## Mathematics Department

### KS3 Intent:

Our Key Stage 3 curriculum provides pupils with an opportunity to continue to develop the Mathematic skills that are essential for everyday life and the next stage of their education. The curriculum builds on knowledge and skills developed at Key Stage 2 with a focus on developing pupils reasoning and problems solving skills whilst providing regular opportunities for pupils to recall and consolidate prior learning. We aim to give pupils regular opportunities to develop fluency through independent practice as well as the opportunity to develop reasoning and problem-solving skills justifying and proving their solutions along the way. Pupils will be able to develop their Mathematical ideas making links with other subject areas. Key Stage 3 Mathematics significantly contributes to pupils cultural capital development through the interconnection of Mathematical ideas and concepts with a focus on how Mathematics can be applied to the real world. Our curriculum is fully inclusive with high ambition for all pupils, by the end of Key Stage 3 Mathematics all pupils need to be able to move fluently between representations of Mathematical ideas and concepts. The Curriculum plan is clearly set out with a focus on the sequence and structure of how subject content is taught.

### Implementation:

 Year Term Topic Knowledge, skills and understanding Window for Assessment 7 1 Using a calculator Algebra – formulae, equations, variables Ratio – notation, bar model, proportional quantities Statistics – Frequency tables, stem and leaf, averages Geometry – angles, properties of shapes, symmetry Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Arithmetic Assessment – September   Assessment in line with whole school data point 2 Number – negative numbers, fractions Geometry – transformations, metric system Algebra - sequences Geometry – angles Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment in line with whole school data point 3 Number – percentages, decimals Statistics – probability Geometry – angles, area and perimeter Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment in line with whole school data point 8 1 Algebra – factorising, complex equations, substitution Ratio – problem solving Number – fractions Geometry – constructions, nets Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment in line with whole school data point 2 Number – decimals Geometry – angles, bearings, metric-imperial, transformations Statistics - probability Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment in line with whole school data point 3 Number – index notations Algebra – sequences Geometry – circles, volume, surface area Number - percentages Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment in line with whole school data point

### KS4 Intent:

At Key Stage 4 our curriculum continues to provide pupils with an opportunity to develop the Mathematic skills that are essential for everyday life and the next stage of their education whilst building on knowledge and skills developed at Key Stage 3. Pupils will continue to develop fluency, mathematical reasoning and demonstrate problem solving skills. They should also apply their Mathematical knowledge wherever relevant in other subjects and real life. Key Stage 4 Mathematics significantly contributes to pupils Cultural Capital development through the interconnection of Mathematical ideas and concepts with a focus on how Mathematics can be applied to the real world. Our curriculum is fully inclusive with high ambition for all pupils, by the end of Key Stage 4 Mathematics all pupils need to be able to move fluently between representations of Mathematical ideas and concepts. The Curriculum plan is clearly set out with a focus on the sequence and structure of how subject content is taught.

### Implementation:

 Year Term Topic Knowledge, skills and understanding Window for Assessment 9 1 Algebra – inequalities, graphs, simultaneous equations, quadratics Number – direct and inverse proportion Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment - October & December 2 Geometry – Pythagoras’ Theorem, circles, angles, prisms Number – percentages, standard form Statistics – grouped data Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment - March 3 Geometry – accuracy, loci, trigonometry, transformations, compound units Statistics – probability Number – fractions, prime factorisation, surds Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment - June 10 1 Algebra – identities, indices, functions, y = mx + c, quadratics, perpendicular lines Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment - October & December 2 Number – percentage Geometry – similarity, congruence, prisms, plans and elevations Statistics – scatter diagrams Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Mock exam - March 3 Geometry – vectors, circle theorems, trigonometry, transformations Statistics – probability, histograms Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Assessment - June 11 1 Algebra – quadratics, functions, proof Number – fractions, percentages, proportion Geometry – vectors, compound units Statistics - grouped data Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Mock exam - September 2 Algebra – further proof, further functions Revision Reasoning, problem solving, critical thinking, data analysis, analysing relationships, applying knowledge, making predictions, evaluating accuracy Mock exam - January Weekly mock exam 3 Revision Examination - June

### KS5 Intent:

Subject content at A level Mathematics is split into three main areas, Pure Mathematics, Mechanics and Statistics. These modules are all initially studied during Year 12 and are delivered through a series of units focusing on building new concepts and ideas step by step as well as allowing regular opportunities for consolidation prior learning.  These skills are then extended to further study during Year 13. A level Maths significantly contributes to pupils Cultural Capital development through the interconnection of Mathematical ideas and concepts with a focus on how Mathematics can be applied to model situations in the real world. Problem solving is used in a variety of context with pupils reasoning and justifying their Mathematical ideas. We aim to prepare all pupils for further study and employment in a wide range of disciplines involving the use of Mathematics.

### Implementation:

 Year Term Topic Knowledge, skills and understanding Window for Assessment 12 1 Surds                                                      Quadratic Equations Equations                                                               Polynomials                                                           Coordinate Geometry                                                Binomial expansion                                                              Exponentials                                                         Problem solving                                                   Probability                                                             Trigonometry                                                        Graphs   Differentiation      Integration Interpret and communicate solutions in the context of the original problem. Understand that many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy. Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions, including those obtained using numerical methods. Understand the concept of a mathematical problem-solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle. Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics. Translate a situation in context into a mathematical model, making simplifying assumptions. Use a mathematical model with suitable inputs to engage with and explore situations Interpret the outputs of a mathematical model in the context of the original situation Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate. Understand and use modelling assumptions. Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion. Disproof by counter example. Proof by contradiction Assessment – October & December 2 Vectors                                  Kinematics                                             Forces and Newton's laws of motion      Variable acceleration                                                Data Collection                                                     Data Processing, presentation and interpretation                                                       Binomial distribution Hypothesis testing Interpret and communicate solutions in the context of the original problem. Understand that many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy. Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions, including those obtained using numerical methods. Understand the concept of a mathematical problem-solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle. Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics. Translate a situation in context into a mathematical model, making simplifying assumptions. Use a mathematical model with suitable inputs to engage with and explore situations Interpret the outputs of a mathematical model in the context of the original situation Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate. Understand and use modelling assumptions. Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion. Disproof by counter example. Proof by contradiction Assessment – February & March 3 Proof                                      Trigonometry                                                        Vectors  Functions Differentiation Interpret and communicate solutions in the context of the original problem. Understand that many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy. Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions, including those obtained using numerical methods. Understand the concept of a mathematical problem-solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle. Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics. Translate a situation in context into a mathematical model, making simplifying assumptions. Use a mathematical model with suitable inputs to engage with and explore situations Interpret the outputs of a mathematical model in the context of the original situation Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate. Understand and use modelling assumptions. Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion. Disproof by counter example. Proof by contradiction Assessment - June 13 1 Sequences and series                                                Trigonometric functions                                               Forces and motion                                                Trigonometric identities               Further algebra    Further differentiation                                      Probability                                                             Integration Interpret and communicate solutions in the context of the original problem. Understand that many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy. Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions, including those obtained using numerical methods. Understand the concept of a mathematical problem-solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle. Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics. Translate a situation in context into a mathematical model, making simplifying assumptions. Use a mathematical model with suitable inputs to engage with and explore situations Interpret the outputs of a mathematical model in the context of the original situation Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate. Understand and use modelling assumptions. Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion. Disproof by counter example. Proof by contradiction Assessment – October & December 2 Moments of forces                                                A model for friction                                                Numerical methods                                                Parametric equations                                                Kinematics                             Projectiles Differential equations Statistical distributions                                          Hypothesis testing Interpret and communicate solutions in the context of the original problem. Understand that many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy. Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions, including those obtained using numerical methods. Understand the concept of a mathematical problem-solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle. Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics. Translate a situation in context into a mathematical model, making simplifying assumptions. Use a mathematical model with suitable inputs to engage with and explore situations Interpret the outputs of a mathematical model in the context of the original situation Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate. Understand and use modelling assumptions. Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion. Disproof by counter example. Proof by contradiction Assessment – February & March 3 Revision Examination - June