# Mathematics

Not everything that can be counted counts, and not everything that counts can be counted.

Our aim is for all students to experience that mathematics is an exciting and creative subject, one which underpins and explains the world around us. Mathematics is critical to all students whatever their eventual destinations: Mathematics underpins many of our interactions with the world in everyday life; is critical to science, technology and engineering, to financial literacy and to most forms of employment. Alongside learning the key foundational knowledge of mathematics, students will explore how to apply their mathematical knowledge to problem solving contexts.

Year 7 and 8 students are taught in mixed attainment groupings, ensuring all students have access to a broad and challenging curriculum, with students then moving into Foundation or Higher Tier classes from Year 9 onwards.

Higher Tier exams test more challenging content and enable students to reach the higher grades (6 to 9), whereas Foundation Tier entries are the best option for students aiming to secure a grade 4 or 5 (equivalent to a C grade in the old A*-G graded GCSE).

## Curriculum Overview

In Year 7 and 8 students focus on securing key foundational knowledge that will be returned to throughout their time at King Alfred’s, exploring big questions such as ‘how does ratio and proportion underpin most of the mathematics we encounter in our daily lives?’ and ‘how does algebra help us generalise patterns and provide us with new strategies to answer mathematical problems?’. From Year 9, students will be able to build on their secure mathematical foundations in either Foundation or Higher Tier classes exploring big questions such as ‘how are statistics used to summarise, communicate and analyse data’ and ‘how can you prove a mathematical statement?’. In Year 11, students sit their Mathematics GCSE which can then lead into a number of choices in Sixth Form from Level 3 Core Maths (equivalent to half an A Level) to Maths and Further Maths A Level.

## Year 7 Topics

Term 1-2: powers and roots – odds, evens, squares, and cubes; place value – number system, multiplying and dividing by powers of 10, rounding and estimating; number properties – factors, multiples, primes, HCF and LCM; and fractions, decimals and percentages – moving between representations.

Term 3-4: addition and subtraction strategies – whole number and decimal operations; angles and lines – angle rules, angles in parallel lines, and bearings; multiplication and division strategies – whole number and decimal operations; and angles in polygons – angles in triangles, quadrilaterals and regular and irregular polygons.

Term 5-6: integer operations – operations with negatives and order of operations; ratio – simplifying, equivalence, and sharing in a ratio; and proportion – direct proportion, unitary method and exchange rates.

## Year 8 Topics

Term 1-2: fractions and percentages of amounts – fractions and percentages of amounts, reverse calculations, percentage increase and decrease; solving equations – algebraic expressions, solving equations, and substitution; adding and subtraction fractions; and standard form – power laws, converting to and from standard form, and calculations with standard form.

Term 3-4: multiplying and dividing fractions; manipulating algebra – simplifying expressions, expanding brackets, and factorising expressions; probability – calculating probability, sample space diagrams, two way tables and frequency trees; and solving equations – forming and solving equations from contexts, and solving equations with unknowns on both sides.

Term 5-6: perimeter and shape properties – perimeter of simple and compound shapes; calculator skills; area – area of rectangles, parallelograms, triangles, trapezia and compound shapes; and sequences – categorising sequences, finding and using nth terms, and Fibonacci-type sequences.

## Year 9 Foundation Topics

Term 1-2: prime factorisation – prime factorisation, HCF and LCM; decimals and fractions – ordering values, and adding and subtracting fractions; algebra skills – power laws, factorising and expanding expressions, and substitution; and multiplying and dividing fractions.

Term 3-4: percentages – percentage representations, multipliers, and reverse calculations; sequences - categorising sequences, finding and using nth terms, and Fibonacci-type sequences; ratio – sharing in a ratio, and ratio, fractions and percentages in worded questions; and angles in bearings – angles in polygons and exterior angles.

Term 5-6: area and surface area – area of shapes, surface area of solids, and plans and elevations; solving equations – forming and solving equations, and unknowns on both sides; calculator skills – rounding to decimals and significant figures, and estimation; and introduction to pythagoras.

## Year 9 Higher Topics

Term 1-2: rational numbers – fraction operations and recurring decimals; indices – power laws, standard form, fractional and negative indices; surds – multiplying and dividing surds and rationalising the denominator; and equations and formulae – forming and solving equations, rearranging formulae, and substitution into formulae.

Term 3-4: percentages – multipliers, reverse percentages and compound interest; area and perimeter – area and circumference of circles, area and perimeter of sectors, and surface area of cylinders, spheres and cones; Pythagoras – pythagoras’ theorem in 2D and 3D; and sequences – nth term of linear and quadratic sequences.

Term 5-6: volume and density – volumes of solids and density calculations; linear graphs – equations of linear graphs, sketching linear graphs and parallel and perpendicular lines; direct and inverse proportion; and distance and speed-time graphs – calculating speed, gradient of non-linear graphs, area under curves.

## Year 10 Foundation Topics

Term 1-2: solving equations  - solving multi-step equations and forming and solving equations; calculator skills; Pythagoras – pythagoras’ theorem, midpoints of line segments, and lengths of line segments; and linear graphs – plotting linear graphs and equations of straight line graphs.

Term 3-4: speed – calculating speed, distance and time and distance-time graphs; compound interest – percentage multipliers and compound increase and decrease; averages and range – calculating averages and range, frequency and grouped frequency tables, and stem and leaf diagrams; and circles – area and circumference of circles, arc length, and area of sectors.

Term 5-6: probability – theoretical probability, sample space diagrams, two way tables, and frequency trees; solving and drawing inequalities; graphs and charts – drawing and interpreting bar charts, pie charts, and scatter diagrams; probability diagrams – independent and dependent tree diagrams and venn diagrams; and quadratics – plotting and factorising quadratics.

## Year 10 Higher Topics

Term 1-2: quadratic graphs – plotting, factorising and solving quadratics and quadratic inequalities, completing the square and the discriminant; and transformations and congruency – reflections, rotations and translations.

Term 3-4: transformations and similarity – enlargements and length, area and volume scale factors; simultaneous equations – solving linear and quadratic simultaneous equations graphically and algebraically; right angled trigonometry – finding missing sides and angles, bearings and 3D trigonometry; and averages and range – averages and range, sampling, capture-recapture, and stem-and-leaf diagrams.

Term 5-6: non-right angles trigonometry – sine and cosine rules, and area of a triangle; distance, speed-time graphs – calculating speed, distance, and time, gradient of non-linear graphs and area under a curve; representing data – frequency polygons, box plots, cumulative frequency graphs and histograms; and probability – sample space diagrams, and tree diagrams.

## Year 11 Foundation Topics

Term 1-2: congruence and transformations – congruency, translations, reflections, rotations and vector arithmetic; quadratic and non-linear graphs – plotting, factorising and solving quadratics and cubic and reciprocal graphs; and volumes and density – volumes of solids and density calculations.

Term 3-4: similarity and transformations – similarity and enlargement, and fractional and negative enlargements; surface area of solids; rearranging formulae; right-angled trigonometry; and errors and bounds.

## Year 11 Higher Topics

Term 1-2: probability – two-way tables, set notation and venn diagrams; algebraic fractions – rearranging formulae, simplifying algebraic fractions and operations with algebraic fractions; functions – function notation, composition and inverses; and types of graph – trigonometric graphs, reciprocal graph, exponential graphs and cubic graphs.

Term 3-4: iteration – identifying solution intervals, and fixed point iteration; algebraic proof; circle theorems; vectors – notation, magnitude and vector geometry; loci and constructions; and sketching 2D inequalities.