Calculations with Percentages

Students learn how to find a percentage of an amount using calculator and non-calculator methods.  As learning progresses they use decimal multipliers to find a percentage change and calculate a simple interest in financial mathematics.

This topic follows on from Fractions, Decimals and Percentages and takes place in Year 8 Term 5.


Calculations with Percentages Lessons
Prerequisite Knowledge
  • Work interchangeably with terminating decimals and their corresponding fractions.
  • Define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal
  • Interpret fractions and percentages as operators
Key Concepts
  • A percentage is a fraction out of 100, so 52% is the same as 52/100, which as the decimal equivalent of 0.52.
  • Finding a percentage of an amount without the use of a calculator can be done by equivalent fractions or by finding 10% first.  Another method could be to change the percentage to a decimal and multiply the decimal by the quantity
  • If something increases by 20% the total percentage is 120%.  This has an equivalent decimal multiplier of 1.2.
  • If something decreases by 20% the total percentage is 80%.  This has an equivalent decimal multiplier of 0.8.
  • The original amount is 100%.  To find the original amount students should use equivalent ratios.
  • The word ‘of’ means to multiply.
Working mathematically

Develop fluency

  • Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals and fractions.

Reason mathematically

  • Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations

Solve problems

  • Begin to model situations mathematically and express the results using a range of
    formal mathematical representations.
Subject Content

Ratio, proportion and rates of change

  • Solve problems involving percentage change, including:
    • percentage increase,
    • decrease
    • original value problems
    • and simple interest in financial mathematics

Number

  • Define percentage as ‘number of parts per hundred’
  • Interpret percentages and percentage changes as a fraction or a decimal and interpret these multiplicatively
  • Express one quantity as a percentage of another,
  • Compare two quantities using percentages,
  • Work with percentages greater than 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

Trigonometric Identities Sin, Cos and Tan

How to introduce the sin, cos and tan trigonometric identities.

Calculating a Reverse Percentage

How to teach calculating the original amount after a percentage change.

Comparing Datasets using the Mean and Range

The importance of the range when comparing comparing datasets.