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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.

- 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 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.

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.

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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