# Maths

__Curriculum Intent__

__Curriculum Intent__

Mathematics provides an efficient way of building mental regulation, encourages logical thinking and mental tenacity. Our aim is to enable students to use Mathematics as a form of communication that they apply on a daily basis and secure mathematical reasoning which they can use and implement independently to understand the world. Students are able to think critically and to reason while also developing their resilience and confidence.

Moreover, the curriculum enables students to gain the basic computational skills, quantitative reasoning and spatial ability while also providing them with the skills to solve sophisticated mathematical concepts and procedures. Our curriculum gives students the opportunity to develop their metacognitive skills by constructing relationships between new processes and what they already knew. Students are given frequent opportunities to explore varied Mathematical problems with increasing difficulty over time to develop their fluency so that they are able to understand concepts and are able to recall and apply knowledge accurately and rapidly.

The principal idea behind our curriculum design is to support students to be able to perform simpler tasks so they can progress on to perform more complex tasks. Each step builds carefully from the previous step, building on students’ prior knowledge to develop new skills. Our curriculum is designed to use skills that students have already learnt in different contexts (sometimes called ‘interleaving’) whenever we can. This helps our students to remember and to make connections between different parts of the curriculum.

__Student Learning Journey__

The national curriculum for mathematics aims to ensure that all pupils:

*become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.**reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language**can solve problems by applying their mathematics to a variety of routine and nonroutine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.*

__Key Stage 3 Mathematics__

__Key Stage 3 Mathematics__

**At KS3**, in line with the National Curriculum the programme of study is broad and organised into distinct strands (number, algebra, geometry, proportion, statistics, probability), but pupils consolidate on their knowledge from KS2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They learn all the foundations for the harder concepts they will need for GCSE and A Level.

**In Year 7** students will focus on developing fluency in maths by consolidating their numerical and mathematical skills from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots. This is developed more formally where different interpretations of fractions and introducing ratio are linked. They explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally. They extend and formalise their knowledge of ratio and proportion in working with measures and geometry. They are able to plot and interpret graphs for the first time. Students also begin to see the link between arithmetic sequences and graph. The cumulative nature of the curriculum means that students apply algebraic reasoning in new contexts.

**In Year 8** students will build on the knowledge accumulated in Year 7 and continue to apply focus to developing the skills of all the different strands. They learn calculator skills while using more complex geometry calculations. Students will build on their prior knowledge of perimeter and area to include volume. They will also be able to solve increasingly complex angles problems including those involving parallel lines or polygons. Students will study the data handling cycle in depth, drawing and interpreting a range of charts and graphs and also calculating measures of central tendency. Algebra skills are revisited with a new focus on factorising and solving equations. Students also begin to see the link between proportion and graphs as their knowledge of ratio and proportion expands.

**In Year 9** the curriculum for this stage of students’ education has been designed to build upon their knowledge of percentages to enable them to compare quantities and combine it with their knowledge of proportion. Students will also study different methods of sampling and how to interpret grouped data. Students will also have the opportunity build on their knowledge of angles in polygons and angles associated with parallel lines and will study Pythagoras’ theorem and trigonometry while having the opportunity to combine this with 3D shapes. Algebra skills become more advanced, with simultaneous equations being introduced, as well as use of quadratics in graphs.

__Key Stage 4 Mathematics__

__Key Stage 4 Mathematics__

**At KS4**, students will follow the Edexcel programme of study. The curriculum splits into two tiers, foundation and higher, and for students begin to follow different programmes of study. All students begin their two year GCSE course by revisiting key threshold concepts – this is basic number and algebra skills for foundation, and more advanced number skills for higher. Throughout the year, students will be exam questions regularly to prepare them fully for their trial exam at the end of the year. Underpinning the curriculum areas, will be the opportunity to explore how the skills they are developing can be used in real life situations. Students are regularly required to combine different areas mathematics to solve problems.

**In Year 10 Foundation**, the curriculum provides students with the opportunity to build upon their knowledge of shape to enable them to calculate area, perimeter and volume and develop their skills on prisms including constructions and transformations. Students will also build on their understanding of ratio and proportion while applying it to graph and use ratio with decimals. They are able to link equation and proportion. Students will learn probability extensively building on work from Key Stage 3 by looking at combined events as well as mutually exclusive and exhaustive events while also learning about the tree diagram.

In Year 10 Higher, the curriculum for this stage has been designed to build upon their knowledge of percentages to enable them to calculate compound interest as well as calculating direct proportion. Students will also have the opportunity to interpret grouped data, as well as being introduced to histograms and cumulative frequency curves to represent grouped data. Students will build on the knowledge of Pythagoras’ theorem and trigonometry in right angled triangles to more complex trigonometric problems. They will also carry out various constructions.

In year 11 Foundation, the curriculum is designed to prepare students to their final exams as well as providing the opportunity to access mathematics from the next stage of study. Throughout the year, students will be exposed to regular exam questions and exam papers to prepare them fully for their exam at the end of the year. Students develop their knowledge of index laws and apply their understanding of standard form to calculate using standard form. They use their knowledge of inverse operations and apply to rearranging formula. They build upon their knowledge of solving simultaneous equations and apply it to graphs and further non linear graphs.

In year 11 Higher, the curriculum is designed to prepare students to their final exams as well as providing the opportunity to access mathematics from the next stage of study. Throughout the year, students will be exposed to regular exam questions and exam papers to prepare them fully for their exam at the end of the year. Students develop their knowledge of trigonometry while studying trigonometry in non-right-angled triangles. They also build upon their knowledge of previous years to enable them to access topics at A Level. They learn about transformation of functions, circle theorems, iterations and algebraic fractions which are fundamentals of A Level Mathematics.

__Key Stage 5 Mathematics__

__Key Stage 5 Mathematics__

**At KS5**, students will follow a two-year course based on Edexcel.

**In year 12**, students build upon their knowledge of algebra by increasing rigour with the introduction of formal proof. They study calculus where they calculate gradients of non-linear functions using differentiation and also calculate areas under curves accurately using integration. Students will have the opportunity to apply their study of calculus to calculate forces and motion, as well as studying how to interpret data using more formal probability models compared to their prior stage of study. Throughout the statistics module, students will have the opportunity to study a large data set and become familiar with how to use the techniques developed in class to analyse it. Throughout the year, students will be exposed to regular exam questions and exam papers to prepare them fully for their exam at the end of the year.

**In Year 13**, students build upon their knowledge of calculus by increasing their skill set for differentiation and integration. Students will spend time studying how to use inverse and reciprocal trigonometric functions and also convert compound angles using trigonometric identities. Students will advance from trial and improvement seen at GCSE to use more rigorous and reliable numerical methods to find approximations to equations. The mechanics modules will build upon the AS level by looking at systems of forces in motion as well as introducing gravity. Students will continue to analyse the large data set, this time looking at how to manipulate continuous data and use hypothesis testing to determine if correlation is significant. Throughout the year, students will be exposed to regular exam questions and exam papers to prepare them fully for their exam at the end of the year.

__How is Maths Taught?__

Each Maths lesson starts with a **retrieval activity** where students have to complete a set of questions based on content learnt previously to strengthen the memory. The activity also includes questions that draw on **prior learning** and link to the **new content** in order to make the lesson meaningful to students. The learning objective is broken down into **explicit success criteria** and shared with the students at the start of the lesson. **Modelling** is used to illustrate examples and allow students to work together towards shared high standards. **Teachers use scaffolding** during the lesson to bridge the gaps and help students to succeed. **Teachers assess students’ understanding** by using questioning and mini whiteboards before they are set independent work. During **independent work**, the teacher intentionally circulates to check for key elements that demonstrate success. Support is then provided to students as required while they are working independently. Students receive **instant feedback throughout the lessons** where they can identify their strengths and areas for development as they **self- assess or peer mark the work set**. This marking is completed using the green pen. Students complete **mini assessments** at the end of each unit, end of half term and end of term where they have the opportunities to demonstrate the understanding of the mathematical concepts in exam conditions. They are then given **written feedback** and time is built in to the lessons to enable students to complete a task based on the outcome of the assessment that they completed. Students are supported to improve their work by correcting errors, addressing misconceptions and deepening their understanding of a given topic **The ****Diagnostic Therapy Testing model (DTT)** is used throughout the scheme of learning as teachers will regularly set homework and starter activities based on the areas identified during the assessments.

__Home Learning__

__Home Learning__

Homework is set on a weekly basis for each class. In Key stage 3 retrieval homework as well as homework based on new content is set on Mathswatch. Whereas in Key stage 4 homework is a combination of retrieval work from Mathswatch and exam questions from either the Edexcel workbook or worksheets. In Key stage 5 students must demonstrate a high degree of skill in independent study and homework is set from the textbooks and exam questions.