# 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.

### Year 8

Learners begin Year 8 by considering percentages as another representation of fractions. Bar models provide an excellent representation of percentage change and equivalence between amounts, hence are used throughout the unit to deepen understanding. As in Year 7, algebra is used to generalise and extend mathematical thinking. Next, sequences are derived from the same geometric patterns and other contexts. Different types of sequences are explored including linear, non-linear, arithmetic and geometric. In Year 7 students explored the nature of equality and solved equations with one unknown where the unknown appeared on one side. In Unit 3 learners formalise methods for solving equations. Learners use inverse operations to transform equations with one and two steps and encounter equations involving a single bracket. Inequalities are then derived from the same contexts that were met in the previous unit.

In the second half-term learners prepare to study linear graphs. This begins by learning about ratios. Bar models, double number lines and graphs are used to connect ratio notation with prior learning. 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. 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. This is the foundation for exploring similarity and trigonometry later.

Throughout Year 7, learners’ proportional reasoning was developed through experiences in multiplication, division and fractions. Learners study linear graphs and real life graphs and consider the functional relationships between different variables, including piecewise functions. Next, learners examine proportional relationships in familiar contexts before looking at the meaning of direct proportion in abstract. Students are encouraged to compare different approaches to solving problems involving direct proportion.

With a secure foundation in basic algebra, learners will be ready to tackle problems in geometry and statistics. In the late spring learners return to angles by considering the angle sum theorem in polygons, and bearings. Learners learn about the properties of circles and mensuration of 3D shapes. Learners will be challenged to think carefully about proof and develop their spatial reasoning. In the first unit of the last half-term, learners study univariate data. The unit presents a series of inquiry questions and students make hypotheses in relation to these. Each of the statistical methods taught in this unit are used to construct an argument for or against some given hypotheses. In the second unit of the half-term, students extend their understanding of statistical diagrams and measures to bivariate data. The difference between correlation and causation are introduced and the idea of an explanatory variable.

## 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 A-Level 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.