In year 7 students start by consolidating key number skills from Primary school; initially they do this via an introduction to algebra. The discovery of variables and expressions and manipulation of terms gives them important practice of addition, subtraction and negative numbers. This ensures students have a sense of progress whilst delivering arithmetic skills. As they progress through the Autumn they develop their knowledge of fractions and build in confidence working with mixed numbers, decimals and percentages interchangeably.
Moving into the Spring term students will have their first taste of geometry, specifically area and volume of polygons and prisms and here they can put number and algebra skills to use in context. They will also learn about the properties of polygons and be given key definitions that will be used from year 8 onwards. A unit on conversions between different metric units of measure adds a layer of depth to their work with shapes. In this term we will also begin to work with percentages in calculations, focussing specifically on calculations using written non calculator methods.
In the Summer term we return to algebra skills, investigating patterns and sequences and learning to solve simple linear equations. Students will then benefit from plotting graphs from these sequences and equations so they have a visual representation of the relationships they have been studying. This term also includes the introduction of ratio and scale which can be applied to the geometry work from Spring term. The year finishes with an introduction to statistics in which students will learn about different types of data and how it can be represented and analysed. Throughout the year they will have applied simple averages to number problems and will now look to calculate averages from data presented in a table.
In year 7 students will also study some elements of computing, including binary numbers and algorithms and flowcharts.
In Year 8 we develop the key ideas from the introduction to algebra in Year 7 and show them how to apply these ideas to quadratic expressions, including looking at the difference of two squares and simple rearranging of formulae. Looking at the number strand, students build on their knowledge of square and cube numbers by looking at indices laws and the concept of surds and irrational numbers. They also are introduced to standard form as a way of writing and working with very large and very small numbers. The Autumn term is when we approach probability for the first time, refreshing and consolidating ideas form primary school and formalising these ideas with the correct terminology. Students work in geometry this term is based around circles and parts of circles, ensuring students have the correct language to use, can name all the parts of a circle and can find the area and circumference. We will also learn facts about angles in polygons and parallel lines, and the method for how to accurately construct geometric shapes.
The Spring term builds some important calculator skills as students revisit percentages, learning how to apply direct proportion using multipliers as an alternative to written methods. This work will be supported by the ratio problem solving unit which also looks at proportionality in different contexts. Students algebra skills are developed by learning to solve equations that have variables on both sides and finding the nth term for non-linear sequences. Their earlier study of volume is stretched by applying it to curved shapes and the concept of surface area is introduced allowing for complex questions combining the 2 skills.
The Summer term finds us coming back to number, both developing the surds skills from Autumn term and beginning to use upper and lower bounds to investigate the accuracy of rounded values. Inverse proportion is introduced and used to solve work rate problems and students will also learn how to find the equation of any straight line. Pythagoras’ theorem gives students tools to find the length of a side of a right-angled triangle and in statistics we will plot cumulative frequency and scatter graphs to represent different types of data.
In year 8 we will look at some elements of computing again, building upon their prior knowledge of algorithms and introducing hexadecimal coding.
The Autumn term starts off with a new number skill, learning how to work with recurring decimals which means students can now order numbers using fractions and decimals. Their indices knowledge from year 8 is stretched by the introduction of two new laws (fractional and negative indices) and these are then applied to index number problems including equations. We will also take their algebra skills and show them how to factorise quadratics to solve when there are 1 or 2 solutions and introduce inequalities to solve algebraic problems when relationships not equal. The probability terminology learned in year 8 will support the acquisition of new probability skills including the use of probability trees and Venn diagrams to represent different data sets. In geometry the principles of congruence and similarity and introduced and contrasted to each other and we also learn how to accurately construct triangles to make the link between this and congruency conditions. A unit on statistics extends their cumulative frequency knowledge so that students can represent the same dataset using bow plots and frequency polygons.
In the Spring the surds skills from year 8 are built upon to include rationalising surds to prepare for including them in equations later and percentages are revisited to include compound percentage change such as occurs in banking interest. There are significant introductions in geometry this term, including vector arithmetic, bearings and right angled trigonometry which pulls respectively on number, angle and Pythagoras’ theorem. We also look at speed, density and pressure and vary the metric units to improve fluency with units.
The Summer term formalises students earlier experiences with direct proportion, showing them how to represent directly proportional relationships using algebra and constants. We will improve graphing skills in this term; looking at both linear graphs with perpendicular and parallel line and graphs of real life scenarios. Students will learn how to do transformations of shapes and points on graphs, using their newly acquired vector skills. They will finish the year with fraction and averages problem solving work, applying and stretching their previous learning.
As students enter Key stage 4 they learn the final skills needed for their Nationally recognised qualifications at the end of year 11. In Maths these skills build and develop their learning from Key Stage 3 and acquire knowledge on a few discrete units of learning.
Autumn starts by extending knowledge on surds, equations and right angled triangles, encouraging students to apply their foundational knowledge to new questions. They then are introduced to histograms, algebraic Venn diagrams and algebraic inverse proportion.
In the Spring we will learn alternative ways to solve quadratic equations, so that students have a variety of ways to approach common questions and we will combine this with algebraic fractions that can be linear or quadratic. As well as looking at iteration as a method of solving equations, students will learn how to prove congruency rules and draw and interpret velocity time graphs.
In the Summer term, we will revisit simultaneous equations including non linear equations and stretching to equations of circles for the most ambitious students. Students will also learn to graph inequalities and apply their constructions skills to questions involving loci.
In year 11 the application of prior knowledge is paramount and a lot of time is devoted to understanding how knowledge and skills from different areas of Maths interact and can be used to make sense of complex problems.
Students who demonstrate a sound understanding of foundational maths concepts will sit the Higher tier paper and will practise advanced mathematics in areas such as ratio and solving equations. They will also learn about circle theorems, which builds on previous geometry topics such as congruency, parallel lines, angles and triangle facts and gives them the opportunity to apply them to a new context. This year they will also learn how to graph and identify regions on graphs that satisfy inequalities, use trigonometry for non-right angled triangles, find iterative solutions to equations and manipulate vectors and functions.
When studying at the Foundation tier of entry, year 11 is spent securing the key knowledge and adding more challenge to existing skills. An example of this would be that students who are already familiar with Volume and surface area, will spend time working with curved shapes which are more challenging, and using the formulas to work backwards from volume to find a missing dimension or angle.
Throughout year 11 all students will revisit all the main strands of Number, Algebra, Geometry, Probability, Ratio and Statistics and the time spent studying in each will vary according to the tier of entry and the individual class. At the end of the year, all students will be prepared for sitting a Nationally recognised qualification as well as having a broad understanding of Maths and its applications outside the classroom.
The curriculum prepares students for continuing their education with an A Level in Maths by offering lots of opportunities to study the most challenging content which is the basis for further study. All students will leave with a comprehensive understanding of algebra, statistics and number which are the key elements that are developed at A Level study. Students who demonstrate passion and aptitude for Mathematics at Key Stage 4 may be able to study Further Maths in addition to their normal maths lessons, which gives them an introduction to A Level content and bridges the gap between A Level and GCSE.
At Harris Greenwich, we offer courses in A Level Mathematics and A Level Further Mathematics. Students study elements of Pure Mathematics, Mechanics and Statistics over 2 years and learn to apply their skills to solve challenging problems solving questions.
Year 12 Mathematics
Our provision consolidates and extend GCSE mathematics during the early stages of the course. In the Autumn term, students explore the idea of functions, graphs and mathematical modelling. In the Spring term, Trigonometric equations and their corresponding graphs are examined alongside the notion of the effect of small changes to functions. Calculus and its applications are studied at this time. During the Summer term, students experience the application of Mathematics in areas of Mechanics and Statistics. The notion of constant acceleration, free fall, Forces and vectors are studied at this time. Discrete probability distributions, Hypothesis testing and various forms of data representation are also explored.
Year 13 Mathematics
During the Autumn term, our A level students revisit Differentiation and Integration by exploring the rate of change in other types of functions; Logarithmic, exponential, trigonometric functions etc. Students also examine the use of parametric equations to model multi-dimensional real-life problems. During the Spring term students study numerical iterative methods, vectors and further integration. In the Summer term Moments, projectile motions, forces and Normal distribution are studied.
Please find attached the 2019/2020 curriculum map for Maths, as well as a narrative of how that curriculum builds over time