Calculations with Percentages

Scheme of work: Key Stage 3: Year 8: Term 5: Calculations with Percentages

Prerequisite Knowledge

  • Work interchangeably with terminating decimals and their corresponding fractions.
  • Define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal.
  • Interpret fractions and percentages as operators.

Key Concepts

  • A percentage is a fraction of 100, so 52% is the same as 52/100, the decimal equivalent of 0.52.
  • Finding a percentage of an amount without the use of a calculator can be done by equivalent fractions or by finding 10% first.  Another method could be to change the percentage to a decimal and multiply the decimal by the quantity
  • If something increases by 20% the total percentage is 120%.  This has an equivalent decimal multiplier of 1.2.
  • If something decreases by 20% the total percentage is 80%.  This has an equivalent decimal multiplier of 0.8.
  • The original amount is 100%.  To find the original amount students should use equivalent ratios.
  • The word ‘of’ means to multiply.

Working Mathematically

  • Develop fluency
    • Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals and fractions.
  • Reason mathematically
    • Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations
  • Solve problems
    • Begin to model situations mathematically and express the results using a range of
      formal mathematical representations.

Subject Content

  • Ratio, proportion and rates of change
    • Solve problems involving percentage change, including:
      • percentage increase,
      • decrease
      • original value problems
      • and simple interest in financial mathematics
  • Number
    • Define percentage as ‘number of parts per hundred’
    • Interpret percentages and percentage changes as a fraction or a decimal and interpret these multiplicatively
    • Express one quantity as a percentage of another,
    • Compare two quantities using percentages,
    • Work with percentages greater than 100%

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