England

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Skills available for England year 8 maths curriculum

Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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Programme of Study: Key Stage 3, Year 8 Programme of Study: Key Stage 3, Year 8

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Working mathematically

Develop fluency

Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots.

Select and use appropriate calculation strategies to solve increasingly complex problems.

Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.

Substitute values in expressions, rearrange and simplify expressions, and solve equations.

Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs].

Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions.

Use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

Reason mathematically

Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.

Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.

Identify variables and express relations between variables algebraically and graphically.

Make and test conjectures about patterns and relationships; look for proofs or counter-examples.

Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.

Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.

Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

Solve problems

Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems.

Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.

Begin to model situations mathematically and express the results using a range of formal mathematical representations.

Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Number

Understand and use place value for decimals, measures and integers of any size.

Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥.

Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property.

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.

Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.

Recognise and use relationships between operations including inverse operations.

Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations.

Interpret and compare numbers in standard form A × 10n1 ≤ A < 10, where n is a positive or negative integer or zero.

Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).

Define percentage as 'number of parts per hundred', interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%.

Interpret fractions and percentages as operators.

Use standard units of mass, length, time, money and other measures, including with decimal quantities.

Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures].

Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b.

Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.

Appreciate the infinite nature of the sets of integers, real and rational numbers.

Algebra

Use and interpret algebraic notation, including:

ab in place of a × b

3y in place of y + y + y and 3 × y

a2 in place of a × a, a3 in place of a × a × a; a2b in place of a × a × b

a/b in place of a ÷ b

coefficients written as fractions rather than as decimals

brackets

Substitute numerical values into formulae and expressions, including scientific formulae.

Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors.

Simplify and manipulate algebraic expressions to maintain equivalence by:

collecting like terms

multiplying a single term over a bracket

taking out common factors

expanding products of two or more binomials

Understand and use standard mathematical formulae; rearrange formulae to change the subject.

Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement).

Work with coordinates in all four quadrants.

Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane.

Interpret mathematical relationships both algebraically and graphically.

Reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically.

Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations.

Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs.

Generate terms of a sequence from either a term-to-term or a position-to-term rule.

Recognise arithmetic sequences and find the nth term.

Recognise geometric sequences and appreciate other sequences that arise.

Ratio, proportion and rates of change

Change freely between related standard units [for example time, length, area, volume/capacity, mass].

Use scale factors, scale diagrams and maps.

Express one quantity as a fraction of another, where the fraction is less than one and greater than one.

Use ratio notation, including reduction to simplest form.

Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio.

Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction.

Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.

Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics.

Solve problems involving direct and inverse proportion, including graphical and algebraic representations.

Use compound units such as speed, unit pricing and density to solve problems.

Interpret and compare numbers in standard form A × 10ⁿ1 ≤ A < 10, where n is a positive or negative integer or zero.

Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and ⁷/₂ or 0.375 and ³/₈).

a² in place of a × a, a³ in place of a × a × a; a²b in place of a × a × b

^a/_b in place of a ÷ b