# Calculations with Percentages

Scheme of work: Key Stage 3: Year 8: Term 5: Calculations with Percentages

#### 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 of 100, so 52% is the same as 52/100, 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 â€˜ofâ€™ 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 â€˜number of parts per hundredâ€™
• 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%

## Calculations with Percentages Resources

### Mr Mathematics Blog

#### Regression, Correlation and Hypothesis Testing

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing

#### 3D Vectors – Year 2

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Pure 2: 3D Vectors

#### Parametric Equations

Edexcel A-Level Mathematics Year 2: Pure 2: Parametric Equations