• Represent problems mathematically, making correct use of symbols, words, diagrams, tables and graphs.
  • Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT.
  • Understand the significance of a counter-example.
  • Understand the relationship between ratio and proportion; solve simple problems about ratio and proportion using informal strategies.


  • Solve more demanding problems and investigate in a range of contexts: number and measures.
  • Identify the necessary information to solve a problem; represent problems and interpret solutions in algebraic or graphical form, using correct notation.
  • Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for calculation.
  • Use logical argument to establish the truth of a statement; give solutions to an appropriate degree of accuracy in the context of the problem.
  • Suggest extensions to problems, conjecture and generalise; identify exceptional cases or counter-examples.
  • Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.


  • Solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a range of contexts.
  • Present a concise, reasoned argument, using symbols, diagrams and graphs and related explanatory text.
  • Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole; compare two ratios; interpret and use ratio in a range of contexts, including solving word problems.

Key Vocabulary:

  • problem, solution, answer, method, results, reasons, evidence, best estimate, degree of accuracy, explain, justify, prove, deduce, conclude, conclusion, counter-example, exceptional case.

Suggested Lesson Outcomes:



Teaching & Learning Resources:

Solving Problems Resources
Ratio Resources
Proportion Resources