Tracking Maths Objectives by Year – Calculating – Year 6 to 9

Year 6 / Progression into Year 7 / Year 7 / Year 8 / Year 9 / Exceptional Performance
Calculate mentally with integers and decimals:
U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U / Consolidate and extend mental methods of calculation to include decimals, fractions and percentages / Extend mental methods of calculation to include decimals, fractions and percentages / 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 / Know and use the index laws for multiplication and division of positive integer powers
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 three-digit 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 two-digit integer; extend division to dividing
three-digit integers by a two-digit 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 whole-number
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 / Understand and use proportionality and calculate the result of any proportional change using multiplicative methods
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
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 / Change the subject of a formula
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 / 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