# 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

Expressing One Number as a Percentage of Another

Solve Problems Involving Percentage Change

Finding the Original Value

Simple Interest in Financial Mathematics

##### 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.

##### Calculations with Percentages 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%

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