• Recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes.
  • Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers.
  • Recognise that equations of the form y = mx + c correspond to straight-line graphs.
  • Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.
  • Plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT.


  • Use the prime factor decomposition of a number.
  • Use ICT to estimate square roots and cube roots.
  • Use index notation for integer powers and simple instances of the index laws.
  • Given values for m and c, find the gradient of lines given by equations of the form y = mx + c.
  • Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations, including distance–time graphs.
  • Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form to another to gain a different perspective on the problem.
  • Simplify or transform algebraic expressions by taking out single-term common factors.
  • Use formulae from mathematics and other subjects; substitute numbers into expressions and formulae; derive a formula and, in simple cases, change its subject.
  • Generate points and plot graphs of linear functions (y given implicitly in terms of x), e.g. ay + bx=0, y + bx + c= 0, on paper and using ICT.
  • Solve increasingly demanding problems; explore connections in mathematics across a range of contexts: algebra.


  • Know and use the index laws (including in generalised form) for multiplication and division of positive integer powers; begin to extend understanding of index notation to negative and fractional powers, recognising that the index laws can be applied to these as well.
  • Investigate the gradients of parallel lines and lines perpendicular to these lines.
  • Plot graphs of simple quadratic and cubic functions, e.g. y=x2, y= 3x2 + 4, y = x3.
  • Square a linear expression, expand the product of two linear expressions of the form x ± n and simplify the corresponding quadratic expression; establish identities such as a2 – b2 = (a + b)(ab).
  • Solve linear inequalities in one variable, and represent the solution set on a number line; begin to solve inequalities in two variables.
  • Derive and use more complex formulae, and change the subject of a formula.

Key Vocabulary:

  • Multiple, LCM, prime factor, prime factor decomposition, LCD, algebraic proof, gradient, function, variable, proportion, proportionality.

Suggested Lesson Outcomes:



Teaching & Learning Resources:

Index Laws Resources
LCM Resources
HCF Resources
PFD Resources
Graphs Resources
Gradient Resources
y=mx c Resources
Formulae Resources
Inequalities Resources
Quadratics Resources