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 percentage of an amount, percentage change and reverse percentages.

This unit takes place in Term 2 of Year 10 and follows on from working with fractions and mixed numbers.


Percentages Lessons
4 Part Lesson
Calculating a Repeated Percentage Change
4 Part Lesson
Reverse Percentages
4 Part Lesson
Percentage Increases
4 Part Lesson
Percentage Decreases
4 Part Lesson
Percentages of an Amount Non-Calculator Methods
4 Part Lesson
Percentages of an Amount Calculator Methods
4 Part Lesson
Writing Percentages
4 Part Lesson
Converting between fractions decimals and percentages
4 Part Lesson
Compound Percentage Increases
4 Part Lesson
Compound Percentage Decrease
Additional Resources
Extended Learning
Percentages of an Amount – Non Calculator
Extended Learning
Growth and Decay
Problem Solving
Real World Percentage Problems
Extended Learning
Percentage Changes
Extended Learning
Reverse Percentages
Problem Solving
Fractions, Decimals and Percentages
Problem Solving
Compound Percentages
Revision
Reverse Percentages
Revision
Non-Calculator Percentage Problems
Revision
Percentage Changes
Revision
Fractions, Decimals and Percentages
Revision
Compound Percentage Changes

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

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.

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 1/65rather than 65/100.

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