Key Stage 3 Maths

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The current Key Stage 3 mathematics curriculum states the following aims:

  • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

  • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language

  • solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Key Stage 3 maths is split into 7 areas:
  1. Working mathematically

  • Improve students’ ability to work more fluently within mathematical contexts.

  • Improve students’ ability to reason logically and mathematically in various contexts.

  • Improve students’ ability to solve problems, using various techniques.


  1. Number

  • Understand and apply calculation using the operators.

  • Work with decimals, fractions and percentages.

  • Work with exponents and roots.

  • Calculate using various units.

  • Learn the skills of estimation.

  • Explore how to use calculators.

  • Understand the differences between real numbers, integers and rational numbers.

  • Learn how to use calculate errors that occur when approximating using inequalities expressed in the form a < x ≤ b.

  1. Algebra

  • Understanding algebraic notation.

  • Understanding how to substitute values into expressions and equations.

  • Learn how to change the subject of formulae.

  • Work with coordinates in all four quadrants.

  • Recognise, sketch and produce graphs of linear and quadratic functions on a cartesian plane.

  •  Interpret graphical relationships and algebraically.

  • Model situations using algebra.

  • Reduce a linear equation into the form y = mx + c.

  • Understand simultaneous equations and how to solve them approximately using a graph.

  • Recognise different kinds of sequences and find the nth term for arithmetic sequences.

  1. Ratio, proportion and rates of change

  • Solve problems of direct and indirect proportion.

  • Convert between units.

  • Understand and use ratio notation.

  • Use scale factors, scale diagrams and maps.

  • Understand the relationship between ratios and fractions.

  • Solve percentage change problems.

  1. Geometry and measures

  • Use various formulae to find the area of certain shapes such as trapeziums, triangles, parallelograms, circles. In addition, find the

  • Find the volume of various 3d shapes and prisms.

  • Scale drawing, including the interpretation of geometric figures.

  • Drawing various geometric figures using a compass/protractor and ruler.

  • Understanding congruence in triangles and similarity between shapes.

  • Describing and performing transformations, reflections, enlargements and rotations.

  • Understanding how triangles can be used to deduce the size of any angle within a regular polygon.

  • Interpret mathematical relationships both algebraically and geometrically.

  • Understand angle relationships between pairs of parallel lines.

  • Use Pythagoras’ theorem to solve right-angled triangle problems.

  • Understand the properties of 3D shapes to solve problems.

  1. Probability

  • Understand how concepts of set theory such as union, an intersection can be used within probabilistic contexts in Venn diagrams, tables and grids.

  • Use the appropriate language to describe the probability of an event or outcome and place an event on a scale from 0-1.

  • Understand the differences between theoretical and experimental probability.

  • Understand that the probabilities of all possible outcomes equal 1.

  • Describe a probability as a fraction.

  • Understanding the difference between a mutually exclusive outcome, independent outcome, single events and combined events.

Deck of Cards

  1. Statistics

  • Describe, interpret and compare observed distributions of a single variable through appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

  • Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

  • Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

How Redbridge Tuition can help:

We offer a free 15-minute consultation to discuss your child’s needs:


At Redbridge Tuition, our aim to ensure that all key stage 3 students become fluent and strong in the fundamentals of mathematics, thereby giving them a strong platform to undertake GCSE Mathematics confidently. This is done through mathematical reasoning and problem-solving, applying concepts learned to routine and non-routine problems.

Based on the National Curriculum, we consolidate their knowledge from Key Stage 2, then extend their understanding.

We place a high value on problem-solving in our Key Stage 3 lessons. This helps students to reason mathematically, to interpret what can and cannot be inferred from a mathematical problem and to formulate their answers and arguments.

Both our Seven Kings Centre and our Loughton Centre has specialist maths tutors who are not only great mathematicians but are also brilliant tutors with a great deal of experience

Students are taught the art of problem structuring and mathematical modelling. They are taught how to select appropriate techniques and methods to solve unfamiliar problems.

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