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


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.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Calculating the Volume of a Pyramid

When calculating the volume of a pyramid we can substitute the values of the length, width and perpendicular height into the formula V = 1/3 lwh.  In my experience this is often provided for the students with little explanation as to why a volume of a pyramid is exactly one third the volume of a […]

Solving 3D Problems using Trigonometry

When teaching solving 3D problems using trigonometry we begin the lesson with a recap of Pythagoras’ Theorem and the three trigonometric ratios.  We do this by matching the ratio and equations to the respective right-angled triangle.   Students are encouraged to work in pairs and to show the diagrams as part of the working out on […]

Rounding to a significant figure

When I teach rounding to a significant figure, I ask the class to discuss in pairs or small groups a definition for the word significant.  It is a word that all the students have heard before but not all are able to define. After 2 or 3 minutes of conversation I ask the students to […]