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# Functional skills in mathematics

## Introduction

The term ‘functional’ should be considered in the broad sense of providing learners with the skills and abilities they need to take an active and responsible role in their communities, in their everyday life, workplace and in educational settings. Functional mathematics requires learners to be able to use mathematics in ways that make them effective and involved as citizens, able to operate confidently in life and to work in a wide range of contexts.

## Functional skills in the mathematics programme of study

The revised mathematics programme of study for key stage 3 embeds the level 1 functional skills standards in mathematics. As well as overlaps in the language used, there are deliberate structural similarities (summarised in Links with functional skills). Functional skills are a subset of the key processes set out in the programme of study. All teaching needs to contribute to the development of the key processes. The key processes of representing, analysing, interpreting, evaluating, communicating and reflecting, comprise the skills necessary to be functional in mathematics.

The range and content set out in the programme of study goes beyond that which is likely to be required in the assessment of functional skills at level one.

The key stage 3 programme of study lays the groundwork for pupils to apply their mathematics to real contexts in key stage 4. In addition, it requires that pupils be introduced to a range of real-life uses of mathematics, including its role in the modern workplace.

### Level 1 functional skill standard: representing - making sense of situations and representing them

• Recognise that a situation has aspects that can be represented using mathematics

• Make an initial model of a situation using suitable forms of representation

• Decide on the methods, operations and tools, including ICT, to use in a situation

• Select the mathematical information to use.

### Key stage 3 programme of study key processes: representing

• Identify the mathematical aspects of a situation or problem

• Simplify the situation or problem in order to represent it mathematically, using appropriate variables, symbols, diagrams and models

• Choose between representations, select mathematical information, methods and tools to use Select mathematical information, methods and tools to use.

### Level 1 functional skill standard: analysing – processing and using the mathematics

• Use appropriate mathematical procedures Examine patterns and relationships

• Change values and assumptions or adjust relationships to see the effects on answers in the model

• Find results and solutions.

### Key stage 3 programme of study key processes: analysing

• Use appropriate mathematical procedures

• 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

• Work logically towards results and solutions, recognising the impact of constraints and assumptions.

### Level 1 functional skill standard: interpreting – interpreting and communicating the results of the analysis

• Interpret results and solutions

• Draw conclusions in the light of the situation

• Consider the appropriateness and accuracy of the results and conclusions.

### Key stage 3 programme of study key processes: interpreting and evaluating

Form convincing arguments based on findings and make general statements

Relate findings to the original context, identifying whether they support or refute conjectures

Consider the assumptions made and the appropriateness and accuracy of results and conclusions

### Level 1 functional skill standard: interpreting – interpreting and communicating the results of the analysis

• Choose appropriate language and forms of presentation to communicate results and conclusions.

### Key stage 3 programme of study key processes: communicating and reflecting

• Communicate findings effectively, Engage in mathematical discussion of results.

## Planning for functional skills

The key concept of competence emphasises the need for pupils to be able to adapt and apply their understanding in a widening range of contexts within the classroom and beyond. This is also at the heart of functional skills. In this way functional skills are much more than a set of technical competencies in mathematics; pupils have to use mathematics to tackle tasks and problems. All teaching needs to be designed in a way that contributes to the development of functional skills.

When planning opportunities for pupils to develop and understand functional skills you should consider if you have:

• provided opportunities for different skills you are focusing on in representing, analysing and interpreting to be developed in combination

• ensured that pupils understand that they are learning skills that they will use and apply in a variety of contexts

• given pupils the chance to select the skills and tools (including ICT) they need for a particular task

• provided opportunities for pupils to apply these skills for real purposes and contexts beyond the classroom.

For example, a project for year 9 pupils – ‘How fair is our society?’ – required them to work in small groups to identify a question they would like to investigate, for example: Is there still slavery today? How is wealth distributed in our society? Do minority ethnic students do less well at school? Who is in prison? How does where you are born in the world affect your life expectancy? They then had to identify suitable data – searching on the internet and interrogating a variety of sources using critical judgement – to decide on the veracity and reliability of the data found. The data was then analysed and represented in such a way that they could answer their question, presenting their findings on a poster and through a presentation to their peers.

This project has the potential to be developed in conjunction with ICT, English and citizenship colleagues as it addresses wider curricular issues and also offers opportunities to develop functional skills in ICT and English as well as mathematics.