Mathematics
Key Stage 3 Overview
The HHS Mathematics department follows a tailored version of a mastery scheme of work. The curriculum is a spiral curriculum, which means prior learning is revisited and extended year upon year.

Year 7 begins with an examination of the number system, followed by preparing learners for generalising with algebra. The themes in the autumn are built upon later in the spring, and the year ends with an in depth study of fractions.

In Year 8, learners begin by studying percentages before revisiting and extending the algebra learned 6 months prior. Learners then study a carefully sequenced set of topics to understand how algebra relates to the coordinate system. The end of the year applies some of this knowledge to geometry and statistics.

In Year 9, learners build on their learning in Year 8 by studying probability, more challenging algebra, and trigonometry. The topics in the summer, quadratic equations and exponential growth, are designed to draw on themes from the whole of KS3.
Learning Journey & Sequencing Rationale
Year 7
Year 7 begins by asking students to think more deeply about the number system, and the structures of numbers in general. Learners experience a range of number and numeral systems to develop their understanding of the base 10 place value system.Learners also explore the axioms of number and which operations they can be applied to. Generalisations such as algebra are introduced to communicate and explain mathematical ideas. Learners will then be introduced to factors, multiples and important sets of numbers such as prime numbers, square numbers and cube numbers. Once the fundamental concepts have been introduced students are given the opportunity to develop their understanding, conjecture, problem solve and generalise in a series of structured tasks. After this has been secured, learners develop their algebraic reasoning, focusing on directed numbers and using algebraic notation. Finally, learners study prime factorisation and use is it to determine the highest common factor and lowest common multiple.
Later in the spring, learners are exposed to a range of new knowledge and skills in 2D geometry, which will provide the foundation for further work in Years 8 and 9. This work also provides more contexts for students to practice the algebraic reasoning developed in Autumn term. Learners work with angles and revise facts involving angles. Learners explore and clarify definitions of parallel lines, perpendicular lines, and polygons. Learners are encouraged to conjecture and prove. Generalisations are expressed algebraically, and learners set up and solve equations involving special types of triangle and quadrilaterals.
In the summer learners will construct/draw triangles using initial information and conversely will deduce properties of triangles from completed constructions. The concept of area as a measurable quantity is introduced, and every opportunity is used to explore prior learning about arrays and formulae.
Lastly, at the end of the year, learners formally explore fractions and their relation to decimals. The extension of the number system to rational numbers is a highly important stage in learners’ mathematical development. Fractions are considered simultaneously as a number, as a way of expressing division, as a continuous partwhole model and as a discrete part of a larger set. Students find fractions of amounts by considering the multiplication of an amount by a fraction. Bar models, line models and rectangular representations are used heavily throughout to represent the fractional amounts.
autumn 1  the number system
Skills 

Knowledge 

Rationale 
This module is fundamentally about asking students to think more deeply about the number system, and the structures of numbers in general. The module begins with the ‘Numbers and Numerals’ unit, in which learners experience a range of number and numeral systems to develop their understanding of the base 10 place value system from primary years. In ‘Axioms and Arrays,’ learners develop their understanding of different models for multiplication and division. Learners also explore the axioms of number and which operations they can be applied to. Generalisations such as algebra are introduced to communicate and explain mathematical ideas. Learners will then be introduced to factors, multiples and important sets of numbers such as prime numbers, square numbers and cube numbers. Once the fundamental concepts have been introduced students are given the opportunity to develop their understanding, conjecture, problem solve and generalise in a series of structured tasks. Lastly, learners develop an explicit understanding of the order of operations based on the equal priority of addition with subtraction and multiplication with division. They will understand the higher priority of multiplication with division in written calculations and understand the use of brackets and vincula to manipulate this priority order. 
autumn 2  expressionS and equations
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Knowledge 

Rationale 
This module provides learners with the opportunity to develop their algebraic reasoning, while extending their knowledge of the number system. It provides a thorough introduction to the key concepts and procedures in algebra that underpin the rest of secondary mathematics. This first unit focuses on directed numbers. It provides opportunities to interpret negative quantities in practical situations. Students will have experienced negative numbers in context from primary education. Understanding is developed by placing number on a number line and using the number line as a representation for addition and subtraction of negative numbers as well as a scaling model for multiplying and dividing. In the second unit, ‘expressions, equations and inequalities,’ students use algebraic notation and make links to work on the basic properties of arithmetic established in the previous module. Once familiarity with this notation system has been developed, students will explore representations of equality. Finally, learners will explore counting strategies in growing dot patterns, supporting the later study of sequences 
spring 1  2D Geometry
Skills 

Knowledge 

Rationale 
This module has two purposes. First is to expose learners to a range of new knowledge and skills in 2D geometry, which will provide the foundation for further work in Years 8 and 9. Second, to provide more contexts for students to practice the algebraic reasoning developed in Autumn term. The first unit covers angles. Learners describe, classify and identify types of angles using clear vocabulary, and measure and draw angles accurately. Learners revise facts involving angles from experiences in primary school. Learners explore and clarify definitions of parallel lines and perpendicular lines, and use rules around corresponding, alternate and cointerior angles. Students being to formulate equations to show relationships between angles using the angle facts. Next learners, study the geometric properties of polygons before focusing more closely on triangles and quadrilaterals. Learners are encouraged to conjecture and prove. Special types of triangles and quadrilaterals are defined. Generalisations are expressed algebraically, and learners set up and solve equations involving special types of triangle and quadrilaterals. Lastly, students construct triangles and quadrilaterals. The unit begins by introducing the anatomy of a circle. The minimum conditions for constructing triangles are explored and thereby informally introducing congruence. Students will construct/draw triangles using initial information and conversely will deduce properties of triangles from completed constructions. 
spring 2  the cartesian plane
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Rationale 
In this module, learners start to apply what they have learned about algebra and geometry in the Cartesian grid. First learners study coordinates in all four quadrants. Learners will be familiar with coordinates from work at primary school and in other subjects. The tasks in this unit will give learners opportunities to apply their understanding from previous units including negative numbers and geometric properties of triangles and quadrilaterals. Next, the concept of area as a measurable quantity is introduced. This begins by revisiting arrays. Reasoning about calculating the area of shapes is built up by decomposing shapes and connecting to existing knowledge. The generalised expressions for finding the area of shapes are used to introduce rearranging formulae. Lastly, learners are expected to consider how transformations acting on an object produce different images. Reflection and rotation are introduced through previous experience of line and rotational symmetry. There is a focus on language and consideration of the amount of information required to perform each transformation. The transformations are sorted by whether they result in a congruent image. This is the foundation for exploring similarity and trigonometry later. 
summer 1  fractions
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Rationale 
In this module learners formally explore fractions and their relation to decimals. The extension of the number system to rational numbers is a highly important stage in learners’ mathematical development. To begin, learners revisit the composition of numbers developed in unit 3. The uniqueness of the prime number decomposition is explored. This is used to show properties of particular numbers e.g. if a number is a square or cube number and therefore identify square and cube roots. Prime factorisation is used to determine the highest common factor and lowest common multiple. During this unit, indices are used for powers greater than 2 for the first time. The next two units are dedicated to fractions, building on knowledge of fractions from KS2. Unit 14 has learnings exploring multiple interpretations of fractions. Fractions are considered simultaneously as a number, as a way of expressing division, as a continuous partwhole model and as a discrete part of a larger set. The notion of a percentage is dealt with briefly. Learners compare two or more fractions in a set and order them by their size. In Unit 15, learners extend their understanding of applying the four operations to noninteger values. Students find fractions of amounts by considering the multiplication of an amount by a fraction. Bar models, line models and rectangular representations are used heavily throughout to represent the fractional amounts. Teachers should encourage students to use these to help them solve and demonstrate understanding of the problems even where not stated explicitly. 
summer 2  ratio and proportion
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Knowledge 

Rationale 
In this module, learners extend their understanding of fractions to percentages and ratio. This module forms an important bridge towards proportional reasoning. Unit 16 explores ratio notation, language, representations and contexts. The ratio notation of 𝑎: 𝑏 is unpicked using bar models. Learners work on a series of problems that require them to use all of these relationships. Bar models, double number lines and line graphs are used throughout this unit to help develop and expand learners’ conceptual understanding of ratio. In the final unit of Year 7, learners work with percentages as another representation of ratios and fractions. The different ways of interpreting fractions are again referenced. The unit progresses to the use of percentages to compare quantities and find a given percentage of a quantity. Learners then increase and decrease quantities by a given percentage and find the original quantity given a percentage of the quantity. Bar models provide an excellent representation of percentage change and equivalence between amounts, hence are used throughout the unit to deepen understanding. 
knowledge OrganiserS
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 ALevel 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.
Maths mastery intro