Calculations with Percentages

Students learn how to find a percentage of an amount using calculator and non-calculator methods.  As learning progresses they use decimal multipliers to find a percentage change and calculate a simple interest in financial mathematics.

This topic follows on from Fractions, Decimals and Percentages and takes place in Year 8 Term 5.


Calculations with Percentages Lessons


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 out of 100, so 52% is the same as 52/100, which as 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.

Calculations with Percentages 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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