Mathematics

Mathematics

Curriculum Intent

At Trinity, we believe that Mathematics is fundamental to the growth of our students and their preparation for the world beyond school. We believe all students are capable of success in Mathematics, and as such teach our students through a challenging curriculum that promotes mathematical thinking.

Through a carefully sequenced five-year journey, students will begin by building foundations in their mathematical understanding in Year 7. Each year, they will embed and increase their depth on understanding, while meeting new concepts and ideas to take their learning to the next level. The students that grasp concepts with relative ease will be stretched through challenge tasks to develop higher order thinking skills, while those who need it will be supported through scaffolded examples.

There are five main strands that form the Mathematics curriculum; Number, Algebra, Geometry & Measure, Statistics & Probability and Ratio & Proportion. The structure of our curriculum highlights the links across these strands so students should see how the smaller ideas and concepts fit together to form the bigger picture of Mathematics. While we move through our five-year journey, there are three objectives that are consistently embedded throughout. These are:

Fluency - Each new concept is explored and modelled through carefully planned activities, and then practiced by students to ensure students can apply the concept successfully.

Reasoning - Students will have to reason mathematically, both written and verbally, at each stage of their learning. Correct mathematical vocabulary is reinforced through discussion and there are high expectations on how to present written work in a mathematically correct way.

Problem solving – Arguably the most valuable skill developed in Mathematics, students will solve problems by applying their understanding of newly secured knowledge and previously learned skills.

Having these objectives running through everything that we teach in Mathematics, ensures that we prepare our students fully for external examinations, but also for using Mathematics beyond the classroom in day-to-day life.

Beyond our five-year journey and into Key Stage 5, our lesson structure changes but the three key objectives are still very much at the fore-front of what we do.

Outside of the classroom, we offer a range of activities to students to nurture their passion for the subject. We participate in the UKMT Maths Challenges across all key stages, there is a Maths club in Key Stage 3 and we teach a Further Mathematics after school at Key Stage 4 for our most dedicated students.

Strengths of the Department

Lessons in Maths are exciting and varied and promote problem solving skills, working with peers and independent learning. Pupils in Maths can expect to be challenged and stretched and are encouraged to discover and explore Mathematical concepts for themselves.

Achievements

As well as consistently achieving GCSE results above the national average, the Maths department at Trinity provide students with a variety of extra-curricular activities to help develop their understanding of the subject. We run a hugely popular extra-curricular Maths club where students develop their understanding and are encouraged to explore problems and look at Maths in the real world. We also have strong links with the University of Manchester who have worked with us to stretch and challenge our students through master classes in particular topics and also via a code breaking competition each year. In addition, we offer students the opportunity to complete the UKMT Maths Challenge each year. A very popular event was the Enigma project where a real Enigma machine was brought into school and students were taught about the mathematics of code breaking and how it helped to end the war.

Exam Board: AQA

Mathematics Curriculum

Year 7Year 8Year 9Year 10Year 11Year 12Year 13
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Place Value and ordering (Including: number lines, rounding, range, median and powers of 10)

Fraction, decimal and percentage equivalence (Including: pie charts)

 Addition and subtraction (Including: Perimeter, money, frequency tress and bar charts)

Multiplication and division: (Including: powers of 10, HCF, LCM, area, Mean, percentages of amounts and BIDMAS)

Fractions and percentages of amounts

 Directed number (Including: using the 4 operations, ordering, solving simple equations and BIDMAS)

Adding and subtracting fractions (Including: mixed and improper fractions)

 Construction and measuring (Including: labelling lines and angles, draw and measure angles, parallel and perpendicular lines, types of triangles and quadrilaterals, Constructing triangles and pie charts)

Geometric reasoning (Including: calculating missing angles in a triangle, in a quadrilateral, at a point, on a line and vertically opposite angles)

 Developing number sense (Including: Mental arithmetic strategies and estimation)

Sets and probability (Including: Set notation and Venn diagrams)

Prime numbers and proof (Including: prime, square and triangle numbers, product of prime factors, powers and roots)

 Exploring sequences

Understanding and using algebraic notation (Including: function machines, inverse operations, substitution and representing functions graphically)

Equality and equivalence (Including: forming and solving simple equations and collecting like terms)
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Ratio and scale (Including: circumference of a circle)

Multiplicative change (Including: scale factors, simple direct proportion, scale diagrams and maps)

Multiplying and dividing fractions (Including: reciprocals)

 Working in the Cartesian plane (Including: equation of a straight line, parallel lines, real life graphs)

Representing data (Including: scatter graphs, grouped data and two-way tables)

Probability (Including: sample space diagrams and Venn diagrams)

 Brackets, equations and inequalities (Including: expand and factorise, solving equations and inequalities)

Sequences

Indices

 Fractions and percentages (Including: percentage increase and decrease, using multipliers)

Standard index form

Number sense (Including: mental strategies, metric units, estimation and BIDMAS)

 Angles in parallel lines and polygons

Area of trapezia and circles (Including: area of parts of a circle and compound shapes)

Line symmetry and reflection

 Data handling cycle (Including: types of data, questionnaires, multiple bar charts, pie charts, misleading graphs)

Measures of location and dispersion (Including: mean, median, mean from grouped data, mode, modal class and comparing distributions)
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Straight line graphs (including: finding equations, y=mx + c, parallel and perpendicular lines)

Forming and solving equations and inequalities (Including: changing the subject of a formula)

Testing conjectures (Including: expanding double brackets)

 Three dimensional shapes (Including: prisms and non-prisms, volume, surface area, cylinders)

Constructions and congruency (Including: nets, scale drawings, perpendicular bisectors, congruency)

 Numbers (Including: rational and irrational numbers, fractions, HCF, LCM and standard form)

Using percentages (Including: percentage change, multipliers, reverse percentages, repeated percentage change, compound interest)

Maths and money (Including: Bills and bank statements, Interest, best buys, VAT)

 Deduction (Including: angle rules, algebra rules, solving equations, reasoning)

Rotation and translation (Including: rotational symmetry)

Pythagoras’ Theorem

 Enlargement and similarity

Solving ratio and proportion problems (Including: proportion graphs, conversion graphs, best buys)

Rates (Including: speed, density and compound units)

 Probability (Including: relative frequency and independent events)

Algebraic representation (Including: drawing and reading from quadratics, reciprocal graphs and representing inequalities)

 

Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Congruence, similarity and enlargement (Including Higher content: area and volume of similar shapes, proof of congruency, negative scale factors

Trigonometry (Including Higher content: 3D Trig, Sine and cosine rules, area of a triangle using sine)

 Representing solutions of equations and inequalities (Including Higher content: identify regions, solve quadratics by factorising)

Simultaneous equations (Including Higher content: solve simultaneous equations with one linear and one quadratic)

 Angles and bearings

Working with circles (Including: area and circumference, arcs and sectors, area and volume related to circles- cylinder, cone, sphere. Also including Higher content: Circle theorems, equation of a circle)

Vectors

 Ratio and fractions (Including: best buys and currency conversions. Also including Higher content: area and volume ratios)

Percentages and interest (Including: interest and depreciation, finding original values. Also included Higher content: Iterative methods)

Probability (Including mutually exclusive and independent events, tree diagrams and Venn diagrams. Also including Higher content: conditional probabilities)

 Collecting, representing and interpreting data (Including: sampling, time series, grouped data, correlation, lines of best fit, frequency polygons, compare distributions. Also included Higher content: cumulative frequency, box plots and histograms) Non-calculator methods (Including Higher content: surds)

Types of number and sequences (Including: arithmetic and geometric sequences. Also including Higher content: nth term of a quadratic sequence)

Indices and roots (Including: standard index for. Also including Higher content: fractional indices, recurring decimals, upper and lower bounds)
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Gradients and lines (Including Higher content: perpendicular lines)

Non-linear graphs (Including: quadratic and cubic graphs, reciprocal graphs. Also including Higher content: exponential graphs, equation of a tangent)

Using graphs (Including: reflection, speed, distance, time graphs and real life graphs. Also including Higher content: area under a curve)

 Expanding and factorising (Including: solving quadratic equations and algebraic fractions. Also including Higher content: completing the square and the quadratic formula)

Changing the subject (including volume of a pyramid. Also including Higher content: changing the subject when the subject appears more than once and iteration)

Functions (including Higher content: composite and inverse functions)

 Multiplicative reasoning (Including: scale and enlargement, proportion, pressure and density)

Geometric reasoning (Including: angle facts, Pythagoras and trigonometry. Also including Higher content: geometric proofs)

Algebraic reasoning (Including: complex indices, nth term, sequences. Also including Higher content: algebraic proof)

 Transforming and constructing (Including: loci. Also including Higher content: trig graphs and transforming graphs)

Listing and describing (Including: sample space, Venn diagrams, scatter graphs, plans and elevations)

Show that… (Including: equivalence, angles, congruent triangles. Also including Higher content: formal proof of congruent triangles)
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Algebra and Functions:
Surds, equations and Binomial Expansion.Coordinate Geometry:
Straight lines and problems.Further Algebra:
Polynomial Division and Factor Theorem.Trigonometry:
Solving equations and proving identities.		 Vectors:
Notation, magnitude, solving vector problems.Differential Calculus:
Differentiation and its applications.Integral Calculus:
Integration and its applications.Exponentials and Logarithms:
The exponential number and logarithms including the natural logarithm.		 Sampling:
Understanding advantages and disadvantages of different methods.Data:
Measures of tendency and spread. Correlation and regression.Probability:
Venn Diagrams, Tree diagrams and notation.Distributions and Hypothesis Testing:
The Binomial Distribution and testing for changes to probability.		 Quantities in Mechanics:
Units and notation.Kinematics:
Solving problems where acceleration is constant. Real life graphs.Forces:
Considering problems where forces are acting on a particle.Variable Acceleration:
Using calculus to solve problems where acceleration is not constant.		 REVISION AND EXAMINATIONS Year 13 Introduction

Algebraic and Partial Fractions:
Reducing an algebraic fraction into its partial fractions.

Functions and Modelling:
The modulus function and domain, range and mappings.

Proof:
Proof by contradiction
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Sequences and Series:
Arithmetic and Geometric.Binomial Expansion:
Using negative and fractional powers.Trigonometry:
Addition and Double Angle Formula.		 Parametric Equations: Using a parameter to describe curves.

Differentiation:
Product rule, chain rule and quotient rule.

Numerical Methods:
Iteration and the Newton-Raphson Method.

 Integration:
Integration methods and differential equations.Vectors:
3D Vector problems.Regression and Correlation
Probability:
Testing for zero correlation.		 Normal Distribution:
Testing for a Normal Distribution.Moments:
Turning effect of a force.Forces:
Forces applied at angles.Kinematics:
Vectors with constant acceleration.		 REVISION AND A-LEVEL EXAMINATIONS

Further Mathematics Curriculum

Year 10Year 11Year 12Year 13
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Simultaneous Equations in three variables:
Progressing from two variables to three (or more) variables.Quadratic Simultaneous Equations:
Progressing from two variables to three (or more) variables.		 Polynomial Division
The Factor Theorem and Cubic Equations:
Dividing polynomial expressions.Pascal’s Triangle and Binomial Expansion:
Expanding brackets with higher positive powers.Review:
Recall Autumn 1 and facts from Mathematics that are useful moving forwards.		 Matrices and operations:
Adding and multiplying Matrices.Matrix Transformations:
Rotations, Reflections and Enlargements in 2D space.Review:
Recall Autumn 1 and Autumn 2.		 Further Trigonometry:
Understanding Trigonometric graphs and the structure of the functions.Trigonometric Identities and Equations:
Finding multiple solutions and proving identitiesReview:
Recall selected topics from Year 10.		 Sequences:
Considering the limiting value of a converging sequence.Functions:
Composite and Inverse Functions and their domain and range.Review:
Recall selected topics from Year 10.
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Review:
Year 10 Further Maths		 Differentiation:
First principles and differentiation of polynomials.Finding Tangents and Normals:
Finding the equation of the normal or tangent to a curve.		 Increasing and Decreasing Functions:
Analysing where functions are increasing or decreasing using differentiation.Optimisation:
Finding maximum and minimum values using differentiation and applying this to a real life context.		 Equation of a circle:
The equation of a circle not centred at the origin.Co-ordinate Geometry and problems:
Using lines to solve problems in 2D space.Algebraic Fractions:
Four operations on algebraic fractions.		 Geometry and proofs:
Generalisation of the circle theorems and their proofs.
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Complex Numbers and Argand Diagrams:
The complex numbers and their representation in space.Roots of Polynomials:
The sum and products of roots of an equation.Matrices and transformations:
Enlargement, reflection, rotation around any angle.		 Series and Proof by Induction:
Formulae for sums of squares and cubes and proving results inductively.Vectors:
The scalar product and vector equations for lines and planes.Calculus – Volume of Revolution:
Rotating curves around the co-ordinate axes.		 Inequalities (FP1):
Solving rational expression inequalities.Conic Sections 1 (FP1):
Parabolas and Hyperbolae.Pre-requites (FM1):
Forces, Friction and kinematics.Momentum and Impulse (FM1):
Conservation of momentum.		 t-formulae (FP1):
solving equations and identities using expressions.Vectors (FP1):
The Vector ProductNumerical (FP1)
differential equations:
Euler’s Method.Work, energy and power (FM1): Different types of energy.Elastic Collisions (FM1):
Using Newton’s law on collisions.		 REVISION AND AS EXAMINATIONS Year 13 Introduction

Complex Numbers:
Modulus and argument. De Moivre’s Theorem.

Pre-requisites for Y13:
A-Level Mathematics.
Autumn 1
Autumn 2
Spring 1
Spring 2
Summer 1
Summer 2
Series:
Method of differencesMethods in Calculus:
Improper Integrals and power series.Volume of Revolution:
Modelling problems		 Polar Coordinates:
Using alternative coordinate systems.Hyperbolic Functions:
Hyperbolic Sine, Cosine and Tangent.Differential Equations:
Integrating factors and second order differentiation equations.		 Vectors:
Straight LinesConic Sections 2:
Ellipses and Hyperbolae.Modulus Inequalities:
Modulus Functions in rational expressions.Elastics:
Hooke’s Law.		 Trigonometry:
Modelling with t-formulae.Taylor Series:
Polynomial expressions for functions.Methods in Calculus:
Leibniz and L’Hopital.Reducible Differential Equations:
First and Second order differential equations.Elastic Collisions:
Oblique impacts.		 REVISION AND A-LEVEL EXAMINATIONS
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