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					The Interactive Scheme of Work Creator
Strand   Topic   Band   Order   YoT   Module




MPA      REPR     1      1      7




MPA      REPR     1      2      8




MPA      REPR     1      3      9




MPA      REPR     1      4      10



MPA      REPR     1      5      11



MPA      REPR     1      6      11




MPA      ANAR     1      1      7




MPA      ANAR     1      2      8




MPA      ANAR     1      3      9




MPA      ANAR     1      4      10
MPA   ANAR   1   5    11




MPA   ANAR   1   6    11


MPA   ANAP   1   1    7

MPA   ANAP   1   2    7

MPA   ANAP   1   3    7

MPA   ANAP   1   4    7

MPA   ANAP   1   5    7

MPA   ANAP   1   6    8

MPA   ANAP   1   7    8

MPA   ANAP   1   8    8

MPA   ANAP   1   9    8

MPA   ANAP   1   10   8

MPA   ANAP   1   11   9

MPA   ANAP   1   12   9

MPA   ANAP   1   13   9

MPA   ANAP   1   14   9

MPA   ANAP   1   15   9

MPA   ANAP   1   16   10

MPA   ANAP   1   17   10

MPA   ANAP   1   18   10

MPA   ANAP   1   19   10

MPA   ANAP   1   20   10

MPA   ANAP   1   21   11

MPA   ANAP   1   22   11
MPA   ANAP    1   23   11

MPA   ANAP    1   24   11

MPA   ANAP    1   25   11


MPA   IEVAL   1   1    7




MPA   IEVAL   1   2    8




MPA   IEVAL   1   3    9




MPA   IEVAL   1   4    10




MPA   IEVAL   1   5    11




MPA   IEVAL   1   6    11



NUM   PVOR    1   1    7


NUM   PVOR    2   2    7


NUM   PVOR    3   3    7


NUM   PVOR    1   4    8
NUM   PVOR    2   5    8


NUM   PVOR    3   6    8



NUM   PVOR    1   7    9


NUM   PVOR    3   8    9
NUM   PVOR    1   9    10

NUM   PVOR    1   10   10


NUM   PVOR    3   11   10


NUM   PVOR    1   12   11

NUM   PVOR    3   13   11
NUM   PVOR    3   14   11
NUM   PNIPR   1   1    7


NUM   PNIPR   1   2    7



NUM   PNIPR   1   3    7




NUM   PNIPR   1   4    8




NUM   PNIPR   1   5    8



NUM   PNIPR   1   6    8

NUM   PNIPR   1   7    9
NUM   PNIPR   1   8    9

NUM   PNIPR   1   9    9


NUM   PNIPR   1   10   10


NUM   PNIPR   1   11   10


NUM   PNIPR   1   12   11

NUM   PNIPR   1   13   11


NUM   FDPRP   1   1    7
NUM   FDPRP   2   2    7



NUM   FDPRP   3   3    7


NUM   FDPRP   3   4    7



NUM   FDPRP   3   5    7




NUM   FDPRP   1   6    8




NUM   FDPRP   2   7    8




NUM   FDPRP   3   8    8


NUM   FDPRP   3   9    8




NUM   FDPRP   3   10   8




NUM   FDPRP   1   11   9


NUM   FDPRP   2   12   9



NUM   FDPRP   3   13   9



NUM   FDPRP   3   14   9



NUM   FDPRP   1   15   10


NUM   FDPRP   2   16   10
NUM   FDPRP   3   17   10



NUM   FDPRP   3   18   10


NUM   FDPRP   1   19   11


NUM   FDPRP   3   20   11


NUM   FDPRP   3   21   11


NUM   NOPS    1   22   7

NUM   NOPS    1   23   7
NUM   NOPS    1   24   8

NUM   NOPS    1   25   8


NUM   NOPS    1   26   9


NUM   NOPS    1   27   9


NUM   NOPS    1   28   10



NUM   NOPS    1   29   11


NUM   MCM     1   1    7



NUM   MCM     2   2    7


NUM   MCM     3   3    7


NUM   MCM     1   4    8




NUM   MCM     2   5    8
NUM   MCM    3   6    8


NUM   MCM    1   7    9


NUM   MCM    3   8    9


NUM   MCM    3   9    10


NUM   MCM    1   10   11


NUM   WCM    1   1    7


NUM   WCM    1   2    7


NUM   WCM    1   3    8



NUM   WCM    1   4    8




NUM   WCM    1   5    9



NUM   CALC   1   6    7


NUM   CALC   1   7    7



NUM   CALC   1   8    8


NUM   CALC   1   9    8




NUM   CALC   1   10   9




NUM   CALC   1   11   10


NUM   CALC   1   12   10
NUM   CALC    1   13   11

NUM   CALC    1   14   11


NUM   CALC    1   15   11


NUM   CHECK   1   1    7


NUM   CHECK   1   2    8
NUM   CHECK   1   3    9
NUM   CHECK   1   4    10
NUM   CHECK   1   5    11

ALG    EFI    1   1    7


ALG    EFI    2   2    7


ALG    EFI    2   3    7


ALG    EFI    2   4    7



ALG    EFI    3   5    7



ALG    EFI    1   6    8


ALG    EFI    1   7    8


ALG    EFI    2   8    8


ALG    EFI    2   9    8


ALG    EFI    2   10   8



ALG    EFI    3   11   8



ALG    EFI    1   12   9

ALG    EFI    1   13   9
ALG   EFI   2   14   9


ALG   EFI   2   15   9


ALG   EFI   2   16   9


ALG   EFI   1   17   9


ALG   EFI   1   18   9


ALG   EFI   3   19   9


ALG   EFI   1   20   10


ALG   EFI   1   21   10




ALG   EFI   2   22   10


ALG   EFI   2   23   10



ALG   EFI   2   24   10




ALG   EFI   3   25   10




ALG   EFI   1   26   11



ALG   EFI   1   27   11


ALG   EFI   2   28   11


ALG   EFI   2   29   11

ALG   EFI   2   30   11
ALG   EFI   2   31   11


ALG   EFI   2   32   11




ALG   EFI   2   33   11


ALG   EFI   3   34   11


ALG   SFG   1   1    7


ALG   SFG   1   2    7

ALG   SFG   2   3    7



ALG   SFG   3   4    7



ALG   SFG   3   5    7


ALG   SFG   1   6    8



ALG   SFG   1   7    8


ALG   SFG   2   8    8


ALG   SFG   3   9    8




ALG   SFG   3   10   8


ALG   SFG   1   11   9


ALG   SFG   1   12   9

ALG   SFG   2   13   9
ALG   SFG   2   14   9




ALG   SFG   3   15   9



ALG   SFG   4   16   9



ALG   SFG   4   17   9



ALG   SFG   1   18   10


ALG   SFG   2   19   10


ALG   SFG   2   20   10



ALG   SFG   3   21   10



ALG   SFG   3   22   10



ALG   SFG   2   23   11


ALG   SFG   2   24   11


ALG   SFG   3   25   11


ALG   SFG   3   26   11



ALG   SFG   2   27   11




ALG   SFG   2   28   11
ALG    SFG   3   29   11




ALG    SFG   3   30   11


GEOM   GR    1   1    7


GEOM   GR    1   2    7



GEOM   GR    2   3    7


       GR    4   4    7



GEOM   GR    1   5    8




GEOM   GR    2   6    8



GEOM   GR    3   7    8


GEOM   GR    4   8    8


GEOM   GR    1   9    9


GEOM   GR    1   10   9



GEOM   GR    2   11   9



GEOM   GR    2   12   9


GEOM   GR    3   13   9

GEOM   GR    4   14   9


GEOM   GR    1   15   10
GEOM    GR     1   16   10




GEOM    GR     2   17   10




GEOM    GR     3   18   10



GEOM    GR     4   19   10


GEOM    GR     4   20   10


GEOM    GR     1   21   11




GEOM    GR     2   22   11




GEOM    GR     4   23   11


GEOM    GR     4   24   11


GEOM    GR     1   25   11

GEOM    GR     2   26   11
GEOM    GR     3   27   11

GEOM    GR     4   28   11


GEOM    GR     4   29   11


GEOM    GR     4   30   11

GEOM   TCOOR   1   1    7
GEOM   TCOOR   2   2    7
GEOM   TCOOR   2   3    7
GEOM   TCOOR   2   4    7
GEOM   TCOOR   6   5    7


GEOM   TCOOR   2   6    7


GEOM   TCOOR   2   7    8

GEOM   TCOOR   2   8    8


GEOM   TCOOR   4   9    8


GEOM   TCOOR   5   10   8
GEOM   TCOOR   6   11   8
GEOM   TCOOR   2   12   9

GEOM   TCOOR   2   13   9


GEOM   TCOOR   2   14   9


GEOM   TCOOR   3   15   9




GEOM   TCOOR   4   16   9




GEOM   TCOOR   5   17   9

GEOM   TCOOR   6   18   9


GEOM   TCOOR   2   19   10



GEOM   TCOOR   2   20   10




GEOM   TCOOR   4   21   10




GEOM   TCOOR   6   22   10
GEOM   TCOOR   4   23   11


GEOM   TCOOR   6   24   11




GEOM   TCOOR   6   25   11


GEOM   TCOOR   6   26   11
GEOM   TCOOR   6   27   11


GEOM    CL     1   1    7


GEOM    CL     1   2    7

GEOM    CL     1   3    7




GEOM    CL     1   4    8


GEOM    CL     1   5    8
GEOM    CL     1   6    8

GEOM    CL     1   7    9

GEOM    CL     1   8    9

GEOM    CL     1   9    9


GEOM    CL     1   10   10


GEOM    CL     1   11   10



GEOM   MMEN    1   1    7



GEOM   MMEN    1   2    7


GEOM   MMEN    3   3    7

GEOM   MMEN    3   4    7
GEOM    MMEN   1   5    8


GEOM    MMEN   1   6    8

GEOM    MMEN   3   7    8


GEOM    MMEN   3   8    8



GEOM    MMEN   1   9    9




GEOM    MMEN   2   10   9



GEOM    MMEN   3   11   9
GEOM    MMEN   3   12   9

GEOM    MMEN   1   13   10


GEOM    MMEN   3   14   10

GEOM    MMEN   3   15   10


GEOM    MMEN   1   16   11


GEOM    MMEN   3   17   11

GEOM    MMEN   3   18   11


GEOM    MMEN   3   19   11


GEOM    MMEN   1   20   11

GEOM    MMEN   3   21   11

GEOM    MMEN   3   22   11

STATS   SPEC   1   1    7

STATS   SPEC   1   2    7
STATS   SPEC   1   3    7




STATS   SPEC   1   4    7


STATS   SPEC   1   5    8


STATS   SPEC   1   6    8


STATS   SPEC   1   7    8


STATS   SPEC   1   8    8

STATS   SPEC   1   9    9


STATS   SPEC   1   10   9




STATS   SPEC   1   11   9




STATS   SPEC   1   12   9


STATS   SPEC   1   13   10

STATS   SPEC   1   14   10


STATS   SPEC   1   15   10



STATS   SPEC   1   16   10



STATS   SPEC   1   17   11


STATS   SPEC   1   18   11

STATS   SPEC   1   19   11


STATS   SPEC   1   20   11
STATS   SPEC   1   21   11




STATS   PREP   1   1    7




STATS   PREP   2   2    7




STATS   PREP   1   3    8




STATS   PREP   2   4    8




STATS   PREP   1   5    9



STATS   PREP   2   6    9




STATS   PREP   3   7    9




STATS   PREP   1   8    10




STATS   PREP   2   9    10




STATS   PREP   1   10   11


STATS   PREP   1   11   11


STATS   PREP   2   12   11


STATS   PREP   2   13   11
STATS   INTR   1   1    7



STATS   INTR   1   2    7



STATS   INTR   1   3    7


STATS   INTR   1   4    8


STATS   INTR   1   5    8

STATS   INTR   1   6    8


STATS   INTR   1   7    9


STATS   INTR   1   8    9



STATS   INTR   1   9    9



STATS   INTR   1   10   10




STATS   INTR   1   11   10




STATS   INTR   1   12   10


STATS   INTR   1   13   11


STATS   INTR   1   14   11


STATS   INTR   1   15   11


STATS   INTR   1   16   11


STATS   PROB   1   1    7
STATS   PROB   1   2    7




STATS   PROB   1   3    7




STATS   PROB   1   4    8




STATS   PROB   1   5    8




STATS   PROB   1   6    8



STATS   PROB   1   7    9


STATS   PROB   1   8    9



STATS   PROB   1   9    9


STATS   PROB   1   10   10




STATS   PROB   1   11   10




STATS   PROB   1   12   10



STATS   PROB   1   13   11
STATS   PROB   1   14   11



STATS   PROB   1   15   11
active Scheme of Work Creator
                                   Objective                               NC Level



        Identify the necessary information to understand or simplify a
        context or problem; represent problems, making correct use
        of symbols, words, diagrams, tables and graphs; use                   5
        appropriate procedures and tools, including ICT

        Identify the mathematical features of a context or problem;
        try out and compare mathematical representations; select
                                                                              5
        appropriate procedures and tools, including ICT

        Break down substantial tasks to make them more
        manageable; represent problems and synthesise information
        in algebraic, geometrical or graphical form; move from one            6
        form to another to gain a different perspective on the
        problem
        Compare and evaluate representations; explain the features
        selected and justify the choice of representation in relation to      7
        the context
        Choose and combine representations from a range of
        perspectives; introduce and use a range of mathematical
                                                                              8
        techniques, the most efficient for analysis and most effective
        for communication
        Systematically model contexts or problems through precise
        and consistent use of symbols and representations, and                8
        sustain this throughout the work
        Classify and visualise properties and patterns; generalise in
        simple cases by working logically; draw simple conclusions
        and explain reasoning; understand the significance of a               4
        counter-example; take account of feedback and learn from
        mistakes
        Visualise and manipulate dynamic images; conjecture and
        generalise; move between the general and the particular to
        test the logic of an argument; identify exceptional cases or
        counter-examples; make connections with related contexts

        Use connections with related contexts to improve the analysis
        of a situation or problem; pose questions and make
        convincing arguments to justify generalisations or solutions;
        recognise the impact of constraints or assumptions

        Identify a range of strategies and appreciate that more than
        one approach may be necessary; explore the effects of
        varying values and look for invariance and covariance in
        models and representations; examine and refine arguments,
        conclusions and generalisations; produce simple proofs
Make progress by exploring mathematical tasks, developing
and following alternative approaches; examine and extend
generalisations; support assumptions by clear argument and
follow through a sustained chain of reasoning, including proof

Present rigorous and sustained arguments; reason
inductively, deduce and prove; explain and justify
assumptions and constraints
Make accurate mathematical diagrams, graphs and
constructions on paper and on screen
Calculate accurately, selecting mental methods or calculating
devices as appropriate
Manipulate numbers, algebraic expressions and equations,
and apply routine algorithms
Use accurate notation, including correct syntax when using
ICT
Record methods, solutions and conclusions; estimate,
approximate and check working
Make accurate mathematical diagrams, graphs and
constructions on paper and on screen
Calculate accurately, selecting mental methods or calculating
devices as appropriate
Manipulate numbers, algebraic expressions and equations,
and apply routine algorithms
Use accurate notation, including correct syntax when using
ICT
Record methods, solutions and conclusions; estimate,
approximate and check working
Make accurate mathematical diagrams, graphs and
constructions on paper and on screen
Calculate accurately, selecting mental methods or calculating
devices as appropriate
Manipulate numbers, algebraic expressions and equations,
and apply routine algorithms
Use accurate notation, including correct syntax when using
ICT
Record methods, solutions and conclusions; estimate,
approximate and check working
Make accurate mathematical diagrams, graphs and
constructions on paper and on screen
Calculate accurately, selecting mental methods or calculating
devices as appropriate
Manipulate numbers, algebraic expressions and equations,
and apply routine algorithms
Use accurate notation, including correct syntax when using
ICT
Record methods, solutions and conclusions; estimate,
approximate and check working
Make accurate mathematical diagrams, graphs and
constructions on paper and on screen
Calculate accurately, selecting mental methods or calculating
devices as appropriate
Manipulate numbers, algebraic expressions and equations,
and apply routine algorithms
Use accurate notation, including correct syntax when using
ICT
Record methods, solutions and conclusions; estimate,
approximate and check working
Interpret information from a mathematical representation or
context; relate findings to the original context; check the
accuracy of the solution; explain and justify methods and
conclusions; compare and evaluate approaches
Use logical argument to interpret the mathematics in a given
context or to establish the truth of a statement; give accurate
solutions appropriate to the context or problem; evaluate the
efficiency of alternative strategies and approaches

Justify the mathematical features drawn from a context and
the choice of approach; generate fuller solutions by
presenting a concise, reasoned argument using symbols,
diagrams, graphs and related explanations
Make sense of, and judge the value of, own findings and
those presented by others; judge the strength of empirical
evidence and distinguish between evidence and proof; justify
generalisations, arguments or solutions
Show insight into the mathematical connections in the
context or problem; critically examine strategies adopted and
arguments presented; consider the assumptions in the model
and recognise limitations in the accuracy of results and
conclusions
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
Understand and use decimal notation and place value;
multiply and divide integers and decimals by 10, 100, 1000,       4
and explain the effect
Compare and order decimals in different contexts; know that
when comparing measurements the units must be the same

Round positive whole numbers to the nearest 10, 100 or
1000, and decimals to the nearest whole number or one
decimal place
Read and write positive integer powers of 10; multiply and
divide integers and decimals by 0.1, 0.01
Order Decimals
Round positive numbers to any given power of 10; round
decimals to the nearest whole number or to one or two
                                                                  5
decimal places

Extend knowledge of integer powers of 10; recognise the
equivalence of 0.1, 1⁄10 and 10^(–1); multiply and divide by
any integer power of 10
Use rounding to make estimates and to give solutions to
problems to an appropriate degree of accuracy
Express numbers in standard index form, both in
conventional notation and on a calculator display
Convert between ordinary and standard index form
representations
Round to a given number of significant figures; use significant
figures to approximate answers when multiplying or dividing
large numbers
Use standard index form to make sensible estimates for
                                                                  8
calculations involving multiplication and/or division
Understand how errors can be compounded in calculations

Understand upper and lower bounds                                 EP
Understand negative numbers as positions on a number line;
order, add and subtract integers in context
Recognise and use multiples, factors, primes (less than 100),
common factors, highest common factors and lowest common
multiples in simple cases; use simple tests of divisibility

Recognise the first few triangular numbers; recognise the
squares of numbers to at least 12 × 12 and the
corresponding roots
Add, subtract, multiply and divide integers

                                                                  5


Use multiples, factors, common factors, highest common
factors, lowest common multiples and primes; find the prime
                                                                  6
factor decomposition of a number, e.g. 8000 = 2^6 × 5^3

Use squares, positive and negative square roots, cubes and
cube roots, and index notation for small positive integer         6
powers
Use the prime factor decomposition of a number
Use ICT to estimate square roots and cube roots
Use index notation for integer powers; know and use the
index laws for multiplication and division of positive integer
powers
use index notation with negative and fractional powers,
recognising that the index laws can be applied to these as
well
know that n^(1/2) = root(n) and n^(1/3) = CubeRoot(n) for
any positive number n
Use inverse operations, understanding that the inverse
operation of raising a positive number to power n is raising
the result of this operation to power 1/n
Understand and use rational and irrational numbers                EP
Express a smaller whole number as a fraction of a larger one;
simplify fractions by cancelling all common factors and
identify equivalent fractions; convert terminating decimals to
fractions, e.g. 0.23 = 23/100 ; use diagrams to compare two
or more simple fractions
Add and subtract simple fractions and those with common
denominators; calculate simple fractions of quantities and
measurements (whole-number answers); multiply a fraction
by an integer
Understand percentage as the ‘number of parts per 100’;
calculate simple percentages and use percentages to compare
simple proportions
Recognise the equivalence of percentages, fractions and
                                                                    6
decimals
Understand the relationship between ratio and proportion;
use direct proportion in simple contexts; use ratio notation,
simplify ratios and divide a quantity into two parts in a given
ratio; solve simple problems involving ratio and proportion
using informal strategies
Recognise that a recurring decimal is a fraction; use division
to convert a fraction to a decimal; order fractions by writing
                                                                    6
them with a common denominator or by converting them to
decimals
Add and subtract fractions by writing them with a common
denominator; calculate fractions of quantities (fraction
                                                                    6
answers); multiply and divide an integer by a fraction

Interpret percentage as the operator ‘so many hundredths of’
and express one given number as a percentage of another;
                                                                    6
calculate percentages and find the outcome of a given
percentage increase or decrease
Use the equivalence of fractions, decimals and percentages to
                                                                    6
compare proportions
Apply understanding of the relationship between ratio and
proportion; simplify ratios, including those expressed in
different units, recognising links with fraction notation; divide
                                                                    6
a quantity into two or more parts in a given ratio; use the
unitary method to solve simple problems involving ratio and
direct proportion
Understand the equivalence of simple algebraic fractions;
know that a recurring decimal is an exact fraction
Use efficient methods to add, subtract, multiply and divide
fractions, interpreting division as a multiplicative inverse;
cancel common factors before multiplying or dividing

Recognise when fractions or percentages are needed to
compare proportions; solve problems involving percentage
changes
Use proportional reasoning to solve problems, choosing the
correct numbers to take as 100%, or as a whole; compare
two ratios; interpret and use ratio in a range of contexts

Distinguish between fractions with denominators that have
only prime factors 2 or 5 (terminating decimals), and other
fractions (recurring decimals)
Understand and apply efficient methods to add, subtract,
multiply and divide fractions, interpreting division as a
multiplicative inverse
Understand and use proportionality and calculate the result of
any proportional change using multiplicative methods

Calculate an original amount when given the transformed
amount after a percentage change; use calculators for
reverse percentage calculations by doing an appropriate
division
Use an algebraic method to convert a recurring decimal to a
fraction
Calculate an unknown quantity from quantities that vary in
direct proportion using algebraic methods where appropriate

Understand and use direct and inverse proportion; solve
problems involving inverse proportion (including inverse
squares) using algebraic methods
Understand and use the rules of arithmetic and inverse
operations in the context of positive integers and decimals

Use the order of operations, including brackets
Understand and use the rules of arithmetic and inverse
                                                                 6
operations in the context of integers and fractions
Use the order of operations, including brackets, with more
complex calculations
Understand the effects of multiplying and dividing by
numbers between 0 and 1; consolidate use of the rules of
arithmetic and inverse operations
Understand the order of precedence of operations, including
powers
Recognise and use reciprocals; understand ‘reciprocal’ as a
multiplicative inverse; know that any number multiplied by its
reciprocal is 1, and that zero has no reciprocal because
division by zero is not defined
Use a multiplier raised to a power to represent and solve
problems involving repeated proportional change, e.g.
compound interest
Recall number facts, including positive integer complements
to 100 and multiplication facts to 10 × 10, and quickly derive
associated division facts
Strengthen and extend mental methods of calculation to
include decimals, fractions and percentages, accompanied
where appropriate by suitable jottings; solve simple problems
mentally
Make and justify estimates and approximations of calculations

Recall equivalent fractions, decimals and percentages; use
known facts to derive unknown facts, including products
involving numbers such as 0.7 and 6, and 0.03 and 8

Strengthen and extend mental methods of calculation,
working with decimals, fractions, percentages, squares and
square roots, and cubes and cube roots; solve problems
mentally
Make and justify estimates and approximations of calculations

Use known facts to derive unknown facts; extend mental
methods of calculation, working with decimals, fractions,
percentages, factors, powers and roots; solve problems
mentally
Make and justify estimates and approximations of calculations

Make and justify estimates and approximations of calculations
by rounding numbers to one significant figure and multiplying
or dividing mentally
Use surds and pi in exact calculations, without a calculator;
rationalise a denominator such as 1/root(3) = root(3)/3

Use efficient written methods to add and subtract whole
numbers and decimals with up to two places
Multiply and divide three-digit by two-digit whole numbers;
extend to multiplying and dividing decimals with one or two
places by single-digit whole numbers
Use efficient written methods to add and subtract integers
and decimals of any size, including numbers with differing
numbers of decimal places
Use efficient written methods for multiplication and division of
integers and decimals, including by decimals such as 0.6 or
0.06; understand where to position the decimal point by
considering equivalent calculations
Use efficient written methods to add and subtract integers
and decimals of any size; multiply by decimals; divide by
decimals by transforming to division by an integer

Carry out calculations with more than one step using brackets
and the memory; use the square root and sign change keys

Enter numbers and interpret the display in different contexts
(decimals, percentages, money, metric measures)

Carry out more difficult calculations effectively and efficiently
using the function keys for sign change, powers, roots and
fractions; use brackets and the memory

Enter numbers and interpret the display in different contexts
(extend to negative numbers, fractions, time)
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; use the
constant, pi and sign change keys; use the function keys for
powers, roots and fractions; use brackets and the memory

Use an extended range of function keys, including the
reciprocal and trigonometric functions
Use standard index form, expressed in conventional notation
and on a calculator display; know how to enter numbers in
standard index form
Use calculators to explore exponential growth and decay,
using a multiplier and the power key
Calculate with standard index form, using a calculator as
appropriate
Use calculators, or written methods, to calculate the upper
and lower bounds of calculations in a range of contexts,
particularly when working with measurements
Check results by considering whether they are of the right
order of magnitude and by working problems backwards               5

Select from a range of checking methods, including
                                                                   6
estimating in context and using inverse operations
Check results using appropriate methods                            5
Check results using appropriate methods                            5
Check results using appropriate methods                            5
Use letter symbols to represent unknown numbers or
variables; know the meanings of the words term, expression
and equation
Understand that algebraic operations follow the rules of
arithmetic
Simplify linear algebraic expressions by collecting like terms;
multiply a single term over a bracket (integer coefficients)

Construct and solve simple linear equations with integer
coefficients (unknown on one side only) using an appropriate       6
method (e.g. inverse operations)
Use simple formulae from mathematics and other subjects;
substitute positive integers into linear expressions and
formulae and, in simple cases, derive a formula

Recognise that letter symbols play different roles in
equations, formulae and functions; know the meanings of the
words formula and function
Understand that algebraic operations, including the use of
brackets, follow the rules of arithmetic; use index notation for
small positive integer powers
Simplify or transform linear expressions by collecting like
terms; multiply a single term over a bracket
Construct and solve linear equations with integer coefficients
(unknown on either or both sides, without and with brackets)
using appropriate methods (e.g. inverse operations,
transforming both sides in same way)
Use graphs and set up equations to solve simple problems
involving direct proportion
Use formulae from mathematics and other subjects;
substitute integers into simple formulae, including examples
that lead to an equation to solve; substitute positive integers
into expressions involving small powers, e.g. 3x^2 + 4 or
2x^3 ; derive simple formulae
Distinguish the different roles played by letter symbols in
equations, identities, formulae and functions
Use index notation for integer powers and simple instances of
the index laws
Simplify or transform algebraic expressions by taking out
single-term common factors; add simple algebraic fractions

Construct and solve linear equations with integer coefficients
(with and without brackets, negative signs anywhere in the
equation, positive or negative solution)
Use systematic trial and improvement methods and ICT tools
to find approximate solutions to equations such x^2 + x = 20

Use algebraic methods to solve problems involving direct
proportion; relate algebraic solutions to graphs of the
equations; use ICT as appropriate
Explore ways of constructing models of real-life situations by
drawing graphs and constructing algebraic equations and
inequalities
Use formulae from mathematics and other subjects;
substitute numbers into expressions and formulae; derive a
formula and, in simple cases, change its subject
Know and use the index laws in generalised form for
multiplication and division of integer powers
Square a linear expression; expand the product of two linear
expressions of the form xn± and simplify the corresponding
quadratic expression; establish identities such as a^2 - b^2
= (a+b)(a-b)
Solve linear equations in one unknown with integer and
fractional coefficients; solve linear equations that require
prior simplification of brackets, including those with negative
signs anywhere in the equation
Solve linear inequalities in one variable; represent the
solution set on a number line
Solve a pair of simultaneous linear equations by eliminating
one variable; link a graph of an equation or a pair of
equations to the algebraic solution; consider cases that have     7
no solution or an infinite number of solutions

Derive and use more complex formulae; change the subject
of a formula, including cases where a power of the subject
appears in the question or solution, e.g. find given that A =
(pi)r^2
Factorise quadratic expressions, including the difference of
two squares, e.g. x^2 - 9 = (x+3)(x-3); cancel common
factors in rational expressions eg, 2(x+1)^2 / (x+1)

Simplify simple algebraic fractions to produce linear
expressions; use factorisation to simplify compound algebraic
fractions
Solve equations involving algebraic fractions with compound
expressions as the numerators and/or denominators

Solve linear inequalities in one and two variables; find and
represent the solution set
Explore ‘optimum’ methods of solving simultaneous equations
in different forms
Solve quadratic equations by factorisation
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         EP
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
Describe integer sequences; generate terms of a simple
sequence, given a rule (e.g. finding a term from the previous
term, finding a term given its position in the sequence)

Generate sequences from patterns or practical contexts and
describe the general term in simple cases
Express simple functions in words, then using symbols;
represent them in mappings
Generate coordinate pairs that satisfy a simple linear rule;
plot the graphs of simple linear functions, where y is given
explicitly in terms of x, on paper and using ICT; recognise
straight-line graphs parallel to the x-axis or y-axis

Plot and interpret the graphs of simple linear functions arising
from real-life situations, e.g. conversion graphs
Generate terms of a linear sequence using term-to-term and
position-to-term rules, on paper and using a spreadsheet or
graphics calculator
Use linear expressions to describe the term of a simple
arithmetic sequence, justifying its form by referring to the
activity or practical context from which it was generated

Express simple functions algebraically and represent them in
mappings or on a spreadsheet
Generate points in all four quadrants and plot the graphs of
linear functions, where y is given explicitly in terms of x, on
paper and using ICT; recognise that equations of the form y=
mx + c correspond to straight-line graphs
Construct linear functions arising from real-life problems and
plot their corresponding graphs; discuss and interpret graphs
arising from real situations, e.g. distance–time graphs

Generate terms of a sequence using term-to-term and
position-to-term rules, on paper and using ICT
Generate sequences from practical contexts and write and
justify an expression to describe the thn term of an arithmetic
sequence
Find the inverse of a linear function
Generate points and plot graphs of linear functions, where y
is given implicitly in terms of x (e.g. ay + bx = 0, y + bx + c
= 0 ), on paper and using ICT; find the gradient of lines given
by equations of the form , given values for m and c

Construct functions arising from real-life problems and plot
their corresponding graphs; interpret graphs arising from real
situations, e.g. time series graphs
Use ICT to explore the graphical representation of algebraic
equations and interpret how properties of the graph are
related to features of the equation, e.g. parallel and
perpendicular lines
Interpret the meaning of various points and sections of
straight-line graphs, including intercepts and intersection,
e.g. solving simultaneous linear equations
Find the next term and the nth term of quadratic sequences
and explore their properties; deduce properties of the
sequences of triangular and square numbers from spatial
patterns
Plot the graph of the inverse of a linear function
Understand that equations in the form y=mx+c represent a
straight line and that m is the gradient and c is the value of
the y -intercept; investigate the gradients of parallel lines and
lines perpendicular to these lines
Explore simple properties of quadratic functions; plot graphs
of simple quadratic and cubic functions, e.g. y=x^2, y=3x^2
+ 4, y=x^3
Understand that the point of intersection of two different lines
in the same two variables that simultaneously describe a real
situation is the solution to the simultaneous equations
represented by the lines
Identify the equations of straight-line graphs that are
parallel; find the gradient and equation of a straight-line
graph that is perpendicular to a given line
Plot graphs of more complex quadratic and cubic functions;
estimate values at specific points, including maxima and
minima
Find approximate solutions of a quadratic equation from the
graph of the corresponding quadratic function
Identify and sketch graphs of linear and simple quadratic and
cubic functions; understand the effect on the graph of
addition of (or multiplication by) a constant
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= 1/x, x≠0 ), exponential functions ( y=kx= for
integer values of x and simple positive values of k) and
trigonometric functions, on paper and using ICT
Apply to the graph y=f(x) the transformations y=f(x)+a,
y=f(ax), y=f(x+a) and y=af(x) for linear, quadratic, sine and
cosine functions
Use correctly the vocabulary, notation and labelling
conventions for lines, angles and shapes
Identify parallel and perpendicular lines; know the sum of
angles at a point, on a straight line and in a triangle;
recognise vertically opposite angles
Identify and use angle, side and symmetry properties of
triangles and quadrilaterals; explore geometrical problems
involving these properties, explaining reasoning orally, using
step-by-step deduction supported by diagrams
Use 2-D representations to visualise 3-D shapes and deduce
some of their properties
Identify alternate angles and corresponding angles;
understand a proof that: (i) the angle sum of a triangle is
180° and of a quadrilateral is 360°, (ii) the exterior angle of a
triangle is equal to the sum of the two interior opposite
angles
Solve geometrical problems using side and angle properties of
equilateral, isosceles and right-angled triangles and special
quadrilaterals, explaining reasoning with diagrams and text;
classify quadrilaterals by their geometrical properties

Know that if two 2-D shapes are congruent, corresponding
sides and angles are equal
Visualise 3-D shapes from their nets; use geometric
properties of cuboids and shapes made from cuboids; use
simple plans and elevations
Distinguish between conventions, definitions and derived
properties
Explain how to find, calculate and use: (i) the sums of the
interior and exterior angles of quadrilaterals, pentagons and
hexagons; (ii) the interior and exterior angles of regular
polygons
Know the definition of a circle and the names of its parts;
explain why inscribed regular polygons can be constructed by
equal divisions of a circle
Solve problems using properties of angles, of parallel and
intersecting lines, and of triangles and other polygons,
justifying inferences and explaining reasoning with diagrams
and text
Understand congruence and explore similarity
Investigate Pythagoras’ theorem, using a variety of media,
through its historical and cultural roots including ‘picture’
proofs
Distinguish between practical demonstration and proof in a
geometrical context
Solve multi-step problems using properties of angles, of
parallel lines, and of triangles and other polygons, justifying
inferences and explaining reasoning with diagrams and text

Know that the tangent at any point on a circle is
perpendicular to the radius at that point; explain why the
perpendicular from the centre to the chord bisects the chord

Know that if two 2-D shapes are similar, corresponding
angles are equal and corresponding sides are in the same
ratio; understand from this that any two circles and any two
squares are mathematically similar while in general any two
rectangles are not
Understand and apply Pythagoras’ theorem when solving
                                                                   7
problems in 2-D and simple problems in 3-D
Understand and use trigonometric relationships in right-
angled triangles, and use these to solve problems, including       8
those involving bearings
Show step-by-step deduction in solving more complex
geometrical problems
Prove and use the facts that: (I) the angle subtended by an
arc at the centre of a circle is twice the angle subtended at
any point on the circumference; (ii) the angle subtended at
the circumference by a semicircle is a right angle; (iii) angles
in the same segment are equal; (iv) opposite angles on a
cyclic quadrilateral sum to 180°
Understand and use Pythagoras’ theorem to solve 3-D
                                                                   EP
problems
Use trigonometric relationships in right-angled triangles to
solve 3-D problems, including finding the angles between a         EP
line and a plane
Understand the necessary and sufficient conditions under
which generalisations, inferences and solutions to geometrical
problems remain valid
Prove and use the alternate segment theorem
Prove the congruence of triangles and verify standard ruler
and compass constructions using formal arguments
Calculate the area of a triangle using the formula 1/2absinC
                                                                   8
Draw, sketch and describe the graphs of trigonometric
functions for angles of any size, including transformations
involving scalings in either or both of the xand y directions

Use the sine and cosine rules to solve 2-D and 3-D problems

Understand and use the language and notation associated
with reflections, translations and rotations
Recognise and visualise the symmetries of a 2-D shape
Transform 2-D shapes by: (i) reflecting in given mirror lines;
(ii) rotating about a given point; (iii) translating
Explore these transformations and symmetries using ICT
Use conventions and notation for 2-D coordinates in all four
quadrants; find coordinates of points determined by
geometric information
Identify all the symmetries of 2-D shapes


Transform 2-D shapes by rotation, reflection and translation,
on paper and using ICT
Try out mathematical representations of simple combinations
of these transformations
Understand and use the language and notation associated
with enlargement; enlarge 2-D shapes, given a centre of
enlargement and a positive integer scale factor; explore
enlargement using ICT
Make scale drawings
Find the midpoint of the line segment AB, given the
coordinates of points A and B
Identify reflection symmetry in 3-D shapes
Recognise that translations, rotations and reflections preserve
length and angle, and map objects on to congruent images

Devise instructions for a computer to generate and transform
shapes
Explore and compare mathematical representations of
combinations of translations, rotations and reflections of 2-D
shapes, on paper and using ICT
Enlarge 2-D shapes, given a centre of enlargement and a
positive integer scale factor, on paper and using ICT; identify
the scale factor of an enlargement as the ratio of the lengths
of any two corresponding line segments; recognise that
enlargements preserve angle but not length, and understand
the implications of enlargement for perimeter

Use and interpret maps and scale drawings in the context of
mathematics and other subjects
Use the coordinate grid to solve problems involving
translations, rotations, reflections and enlargements
Transform 2-D shapes by combinations of translations,
rotations and reflections, on paper and using ICT; use
congruence to show that translations, rotations and
reflections preserve length and angle
Use any point as the centre of rotation; measure the angle of
rotation, using fractions of a turn or degrees; understand that
translations are specified by a vector
Enlarge 2-D shapes using positive, fractional and negative
scale factors, on paper and using ICT; recognise the similarity
of the resulting shapes; understand and use the effects of        7
enlargement on perimeter

Find the points that divide a line in a given ratio, using the
properties of similar triangles; calculate the length of AB,
given the coordinates of points A and B
Understand and use the effects of enlargement on areas and
volumes of shapes and solids
Understand and use vector notation to describe
transformation of 2-D shapes by combinations of
translations; calculate and represent graphically the sum of
two vectors
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
Use a ruler and protractor to: (i) measure and draw lines to
the nearest millimetre and angles, including reflex angles, to
the nearest degree; (ii) construct a triangle, given two sides
and the included angle (SAS) or two angles and the included
side (ASA)
Use ICT to explore constructions
Use ruler and protractor to construct simple nets of 3-D
shapes, e.g. cuboid, regular tetrahedron, square-based
pyramid, triangular prism
Use straight edge and compasses to construct: (i) the
midpoint and perpendicular bisector of a line segment; (ii)
the bisector of an angle; (iii) the perpendicular from a point
to a line; (iv) the perpendicular from a point on a line; (v) a
triangle, given three sides (SSS)
Use ICT to explore these constructions
Find simple loci, both by reasoning and by using ICT, to
produce shapes and paths, e.g. an equilateral triangle
Use straight edge and compasses to construct triangles, given
right angle, hypotenuse and side (RHS)
Use ICT to explore constructions of triangles and other 2-D
shapes
Find the locus of a point that moves according to a simple
                                                                  7
rule, both by reasoning and by using ICT
Understand from experience of constructing them that
triangles given SSS, SAS, ASA or RHS are unique, but that
triangles given SSA or AAA are not
Find the locus of a point that moves according to a more
complex rule, both by reasoning and by using ICT
Choose and use units of measurement to measure, estimate,
calculate and solve problems in everyday contexts; convert
one metric unit to another, e.g. grams to kilograms; read and
interpret scales on a range of measuring instruments

Distinguish between and estimate the size of acute, obtuse
and reflex angles
Know and use the formula for the area of a rectangle;
calculate the perimeter and area of shapes made from
rectangles
Calculate the surface area of cubes and cuboids
Choose and use units of measurement to measure, estimate,
calculate and solve problems in a range of contexts; know
rough metric equivalents of imperial measures in common
use, such as miles, pounds (lb) and pints

Use bearings to specify direction
Derive and use formulae for the area of a triangle,
parallelogram and trapezium; calculate areas of compound
shapes
Know and use the formula for the volume of a cuboid;
calculate volumes and surface areas of cuboids and shapes
made from cuboids
Solve problems involving measurements in a variety of
contexts; convert between area measures (e.g. mm2 to cm2,
cm2 to m2, and vice versa) and between volume measures
(e.g. mm3 to cm3, cm3 to m3, and vice versa)
Interpret and explore combining measures into rates of
change in everyday contexts (e.g. km per hour, pence per
metre); use compound measures to compare in real-life
contexts (e.g. travel graphs and value for money), using ICT
as appropriate
Know and use the formulae for the circumference and area of
a circle
Calculate the surface area and volume of right prisms
Understand and use measures of speed (and other compound
measures such as density or pressure); solve problems
involving constant or average rates of change
Solve problems involving lengths of circular arcs and areas of
sectors
Solve problems involving surface areas and volumes of
cylinders
Apply knowledge that measurements given to the nearest
whole unit may be inaccurate by up to one half of the unit in
either direction and use this to understand how errors can be
compounded in calculations
Solve problems involving surface areas and volumes of
cylinders, pyramids, cones and spheres
Understand and use the formulae for the length of a circular
arc and area and perimeter of a sector
Consider the dimensions of a formula and begin to recognise
the difference between formulae for perimeter, area and
volume in simple contexts
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
Understand the difference between formulae for perimeter,
area and volume by considering dimensions
Suggest possible answers, given a question that can be
addressed by statistical methods
Decide which data would be relevant to an enquiry and
possible sources
Plan how to collect and organise small sets of data from
surveys and experiments: (i) design data collection sheets or
questionnaires to use in a simple survey; (ii) construct         4
frequency tables for gathering discrete data, grouped where
appropriate in equal class intervals
Collect small sets of data from surveys and experiments, as
planned                                                          4

Discuss a problem that can be addressed by statistical
methods and identify related questions to explore
Decide which data to collect to answer a question, and the
degree of accuracy needed; identify possible sources;
consider appropriate sample size
Plan how to collect the data; construct frequency tables with
equal class intervals for gathering continuous data and two-
way tables for recording discrete data
Collect data using a suitable method (e.g. observation,
controlled experiment, data logging using ICT)
suggest a problem to explore using statistical methods, frame
questions and raise conjectures
Discuss how different sets of data relate to the problem;
identify possible primary or secondary sources; determine the
sample size and most appropriate degree of accuracy
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 gathering
large discrete and continuous sets of raw data, choosing
suitable class intervals; design and use two-way tables

Gather data from specified secondary sources, including
printed tables and lists, and ICT-based sources, including the
internet
Independently devise a suitable plan for a substantial
statistical project and justify the decisions made
Identify possible sources of bias and plan how to minimise it

Break a task down into an appropriate series of key
statements (hypotheses), and decide upon the best methods
for testing these
gather data from primary and secondary sources, using ICT
and other methods, including data from observation,
controlled experiment, data logging, printed tables and lists

Consider possible difficulties with planned approaches,
including practical problems; adjust the project plan
accordingly
Deal with practical problems such as non-response or missing
data
Identify what extra information may be required to pursue a
further line of enquiry
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

Calculate statistics for small sets of discrete data: (i) find the
mode, median and range, and the modal class for grouped
data; (ii) calculate the mean, including from a simple               5
frequency table, using a calculator for a larger number of
items
Construct, on paper and using ICT, graphs and diagrams to
represent data, including: (i) bar-line graphs; (ii) frequency
                                                                     5
diagrams for grouped discrete data; (iii) simple pie charts

Calculate statistics for sets of discrete and continuous data,
including with a calculator and spreadsheet; recognise when
it is appropriate to use the range, mean, median and mode
and, for grouped data, the modal class
Construct graphical representations, on paper and using ICT,
and identify which are most useful in the context of the
problem. Include: (i) pie charts for categorical data; (ii) bar
charts and frequency diagrams for discrete and continuous
data; (iii) simple line graphs for time series; (iv) simple
scatter graphs; (v) stem-and-leaf diagrams
Calculate statistics and select those most appropriate to the
problem or which address the questions posed
Select, construct and modify, on paper and using ICT,
suitable graphical representations to progress an enquiry and
identify key features present in the data. Include: (i) line
graphs for time series; (ii) scatter graphs to develop further
understanding of correlation;
Work through the entire handling data cycle to explore
relationships within bivariate data, including applications to
global citizenship, e.g. how fair is our society?
Use an appropriate range of statistical methods to explore
and summarise data; including estimating and finding the
mean, median, quartiles and interquartile range for large data
sets (by calculation or using a cumulative frequency diagram)

Select, construct and modify, on paper and using ICT,
suitable graphical representation to progress an enquiry and
identify key features present in the data. Include: (i)
cumulative frequency tables and diagrams; (ii) box plots; (iii)
scatter graphs and lines of best fit (by eye)
Use an appropriate range of statistical methods to explore
and summarise data; including calculating an appropriate
moving average for a time series
Use a moving average to identify seasonality and trends in
time series data, using them to make predictions
Select, construct and modify, on paper and using ICT,
suitable graphical representation to progress an enquiry,
including histograms for grouped continuous data with equal
class intervals
Construct histograms, including those with unequal class
                                                                     EP
intervals
Interpret diagrams and graphs (including pie charts), and
draw simple conclusions based on the shape of graphs and            5
simple statistics for a single distribution
Compare two simple distributions using the range and one of
the mode, median or mean
                                                                    5


Write a short report of a statistical enquiry, including
appropriate diagrams, graphs and charts, using ICT as               5
appropriate; justify the choice of presentation
Interpret tables, graphs and diagrams for discrete and
continuous data, relating summary statistics and findings to
the questions being explored
Compare two distributions using the range and one or more
of the mode, median and mean
Write about and discuss the results of a statistical enquiry
using ICT as appropriate; justify
Interpret graphs and diagrams and make inferences to
support or cast doubt on initial conjectures; have a basic
understanding of correlation
Compare two or more distributions and make inferences,
using the shape of the distributions and appropriate statistics

Review interpretations and results of a statistical enquiry on
the basis of discussions; communicate these interpretations
and results using selected tables, graphs and diagrams

Analyse data to find patterns and exceptions, and try to
explain anomalies; include social statistics such as index
numbers, time series and survey data
Appreciate that correlation is a measure of the strength of
association between two variables; distinguish between
positive, negative and zero correlation, using lines of best fit;
appreciate that zero correlation does not necessarily imply ‘no
relationship’ but merely ‘no linear relationship’

Examine critically the results of a statistical enquiry; justify
choice of statistical representations and relate summarised
data to the questions being explored
Interpret and use cumulative frequency diagrams to solve
problems
Recognise the limitations of any assumptions and the effects
that varying the assumptions could have on the conclusions
drawn from data analysis
Compare two or more distributions and make inferences,
using the shape of the distributions and measures of average
and spread, including median and quartiles
Use, interpret and compare histograms, including those with
unequal class intervals
Use vocabulary and ideas of probability, drawing on
experience
                                                                    4
Understand and use the probability scale from 0 to 1; find
and justify probabilities based on equally likely outcomes in
simple contexts; identify all the possible mutually exclusive
outcomes of a single event                                       5




Estimate probabilities by collecting data from a simple
experiment and recording it in a frequency table; compare
experimental and theoretical probabilities in simple contexts
                                                                 5



Interpret the results of an experiment using the language of
probability; appreciate that random processes are
unpredictable
Know that if the probability of an event occurring is p, then
the probability of it not occurring is 1-p ; use diagrams and
tables to record in a systematic way all possible mutually
exclusive outcomes for single events and for two successive
events
Compare estimated experimental probabilities with theoretical
probabilities, recognising that: (i) if an experiment is
repeated the outcome may, and usually will, be different; (ii)
increasing the number of times an experiment is repeated
generally leads to better estimates of probability;

Interpret results involving uncertainty and prediction
Identify all the mutually exclusive outcomes of an
experiment; know that the sum of probabilities of all mutually
exclusive outcomes is 1 and use this when solving problems

Compare experimental and theoretical probabilities in a range
of contexts; appreciate the difference between mathematical
explanation and experimental evidence
Use tree diagrams to represent outcomes of two or more
events and to calculate probabilities of combinations of
independent events
Know when to add or multiply two probabilities: if A and B
are mutually exclusive, then the probability of A or B
occurring is P(A) + P(B), whereas if A and B are independent
events, the probability of A and B occurring is P(A) × P(B)

Understand relative frequency as an estimate of probability
and use this to compare outcomes of experiments

Use tree diagrams to represent outcomes of compound
events, recognising when events are independent and
distinguishing between contexts involving selection both with
and without replacement
Understand that if an experiment is repeated, the outcome
may – and usually will – be different, and that increasing the
sample size generally leads to better estimates of probability
and population parameters
Recognise when and how to work with probabilities associated
with independent and mutually exclusive events when
interpreting data
                                             Possible Possible
Possible Teaching   Hooks for                Teaching Teaching
                                Rich Tasks
   Resources        Learning                 Resource Resource
                                                s        s
                                                                     AAA Math
                                                            AAA Math
                                           Decimal Places            Rounding
Decimal Places Powerpoint   Powers of 10                    Rounding
                                               Jigsaw                 Nearest
                                                            Decimals
                                                                       10th
                            Powers of Ten
  Powers of 10 Website
                           Video from IBM




                             Universcale




   Additions Shortcuts                        Nrich Smallest        AAA Math AAA Math
                               Tutpup
       Powerpoint                            Number Challenge         Add    Subtract



                                                 Factors and
Prime Factors Powerpoint   The Factor Game
                                             Multiples Minni Book


                           Extracting Cube     Finding Square
Number Tables Powerpoint
                           Roots Mentally      Roots Manually
                                                   Nrich Egyptian
BBC Skillswise Introduction    Fractions Clock
                                                      Fractions


                              Folding Fractions    Cynthia Lanius
  How to Add Fractions
                                  Mini Book          Fractions


                                Nrich Sum of      Nrich Fraction and   QuickMath  Nrich
 Percentages Powerpoint         Percentages           Percentage       Percentag Mathland
                                  Problem             Pelmanism            es    Election
                              Nrich Percentages
                                  Pelmanism


                              You Tube Golden                          AAA Math   BBC
     Ratio Powerpoint                               Ratio Jigsaw
                                 Ratio Clip                              Ratio  Skillswise
Bodmas Podcast   Nrich Reaching 50
                          Applications of      Geometry        Coordinat
Properties of 2D shapes     rotational      Interactive free   e         Shape
                            symmetry          sample ATM       challenge facts
Triangle Constructions                     Explain why - Nrich Constructi
                                                               ng
                                                               triangles


                                           Cubic Conundrum     Ominoes
                                                               project




                         Estimate angles
                              game
Census at school
  Crash Test -
    Bowland
                                                APP Year 7 Handling
 Questionnaire design ppt    Census at school
                                                     Data Pack


 Conduct a class survey on   Using excel for
IWB Teacher Led Resources    data collection
                                                                                 Mean,
                                                                     Crickweb'
                                               Nrich Litov's mean               median
 Crickweb's Mean Machine    Mr Reddy's poems                          s mean
                                                 value theorem                 and mode
                                                                      runners
                                                                                 song

                               Mr Barton's
http://www.subtangent.com                      Using Excel to Draw
                               Statistical
   /maths/freqdiag1.php                              Charts
                                Diagrams




                                                Census At School
                              Missing label bar
Kenny's Pouch Constructing
                              charts - 3 starter
          Graphs
                                  activities
                                                   Standards Unit         Mr      Using
 Kenny's Pouch Analysing     CIMT Cricket Player   Understanding       Reddy's   Excel to
   Statistics worksheet           Ratings          Mean, median,       Cricket   calculate
                                                   mode and range      problem   averages




                                 GapMinder




                                                    Beyond the Bar
                                                        Chart




                                                   Standards Unit S2
  Probability vocabulary       CIMT National          Evaluating
      blockbusters                Lottery             Probability
                                                      Statements
                                                                                 Standards
                                                                     Standards
                                                                                  Unit S3
                                                                      Unit S1
                               Mr Barton's       Nrich Experimenting               Using
  Mr Barton's Coin races                                              Ordering
                             Probability Tools     with probability              Probability
                                                                     Probabiliti
                                                                                 Computer
                                                                         es
                                                                                   Games
                                                                     http://ww
                                                                     w.webmat
Probability ESP Experiment   Subtangent coins    Nrich Experimenting hs.co.uk/
  Teacher Led Resources          and dice          with probability  worksheet
                                                                     bankindex
                                                                       .html
Possible Possible Possible
                            Hooks    Hooks
Teaching Teaching Teaching                      Rich    Rich    Rich
                              for      for
Resource Resource Resource                     Tasks   Tasks   Tasks
                           Learning Learning
   s        s        s
AAA Math
Rounding   BBC        YouTube   Rounding
 Nearest Skillswise     Clip     Jigsaw
  100th
                                You Tube
AAA Math    AAA Math AAA Math     Tom
 Multiply    Divide  Decimals    Lehrer
                                New Math

                                  Prime
                                           HCF LCM
                                 Number
                                           Podcast
                                Factoriser
                               Golden
YouTube              Ratio
            Ratio               Ratio
 GCSE               Words
           Jigsaw            Investigati
Question            Jigsaw
                                 on
Bodmas    Year
Podcast   Game
         Rotation
Symmetry symmetry
game     puzzles
Tarsia
jigsaw
mymaths
Play your
  cards
  right
National Curriculum Attainment Targets
         Strand                   Level


Mathematical Processes           Level 4
   and Applications


                                 Level 5




                                 Level 6




                                 Level 7




                                 Level 8




                         Exceptional Performance




  Number and Algebra             Level 4




                                 Level 5
                                Level 6




                                Level 7




                                Level 8




                        Exceptional Performance




Geometry and Measures           Level 4




                                Level 5




                                Level 6




                                Level 7




                                Level 8
                Exceptional Performance




Handling Data           Level 4




                        Level 5




                        Level 6




                        Level 7




                        Level 8



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

				
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