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Using efficient calculator methods for percentages changes can be a tricky experience for students. Sometimes because the numerical methods involved can overwhelm the visual concept but also because students often see two distinct methods. One with a calculator and one without.

I wanted to teach my Year 9 group how to visualise a percentage change to consolidate their understanding of using non-calculator methods and help them use a calculator more efficiently.

For this series of lessons to succeed students had to know the word ‘of’ in maths relates to multiplication and how to convert a percentage to a decimal using mental methods.

When I teach calculating an amount after a percentage change I want students to be able to visualise the change and use the most efficient method. Using the example above their first attempt could be to calculate 40% of £110 and add that on. This is fine I suppose. However, it does lead to difficulties with calculating compound changes and can prove troublesome when dealing with percentage changes of involving decimals.

The graphic is intended to illustrate the sale price as a 40% increase on the cost price of 100%. Therefore Sale Price = 140% of £110. Converting the 140% to a decimal. Sale Price = 1.4 x £110.

Similarly, when calculating a percentage decrease the graphic illustrates the sale price is 35% less than the 100% original cost price. Therefore the sale price = 65% of cost price = 0.65 x £110.

When a profit of 20% has been made the sale price, S, is calculated as 120% of the cost price. Since we’re trying to find the cost price you can either set-up a simple equation or use equivalent ratios to find the original amount.

Again, the same idea applies when a loss has been made. In the case above you can see the sale price was 32% less than the cost price so £289 represents 68% of the original.

A 46% profit has been made on the 100% cost price £425. Therefore the profit = 0.46 x £425 = £195.50.

In the second example the sale price represents 61% of the cost price so a loss has been made. As we saw earlier 0.61C = £259.25. £C = 425. The difference between the cost and sale price £165.75 is the amount lost.

By visualising percentage changes in this way I try to encourage my students to gain a holistic approach to the calculations rather than seeing them as separate methods for separate questions. They are also more likely to intuitively apply other areas of mathematics such as equivalent ratios, setting up and solving equations and converting to decimals in their calculations.

The Geogebra file I use for percentages is freely available on my website. Click here for the download.

How do you teach percentage changes? Have you had success using different approaches?

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