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**Scheme of work: GCSE Higher: Year 10: Term 1: Solving Problems with Percentages**

- Multiply and divide by powers of ten.
- Recognise the per cent symbol (%)
- Understand that per cent relates to number of parts per hundred.
- Write one number as a fraction of another
- Calculate equivalent fractions

- Define percentage as a number of parts per hundred.
- Interpret fractions and percentages as operators
- Interpret percentages as a fraction or a decimal
- Interpret percentages changes as a fraction or a decimal
- Interpret percentage changes multiplicatively
- Express one quantity as a percentage of another
- Compare two quantities using percentages
- Work with percentages greater than 100%;
- Solve problems involving percentage change
- Solve problems involving percentage increase/decrease
- Solve problems involving original value problems
- Solve problems involving simple interest including in financial mathematics
- Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes

- Use the place value table to illustrate the equivalence between fractions, decimals and percentages.
- To calculate a percentage of an amount without calculator students need to be able to calculate 10% of any number by dividing by 10.
- To calculate a percentage of an amount with a calculator students should be able to convert percentages to decimals mentally and use the percentage function.
- Equivalent ratios are useful for calculating the original amount after a percentage change.
- To calculate the multiplier for a percentage change students need to understand 100% as the original amount. E.g., 10% decrease represents 10% less than 100% = 0.9.
- Students need to have a secure understanding of the difference between simple and compound interest.

- Students often consider percentages to be limited to 100%. A key learning point is to understand how percentages can exceed 100%.
- Students sometimes confuse 70% with a magnitude of 70 rather than 0.7.
- Students can confuse 65% with 1/65 rather than 65/100.
- Compound interest is often confused with simple interest, i.e., 10% compound interest = 110% = 1.1
^{2,}not 220% (2.2).

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