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Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include:

- drawing non-linear scales on the x or y axis,
- using the incorrect units when converting between imperial and metric measurements,
- taking inaccurate readings from either axis
- not joining correctly plotted points to make a continuous line
- attempting to draw a bar chart instead of a line graph
- incorrect rounding when reading off currency values

In this blog I will take you through how I teach conversion graphs in a way that addresses each of these misconceptions.

To introduce the main lesson, I explain conversion graphs can be used to represent real-life situations, such as currency exchange rates and converting between metric and imperial measurements.

In the first example we discuss how to convert between GBP and Euros using a pre-drawn conversion graph. I provide a copy of the presentation slide as a handout for the students so they can work through the problems with me.

We work through questions a) to d) one at a time being careful to make sure we draw accurate horizontal and vertical lines from the axes. We discuss that while it is important to be as accurate as possible we should use suitable approximations especially when dealing with currencies.

Before we progress on to the third slide, I challenge the class to use the same conversion graph to convert 400 Euros to Pounds and show me their attempt on mini-whiteboards. A common misconception is that the graph is not big enough to tell. Some students had the right idea but made arithmetic errors due to having no clear writing frame. I demonstrate the method below to feedback.

** € : £**

10 : 7

40 : 28

400 : **280**

As a quick progress check I ask the class to convert £360 to Euros. Nearly all the class correctly applied the ‘build-up’ method starting from either £6 or £12

**€ : £**

6 : 8

60 : 80

360 : **480**

**€ : £**

12 : 17

36 : 51

360 : **510**

I encourage the students to share their different approaches by letting others see the working out on their mini-whiteboards. It is interesting that all the students are confident in their method but cannot understand why we have two seemingly correct answers. I ask the class to discuss the cause of this in pairs. We conclude our readings from the graphs cannot be taken as completely accurate so as we scale up the reading the magnitude of the error increases.

I ask the students to attempt the questions on third slide and then I feedback. I use the Interactive Excel File (click to download) to provide additional examples for those who are struggling.

As we progress through the lesson students are challenged to plot conversion graphs from partially completed data tables. When drawing the grid, I encourage students to choose their own scale depending on the space available to them. All grids must be drawn in pencil and on graph paper.

It does take a while for the students to draw the grid and plot the conversion graph but this is time well spent. When mistakes were made plotting the conversion graphs it was typically due to non-linear axes. We discuss how to use the properties of linear graphs to check for mistakes in either the axes scales, calculated values or incorrectly points.

It was pleasing that students were able to identify mistakes themselves by realising the conversion line was wonky. All students were able to find their mistake and went on to correct it.

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