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:
- 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.
- 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.
- 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.