REPRESENTING
Identify the mathematical aspects of a
situation or problem
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Choose between representations
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Simplify the situation or problem in order to represent it mathematically, using appropriate variables, symbols, diagrams and models
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Select mathematical information, methods and tools to use
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ANALYSING: Use mathematical reasoning
Make connections within mathematics
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Use knowledge of related problems
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Visualise and work with dynamic images
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Identify and classify patterns
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Make and begin to justify conjectures and generalisations, considering special cases and counter-examples
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Explore the effects of varying values and look for invariance and covariance
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Take account of feedback and learn from mistakes
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Work logically towards results and solutions, recognising the impact of constraints and assumptions
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Appreciate that there are a number of different techniques that can be used to analyse a situation
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Reason inductively and deduce
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ANALYSING: Use appropriate mathematical
procedures
Make accurate mathematical diagrams, graphs and constructions on paper and on screen
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Calculate accurately, selecting mental methods or calculating devices as appropriate
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Manipulate numbers, algebraic expressions and equations and apply routine algorithms
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Use accurate notation, including correct syntax when using ICT
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Record methods, solutions and conclusions
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Estimate, approximate and check working
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INTERPRETING AND EVALUATING:
Form convincing arguments based on findings and make general statements
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Consider the assumptions made and the appropriateness and accuracy of results and conclusions
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Be aware of the strength of empirical evidence and appreciate the difference between evidence and proof
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Look at data to find patterns and exceptions
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Relate findings to the original context, identifying whether they support or refute conjectures
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Engage with someone else’s mathematical reasoning in the context of a problem or particular situation
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Consider the effectiveness of alternative strategies
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COMMUNICATING AND REFLECTING
Communicate findings effectively
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Engage in mathematical discussion of results
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Consider the elegance and efficiency of alternative solutions
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Look for equivalence in relation to both the different approaches to the problem and different problems with similar structures
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Make connections between the current situation and outcomes, and situations and outcomes they have already encountered
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