Math Formulas


“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” –


William Paul Thurston


Subject Intent:

Mathematics is an innovative and highly interconnected subject that has provided the solution to some of history’s most complex problems. It is vital to everyday life, and essential for financial literacy. Not to mention being a requirement for most forms of employment.


Our curriculum is a mastery curriculum which aims to provide pupils with a strong foundation for understanding how mathematics works in the wider world, the ability to problem solves, and to reason mathematically, as well as an appreciation of the beauty and power of mathematics.


We built the curriculum with the intent that students will:

  • experience a broad, deep and knowledge-rich curriculum based on frequent exposure to a variety of increasingly complex problems over time. This allows pupils to develop their conceptual understanding and recall skills and gives them the ability to recall relevant knowledge rapidly and accurately.

  • extend their KS2 knowledge by applying skills previously learnt to more complex problems, learning to break these more complex problems into smaller parts, and develop a resilience which allows them to persevere while seeking solutions.

  • be literate and numerate to reason mathematically, by developing justifications and mathematical arguments using appropriate mathematical language.

  • have high expectations for their behaviour and achievement and demonstrate this by actively participating in lessons. Our pupils will respect themselves, and each other as we examine situations where mathematics applies in real life, and demonstrate British Values as they work with each other, and independently, on a wide range of engaging tasks.

  • develop their cultural, moral, social, mental, and physical development by exposing them to a range of increasingly complex problems aimed to open their mind to the wider world, whilst also developing their resilience. Pupils will be exposed to tasks which are designed to excite and spark interest and curiosity.

  • be prepared for life beyond the school by allowing pupils exposure to mathematics in the real world, ensuring pupils can make the link from classroom to career in order to ensure that they do not view learning mathematics as a redundant practise.

  • experience a curriculum that is fully inclusive, enabling all students to access the knowledge and skills regardless of their starting points and barriers to learning.

  • be closely monitored – especially specific groups (such as SEND, DP, MA) – and intervention, where necessary, is planned in order to reduce gaps which will allow students to meet their targets.


Subject Implementation:

  • The curriculum builds from year 7 – 11, focusing on a mastery approach to learning. Key topics are revisited regularly throughout KS3 and KS4 to ensure that pupils are fluent in key skills and develop recall. Subjects on the maths 5-year curriculum map, clearly detail the last time a topic was taught, as well as the next time a topic will be taught.

  • The curriculum is taught over three different pathways, to effectively meet the needs of all pupils within each cohort. These are…

    • ‘Support’ for pupils who achieved less than expected attainment at KS2

    • ‘Core’ for pupils who achieved the expected attainment at KS2

    • ‘Higher’ for pupils who achieved more than the expected attainment at KS2.  

  • Pupils will be exposed to a variety of questions each lesson, designed to improve fluency, and develop rapid recall. Problem solving and reasoning questions will be used expose pupils to more complex mathematics, and allow them to build up a resilience, particularly when dealing with more complex problems.

  • Pupils will be exposed to mathematical vocabulary from KS3 and throughout KS4, which will allow them to break down more complex GCSE problems, and allow them to recall the subject knowledge to answer them effectively.

  • KS3 pupils who develop rapidly, and grasp mathematical concepts more quickly, will be challenged with the use of enrichment tasks and more sophisticated problems before accelerating through to KS4 content. This allows pupils to master their KS3 knowledge more solidly.

  • Summer term in year 11 will be dedicated to exam preparation. This allows year 11 to get a thorough understanding of their GCSE expectations and have adequate experience applying the skills mastered at KS3 and KS4 prior to their formal exam.

  • Pupils will be assessed via a summative assessment every half term, to assess understanding of topics taught and inform planning for the next half term.

  • Assessment for learning during lesson, as well as using Hegarty Maths for homework, will allow teachers to assess pupil understanding on a more daily basis and inform short term planning

  • A blended learning approach is used to promote and develop independent learning in pupils. We use Microsoft TEAMs to set home-learning activities and to consolidate knowledge through the use of knowledge organisers, which are linked to the schemes of learning. Teachers routinely feedback on pupil progress.


Subject Enrichment:

In Mathematics, we believe that mathematical teaching should focus on the needs of the pupil, engraining enrichment activities into the heart of the curriculum itself, rather than being a bolt on. Our pupils are exposed to a variety of tasks, challenges and scenarios developed to enrich their learning and personal development.


  • Activities embedded into each lesson which provoke mathematical thinking

  • Clear links between lesson content and relevance to every-day life. This works to prevent pupils from becoming disenfranchised with mathematics

  • Cultural capital tasks which personalise and tailor the learning to the child, allowing them to develop critical thinking and strengthen their subject knowledge

  • Pupils discuss mathematics influences from outside of the western world, such as the Bengali Number System

  • Pupils are exposed to key, historical and prominent mathematic figures, such as Pythagoras

  • When studying data, pupils will be given the chance to apply this to how society balances data collection and will further develop their critical thinking on this topic as they discuss and analyse followers across social media platforms.  


Subject Impact

  • Ensure the curriculum provides a varied and rich learning opportunity for all pupils from year 7 to year 11. Pupils revisit key concepts throughout their time at Smithills School. Pupils access different questions and problems of increasing difficulty to cement understanding and develop recall.

  • Provide pupils with an education which allows them to develop into outstanding citizens, armed with the knowledge required to actively engage with their local community, UK and beyond.

  • Allow pupils the opportunity to build resilience through problem solving, and enable pupils to apply this resilience and character to the outside world as they navigate into adulthood

  • Provide pupils with a range of vocabulary to allow them to navigate through the real world. Giving pupils an understanding of financial matters, which are necessary for all adults. Allowing pupils to make links between topics taught, vocabulary used and future careers.


The study of mathematics will allow pupils to develop a thirst for knowledge, and an ability to solve problems, not just related to maths, but related to the outside world.

Curriculum Map

Maths Map - Support.png
Maths Map - Core.png
Maths Map - Higher.png

Knowledge and Skills

Red Bold = Support only, Italics = Higher only


Year 7:


Pupils will develop their knowledge of:

  • Number

  • Algebra

  • Geometry and Measures

  • Statistics

  • Ratio and Proportion

  • Probability


Pupils will develop their skills in:

  • Understanding the requirement of calculations, place value and properties of number needed to access the full five-year curriculum.

  • Analysing and displaying data.

  • Key mathematical vocabulary and the language of algebra and their understanding of algebraic manipulation.

  • Number rules and their relationships.

  • Solve equations using balancing method and explore trial and improvement methods for non-linear equations.

  • How to calculate with fractions and mixed number. 

  • Understanding of the relationship between fractions, decimals and percentages.  Students will convert between fractions, decimals and percentages.

  • Decimals and estimation including situations involving finance and measures.

  • Fractions and their relationship with decimals and percentages.

  • The language of probability and how to calculate simple probabilities.

  • Angle rules, and how to apply these to find missing angles and develop an understanding of angle reasoning for parallel lines.

  • Shape, symmetry, area and perimeter.

  • How to write ratios and use direct proportion to solve basic problems and Cover proportional reasoning in context, for example recipes.

  • Converting between imperial and metric units. 

  • Use sequences to extend their learning to basic straight-line graphs.

  • Congruent shapes and the four mathematical transformations.

  • The surface area and volume of 3D Shapes.

  • Finding the nth term rule for sequences.

  • Recapping coordinates and use substitution to calculate coordinates.


Year 8:


Pupils will develop their knowledge of:

  • Number

  • Algebra

  • Geometry and Measures

  • Statistics

  • Ratio and Proportion

  • Probability


Pupils will develop their skills in:

  • Calculating with negative numbers, powers and roots. 

  • Calculating with larger numbers, going on to use multiplicative reasoning.

  • Calculating using decimals.

  • More complex sums involving multiples and factors.

  • The properties of numbers to include hcf and lcm

  • Venn diagrams to find the HCF and LCM.

  • Laws of indices understanding of powers of 10.

  • Rounding to significant figures and use this to estimate calculations.

  • Area and Volume of shapes.

  • Understanding of basic angle facts.

  • Interpreting data

  • Circumference and area of circles.

  • Using the Pythagoras’ Theorem.

  • Interpreting and displaying data using more complex charts.

  • All four types of transformations and combined transformations.

  • Understanding and applying the different approaches when solving equations.

  • Conversion graphs and distance/time graphs.

  • How to use geometrical equipment to draw accurate drawings.

  • Solving more complex geometrical problems.

  • Generating and writing sequences.

  • The equation of straight lines.

  • The different methods of calculating probabilities and the probabilities of two events which require the use of diagrams.

  • Ratio to maps and scale drawings and bearing.


Year 9

Pupils will develop their knowledge of:

  • Number

  • Algebra

  • Geometry and Measures

  • Statistics

  • Ratio and Proportion

  • Probability


Pupils will develop their skills in:

  • Calculations, place value and properties of number needed to access the full GCSE curriculum.

  • Developing an understanding of standard form, negative and fractional indices, with an introduction to simplifying surds.

  • The manipulation techniques for expressions and formulae.

  • Quadratic expressions and rearranging formulae. 

  • Build on previous years understanding of solving equations.

  • Data interpretation and data display.

  • Converting between fractions, decimals, and percentages.

  • Demonstrating a link between all four areas to support the understanding when applying to problem solving.

  • Calculating with fractions and understanding examples used to explore financial literacy.

  • Solving equations, including inequalities.

  • reasoning and use of mathematical language when applying knowledge of angle facts.


Year 10

Pupils will develop their knowledge of:

  • Number

  • Algebra

  • Geometry and Measures

  • Statistics

  • Ratio and Proportion

  • Probability


Pupils will develop their skills in

  • Comparing averages using calculations and looking at continuous data

  • Understanding of how to compare averages using calculations and looking at continuous data

  • Their knowledge of formulae for the area of shapes and go on to surface area and volume of prisms

  • Introduce spheres, cones and pyramids.

  • The learning of substitution to generate the coordinates to plot graphs. 

  • The different methods that can be used to solve quadratic equations

  • Applying the learning of substitution to generate the coordinates, to plot graphs

  • All four types of transformations covered, including to be able to describe transformations. The key point is to embed a combination of transformations

  • Growth and decay, compound measures and a further understand of direct and inverse proportion

  • Ratio and proportion

  • Introduction of ratio and proportion

  • Further developed to include Venn diagrams and tree diagrams. 

  • The laws of indices including the use of brackets.

  • Congruent and similar shapes. 

  • Reasoning and use of mathematical language when applying knowledge, some of which will have been covered in KS3.

  • Students gain an understanding of the key features of the three trigonometric graphs, developing their understanding of non, right-angled triangles.

  • Trigonometry in 3D is also introduced along with transformation of trigonometric graphs.

  • Using place value to help with converting units


Year 11


Pupils will develop their knowledge of:

  • Number

  • Algebra

  • Geometry and Measures

  • Statistics

  • Ratio and Proportion

  • Probability


Pupils will develop their skills in:

  • Scale drawing and maps which links with the previous learning on ratio.

  • 3D isometric drawing and representations of 3D solids. 

  • The relationship between lengths and angles in right angled triangles.

  • Rediscover and understand the Pythagoras’ theorem. 

  • Calculate circumference and area of circles. 

  • Compound shapes., including finding the surface area and volume of cylinders.

  • Proportional reasoning to answer problems on similarity.  

  • Students will learn to add and subtract simple vectors.

  • Explore similar shapes to solve angle problems.

  • Understanding of vectors to solve geometrical problems in both 2D and 3D.

  • Their understanding of congruence.

  • Drawing linear/quadratic graphs to cubic and reciprocal graphs, extending towards solving simultaneous equations graphically.

  • Algebraic Proof.

  • Advanced algebra for example more complex rearrangement of formulae.

  • Understanding of proportion is developed, the letter K (constant) is introduced and students create equations to describe a proportional relationship.

  • Exponential functions are introduced together with translation of graphs.

  • Exam strategies and answer structures in preparation for the summer exams.

Contact Head of Department:

Mrs Adam -