Teach Secondary 13.8

[ M A T H S P R O B L E M ] Colin Foster (@colinfoster77) is a Reader in Mathematics Education in the Department of Mathematics Education at Loughborough University. He has written many books and articles for mathematics teachers. foster77.co.uk , blog.foster77.co.uk THE DIFFICULTY Five different colours are available for painting a youth centre. Each child in the youth centre chooses their preferred colour. These two charts both show the same data about their choices. In this lesson, students explore the advantages and disadvantages of bar charts and pie charts. Here are answers and some comments. Answer Comments 1 Light blue Easy to see from either chart, but maybe easier from the bar chart. 2 12 Need the bar chart. 3 Orange Easier to be sure from the bar chart. 4 Orange Easier to see (rather than calculate) the fraction from the 90° sector in the pie chart. 5 No Easier to see in the pie chart. 6 2 Need the bar chart. If you want to see the exact frequencies, or differences in frequencies, then the scale on the bar chart is necessary. Most people find the areas of rectangles (on a bar chart) easier to compare visually than the areas of sectors of a circle (on a pie chart). If you want to see proportions, then the pie chart may be easier, especially if the total frequency (as here) is a multiple of 12. Imagining a clockface around the pie chart can often make it easier to draw conclusions without needing to use an angle measurer. The corner of a piece of paper can be useful for comparing with 90°. BAR CHARTSVERSUS PIE CHARTS Students often struggle to compare the benefits offered by different types of statistical charts, says Colin Foster Which chart do you prefer? Why? This question is just to get students thinking about their personal preferences and what they might depend on. THE SOLUTION Try using the two charts to answer these questions. Which chart do you find easier to use for each question? Why? 1.Which was the most popular colour? 2. How many children altogether were in the youth centre? 3.Which colour was three times as popular as another colour? 4.Which colour did a quarter of the children choose? 5. Did more than half of the children choose some kind of blue? 6. How many more children chose orange than dark blue? Checking for understanding Make up some data like these and represent them in both a bar chart and a pie chart. Invent 3 questions that are easier to answer using the bar chart, and 3 questions that are easier to answer using the pie chart. See if your partner agrees. 10 teachwire.net/secondary