than one criterion
understand vocabulary relating to handling data
collect and sort data to test a simple hypothesis
record results in simple lists, tables, pictograms and block graphs
communicate their findings, using the simple lists, tables, pictograms and block graphs they have
recorded
begin to use halves and quarters and relate the concept of half of a small quantity to the concept of half
of a shape
count sets of objects reliably
begin to understand the place value of each digit; use this to order numbers up to 100
discuss their work using mathematical language                                                                 7A2
begin to represent their work using symbols and simple diagrams
explain why an answer is correct
select the mathematics they use in some classroom activities
predict what comes next in a simple number, shape or spatial pattern or sequence and give reasons for
their opinions                                                                                            7A1
apply to the graph y = f(x ) the transformations y = f(x ) + a , y = f(ax ), y = f(x +a ) and y = a f(x )
for linear, quadratic, sine and cosine functions
recognise limitations in the accuracy of measurements and judge the proportional effect on
solutions
solve problems involving more complex shapes and solids, including segments of circles and
frustums of cones
prove and use the alternate segment theorem
prove the congruence of triangles and verify standard ruler and compass constructions using
formal arguments
solve exactly, by elimination of an unknown, two simultaneous equations in two unknowns, where
one is linear in each unknown and the other is linear in one unknown and quadratic in the other or
of the form x 2 + y 2 = r 2
solve quadratic equations by factorisation, completing the square and using the quadratic formula,
including those in which the coefficient of the quadratic term is greater than 1
derive relationships between different formulae that produce equal or related results
know and understand that the intersection points of the graphs of a linear and quadratic function
are the approximate solutions to the corresponding simultaneous equations
construct the graphs of simple loci, including the circle x 2 + y 2 = r 2; find graphically the
intersection points of a given straight line with this circle and know this represents the solution to
the corresponding two simultaneous equations
plot and recognise the characteristic shapes of graphs of simple cubic functions (e.g. y = x 3),
reciprocal functions (e.g. y = ,    x ≠ 0), exponential functions (y = k to the power x for integer
values of x and simple positive values of k) and trigonometric functions, on paper and using ICT
understand and use direct and inverse proportion; solve problems involving inverse proportion
(including inverse squares) using algebraic methods
use surds and π in exact calculations, without a calculator; rationalise a denominator such as one
over square root of three = square root of three over three
check results using appropriate methods
use calculators, or written methods, to calculate the upper and lower bounds of calculations in a
range of contexts, particularly when working with measurements
select and justify a sampling scheme and a method to investigate a population, including random
and stratified sampling
understand how different methods of sampling and different sample sizes may affect the reliability
of conclusions drawn
construct histograms, including those with unequal class intervals
use, interpret and compare histograms, including those with unequal class intervals
recognise when and how to work with probabilities associated with independent and mutually
exclusive events when interpreting data
understand and use rational and irrational numbers
understand upper and lower bounds
use the sine and cosine rules to solve 2-D and 3-D problems
calculate the area of a triangle using the formula       ab sin C
understand the difference between formulae for perimeter, area and volume by considering
dimensions
understand the necessary and sufficient conditions under which generalisations, inferences and
solutions to geometrical problems remain valid
draw, sketch and describe the graphs of trigonometric functions for angles of any size, including
transformations involving scalings in either or both of the x and y directions
calculate and represent graphically the sum of two vectors, the difference of two vectors and a
scalar multiple of a vector; calculate the resultant of two vectors
understand and use the commutative and associative properties of vector addition
solve simple geometrical problems in 2-D using vectors
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                 use mathematical language and symbols effectively in presenting convincing conclusions or
                 findings; critically reflect on own lines of enquiry when exploring; search for and appreciate more
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                 present rigorous and sustained arguments; reason inductively, deduce and prove; explain and
                 justify assumptions and constraints
                 justify and explain solutions to problems involving an unfamiliar context or a number of features or
                 variables; comment constructively on reasoning, logic, process, results and conclusions



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                                                                                8S2S2

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        5
        5




        5

        6




        6
        6
        6

        6
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        7
        7

        6
Progression maps: Shape and space
Step 1
   Identify lines of symmetry in simple shapes and recognise shapes with no lines of symmetry. View step
Step 2
   Classify polygons, using criteria such as number of right angles, whether or not they are regular, and symmetry properties.
Step 3
   Recognise perpendicular and parallel lines, and properties of rectangles. View step
Step 4
   Recognise and visualise the transformation and symmetry of 2-D shapes, including reflection in given mirror lines
   Construct 3-D models by linking given faces or edges. View step
Step 5
   Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle and recognise
   Use a ruler and protractor to measure and draw lines to the nearest millimetre and angles, including reflex angles, to the ne
   Recognise and visualise the transformation and symmetry of a 2-D shape:
     reflection in given mirror lines and line symmetry;
     rotation about a given point and rotational symmetry. View step
Step 6
   Transform 2-D shapes by simple combinations of rotations, reflections and translations, on paper and using ICT; identify all
Step 7
   Use a straight edge and compasses to construct:
     the midpoint and perpendicular bisector of a line segment;
     the bisector of an angle;
     the perpendicular from a point to a line;
     the perpendicular from a point on a line.
   Construct a triangle, given three sides (SSS); use ICT to explore these constructions. View step
   Identify alternate and corresponding angles; understand a proof that the sum of the angles of a triangle is 180° and of a qua
   Classify quadrilaterals by their geometric properties. View step
   Enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor. View step
Step 8
   Know that translations, rotations and reflections preserve length and angle, and map objects on to congruent images. View
   Visualise and use 2-D representations of 3-D objects; analyse 3-D shapes through 2-D projections, including plans and elev
Step 9
   Explain how to find, calculate and use the interior and exterior angles of regular polygons. View step
   Enlarge 2-D shapes by a positive whole-number or fractional scale factor. View step
   Find the locus of a point that moves according to a given rule, both by reasoning and by using ICT. View step
Step 10
   Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying i
 nd symmetry properties. View step



 on in given mirror lines and line symmetry.


n a triangle and recognise vertically opposite angles. View step
ng reflex angles, to the nearest degree. View step




and using ICT; identify all the symmetries of 2-D shapes. View step




angle is 180° and of a quadrilateral is 360°. View step



 congruent images. View step
s, including plans and elevations. View step




other polygons, justifying inferences and explaining reasoning with diagrams and text. View step
      Progression Maps: Handling data
    Step 1
3      Solve a given problem by organising and interpreting numerical data in simple lists, tables and graphs; for exampl
         simple frequency tables;
         pictograms – symbol representing two units;
         bar charts – intervals labelled in ones and then twos;
         Venn and Carroll diagrams (one criterion).
    Step 2
4      Solve a problem by collecting, organising, representing and interpreting data in tables, charts, graphs and diagram
         tally charts and frequency tables;
         pictograms – symbol representing two, five, ten or twenty units;
         bar charts – intervals labelled in twos, fives, tens or twenties;
         Venn and Carroll diagrams (two criteria).
    Step 3
4   Find the mode and range of a set of data.
    Step 4
    Solve a problem by representing, extracting and interpreting data in tables, graphs and charts. Calculate statistics fo
4   find the mode, median and range;calculate the mean in simple cases.
    Step 5
5      Understand the effect on the mean and median of altering the data. Interpret diagrams and graphs (including pie c
    Step 6
5      Compare two simple distributions using the range and one of the mode, median or mean.
    Step 7
6      Construct, on paper and using ICT:
         pie charts for categorical data;
         bar charts and frequency diagrams for discrete and continuous data;
         simple line graphs for time series;
         simple scatter graphs.
       Identify which are most useful in the context of the problem.
    Step 8
6      Design a survey or experiment to capture the necessary data from one or more sources; determine the sample si
       Communicate interpretations and results of a statistical enquiry using selected tables, graphs and diagrams in sup
    Step 9
7      Select, construct and modify, on paper and using ICT, suitable graphical representations to progress an enquiry, i
       Examine critically the results of a statistical enquiry, and justify the choice of statistical representation in written pre
    Step 10
7      Identify possible sources of bias and plan how to minimise it
e lists, tables and graphs; for example:




in tables, charts, graphs and diagrams, including those generated by a computer; for example:




phs and charts. Calculate statistics for small sets of discrete data:


diagrams and graphs (including pie charts) and draw simple conclusions based on the shape of graphs and simple statistics for a single dist




re sources; determine the sample size and degree of accuracy needed; design, trial and, if necessary, refine data collection sheets; design a
d tables, graphs and diagrams in support, using ICT as appropriate; construct tables for large, discrete and continuous sets of raw data, cho

esentations to progress an enquiry, including scatter graphs to develop further understanding of correlation.
statistical representation in written presentations.
and simple statistics for a single distribution.




efine data collection sheets; design and use two-way tables.
and continuous sets of raw data, choosing suitable class intervals.
      Progression Maps: Probability
    Step 1

    Step 2

    Step 3

    Step 4
       Discuss the chance or likelihood of particular events.
       Use the language associated with probability to discuss events, including those with equally likely outcomes.
    Step 5
5      Understand and use the probability scale from 0 to 1.
       Find and justify probabilities based on equally likely outcomes in simple contexts.
    Step 6
6      Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p.
6      Estimate probabilities from experimental data; understand that:
         if an experiment is repeated, there will be different outcomes;
         increasing the number of times an experiment is repeated generally leads to better estimates of probability.
    Step 7
6      Find and record all possible mutually exclusive outcomes for single events and two successive events in a syste
    Step 8
6      Know that the sum of probabilities of all mutually exclusive outcomes is 1, and use this when solving problems.
       Use a single probability to find an estimate of frequency.
       Find an estimate of the frequency for up to two events.
    Step 9
7      Understand relative frequency as an estimate of probability and use this to compare outcomes of experiments.
    Step 10
8      Find the probability of two or more mutually exclusive events occurring.
8      Find the probability of two independent events occurring
 ose with equally likely outcomes.




 it not occurring is 1 – p.


s to better estimates of probability.

and two successive events in a systematic way.

and use this when solving problems.



compare outcomes of experiments.
3
4



5



5

6
6


6

7
7

7
  Progression maps: Algebra - Sequences, Functions and Graphs
Step 1
   Describe and extend number sequences: count on or back in tens or hundreds, starting from any two- or three-digit numbe
Step 2
   Investigate a general statement about familiar numbers by finding examples that satisfy it. View step
Step 3
   Recognise and extend number sequences formed from counting from any number in steps of constant size, extending beyo
   Read and plot coordinates in the first quadrant. View step
Step 4
   Recognise and extend number sequences, such as the sequence of square numbers, or the sequence of triangular numbe
Step 5
   Read and plot coordinates in all four quadrants. View step
   Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions. View step
Step 6
   Begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the acti
   Express simple functions in symbols; represent mappings expressed algebraically. View step
Step 7
   Plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y = mx + c c
   Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on paper and using ICT
Step 8
   Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real sit
   Given values for m and c, find the gradient of lines given by equations of the form y = mx + c. View step
Step 9
   Find the next term and the nth term of quadratic sequences and explore their properties. View step
   Know simple properties of quadratic functions. View step
Step 10
   Plot the graphs of simple quadratic and cubic functions, e.g. y = x², y = 3x², y = x³. View step
two- or three-digit number. View step



stant size, extending beyond zero when counting back. View step


ence of triangular numbers. View step




rm by referring to the activity or practical context from which it was generated. View step


 s of the form y = mx + c correspond to straight-line graphs. View step
e, on paper and using ICT. View step

raphs arising from real situations. View step
        Progression maps: Number – FDPRP
2     Step 1
         Recognise unit fractions such as
         ,
         ,
         ,
         ,
         ... and use them to find fractions of shapes and numbers. View step
      Step 2
3        Recognise simple fractions that are several parts of a whole, such as
         or
         , and mixed numbers, such as
         ; recognise the equivalence of simple fractions (e.g. fractions equivalent to
         ,
         or
         ). View step
      Step 3
         Relate fractions to division and to their decimal representations. View step
         Order a set of fractions such as 2, 2
         ,1
         ,2
         ,1
         and position them on a number line. View step
3/4      Use decimal notation for tenths and hundredths. View step
      Step 4
5        Reduce a fraction to its simplest form by cancelling common factors. View step
         Use a fraction as an 'operator' to find fractions of numbers or quantities (e.g.
         of 32,
         of 40,
         of 400 cm). View step
4        Understand percentage as the number of parts in every 100 and find simple percentages of small whole-numbe
      Step 5
5        Solve simple problems involving ratio and proportion. View step
         Begin to add and subtract simple fractions and those with common denominators. View step
5        Simplify fractions by cancelling all common factors and identify equivalent fractions. View step
      Step 6
5        Recognise the equivalence of percentages, fractions and decimals; calculate simple percentages and use perce
         Multiply and divide a fraction by an integer. View step
      Step 7
6        Use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and
         Order fractions by writing them with a common denominator or by converting them into decimals. View step
         Divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems in
      Step 8
6        Add and subtract fractions by writing them with a common denominator. View step
6        Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole. V
      Step 9
7        Use efficient methods to add, subtract, multiply and divide fractions. View step
      Step 10
7        Understand and use proportionality and calculate the result of any proportional change using multiplicative meth
e percentages of small whole-number quantities. View step


nators. View step
ractions. View step

te simple percentages and use percentages to compare simple proportions. View step


oportions; calculate percentages and find the outcome of a given percentage increase or decrease. View step
 g them into decimals. View step
hod to solve simple word problems involving ratio and direct proportion. View step


ers to take as 100%, or as a whole. View step



 nal change using multiplicative methods. View step
      Progression maps: Number – Written calculation
    Step 1
    Step 2
2      Use informal pencil and paper methods to support, record or explain HTU ± TU, HTU ± HTU. View step
       Develop and refine written methods for column addition and subtraction for two whole numbers less then 1000, and for
    Step 3
      Extend efficient written methods to:
3      column addition/subtraction of two integers less than 10000; View step
3      short multiplication of HTU or TU by U; View step
       long multiplication of TU by TU; View step
       short division of HTU by U (with integer remainder). View step
3      Use all four operations to solve simple word problems involving numbers and quantities including time, explaining meth
4   Step 4
      Extend written methods to:
       column addition and subtraction of numbers involving decimals; View step
5      long multiplication of a three-digit by a two-digit integer; View step
       short division of TU by U (mixed-number answer); View step
       division of HTU by TU (long division, whole-number answer); View step
5      short division of numbers involving decimals. View step
4      Identify and use the appropriate operations (including combinations of operations) to solve word problems involving nu
    Step 5
       Know and use the order of operations including brackets. View step
4      Check a result by considering whether it is of the right order of magnitude and by working the problem backwards. View
    Step 6
5      Use standard column procedures for multiplication and division of integers and decimals, including by decimals such a
5      Enter numbers in a calculator and interpret the display in different contexts. View step
    Step 7
7      Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to
    Step 8
       Use a calculator efficiently and appropriately, including using the reciprocal key. View step
    Step 9
    Step 10
± HTU. View step
numbers less then 1000, and for addition of more than two such numbers. View step




s including time, explaining methods and reasoning. View step




olve word problems involving numbers and quantities, and explain methods and reasoning. View step


ng the problem backwards. View step

ls, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations. View ste


bers of any size, knowing not to round during intermediate steps of a calculation. View step
ring equivalent calculations. View step
      Progression maps: Number – Place value
    Step 1
2      Read, write and order whole numbers to at least 1000; know what each digit represents. View step
    Step 2
3      Read and write the vocabulary of comparing and ordering numbers. Use symbols correctly, including less than (
3      Round any positive integer less than 1000 to the nearest 10 or 100. View step
    Step 3
4      Multiply and divide any positive integer up to 10000 by 10 or 100 and understand the effect. View step
       Round a number with one or two decimal places to the nearest integer. View step
    Step 4
       Understand and use decimal notation and place value. View step
       Order a given set of positive and negative integers. View step
       Compare and order a mixed set of numbers or measurements with up to three decimal places. View step
    Step 5
5      Multiply and divide decimals mentally by 10 or 100, and integers by 1000, and explain the effect. View step
       Round positive whole numbers to the nearest 10, 100 or 1000 and decimals to the nearest whole number or one
       Find the difference between a positive and negative integer, or between two negative integers, in a context such
    Step 6
       Round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two
       Multiply and divide integers and decimals by 0.1, 0.01. View step
    Step 7
       Use rounding to make estimates; round numbers to the nearest whole number or to one or two decimal places.
    Step 8
       Begin to write numbers in standard form. View step
7      Round numbers to a given number of significant figures. View step
    Step 9
       Understand upper and lower bounds. View step
    Step 10
       Estimate calculations by rounding numbers to one significant figure and multiplying or dividing mentally. View ste
it represents. View step

mbols correctly, including less than (<), greater than (>), equals (=). View step


stand the effect. View step




ree decimal places. View step

nd explain the effect. View step
s to the nearest whole number or one decimal place. View step
o negative integers, in a context such as temperature or the number line. View step

earest whole number or to one or two decimal places. View step


ber or to one or two decimal places. View step




ltiplying or dividing mentally. View step
      Progression maps: Number – Mental calculation
    Step 1
       Know by heart all addition and subtraction facts for each number to 20. View step
       Add and subtract mentally a 'near multiple of 10' to or from a two-digit number. View step
3      Understand division as grouping or sharing and recognise that division is the inverse of multiplication. View step
       Know by heart facts for the 2, 5 and 10 multiplication tables. View step
    Step 2
3      Use known number facts and place value to add or subtract mentally, including any pair of two-digit whole numb
       Know by heart multiplication facts for the 2, 3, 4, 5 and 10 times tables. View step
       Derive quickly division facts corresponding to the 2, 3, 4, 5 and 10 multiplication tables. View step
       Find remainders after division. View step
    Step 3
4      Know by heart all multiplication facts up to 10 × 10. View step
       Find differences by counting up through next multiple of 10, 100 or 1000, e.g. calculate mentally a difference su
       Use known number facts and place value to consolidate mental addition and subtraction. View step
    Step 4
       Derive quickly division facts corresponding to multiplication tables up to 10 × 10. View step
    Step 5
4      Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompa
    Step 6
       Consolidate and extend mental methods of calculation, working with decimals, fractions and percentages, squa
    Step 7
       Make and justify estimates and approximations of calculations. View step
    Step 8
    Step 9
    Step 10
ber. View step
e inverse of multiplication. View step


ding any pair of two-digit whole numbers. View step

ation tables. View step



g. calculate mentally a difference such as 8006 – 2993. View step
d subtraction. View step

× 10. View step

 fractions and percentages, accompanied where appropriate by suitable jottings; solve simple word problems mentally. View step

als, fractions and percentages, squares and square roots, cubes and cube roots; solve word problems mentally. View step
 lems mentally. View step

mentally. View step
      Progression maps: Using and applying mathematics – Communica
    Step 1
2      Discuss work, using mathematical language. Represent work, using symbols and simple diagrams. View step
    Step 2
2      Begin to organise work. Use and interpret mathematical symbols and diagrams. View step
    Step 3
3      Begin to refine ways of recording and use appropriate mathematical symbols correctly. View step
    Step 4
4      Present information and results in a clear and organised way. Present solutions/findings in the context of the pro
    Step 5
       Present and interpret solutions/findings in the context of the problem/task. Begin to develop correct and consiste
    Step 6
5      Show understanding of situations by describing them mathematically, making correct use of symbols, words, dia
    Step 7
6      Choose and use correctly symbols, diagrams and graphs. Present and interpret solutions/findings in the context
    Step 8
7      Interpret, discuss and synthesise information presented in a variety of mathematical forms. Begin to explain rea
    Step 9
8      Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form
    Step 10
       Examine critically, improve and justify the choice of mathematical presentation, explaining features selected. Vie
ematics – Communicating
ls and simple diagrams. View step

ams. View step

ls correctly. View step

ions/findings in the context of the problem/task. View step

Begin to develop correct and consistent use of notation, symbols and diagrams. View step

ng correct use of symbols, words, diagrams, tables and graphs. View step

rpret solutions/findings in the context of the original problem/task. View step

ematical forms. Begin to explain reasons for selection and use of diagrams. View step

graphical form; move from one form of presentation to another to gain a different perspective on the problem/task. View step

ion, explaining features selected. View step
blem/task. View step
      Progression maps: Using and applying mathematics – Problem so
    Step 1
3      Try different approaches to solve a problem. View step
    Step 2
3      Try different approaches and find ways of overcoming difficulties that arise when solving problems. View step
    Step 3
       Use a range of strategies when solving problems. View step
    Step 4
4      Develop strategies for solving problems and use these strategies both in working within mathematics and in app
    Step 5
       Begin to structure an approach when exploring a simple task or solving a problem. Generate and check the nec
    Step 6
5      Identify the necessary information to carry through tasks and solve mathematical problems. Check results and c
    Step 7
       Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techni
    Step 8
6      Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques, methods
    Step 9
       Starting from given problems or contexts, progressively refine or extend the mathematics used to generate fulle
    Step 10
7      Solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a ra
ematics – Problem solving

when solving problems. View step



orking within mathematics and in applying mathematics to practical contexts. View step

roblem. Generate and check the necessary information. View step

 atical problems. Check results and consider whether they are sensible. View step

s, choosing and using efficient techniques for calculation, algebraic manipulation and graphical representation, and resources, including ICT.

nge of efficient techniques, methods and resources, including ICT. View step

e mathematics used to generate fuller solutions. View step

nnections in mathematics across a range of contexts: number, algebra, shape, space and measures, and handling data. View step
tation, and resources, including ICT. View step




nd handling data. View step
      Progression maps: Using and applying mathematics – Reasoning
    Step 1
       Explain why an answer is correct. View step
    Step 2
3      Understand a general statement by finding particular examples that match it. View step
    Step 3
       Try out ideas to find a pattern or solution. View step
    Step 4
5      Make general statements, based on evidence produced, and explain reasoning. View step
    Step 5
6      Solve problems and investigate in a range of contexts, explaining and justifying methods and conclusions; begin
    Step 6
       Draw simple conclusions and explain reasoning; suggest extensions to problems; conjecture and generalise. Vi
    Step 7
6      Use logical argument to establish the truth of a statement; begin to give mathematical justifications and test by c
    Step 8
       Present a concise reasoned argument, using symbols, diagrams, graphs and related explanatory texts. View ste
    Step 9
7      Show some insight into mathematical structure by using pattern and symmetry to justify generalisations, argume
    Step 10
       Appreciate the difference between mathematical explanation and experimental evidence. View step
ematics – Reasoning




ning. View step

ying methods and conclusions; begin to generalise and to understand the significance of a counter-example. View step

blems; conjecture and generalise. View step

thematical justifications and test by checking particular cases. View step

nd related explanatory texts. View step

etry to justify generalisations, arguments or solutions. View step

ntal evidence. View step
mple. View step
      Progression maps: Measures
    Step 1
3      Use units of time and know the relationships between them (second, minute, hour, day, week, month, year). Vie
    Step 2
4      Know and use the relationship between familiar units of length, mass and capacity. View step
    Step 3
4      Understand an area measured in square centimetres (cm²). View step
    Step 4
5      Understand and use the formula in words 'length × breadth' for the area of a rectangle. View step
    Step 5
       Calculate the perimeter and area of simple compound shapes that can be split into rectangles. View step
5      Convert one metric unit to another (e.g. grams to kilograms); read and interpret scales on a range of measuring
    Step 6
       Use units of measure to estimate, calculate and solve problems in everyday contexts involving length, area, volu
    Step 7
6      Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shap
6      Deduce and use formulae for the area of a triangle, a parallelogram and a trapezium; calculate areas of compou
    Step 8
6      Know and use the formulae for the area and circumference of a circle. View step
    Step 9
7      Recognise that measurements given to the nearest whole unit may be inaccurate by up to one half of the unit in
7      Calculate the surface areas and volumes of right prisms; calculate lengths, areas and volumes in right prisms, in
    Step 10
7      Understand and use measures of speed (and other compound measures such as density or pressure) to solve
7      Understand and apply Pythagoras' theorem when solving problems in two dimensions. View step
e, hour, day, week, month, year). View step

apacity. View step



a rectangle. View step

split into rectangles. View step
 pret scales on a range of measuring instruments. View step

y contexts involving length, area, volume, capacity, mass, time, angle and bearings; know rough metric equivalents of imperial measures in d

nd surface areas of cuboids and shapes made from cuboids. View step
 rapezium; calculate areas of compound shapes made from rectangles and triangles. View step



curate by up to one half of the unit in either direction. View step
areas and volumes in right prisms, including cylinders. View step

 uch as density or pressure) to solve problems. View step
dimensions. View step
equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons). View step
    Progression maps: Number – Integers and powers
  Step 1
     Recognise odd and even numbers up to 1000, and some of their properties, including the outcomes of sums or
     Describe and extend number sequences: count on or back in tens or hundreds, starting from any two- or three-d
  Step 2
3    Recognise negative numbers in contexts (e.g. on a number line, on a temperature scale). View step
     Recognise multiples of 2, 3, 4, 5 and 10, up to the tenth multiple. View step
  Step 3
     Recognise and extend number sequences formed by counting from any number in steps of constant size. (See
     Recognise multiples of 6, 7, 8 and 9 up to the tenth multiple. View step
4    Know the squares of numbers up to 10 × 10. View step
     Know all the pairs of factors of any number up to 100. View step
     Know and apply tests of divisibility by 2, 4, 5, 10 or 100. View step
  Step 4
     Factorise numbers to 100 into prime factors. View step
     Recognise and use multiples, factors and primes (less than 100). View step
     Know and apply simple tests of divisibility. View step
  Step 5
     Recognise the first few triangular numbers, squares of numbers to at least 12 × 12 and the corresponding roots
5    Add and subtract positive and negative numbers in context. View step
  Step 6
     Add, subtract, multiply and divide integers. View step
  Step 7
     Use index notation for integer powers and simple instances of the index laws. View step
  Step 8
     Know and use the index laws for multiplication and division of positive integer powers. View step
  Step 9
  Step 10
 , including the outcomes of sums or differences of pairs of odd/even numbers. View step
 eds, starting from any two- or three-digit number. View step

erature scale). View step


mber in steps of constant size. (See progression map for Sequences, Functions and Graphs.) View step




12 × 12 and the corresponding roots. View step




ws. View step

 er powers. View step
3



4




5


6



6

6


7

7
Algebra - Equations, Formulae and Identities
Step 1
   Understand division and recognise that division is the inverse of multiplication. View step
Step 2
   Use symbols correctly including less than (<), greater than (>) and equals (=). View step
   Understand the principles of the commutative, associative and distributive laws as they apply to multiplication. View step
Step 3
   Make general statements about odd and even numbers. View step
   Explain a generalised relationship (formula) in words. View step
Step 4
   Understand and use the relationships between the four operations, and principles of the arithmetic laws. Use brackets. View ste
Step 5
   Use letter symbols to represent unknown numbers or variables. View step
   Know and use the order of operations and understand that algebraic operations follow the same conventions and order as arith
   Construct and solve linear equations with positive integer coefficients (unknown on one side only) using appropriate methods. V
Step 6
   Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using
   Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket. View step
   Substitute integers into simple formulae. View step
Step 7
   Construct and solve linear equations with integer coefficients (with and without brackets, with negative signs anywhere in the eq
Step 8
   Use systematic trial and improvement methods and ICT tools to find approximate solutions to equations such as x³ + x = 20. Vie
   Transform algebraic expressions by factorising to produce a single term multiplied by terms in a bracket. View step
Step 9
   Square a linear expression, expand the product of two linear expressions of the form x ± n and simplify the corresponding quad
Step 10
   Solve a pair of simultaneous linear equations by eliminating one variable; link a graphical representation of an equation or pair o
y to multiplication. View step




hmetic laws. Use brackets. View step


ame conventions and order as arithmetical operations. View step
                       6

                          6
                          6
                          6

                          6

                          6
n a bracket. View step

nd simplify the corresponding quadratic expression. View step

presentation of an equation or pair of equations to the algebraic solution. View step
  Progression maps: Algebra - Sequences, Functions and Graphs
Step 1
   Describe and extend number sequences: count on or back in tens or hundreds, starting from any two- or three-d
Step 2
   Investigate a general statement about familiar numbers by finding examples that satisfy it. View step
Step 3
   Recognise and extend number sequences formed from counting from any number in steps of constant size, ext
   Read and plot coordinates in the first quadrant. View step
Step 4
   Recognise and extend number sequences, such as the sequence of square numbers, or the sequence of triang
Step 5
   Read and plot coordinates in all four quadrants. View step
   Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions. View step
Step 6
   Begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referrin
   Express simple functions in symbols; represent mappings expressed algebraically. View step
Step 7
   Plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y
   Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on paper an
Step 8
   Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising
   Given values for m and c, find the gradient of lines given by equations of the form y = mx + c. View step
Step 9
   Find the next term and the nth term of quadratic sequences and explore their properties. View step
   Know simple properties of quadratic functions. View step
Step 10
   Plot the graphs of simple quadratic and cubic functions, e.g. y = x², y = 3x², y = x³. View step
nctions and Graphs
eds, starting from any two- or three-digit number. View step

s that satisfy it. View step

number in steps of constant size, extending beyond zero when counting back. View step


e numbers, or the sequence of triangular numbers. View step


f simple linear functions. View step

quence, justifying its form by referring to the activity or practical context from which it was generated. View step
raically. View step

ecognise that equations of the form y = mx + c correspond to straight-line graphs. View step
nitions of the sequence, on paper and using ICT. View step

ding graphs; interpret graphs arising from real situations. View step
e form y = mx + c. View step

eir properties. View step


 y = x³. View step

								
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