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KS3 TO KS4

**Our Key Stage 3:**

Working mathematically:

• Developing fluency

• Reasoning mathematically

• Solving problems

Working mathematically through the mathematics content, pupils should be 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 counterexamples

– 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.

#### Mathematics – key stage 3

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.

**Key Stage 4**

Through the mathematics content, pupils should be taught to:

Develop fluency

– consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include powers, roots {and fractional indices}

– select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving multiples of π {and surds}, use of standard form and application and interpretation of limits of accuracy

– consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include quadratic expressions, {and expressions involving surds and algebraic fractions}

– extend fluency with expressions and equations from key stage 3, to include quadratic equations, simultaneous equations and inequalities

– move freely between different numerical, algebraic, graphical and diagrammatic representations, including of linear, quadratic, reciprocal, {exponential and trigonometric} functions

– use mathematical language and properties precisely.

#### Reason mathematically

– extend and formalise their knowledge of ratio and proportion, including trigonometric ratios, in working with measures and geometry, and in working with proportional relations algebraically and graphically

– extend their ability to identify variables and express relations between variables algebraically and graphically

– make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments {and proofs}

– 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

#### Mathematics – key stage 4

– explore what can and cannot be inferred in statistical and probabilistic settings, and express their arguments formally

– assess the validity of an argument and the accuracy of a given way of presenting information.

#### 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 contexts

– make and use connections between different parts of mathematics to solve problems

– model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions

– select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems; interpret their solution in the context of the given problem.

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