Intent

The mathematics curriculum aims to help students become confident problem solvers who enjoy maths. The main goals are to:

• Build strong maths skills through regular practice.
• Encourage logical thinking and the ability to explain their reasoning.
• Develop problem-solving abilities for a variety of real-life situations.
• Improve communication using proper maths terms.
• Create a positive and supportive learning environment to reduce maths anxiety.

Implementation

Our approach to teaching maths includes:

• Focusing on understanding maths concepts deeply to prevent anxiety.
• Encouraging students to take an active role in their learning.
• Teachers demonstrating and explaining key ideas to clear up any confusion.
• Regular reviews and practice to help students remember what they learn.
• Using assessments and feedback to track progress and address learning gaps.
• Offering different tasks to support all students, whether they need more help or a greater challenge.
• Promoting the use of correct maths language to strengthen understanding.

Impact

The impact of this curriculum aims to ensure that:

• Students have a strong and connected understanding of maths and its uses.
• They are well-prepared for future education or work opportunities.
• They become confident and independent problem solvers.
• Students develop a positive attitude towards maths with reduced anxiety.
• They can make connections between maths and other subjects, as well as everyday life.
• They gain valuable knowledge, like understanding the stock market and historical maths discoveries.

• Develop fluent knowledge, skills and understanding of mathematical methods and concepts.
• Acquire, select and apply mathematical techniques to solve problems.
• Reason mathematically, make deductions and inferences and draw conclusions.
• Comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the
  information and context.

Students are expected to bring a full set of mathematical equipment, including a scientific calculator, to each lesson. Independent Learning assignments are set weekly to reinforce learning, utilising resources such as online textbooks and tailored worksheets.

At ALNS, we ensure that students not only grasp the fundamental concepts of mathematics but also find a sense of enjoyment and desire to continue to be life long learners of mathematics. 

Foundation Curriculum Plan

Rounding and Error Intervals:

• Round to the nearest 10, 100, and 1000.
• Round to a given number of decimal places and significant figures.
• Use rounding to significant figures to estimate in simple problems and calculations including worded problems.
• Understand and calculate error intervals.

Percentages:

• Find simple and integer percentages of a quantity.
• Perform percentage increase or decrease.
• Solve percentage change problems given in context.
• Calculate simple and compound interest.

Ratio and Proportion:

• Write a ratio from a real-life situation and reduce it to its simplest form.
• Solve best value problems and use proportion to adapt recipes.
• Solve direct and inverse proportion problems.

Volume and Surface Area:

• Calculate the volume of cuboids and prisms, including cylinders.
• Calculate the surface area of cubes, cuboids, and prisms including cylinders.
• Apply formulae to calculate the volume and surface area of spheres, hemispheres, pyramids, and cones.

Transformations:

• Perform and describe transformations (translations, rotations, reflections, and enlargements).
• Identify and describe transformations using coordinates and vector notation.

Angles and Bearings:

• Understand and calculate angles in various geometric shapes.
• Solve problems involving angles on parallel lines.
• Use bearings to describe direction and solve related problems.

Graphs:

• Plot and interpret coordinates in all four quadrants.
• Draw and analyse linear graphs.
• Understand and interpret distance-time and velocity-time graphs.

Compound Measures:

• Understand and calculate speed, density, and pressure.
• Apply compound measure calculations to real-world problems.

Probability:

• Understand and calculate basic probability.
• Use probability scales from 0 to 1.
• Represent probabilities as fractions, decimals, and percentages.
• Understand and use relative frequency.

Averages:

• Calculate mean, median, mode, and range.
• Interpret and compare different averages.
• Solve problems using averages and range.

Multiples and Factors:

• Find multiples and factors of numbers.
• Recognise prime numbers and find LCM and HCF.
• Perform prime factor decompositions.

Algebraic Manipulation:

• Simplify expressions.
• Expand and factorise simple algebraic expressions.
• Substitute values into algebraic expressions.

Solving Equations:

• Solve linear equations with one variable.
• Solve equations involving brackets and fractions.
• Solve simple simultaneous equations.

Indices and Standard Form:

• Understand and use the laws of indices.
• Perform calculations using standard form.
• Convert numbers to and from standard form.

Triangles, Pythagoras, and Trigonometry:

• Understand and use Pythagoras' theorem.
• Calculate missing sides in right-angled triangles using Pythagoras' theorem.
• Use trigonometric ratios to find missing angles and sides in right-angled triangles.

Higher Curriculum Plan

Surds and Indices:

• Simplify expressions using index laws.
• Calculate with fractional and negative indices.
• Simplify and calculate exactly with surds.
• Expand double brackets with surds.
• Rationalise the denominator of an expression with a surd.

Graphing Inequalities:

• Represent solutions of linear inequalities in two variables on a graph.
• Identify equations of linear graphs.
• Plot graphs of quadratic, cubic, exponential, and reciprocal functions.

Arcs and Sectors:

• Calculate the length of arcs and the area of sectors.
• Apply knowledge to solve problems involving parts of circles.

Solving Quadratics:

• Expand products of binomials.
• Factorise quadratic expressions of the form x2+bx+cx^2 + bx + cx2+bx+c.
• Solve quadratic equations by factorisation, completing the square, and using the quadratic formula.

Circle Theorems:

• Understand and apply various circle theorems to find missing angles and lengths.
• Prove and use theorems related to angles, radii, tangents, and chords.

Similarity and Congruence:

• Understand and apply conditions for similarity and congruence in geometric shapes.
• Solve problems involving similar and congruent shapes.

Conditional Probability:

• Understand and calculate conditional probability.
• Use probability trees and Venn diagrams to solve problems involving conditional probability.

Transformations:

• Perform and describe transformations (translations, rotations, reflections, and enlargements).
• Identify and describe transformations using coordinates and vector notation.

Volume and Surface Area:

• Calculate the volume of cuboids and prisms, including cylinders.
• Calculate the surface area of cubes, cuboids, and prisms including cylinders.
• Apply formulae to calculate the volume and surface area of spheres, hemispheres, pyramids, and cones.

Statistics GCSE:

• Types of Data: Understand different types of data (qualitative, quantitative, discrete, and continuous).
• Sampling: Learn various sampling methods (random, stratified, systematic).
• Collecting Data: Techniques for data collection, including surveys and experiments.
• Interpreting Tables and Charts: Analyse and interpret data from tables and various types of charts (bar charts, pie charts, etc.).
• Averages: Calculate and interpret mean, median, mode, and range.
• Standard Deviation: Understand and calculate standard deviation.
• Scattergraphs: Plot and interpret scattergraphs to identify correlation.
• Spearman's Rank: Calculate and interpret Spearman's rank correlation coefficient.

Probability:

• Understand and calculate basic probability.
• Use probability scales from 0 to 1.
• Represent probabilities as fractions, decimals, and percentages.
• Understand and use relative frequency.

Bounds:

• Understand upper and lower bounds.
• Apply bounds to solve problems involving measurements and calculations.

Simultaneous Equations:

• Solve linear simultaneous equations algebraically and graphically.
• Solve simultaneous equations with one linear and one quadratic equation.

Histograms:

• Construct and interpret histograms for grouped data.
• Understand frequency density and use it to draw histograms.

Iteration:

• Understand and use iterative methods to solve equations.
• Apply iteration to approximate solutions.

Transforming Graphs:

• Recognise and apply transformations to graphs of functions.
• Translate, reflect, stretch, and compress graphs.

Non-Right Angle Trigonometry:

• Use the sine and cosine rules to find missing sides and angles in non-right-angled triangles.
• Solve problems involving areas of triangles using trigonometry.

Vectors:

• Understand and use vector notation.
• Perform vector addition and subtraction.
• Multiply vectors by scalars and understand vector geometry.

Rates of Change:

• Understand and calculate rates of change from graphs and equations.
• Apply knowledge to real-life contexts.

Real-Life Graphs:

• Interpret and analyse real-life graphs, including distance-time and velocity-time graphs.
• Solve problems involving gradients and areas under graphs.
  

Algebraic Proof:

• Understand and construct algebraic proofs.
• Use algebra to prove identities and theorems.