### Mathematics

The aim of key stage 3 mathematics is to ensure that all pupils:

• become fluent in the fundamentals of mathematics, where pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• reason mathematically by developing an argument, justification or proof using mathematical language
• can solve problems by applying their mathematics to a variety of routine and non-routine problems

Through the areas of number, algebra, ratio and proportion, geometry and measures, probability and statistics, pupils are taught to:

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.

## Year 7

Areas of mathematics covered are:

• algebraic thinking
• place value and proportion
• applications of number
• directed number
• fractional thinking
• lines and angles
• reasoning with number

## Year 8

Areas of mathematics covered are:

• proportional reasoning
• representations
• algebraic techniques
• developing number
• developing geometry
• reasoning with data

## Year 9

Areas of mathematics covered are:

• reasoning with algebra
• constructing in 2 and 3 dimensions
• reasoning with number
• reasoning with geometry
• reasoning with proportion
• representations and revision

## Year 10 and 11

You can find further details on the KS4 curriculum below:

Mathematics