## 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.