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Questions that involve calculating a reverse percentage are difficult for two reasons: students do not always understand they are required to work out the original amount after a percentage change and the written method involves multiple lines of working which, without a clear writing frame, can be confusing.

Here are two examples from exam papers on calculating a reverse percentage.

**Question 1**

The normal price of a television is reduced by 20% in a sale.

The sale price of the television is £360

Work out the normal price of the television.

The common misconception was to incorrectly add 20% on to the sale price so £432 is seen as an incorrect answer.

**Question 2**

Anita buys a laptop.

20% VAT is added to the price of the laptop.

Anita then has to pay a total of £400.

What is
the price of the laptop with **no** VAT added?

The most common mistake was to use £400 as 100% instead of 120%, with students working out 20% of 400 and subtracting to get £320.

Some thought that as £400 was 120% they had to find 80% of £400 to get back to the original value.

To overcome these difficulties students, need to understand the original amount, before any percentage change, is represented as 100% . They also need to have a clear model that draws on prior learning to break down the problem.

To address these misconceptions, the lesson starts by reviewing how to calculate an amount after a percentage change using a multiplier. This is because, to calculate the multiplier students must have started at 100% as the original value. I ask students to work on whiteboards so I can check this when feeding back.

To calculate the original amount after a percentage change I model the percentage and amount using equivalent ratios. As you can see in this video.

If students needed more practice I use the following Interactive Excel File to randomly generate more questions and solutions, which you can download by clicking on the image.

When the class can model calculating a reverse percentage we move on to solving more worded, real-life problems. These are included in the Interactive Excel File.

Later, as learning progresses students work independently through the questions on the third slide and then through the worksheet.

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