Solving Problems with 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 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

Fractions, Decimals and Percentages

Fractions Decimals and Percentages

Writing a Percentage

Writing Percentages

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

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
  • 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).

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

Solving Inequalities using a Number Line

June 5, 2019

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values.  Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]

Practical Tips for Using Mini-Whiteboards in a Mathematics Lesson

May 1, 2019

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson.  I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making.  When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback.  […]

Showing Progress during a Mathematics Lesson

April 17, 2019

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]