Strategy

Students can:

• interpret a sector graph

When students read a question that contains a picture, graph, table or diagram they need to read all the information provided and be able to interpret the visual representations that the tables and graphs provide.

At this Stage, students need to collect their own data, create tables and graphs and interpret graphs and tables. It is also vital to expose students to the use of data and graphs in the media and wider community and how they convey meaning and information, sometimes showing a bias or presenting the information in a way to persuade the consumer. This provides an opportunity to discuss how and why scale is used and that it is sometimes used to change how information may be interpreted.

The advantages and disadvantages of different representations of the same data in different graphs should be explicitly taught. Students need to choose an appropriate graph to convey meaning for their information, understanding that some graphs have particular uses e.g. Line graphs should only be used where meaning can be attached to the points on the line between plotted points. Graphs are chosen based on what data is being represented, not based on what the student likes.

Activities to support the strategy

Activity 1 – Interpreting sector graphs

When teaching students how to interpret data from a sector graph, it is important that teachers guide students to consider each of the following:

• identify the graph's title which indicates what the graph is about
• examine the sectors to identify that each sector represents part of a whole. If the sectors are labelled as percentages the total of all the sectors should add to 100%
• consider the sector labels to determine the category of information represented in each sector
• use mathematical methods to perform calculations such as combined percentages and to find missing values.

In this activity students will interpret data from a sector graph Marine-Areas-of-Australias-States-and-Territories (PDF 488.8KB) to make calculations which provide information about the relative size of each Australian state and territory's coastal waters as a percentage of the whole of Australia's marine area.

Ask students to look at the sector graph and identify the title, the key and each of the sectors.

• Have students identify each of the different sectors. Remind students to use the key.
• Ask students to write a statement about the information displayed in the sector graph. Remind them to look at the title for a clue.
• Have students present the information as a table. Ask them to list each of the sectors in the graph with the associated numerical data (percentage value).

Discuss the process required for calculations such as:

• determining missing values
• calculating combined percentages
• calculating total percentages etc.

Test for understanding of the information contained within the graph by asking questions such as:

• List the marine areas of Australia's states and territories in order of percentage size from smallest to largest.

Discuss

• Which state or territory has the largest percentage of marine area?
• Which state or territory has the smallest percentage of marine area?
• What is the Northern Territory's percentage of marine area?
• Which state has approximately half of the marine area of Queensland?
• What fraction of Australia's total marine area are the four smallest states when they are combined?

Upon completion of these questions, students could present the information from the sector graph in a column graph then compare which graph is more appropriate.

Activity 2 – Interpreting sector graphs

1. Collect and display a variety of sector graphs from books, newspapers or the Internet. Discuss:

• What is similar to all of these graphs?
• Are the same colours/patterns always used to show the different sectors?
• Do the graphs all have the same number of sectors?
• Where a key is used to interpret the graph discuss the key with the class.

2. Select 20 lollies (jelly beans/Smarties) of 4 different colours in the same proportions e.g. 5 red, 5 blue, 5 green and 5 yellow.

Place the lollies in colour groups along the circumference of a circle.

3. Draw lines from the centre of the circle to the circumference to divide the circle into colour groups. Label each sector and describe the fractional parts. Discuss:

• What fraction of the circle is represented by each colour?
• What fraction of the circle is not red/yellow?

4. Explain that:

• the sector graph is equal to one whole which is the same as 100%.
• there are four equal sectors in the graph, so each sector must be one-quarter.

5. Using fractions, determine what percentage of the circle is represented by each colour ¼ of 100% = 25%

6. Demonstrate that 50% is half of the sector graph. Students identify pairs of sectors which make up 50%.

7. Repeat, selecting 20 coloured lollies (jelly beans/Smarties) of 4 different colours and in different proportions. e.g. 5 red, 7 blue, 6 green and 2 yellow.

Discuss:

• Which colour group is equal to one-quarter of the circle?
• Is the blue sector more or less than one-quarter of the circle?

Order the coloured sectors from smallest to largest. Emphasise that the highest percentage sector represents the largest quantity.

8. Demonstrate how to determine the size of each sector as:

• a fraction of the whole
• a percentage of the whole

9. Students refer back to the sector graph with equal sectors (quadrants). Use a protractor to measure the angle size of each quadrant (90°).

• calculate the angle size at the centre of the circle percentage
• 90° x 4 = 360°

Using angle size, determine what percentage of the circle is represented by each colour.

10. Repeat step 7 using a different number of lollies (jelly beans/Smarties) such as 5 or 12 or 18 or 54. Discuss graphs.

Further activities

11. Students in pairs, conduct a class survey to collect data on a chosen topic. Record the data in a table.

12. Use the data to construct a sector graph. Use a key to identify each sector. Students demonstrate the relationship between the key and the sectors.

13. Students write their own questions using the graph and key and give to other students to answer.

References

Australian curriculum

ACMSP147: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables

NSW syllabus

MA3-18SP: Uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two way tables. MA3-7NA: compares, orders and calculates with fractions, decimals and percentages