Percentages

August 23, 2016

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

Fractions, Decimals and Percentages

Fractions Decimals and Percentages

Writing a Percentage

Writing Percentages

Non Calculator Percentage of an Amount

Percentages of an Amount Non-Calculator Methods

Calculator Methods Percentage of an Amount

Percentages of an Amount Calculator Methods

Percentage Increase

Percentage Increases

Percentage Decrease

Percentage Decreases

Calculating a Repeated Percentage Change

Calculating a Repeated Percentage Change

Reverse Percentages

Reverse Percentages

Compound Interest

Compound Percentage Increases

Compound Decrease

Compound Percentage Decrease

Revision Lessons

Fractions, Decimals and Percentages

Revising Fractions, Decimals and Percentages

Percentage Changes

Revising Percentage Changes

Compound Percentage Changes

Revising 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.

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 Teaching Resources Term by Term

Year 7 Term 1 Year 7 Term 2 Year 7 Term 3 Year 7 Term 4 Year 7 Term 5 Year 7 Term 6
Year 8 Term 1 Year 8 Term 2 Year 8 Term 3 Year 8 Term 4 Year 8 Term 5 Year 8 Term 6
Year 9 Term 1 Year 9 Term 2 Year 9 Term 3 Year 9 Term 4 Year 9 Term 5 Year 9 Term 6
Year 10 Term 1 Year 10 Term 2 Year 10 Term 3 Year 10 Term 4 Year 10 Term 5 Year 10 Term 6
Year 11 Term 1 Year 11 Term 2 Year 11 Term 3 Year 11 Term 4 Year 11 Term 5

Mr Mathematics Blog

Mathematics OFSTED Inspection – The Deep Dive

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

How to Solve Quadratics by Factorising

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have.   Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

How Write 3 Part Ratios

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out.  This is presented to the class as they come into the lesson.    Writing Equivalent Ratios  A few students immediately go […]