# Mathematics

## Learning Journey & Sequencing Rationale

Mathematics can be applied in practical tasks, real-life problems and within mathematics itself. The course aims to develop deep learning through the mastery of mathematical vocabulary, conceptual understanding and mathematical reasoning used to solve a variety of problems.

The course of study should help you whether working individually or collaboratively to reason logically, plan strategies and improve your confidence in solving complex problems.

During Maths lessons you will learn how to:-

• Use and apply maths in practical tasks, real life problems and within mathematics itself.
• Develop and use a range of methods of computation and apply these to a variety of problems.
• Develop mathematical vocabulary and improve mental calculation.
• Consider how algebra can be used to model real life situations and solve problems.
• Explore shape and space through drawing and practical work using a range of materials and a variety of different representations.
• Use statistical methods to formulate questions about data, represent data and draw conclusions.

Engage in practical and experimental activities in order to appreciate principles of probability.

## unit overview - autumn 1 - probability

 Autumn 1: Probability Skills Convert between fractions, decimals and percentages Determine theoretical probabilities Calculate relative frequency and experimental probability Use probability and relative frequency to find an expected number of outcomes Find probabilities of single and combined events Use representations such as two way tables and tree diagrams to solve probability problems Use the language and notation of set theory, including union and intersection Use Venn diagrams to represent sets Calculate probabilities from Venn diagrams Knowledge Understand the equivalence between fractions, decimals and percentages Understand how probability is used to discuss uncertainty Use the language of probability, including ‘event’, ‘outcome’. ‘trial’, ‘experiment’ etc. Know that probabilities are represented by numbers between 0 and 1, where 0 represents impossibility and 1 represents certainty Recognise the differences between situations involving single and combined events Understand and use the addition and multiplication rules for independent and dependent events Begin to understand and reason with conditional probability Rationale In this module learners briefly revise the equivalence of fractions, decimals and percentages before studying probability and set theory. Learners begin by considering uncertainty and the language of probability in the context of idealised experiments and real contexts before considering combined events. Learners encounter a variety of tools and representations, including bar models and tree diagrams.  This learning is formalised and extended in unit 3, where students encounter set theory for the first time, and use Venn diagrams to represent them. Venn diagrams are also explored thoroughly, consolidating learning from Year 7 and 8. Venn diagrams are used as a model to think about conditional probability.

## knowledge Organiser

A knowledge organiser is an important document that lists the important facts that learners should know by the end of a unit of work. It is important that learners can recall these facts easily, so that when they are answering challenging questions in their assessments and GCSE and A-Level exams, they are not wasting precious time in exams focusing on remembering simple facts, but making complex arguments, and calculations.

We encourage all pupils to use them by doing the following:

• Quiz themselves at home, using the read, write, cover, check method.
• Practise spelling key vocabulary
• Further researching people, events and processes most relevant to the unit.