## 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:

**a identify the mathematical aspects of a situation or problem**

b choose between representations

**c simplify the situation or problem in order to represent it mathematically, using appropriate variables, symbols, diagrams and models**

**d select mathematical information, methods and tools to use.**

**2.2 Analysing**

Use mathematical reasoning

Pupils should be able to:

**a make connections within mathematics**

**b use knowledge of related problems**

c visualise and work with dynamic images

d identify and classify patterns

e make and begin to justify conjectures and generalisations, considering special cases and counter-examples

**f explore the effects of varying values and look for invariance and covariance**

**g take account of feedback and learn from mistakes**

**h work logically towards results and solutions, recognising the impact of constraints and assumptions**

i appreciate that there are a number of different techniques that can be used to analyse a situation

j reason inductively and deduce.

Use appropriate mathematical procedures

Pupils should be able to:

k make accurate mathematical diagrams, graphs and constructions on paper and on screen

**l calculate accurately, selecting mental methods or calculating devices as appropriate**

**m manipulate numbers, algebraic expressions and equations and apply routine algorithms**

**n use accurate notation, including correct syntax when using ICT**

**o record methods, solutions and conclusions**

**p estimate, approximate and check working.**

**2.3 Interpreting and evaluating**

Pupils should be able to:

**a form convincing arguments based on findings and make general statements**

**b consider the assumptions made and the appropriateness and accuracy of results and conclusions**

**c be aware of the strength of empirical evidence and appreciate the difference between evidence and proof**

d look at data to find patterns and exceptions

**e relate findings to the original context, identifying whether they support or refute conjectures**

**f engage with someone else's mathematical reasoning in the context of a problem or particular situation**

**g consider the effectiveness of alternative strategies.**

**2.4 Communicating and reflecting**

Pupils should be able to:

**a communicate findings effectively**

b engage in mathematical discussion of results

c consider the elegance and efficiency of alternative solutions

d look for equivalence in relation to both the different approaches to the problem and different problems with similar structures

e make connections between the current situation and outcomes, and situations and outcomes they have already encountered.