MathsClass

Sector Graphs

Thursday, 12 February 2009 | 3 Comments

In my fourth year of teaching, I’m finally happy with how teaching sector graphs went.

Teaching Yr 8 to draw sector (pie) graphs sounds easy, yet has proven difficult. In producing a sector graph, there are a couple fundamentals drawn together — and connecting seemingly disparate concepts presents a roadblock for many students at our school.

Here’s the sequence of lessons that I used this year:

1. drawing circles and dividing those circles up into sectors given angles. For example, draw the sector graph for the following: Red 180°, Blue 90°, Green 45° and Yellow 45°. Now this may seem simple, but this lesson covers:
   • using a compass
   • using a protractor
   • using a 180° protractor to draw an angle greater than 180°
   • labelling and giving a title to a sector graph
• checking your work by making sure that the angles drawn complete the circle (add to 360°)
• find fractions of a circle, i.e. determining a sector angle giving a fraction. Then applying this to drawing sector graphs. For example, given data like the colour of MP3 Players sold: White ¹⁄₂, Silver ¹⁄₃ and Black ¹⁄₆, draw a sector graph. In this lesson:
• 360° in a circle gets repeated and repeated
• we find fractions of 360° by dividing by the denominator (and multiplying by the numerator if we have a fraction like ⁵⁄₁₂)

1. in lesson 3, we finally draw a sector graph from scratch given raw data. Mind you, the raw data is “nice” – that is, number of people surveyed might be 360, 36, 18, 24, 300 or 1800, which all give nice sector angles. In this lesson, I introduce a scaffold (a table) for manipulating the data prior to drawing a sector graph. For example:

This is where I saw students start to just take to drawing the sector graph with minimal guidance, suggesting they’d “got it”.

4. in the fourth lesson, we applied these new found skills to critique movie posters. Credit here to Dan Meyer for sharing his lesson Pie Charts – Movie Posters. I changed the worksheets a little, including making an instruction sheet that included tables for completing the working out. This was a good lesson, because we had to deal with some problems as a class. Some students didn’t rank every poster, meaning students had different totals to work with (some got 17, some 18… and some the correct 21). These don’t all translate into nice sector angles meaning we had to think about dealing with fractions of a degree (ok, so we basically ignored them and fudged the angles).

Four lessons which seemed to graduate nicely, and as we move on to the next type of graph, sector graphs seem complete.

By the way, Rocky seemed to be the most popular poster.

Image credit: Pie Chart by net_efekt on Flickr (Creative Commons)

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