Mathematics
Maths - Curriculum narrative
Year 7
In year 7 students start by consolidating key number skills from Primary school. Initially they spend a week on number: addition, subtraction, multiplication and division with integers and decimals. This is followed by 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. Each unit concludes with a lesson on real life application of maths in its most basic form for everyday life such as budgeting for basic number, using formula in different contexts such as medicine or purchase hire for algebra. Application of percentages in terms of promotional discounts and sales.
Moving into the Spring term students will build on their knowledge of percentages. They will begin to work with percentages in calculations, focussing specifically on calculations using written non calculator methods. This also links back to fractions covered in the Autumn term and consolidates the use of direct proportion covered explicitly in unit 10 and throughout various units covered so far. 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. Students will be introduced to area and circumference of circles for the first time and will be able to apply their knowledge of substitution into formula from Autumn 1 unit 2. Students will learn how to name the different parts of a circle and use the relationship between the diameter and the circumference to calculate the area and circumference. A unit on conversions between different metric units of measure adds a layer of depth to their work with shapes and continues to consolidate the use of proportion encouraging students to make links and build fluency.
In the Summer term we return to algebra skills, investigating patterns and sequences and learning to solve simple linear equations again emphasising the importance of proportionality in maths. 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. Students will experience various lessons which focus specifically on real life application throughout each unit providing concrete examples of how maths is used around us in everyday life to help students make real life connections and aid understanding.
Year 8
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 laws of indices and the concept of surds and irrational numbers which builds on their number skills from year 7. 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, recalling formula from year 7 to find the area and circumference. Incorporating fractions to find arc lengths, perimeter and area of sectors. 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. Real life application is included here to provide context for surface area. Working in a packaging company which incorporates various number skills from year 7 and Autumn 1.
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 continue to visit real life application, but this is more often incorporated into lessons. Additional lessons are included where appropriate to develop reasoning skills and build on students’ cultural capital supporting financial wellbeing such as pay day loans, percentages and interest and real life data.
Year 9
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.
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 those which occur 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. A unit on statistics extends their cumulative frequency knowledge so that students can represent the same dataset using box plots and frequency polygons.
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 become more cognitively developed real life application is embedded in lessons. We look beyond simple exam success and explore concrete examples that link to careers.
Year 10
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. Higher tier will be introduced to histograms, algebraic Venn diagrams and algebraic inverse proportion. Whereas Foundation will cover standard Venn diagrams and probabilities followed by interpreting equations that describe direct and inverse proportion. Foundation will then do a unit on Data recapping and extending knowledge on line graphs bar charts and pictograms.
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. Foundation will not go as far on these topics and will solve quadratic equations algebraically and by factorising. Foundation will then recap fractions with 4 operations whilst extending knowledge to linear algebraic fractions. They will then go on to do a unit on estimation and bounds whereas Higher will look at iteration as a method of solving equations, Higher students will also learn how to prove congruency rules and draw and interpret velocity time graphs.
In the Summer term, we will revisit linear simultaneous equations with the higher tier moving on to non linear equations and stretching to equations of circles for the most ambitious higher students. Higher Students will also learn to graph inequalities and apply their constructions skills to questions involving loci. Whilst Foundation will focus on solving inequalities and constructing triangles, bisecting angles and perpendicular bisectors.
Both higher and foundation will have been exposed to most of the cross over content by the end of year 10 to enable tiering to take place for year 11.
Year 11
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.
Key Stage 5 Mathematics Narrative
At Harris Academy Greenwich, we are inherently ambitious for our students, supporting them in achieving their full potential in what is a highly rigorous subject. This has resulted in our students exceeding the national average pass rate since the inception of the new A level Mathematics specification. With an emphasis on exam focused techniques and knowledge, we actively encourage deliberate practice which has resulted in students demonstrating clear conceptual understanding of ideas covered in lessons.
Year 12
An outstanding GCSE Mathematics grade provides the necessary groundwork for the study of A level Mathematics at Harris Academy Greenwich. Students with a sincere passion for numbers, problem solving, and critical thinking should choose A level Mathematics. This enthusiasm is what is needed for a possible study of Mathematics and other Mathematics related subjects at university.
For AS (Advanced Subsidiary) Level Mathematics, students study Pure Mathematics and its applied options of Statistics and Mechanics.
Pure Mathematics content include topics like proof, whilst students are familiar with the idea of proof as an algebraic argument of a mathematical statement, this idea will be further developed to include prove by exhaustion and counter example whilst the other types of prove, induction and contradiction is addressed in the second year of study. A ‘big idea’ that is encountered in Pure Mathematics at this level is the notion of rate of change. Average rate of change or instantaneous rate of change is addressed via first principle differentiation of polynomials. Although students are familiar with the equation of a circle. At AS level, this idea is further developed to include circles with centre at points other than the origin and intersection of circles with straight lines. The idea of discriminates is used to further describe the nature of these intersections.
Prior to working on statistical distributions, students’ understanding of the rules of probability and experience of creating basic probability distributions from known probability situations is revisited. This basic understanding is further developed in -preparation for the introduction of binomial distribution. Subsequently, the notion of hypothesis testing is introduced as a tool to make inferential decisions about population parameters based on sample statistics. Edexcel our exam board, has provided a large data set, which will support the assessment of the applied options throughout the A level course. This year, the content of the large data set is primarily focused on weather data in different locations for certain time periods. The data is
provided by the Met Office. The LDS contains the weather data for 5 UK weather stations and 3 weather stations overseas for May–October 1987 and May–October 2015. Students are required to become familiar with the data set in advance of the final assessment.
Although there is a small contingent of students who express concerns of their lack of an anchor with which to draw background understanding of Mechanics, students are encouraged to relate work on Forces and Newton’s laws of motion to their own real-life experiences. An understanding of magnitude and direction when working with vector quantities is paramount as vectors are a natural tool to model mechanic problems.
Year 12 culminates in a PPE (Public Preparation Exams) which consists of a Pure paper (8MA0/01) and a Statistics & Mechanics paper (8MA0/02).
Year 13
At the end of year 12, students are now proficient in the differentiation of polynomials and exponential functions, they are also able to integrate and solve challenging problems which incorporates co-ordinate geometry and calculus. In year 13, the fundamental principles of calculus are explored via a wide range of mathematical functions like; logarithmic, trigonometric and parametric. Students encounter modelling complex real-life problems using differential equations. The techniques of resolving fractional expressions into its partial fractions is employed to integrate logarithmic functions. The inverse trigonometric functions of secant, cosecant, cotangent is introduced in year 13. so also, is small angle approximation of sine, cosine and tangent. The addition and double trigonometric identities are derived and applied to integration and differentiation problems.
In Statistics, students extend their understanding of probability distribution by learning about normal distribution, a continuous probability distribution. This presents a perfect opportunity to examine normal/binomial approximations and further enhances our students’ ability to work with both discrete and continuous probability distributions. Hypothesis test is re-visited. In year 13 this involves making inferences about the population parameters using, the standard normal distribution and product moment correlation coefficient.
Projectile motion is covered in Mechanics. Equipped with an understanding of advanced calculus and trigonometry, students are now able to appreciate, moments and application of forces. They are able to equate zero velocity to turning points and displacement to area under the curve therefore employing the notion of differentiation and integration appropriately. with an enhanced understanding of advanced trigonometry, students are able to resolve forces applied to inclined plane.
The last year of our A level maths programme culminates in three linear examinations papers; Paper 1 (9MA0/01) and Paper 2 (9MA0/02) for AS & A Level Pure Maths contents and Paper 3 (9MA0/03) for Statistics and Mechanics AS & A Level contents.
At Harris Academy Greenwich, our A level Mathematics programme develop our students’ analytical, research and problem-solving skills. Not only are our students equipped to tackle scientific, mechanical, and abstract problems, they develop logic to tackle everyday issues like planning projects, managing budgets and even debating effectively.
