Calculations with Percentages

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

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.

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.

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.