Tracking Maths Objectives by Year – Calculating – Year 6 to 9
Year 6
Calculate mentally with
integers and decimals:
U.t ± U.t, TU × U, TU ÷ U, U.t
× U, U.t ÷ U
Progression into
Year 7
Consolidate and extend mental
methods of calculation to
include decimals, fractions and
percentages
Year 7
Extend mental methods of
calculation to include
decimals, fractions and
percentages
Year 8
Year 9
Exceptional
Performance
Add, subtract, multiply and
divide integers
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
Use efficient written methods
to add and subtract integers
and decimals, to multiply and
divide integers and decimals
by a one-digit integer, and to
multiply two-digit and threedigit integers by a two-digit
integer
Use standard column
procedures to add and subtract
integers and decimals, and to
multiply
two-digit and three-digit
integers by a one-digit or twodigit integer; extend division to
dividing
three-digit integers by a twodigit integer
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 standard column
procedures 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
Relate fractions to
multiplication and division (e.g.
6 ÷ 2 = 1/2 of 6 = 6 × 1/2);
express a quotient as a
fraction or decimal (e.g. 67 ÷ 5
= 13.4 or 132/5); find fractions
and percentages of wholenumber
quantities (e.g. 5/8 of 96, 65%
of £260)
Calculate percentage
increases or decreases and
fractions of quantities and
measurements
(integer answers)
Break a complex
calculation
into simpler steps,
choosing
and using appropriate and
efficient operations and
methods
Use the equivalence of
fractions, decimals and
percentages to compare
proportions; calculate
percentages and find the
outcome of a given
percentage increase or
decrease
Use a calculator to solve
problems involving multi-step
calculations
Use bracket keys and the
memory of a calculator to carry
out calculations with more than
one step; use the square root
key
Check a result by
considering whether it is of
the right order of magnitude
Know and use the index laws for
multiplication and division of
positive integer powers
Understand and use
proportionality and calculate the
result of any proportional
change using multiplicative
methods
Tracking Maths Objectives by Year – Calculating – Year 6 to 9
Understand how the
commutative, associative
and distributive laws, and the
relationships between
operations, including inverse
operations, can be used to
calculate more
efficiently; use the order of
operations, including
brackets
Use letter symbols to
represent unknown
numbers or variables
Substitute integers into
simple formulae
Know and use the order of
operations and understand
that algebraic operations
follow the same
conventions and order as
arithmetic operations
Simplify or transform linear
expressions by collecting like
terms; multiply a single term
over a bracket
Change the subject of a formula
Construct and solve linear
equations with integer
coefficients, using an
appropriate method
Square a linear expression and
expand the product of two linear
expressions of the form x + n;
establish identities
Solve a pair of simultaneous
linear equations by eliminating
one variable; link a graphical
representation of an equation or
a pair of equations to the
algebraic solution
Examine critically the results of
a statistical enquiry and justify
choice of statistical
representation in written
presentations
Identify possible sources of bias
in a statistical enquiry and plan
how to minimise it