Solving Problems with Percentages

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

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).