Solving Problems with Percentages

Students learn how to convert between fractions, decimals and percentages and how to write one number as a percentage of another.  They use this knowledge to calculate a repeated percentage  change and reverse percentages.

This unit takes place in Term 1 of Year 10 and follows on from working with fractions and decimals.


Solving Problems with Percentages Lessons


Prerequisite Knowledge
  • Multiply and divide by powers of ten
  • Recognise the per cent symbol (%)
  • Understand that per cent relates to ‘number of parts per hundred’
  • Write one number as a fraction of another
  • Calculate equivalent fractions

Success Criteria
  • Define percentage as ‘number of parts per hundred
  • Interpret fractions and percentages as operators
  • Interpret percentages as a fraction or a decimal
  • Interpret percentages changes as a fraction or a decimal
  • Interpret percentage changes multiplicatively
  • Express one quantity as a percentage of another
  • Compare two quantities using percentages
  • Work with percentages greater than 100%;
  • Solve problems involving percentage change
  • Solve problems involving percentage increase/decrease
  • Solve problems involving original value problems
  • Solve problems involving simple interest including in financial mathematics
  • Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes.


Key Concepts
  • Use the place value table to illustrate the equivalence between fractions, decimals and percentages.
  • To calculate a percentage of an amount without calculator students need to be able to calculate 10% of any number by dividing by 10.
  • To calculate a percentage of an amount with a calculator students should be able to convert percentages to decimals mentally and use the percentage function.
  • Equivalent ratios are useful for calculating the original amount after a percentage change.
  • To calculate the multiplier for a percentage change students need to understand 100% as the original amount. E.g., 10% decrease represents 10% less than 100% = 0.9.
  • Students need to have a secure understanding of the difference between simple and compound interest.

Common Misconceptions
  • Students often consider percentages to limited to 100%. A key learning point is to understand how percentages can exceed 100%.
  • Students sometimes confuse 70% with a magnitude of 70 rather than 0.7.
  • Students can confuse 65% with 1/65 rather than 65/100.
  • Compound interest is often confused with simple interest, i.e., 10% compound interest = 110% × 110% = 1.12 not 220% (2.2).

 

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