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 9

Learners in Year 9 continue to build on the key themes in algebra, geometry and statistics. Their learning is extended to intermediate topics such as conditional probability, trigonometry and quadratic equations.

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.

Linear simultaneous equations are an important part of mathematical reasoning. The skills and knowledge required to solve equations like these are invaluable for technical and everyday contexts. The first unit focuses on the algebraic representation of linear equations and extends prior knowledge about equations into expressions and equations with two variables. In the second part of the module, learners revise linear graphs and represent systems of linear equations graphically, linking the work earlier in the unit to their work on linear graphs in Year 8.

In the spring, learners will consolidate and extend their knowledge of the geometry of triangles. Learners explore construction and consider its relationship to congruence. A key part of this unit is determining the relationship between the minimum conditions for congruence in and the construction of triangles. Learners then study Pythagoras’ theorem, including some proofs and demonstrations, before moving onto similarity and trigonometry. These units are rich with opportunities to improve visual-spatial reasoning, problem-solving and reasoning skills. There are also plenty of opportunities to link to careers and realistic situations.

Learners dedicate one half-term to studying the features of quadratic expressions, equations and functions. This topic is a foundational topic in KS4 and KS5 mathematics. The module begins by examining quadratic expressions and how they are represented on a graph. The graph is then used to aid learners reason about the behaviour of a quadratic function. The graph is used to help learners interpret the meaning of a solution and link it to prior learning about equations. The module ends with factorising, solving and sketching quadratics.

In this module, learners extend their understanding of the number system into the realm of the logarithmic scale. Gaining an appreciation of exponential relationships and their differences to linear relationships is vital for further scientific study, as well as understanding exponential relationships in everyday life. In the first unit learners explore indices further and extend their understanding to include indices other than positive whole numbers. This is so learners are able to appreciate standard form and use it to describe very large and small numbers. Next, learners explore growth and decay in the context of repeated percentage change. This is linked to exponential relationships more broadly.

Knowledge Organisers