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Curriculum Ideas & School Examples

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KS3 Maths : Key Processes

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2. Key processes

These are the essential skills and processes in mathematics that pupils need to learn to make progress.

2.1 Representing

Pupils should be able to:
  • identify the mathematical aspects of a situation or problem
  • choose between representations
  • simplify the situation or problem in order to represent it mathematically, using appropriate variables, symbols, diagrams and models
  • select mathematical information, methods and tools to use.

2.2 Analysing

(Use mathematical reasoning
Pupils should be able to:
  •  make connections within mathematics
  • use knowledge of related problems
  • visualise and work with dynamic images
  • identify and classify patterns
  • make and begin to justify conjectures and generalisations, considering special cases and counter-examples
  • explore the effects of varying values and look for invariance and covariance
  • take account of feedback and learn from mistakes
  • work logically towards results and solutions, recognising the impact of constraints and assumptions
  • appreciate that there are a number of different techniques that can be used to analyse a situation
  • reason inductively and deduce.

Use appropriate mathematical procedures
Pupils should be able to:

  • make accurate mathematical diagrams, graphs and constructions on paper and on screen
  • calculate accurately, selecting mental methods or calculating devices as appropriate
  • manipulate numbers, algebraic expressions and equations and apply routine algorithms
  • use accurate notation, including correct syntax when using ICT
  • record methods, solutions and conclusions
  • estimate, approximate and check working.

2.3 Interpreting and evaluating

Pupils should be able to:
  • form convincing arguments based on findings and make general statements
  • consider the assumptions made and the appropriateness and accuracy of results and conclusions
  • be aware of the strength of empirical evidence and appreciate the difference between evidence and proof
  • look at data to find patterns and exceptions
  • relate findings to the original context, identifying whether they support or refute conjectures
  • engage with someone else’s mathematical reasoning in the context of a problem or particular situation
  • consider the effectiveness of alternative strategies.

2.4 Communicating and reflecting

Pupils should be able to:
  • communicate findings effectively
  • engage in mathematical discussion of results
  • consider the elegance and efficiency of alternative solutions
  • look for equivalence in relation to both the different approaches to the problem and different problems with similar structures
  • make connections between the current situation and outcomes, and situations and outcomes they have already encountered.

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