Key Stage 3 Maths


If you find yourself in Year 7 at Secondary School then you find yourself among the youngest in your school all over again. You may have lost touch with friends who have gone to a different school and the place is way bigger than you're used to. Undoubtedly, going up to Secondary School takes some getting used to.

All the way up in Maths, there are just 3 topic areas: Number and Algebra; Geometry; Data Handling. During key stage 3, especially at first, you will be concerned with consolidating what you've done at Primary School.

Then you will be broadening and developing your knowledge and understanding toward being ready for your study at GCSE level in years 10 and 11. How easy you find the new work will depend in large part on how fluent you are in arithmetic and how practiced you are in applying the rules of arithmetic in problem solving. If, for example, you haven't begun thinking of fractions as just another kind of division1, this is something you may want to spend some time practicing. If you're not used to thinking about multiplication distributing across addition (and subtraction)2 this too is something you will want to give some attention. Are you aware that any simple arithmetic expression can be re-written as 3 other transpositions? Understanding how numbers work, which is after all very accessible to you just through practice, is relevant to all problem solving and algebra3.

If you are in Year 8 or Year 9 and you don't have this kind of fluency with numbers, you will benefit by revisiting these topics even though you are already doing more complex Maths.

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  1. Any division can be simplified to a whole number given the special case that the numerator is a multiple of the denominator.
  2. We say that multiplication distributes across addition and subtraction, as does division.
  3. Algebra: a tool for solving problems.

During key stage 3 in number and algebra, you will understand proportion more clearly as the relationship between 2 quantities that can be expressed as a ratio or fraction. You will broaden your skills to include powers and roots, understanding these also in terms of their inverses and the laws of arithmetic and solving problems that include powers and roots. You will represent linear equations using graphs that conform to the general formula: y = mx + c. You will solve linear equations and linear simultaneous equations. Your work with indeces will advance as far as index arithmetic and you will use standard form. Your increasing ability with expanding brackets and taking out common factors will afford you at least the possibility of solving some quadratics using factorisation. In geometry, your knowledge will progress as far as Pythagoras' Theorem and trigonometry which you will use along with your prior knowledge in problem solving with a broader range of 2D and 3D shapes including trapezia, circles and composite shapes. In data handling, you will become familiar with grouped data, using larger data sets and deriving statistics - mode, median and mean - from tabulated data.


Handle all real numbers: +ve and -ve, fractions and mixed numbers, factors and multipes and prime numbers, observing the relationship between operation including inverses and reciprocals

Observe the priority of operations (bidmas or bodmas) including with indeces and use integer powers and their associated real roots, index arithmetic and standard form.

Understand and use proportion and ratio in the forms of decimals, fractions and percentages.

Use standard measures of mass, capacity, size, time and money and compound measures such as speed, density and unit pricing.

Use estimation, rounding and bounds in calculation and use an electronic calculator to calculate results accurately.

Use standard algebraic notation including index notation and fractional coefficients.

Understand and use the terms: equation, inequality, formula, expression, terms and factors and simplify and manipulate algebraic expressions, formulae and equations.

Solve linear equations using algebra and graphical representation.

Analyse sequences of numbers for term to term and position to term rules.

Use formulae to solve geometric problems with a range of 2D including circles and composite shapes and with solids and employing known properties of shapes.

Measure and construct geometric figures using ruler, compasses and protractor.

Use and manipulate 2D orthographic coordinates including with geometric transformations.

Use Pythagoras' Theorem and trigonometry in solving geometric problems.

Use and analyse simple and compound probability using tree diagrams and sample spaces.

Describe and interpret distribution of data using graphs, charts and tables and involving discreet, continuous and grouped data.

Understand and use bivariate data using scatter graphs.

Not a complete list.

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