Your Basket 0 items - £0.00

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 percentage of an amount, percentage change and reverse percentages.

This unit takes place in Term 2 of Year 10 and follows on from working with fractions and mixed numbers.

**Prerequisite Knowledge**

- 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

**Success Criteria**

- 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

**Key Concepts**

- 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.

**Common Misconceptions**

- 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 1/65rather than 65/100.

January 13, 2019

When calculating instantaneous rates of change students need to visualise the properties of the gradient for a straight line graph. I use the starter activity to see if they can match four graphs with their corresponding equations. The only clue is the direction and steepness of the red lines in relation to the blue line […]

January 4, 2019

Fractions, decimals and percentages are ways of showing a proportion of something. Any fraction can be written as a decimal, and any decimal can be written as a percentage. In this blog I discuss how to use the place value table and equivalent fractions to illustrate how fractions, decimals and percentages are connected. You can […]

October 26, 2018

In my experience, students, in general, find the concept of a mean straightforward to calculate and understand. However, the mean alone does not provide a complete picture of a set of data. To achieve this, a measure of spread is also required. The range is the simplest measure that can be used for this. Not […]