Mathematics

In the autumn term, learners cover two strands of content:

• number, and
• multiplicative reasoning.

Whilst these topics revisit concepts from Key Stage 3, the focus is on reasoning and understanding notation to support the solution of increasingly complex problems that include information presented in a variety of forms.

The number strand allows opportunities for learners to revise and build on KS3 content for calculation. This is covered mostly through problems, particularly multi-step problems in preparation for GCSE. Learners develop their knowledge of numbers through introduction to surds and quadratic sequences. Consolidation of these two topics takes place at the end of the autumn term when learners focus on understanding powers generally and in particular in standard form. Negative and fractional indices are explored in detail. 

The multiplicative reasoning strand builds on KS3 work on ratio and fractions, highlighting similarities and differences and links to other areas of mathematics, including both algebra and geometry. The bar model is a key tool used to support representing and solving these problems. 

Although percentages are not specifically mentioned in the KS4 national curriculum, they feature heavily in GCSE papers and this block builds on the understanding gained in KS3. Calculator methods are encouraged throughout and are essential for repeated percentage change/growth and decay problems. Use of financial contexts is central to this block, helping students to maintain familiarity with the vocabulary they are likely to use beyond school.

The focus for the spring term is algebra.

Learners develop existing methods for manipulating expressions and solving equations, extending their skills to quadratic and simultaneous equations.

Looking at the difference between equations and inequalities, learners will establish the difference between a solution and a solution set; they will also explore how number lines and graphs can be used to represent the solutions to inequalities. As well as solving equations, emphasis is placed on forming equations from given information. 

Learners then move on to the solution of simultaneous equations by both algebraic and graphical methods. The method of substitution will be dealt with before elimination, considering the substitution of a known value and then an expression. With elimination, all types of equations will be considered, covering simple addition and subtraction up to complex pairs where both equations need adjustment. Links will be made to graphs and forming the equations will be explored as well as solving them. The higher strand will include the solution of a pair of simultaneous equations where one is a quadratic, dealing with factorisation only at this stage. 

The remainder of Year 10 is split into two strands:

• similarity; and
• statistics and probability.

Building on their experience of enlargement and similarity in previous years, this unit extends learners‘ experiences and looks more formally at dealing with topics such as similar triangles. Trigonometry is introduced as a special case of similarity within right-angled triangles. Emphasis is placed throughout the steps on linking the trig functions to ratios, rather than just functions.

In statistics, learners build on KS3 work on the collection, representation and use of summary statistics to describe data. Much of the content is familiar, both from previous study within and beyond mathematics (including Geography and Science) and from everyday life. The steps have been chosen to balance consolidation of existing knowledge with extending and deepening, particularly in terms of interpretation of results and evaluating and critiquing statistical methods and diagrams. The emphasis with these topics is on interpretation (particularly in making comparisons) and not just construction. 

The probability aspect of the summer term also builds on KS3 knowledge and provides a good context in which to revisit fraction arithmetic and conversion between fractions, decimals and percentages. Tables and Venn diagrams are revisited and understanding and use of tree diagrams is developed at both tiers, with conditional probability being a key focus for higher tier students.