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.
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.
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.
Distance learning unit of work on Probability.
This unit covers grades 3 to 5 of the U.K. National Curriculum.
With schools around the United Kingdom closed to most students it is important every child has access to engaging maths lessons through distance learning.
There are three common ways to organise data that fall into multiple sets: two-way tables, frequency diagrams and Venn diagrams. Having blogged about frequency diagrams before I thought I would write about how to draw a Venn Diagram to calculate probabilities. Recapping Two-Way Tables This activity works well to review two-way tables from the previous […]