Mathematics

As we have up to sixty feeder schools, we begin Year 7 recapping non-calculator numeracy skills which allows us to see how students apply their knowledge and gives the opportunity to address any gaps in skills and knowledge without covering too much content. We then move onto drawing, measuring, and calculating with angles and lines, so that those students who find number work challenging are able to succeed. Moving on, we then look at telling the time and calculating time differences using both analogue and digital clocks, ready for our students using this in both languages and in science.

We then return to numbers and begin looking at different types of number, encouraging students to spot patterns with the different types including negative and prime numbers, multiples and factors. This in turn helps to strengthen times tables and problem-solving skills before we switch from numbers to letters and introduce algebra and the writing of expressions, collecting terms, expanding brackets, and reusing their other numeracy skills and knowledge of order of operation for substitution. Moving on, we come back to number patterns and look at different types of sequence, writing rules and using either our newly acquired or revisited algebraic skills to write nth terms.  We then progress to rounding to whole numbers, decimal places, and introducing the idea of significant figures, both in maths to estimate calculations, and their use within the wider world to describe very large and very small numbers. Plotting and sketching is the final topic before the end of the Autumn break; here we apply all the skills covered in the term to not only plot coordinates in all quadrants but also draw straight line graphs using equations.

Spring term begins with fractions and in some cases, where needed, going back to the basics and identifying what a fraction is, drawing them, simplifying and equivalence. Once these are concrete, we begin applying the four rules. Transformation looks at reflections, translations, rotations simply and on axis using the graphical skills learnt last term.  Decimals help us to strengthen numeracy skills and to make links with dealing with money and revisiting rounding. We then move onto collecting and interpreting data, making links with real life and other subject areas. Here again we use our skills from previously learnt topics to make comparisons with multiple sets of data. At this point we complete some more work on algebraic skills, including recapping the topics covered earlier in the year before beginning to solve equations. 

In the Summer term we bring together our knowledge of fractions and decimals to convert between them before making links to percentages, where they use them to calculate percentages of amounts, increasing and decreasing by percentages and using these skills in the real world.  Probability looks at the chance of real-world events occurring and linking these to a number line and a probability scale. Again, using fractional skills to calculate the expected probability of events occurring and not happening. Area and perimeter involve looking at shapes and their properties before calculating areas of rectangle, parallelograms, triangles, trapeziums, circles, and compound shapes. Ratio again brings in some more number work making links to fractions before cancelling, comparing amounts using ratios and solving problems. The final topic in Year 7 is displaying data, where we use our previous knowledge to draw various charts including pie, Venn diagrams and scatter graphs.

Years 8 and 9 build on the Year 7 curriculum and they follow a similar path, but each topic covered goes into more detail and the level of challenge increases.

In Year 8 we start looking, in more detail, at number properties and at other types of numbers such as triangular numbers and completing more difficult calculations with negative numbers. Geometry builds on the angle facts learnt in Year 7 but looks at angles in and around polygons. We also use our angle measure and drawing skills to draw bearing diagrams before using other angle facts to solve problems. We then look at algebra, recapping skills before linking equations and substitution to other areas within mathematics before we rearrange formulae to solve problems. Within approximation we again recap previously learnt skills before we look at upper and lower bounds and what these can do to calculations. Percentages develops further to using multipliers to calculate percentage increases and decreases, calculating reverse percentages, and calculating compound interest and again linking to real life applications.  Sequences again use their number skills, and all learners calculate and use the nth term of linear sequences. Collecting and interpreting data recap the work covered in Year 7 but looks at the average calculations with group data and solving problems and using quartiles and box plot diagrams to compare data.

In the Spring term, we start with algebra, solving more complex equations than in Year 7 and introduce the idea of a quadratic equation, this then links to plotting graphs including quadratic and, in some cases, cubic graphs. We then move onto fractions recapping Year 7 skills and using them to solve problems. Next, we look at transformations using skills from graphing to reflect, translate, rotate and enlarge shapes on axis and identifying transformations. The final topic this term is ratio again we recap Year 7 skills and use them to solve more complex problems.

At the beginning of the summer term we revisit probability but look at calculating probabilities of more than one event occurring so using our knowledge of fraction calculations. We recap basic areas before solving problems involving areas and calculating surface area and volumes of prisms. We also introduce Pythagoras’s theorem and calculate side lengths and use this with area and volume calculations. We then do some decimal consolidation with and without a calculator. Our next topic involves using our drawing and measure skills to construct triangles, bisectors and linking these to loci. The final topic of Year 8 is displaying data, again this recaps some of the topics covered in Year 7 and develops Venn diagram notation.

Year 9 builds on both the Years 7 and 8 topics developing them further ready to start the GCSE course after Spring term. We begin by doing a quick recap of percentages and introduce simple interest and compare it to compound interest. We then review fractions and the four rules before moving onto using these skills with algebraic fractions and changing recurring decimals to fractions using algebra. Estimation and rounding are reviewed now including calculations with significant figures. We then introduce index laws before moving on and reviewing expanding and factorising. During transformations we review all types but introduce the idea of negative scale factors with enlargement and make links to similar shapes including scale factors for area and volume. We then move onto drawing graphs recapping the work done in Years 7 and 8, including noting turning points and lines of symmetry of quadratic graphs and drawing reciprocal graphs. Next, we recap sequences and find the nth term of quadratic sequences. We then revisit averages taking in moving averages and time series and their place in the real world. The final topic this term is construction and loci where we review constructions, loci, and scale drawings.

The Spring term starts with areas and volumes are reviewed again with the addition of spheres, cones, and compound 3D shapes. Followed by a recap of probability before using Venn diagrams and probability trees. We continue with our algebra and solve problems that require us to expand brackets, before we look at using these skills to solve equations that involve inequalities, including using a number line and graphically.  We then review Pythagoras’ Theorem before we introduce and start using trigonometry. The final topic in key stage three brings together their algebraic and graphical skills when we solve simultaneous equations.

At the beginning of the summer term all Year 9 students do one of the three levelled baseline tests produced by Edexcel but adapted to fit the current curriculum at The King’s (The Cathedral) School. This allows us to determine the best level of entry at GCSE for each student, this is reviewed in October of Year 10 and again after mock exams in Year 11 as the content of the two tiers differs greatly. Once testing has been completed students then begin the Edexcel GCSE course either following Higher or Foundation; usually 30 students follow the Foundation course, and all others follow the Higher one.

In Year 10 both tiers continue the spiral curriculum started in Key Stage 3 and builds upon previous learning. Each topic covered starts simply supporting prior knowledge and goes on to deepen understanding of key concepts before extending these further. The course aims to give students the appropriate mathematical skills, develop fluent knowledge and understanding of mathematical methods and concepts to help them progress to a full range of courses in further and higher education and in the wider world. Students will also learn to select and apply mathematical techniques to solve problems, reason mathematically, make deductions and inference before drawing conclusions.

Key Stage 5 will offer options to those students who wish to study mathematics beyond GCSE. Edexcel A-Level Maths is taken by approximately 70 students, who gain a grade 7 or above at GSCE. The Year 12 specification broadly covers the Higher GCSE content but builds and strengthens prior knowledge before developing further and introducing new concepts. We have ordered the topics to allow foundations to be strengthened before they are needed with more difficult topics. The aim of the course is that students understand mathematics and mathematical processes in a way that promotes confidence, fosters enjoyment, and provides a strong foundation for progress to further study. It can extend their range of mathematical skills and techniques to help students understand coherence and progression in mathematics and how different areas of mathematics are connected. At appropriate times in the curriculum, we signpost mathematics in other fields of study and make our students aware of the relevance of mathematics to the world of work and to situations in society in general.  Within the curriculum we will construct mathematical proofs and encourage students to use their mathematical skills and techniques to solve challenging problems that require them to decide on the solution strategy.

Using skills learnt in Key Stages 3 and 4 students draw diagrams and sketch graphs to help explore mathematical situations and interpret solutions. It is our aim and that of Edexcel that all students take increasing responsibility for their own learning and the evaluation of their own mathematical development not only preparing them for the future, but to create a passion for maths beyond the classroom.

Our second option at A-Level is Edexcel Further Mathematics. This is for those students who have achieved a grade 8 and above at GCSE and are passionate about mathematics, with the idea of studying maths beyond school. During Year 12 the students study the entirety of the full A-Level course and sit the examinations for these at the end of Year 12. By doing this all the concepts that are required for Further Maths have been covered and any misconception has already been addressed. Problem solving, proof and mathematical modelling will also be assessed in further mathematics in the context of the wider knowledge which students taking A-Level Further Mathematics will have studied.