2 Objectives To develop understanding of Functional Skills To explore resources and strategies for building towards functionality in the context of probability

3 The level of a functional skills qualification is determined by: the complexity of situations and activities the technical demand associated with these activities a learner’s level of familiarity with the task or activity the level of independence with which a learner can complete the activity. …A learner may understand the content within the coverage and range column at a given level – whether this relates to appreciating a particular point, knowing certain facts or calculations, or understanding various concepts or notions – but the functional skill level is determined by the learner’s ability to use and apply this information for ‘reallife’ and purposeful activities. The content that a learner engages with for a level 2 functional task or activity, for example, could be from a range of higher or lower levels. It is the application of the content, the process skills, the outcome, and the interplay of the level differentiation factors that determine the level, and not the content in isolation. Functional Skills Standards

4 The process skills help pupils both to learn mathematics and to apply their mathematical subject knowledge to situations from life and the world of work. To ensure that they make progress in developing these skills and can function mathematically, pupils need to experience a rich ‘diet’ of applications that includes: increasingly complex applications, including non-routine or multi-step problems and extended enquiries, that require them to analyse a situation and sustain their thinking situations that are unfamiliar (in the sense that they are different from the context where the mathematics was developed), including applications to other subjects or aspects of their lives, and that require them to make connections and transfer their skills, sometimes in creative ways situations or problems that increase the technical demand of the mathematics required to solve them, including the application of more advanced concepts, more difficult procedures, or more rigorous argument and proof opportunities to develop greater independence and autonomy in problem- solving skills, so that they can select and apply a higher level of mathematics for themselves. Secondary mathematics guidance papers

5 The process skills help pupils both to learn mathematics and to apply their mathematical subject knowledge to situations from life and the world of work. To ensure that they make progress in developing these skills and can function mathematically, pupils need to experience a rich ‘diet’ of applications that includes: increasingly complex applications, including non-routine or multi-step problems and extended enquiries, that require them to analyse a situation and sustain their thinking situations that are unfamiliar (in the sense that they are different from the context where the mathematics was developed), including applications to other subjects or aspects of their lives, and that require them to make connections and transfer their skills, sometimes in creative ways situations or problems that increase the technical demand of the mathematics required to solve them, including the application of more advanced concepts, more difficult procedures, or more rigorous argument and proof opportunities to develop greater independence and autonomy in problem- solving skills, so that they can select and apply a higher level of mathematics for themselves. Secondary mathematics guidance papers

6 GCSE changes and Functional Skills Assessment objectives Weighting (%) AO1 Recall and use their knowledge of the prescribed content AO2 Select and apply mathematical methods in a range of contexts AO3 Interpret and analyse problems and generate strategies to solve them 15-25

7 Other qualifications and Functional Skills

8 Bowland maths How well does How Risky is Life? help students develop greater independence ? How well does it develop their ability to work in situations that are unfamiliar (in the sense that they are different from the context where the mathematics was developed)

9 Questioning functionally? What’s the probability of rolling a 4 on a dice? Why is the probability of rolling a four on a dice 1/6? Is it always, sometimes or never true that the probability of rolling a four on a dice 1/6? The probability of rolling a 1 on a dice is 1/6 so the probability of rolling a 4 is 4/6. Do you agree or disagree? What’s the same and what’s different about the probability of rolling a 4 on these two dice?

10 If the probability of an event happening is 0.4, what’s the probability of it not happening? Questioning functionally?