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Students learn how to convert between fractions, decimals and percentages and how to write one number as a percentage of another. They use this knowledge to calculate a repeated percentage change and reverse percentages.

This unit takes place in Term 1 of Year 10 and follows on from working with fractions and decimals.

- 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 ‘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 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% × 110% = 1.1
^{2}not 220% (2.2).

July 3, 2020

Students are challenged to apply their understanding of the mean, mode, median and range to calculate datasets by setting up and solving equations.

June 30, 2020

Five, real-life and functional problem solving questions on compound percentage changes.