Mathematics
Key stage 4 overview
At Key Stage 4, HHS Mathematics department follows the White Rose Year 10 and 11 schemes of work. The schemes of work are adapted for each class to allow everyone to achieve the highest possible grades. The curriculum interweaves topics from previous years into every lesson to encourage regular retrieval of important knowledge.
In Years 10 and 11 every learner will have two maths teachers. These two teachers will teach topics that are different enough for there to be no overlap, but use complimentary mathematical habits and skills.

In Year 10, learners begin by developing their algebraic skills, solving a variety of equations and inequalities. They develop multiple ways to represent the solutions to these equations. At the same time, learners learn how to use trigonometry to solve rightangled triangles, and triangles of any size. In the Spring learners are taught how to solve problems using ratio and proportion, and geometry. Finally, in the summer, learners study statistics, and focus on how to solve numerical problems without a calculator.

In Year 11, learners start by studying graphs and algebraic techniques, building on and refreshing the skills gained in Autumn of Year 10. The Spring is spent on revising topics from Key Stage 3 and 4, with a focus on reasoning and mathematical communication. This develops learners’ ability to communicate while preparing them adequately for their exams in the summer.
Note on revision strategies:
From the Spring of Year 11, learners are supported to revise for their exams in a more targeted way. We use a combination of past exam papers in class and the virtual exam folder on pinpointlearning.co.uk to provide targeted exam practice. This takes place alongside the curriculum delivered in class.
GCSE MATHEMATICS TERM OVERVIEWS
Year 10 Autumn
Autumn (Teacher A): Similarity 


Skills 

Knowledge 

Rationale 
Building on their experience of enlargement and similarity in previous years, this unit extends students‘ experiences and looks more formally at dealing with topics such as similar triangles. ICT is used to demonstrate what changes and what stays the same when manipulating similar shapes. Parallel line angle rules are revisited to support establishment of similarity. Congruency is reintroduced through considering what information is needed to produce a unique triangle. Higher level content extends enlargement to explore negative scale factors, and also looks at establishing that a pair of triangles are congruent through formal proof. Trigonometry is then reintroduced as a special case of similarity within rightangled triangles. Emphasis is placed throughout the steps on linking the functions to ratios, rather than just functions. This key topic is introduced early in Year 10 to allow regular revisiting e.g. when looking at bearings. For the Higher tier, calculation with trigonometry is covered now and graphical representation is covered in Year 11. 
Autumn (Teacher B): Developing algebra 

Skills 

Knowledge 

Rationale 
Students will have covered both equations and inequalities at KS3,and this unit offers the opportunity to revisit and reinforce standard techniques and deepen their understanding. Looking at the difference between equations and inequalities, students 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 needs to be placed on forming equations from given information. This provides an excellent opportunity to revisit other topics in the curriculum such as angles on a straight line/in shapes/parallel lines, probability, area and perimeter etc. Factorising quadratics to solve equations is covered in the Higher strand here and is revisited in the Core strand in Year 11. Students 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, again dealing with factorisation only at this stage. 
Year 10 Spring
Spring (Teacher A): Geometry 


Skills 

Knowledge 

Rationale 
As well as the formal introduction of bearings, this block provides a great opportunity to revisit other materials and make links across the mathematics curriculum. Accurate drawing and use of scales will be vital, as is the use of parallel line angles rules; all of these have been covered at KS3. Students will also reinforce their understanding of trigonometry and Pythagoras from earlier this year, applying their skills in another context as well as using mathematics to model reallife situations. The formulae for arc length and sector area are built up from students’ understanding of fractions They are also introduced to the formulae for surface area and volume of spheres and cones; here higher students can enhance their knowledge and skills of working with area and volume ratios. Higher tier students are also introduced to four of the circle theorems; the remaining theorems will be introduced in Year 11 when these four will be revisited. Students will have met vectors to describe translations during KS3 This will be revisited and used as the basis for looking more formally at vectors, discovering the meaning of − 𝒂 compared to 𝒂 to make sense of operations such as addition, subtraction and multiplication of vectors. This will connect to exploring ‘journeys’ within shapes linking the notation 𝐴𝐵 with 𝒃 − 𝒂 etc. Higher tier students will then use this understanding as the basis for developing geometric proof, making links to their knowledge of properties of shape and parallel lines. 
Spring (Teacher B): Proportions & proportional change 

Skills 

Knowledge 

Rationale 
This block 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 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 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 unlikely to use outside school. This block also builds on KS3 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. 
Year 10 Summer
Summer (Teacher A): Delving into data & expressions 


Skills 

Knowledge 

Rationale 
This block builds 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 criticising statistical methods and diagrams. For students following Higher tier, there is additional content relating to continuous data including histograms, cumulative frequency diagrams, box plots and associated measures such as quartiles and the interquartile range. Again the emphasis with these topics should be on interpretation (particularly in making comparisons) and not just construction. The second part of this module builds on the Autumn term learning of equations and inequalities, providing revision and reinforcement for Foundation tier students and an introduction to algebraic fractions for those following the Higher tier. This also allows all students to revise fraction arithmetic to keep their skills sharp. Algebraic argument and proof are considered, starting with identities and moving on to consider generalised number. 
Summer (Teacher B): Using number 

Skills 

Knowledge 

Rationale 
This block revises and builds on KS3 content for calculation. Mental methods and using number sense are to be encouraged alongside the formal methods for all four operations with integers, decimals and fractions. Where possible this should be covered through problems, particularly multistep problems in preparation for GCSE. The limits of accuracy of truncation are explored and compared to rounding, and Higher tier students will look at all aspects of irrational numbers including surds. Learners then review prime factorisation and associated number content such as HCF and LCM. Sequences is extended for Higher tier to include surds and finding the formula for a quadratic sequence. Finally, learners consolidate the previous two blocks focusing on understanding powers generally, and in particular in standard form. Negative and fractional indices are explored in detail. Again, much of this content will be familiar from KS3, particularly for Higher tier students, so this consolidation material may be covered in less than two weeks allowing more time for general noncalculator and problemsolving practice. To consolidate the index laws, these can be revisited in the next block when simplifying algebraic expressions. 