# Stage 3 - data – displaying and interpreting graphs

## Strategy

Students can:

• determine a suitable scale for data and recording the scale in a key
• draw picture or column graphs using a scale or key
• interpret a given picture or column graph using a scale or key

## Activities to support the strategy

### Activity 1 – surveying the class

Pose the following problem:

What question would you ask the class if you were going to conduct a survey to find out:

• the favourite milkshake flavour
• the most popular fruit
• the preferred team game during sport time

What if your survey included all students in the school and your numbers were large, how could you display the data for large numbers? Discuss the use of symbols, for example, 10 symbols can represent 100.

Draw one car on the whiteboard. One car = 10

Draw two more cars (three in total).

What number would be represented now?

Change the number of symbols to 4, 8, 11, and so on and students determine the matching number.

Repeat, but change the key so that one symbol equals 5 (or 20) and students determine the numbers for 5 cars. Ask the class what the symbol of a car could represent. List the students' suggestions on the whiteboard, for example:

• ways of getting to school.
• types of cars owned by class families
• the number of cars passing the school in a given time period.

Students suggest other symbols that could be used to represent transport themes.

### Activity 2 – picture graphs

Display a variety of tables, with larger numbers for students to discuss. For example

This table records the number of tourist buses visiting a town in one year. Tourist Buses Table

1. Students will use the information to complete a picture graph showing the bus arrivals during the year.

Before they start discuss the following points:

• What are some advantages of using a picture graph?
• What are some disadvantages of using a picture graph?
• Because of the large numbers, can we make the task of showing the numbers in a graph easier?
• Would using a symbol, to represent more than one object, make it easier to present the large numbers?
• What number could each symbol represent? (1 symbol could equal 5 buses, 10 buses). Have students justify their answer.
• If one symbol equals 10 buses, how many symbols would need to be shown for each month? Add another column to the table to show the number of symbols that have to be used.
• What if we need to show five buses, what symbol could be used?
Tourist buses
Month Number of buses
January 75
February 30
March 35
April 55
May 40
June 50
July 65
August 40
September 50
October 55
November 30
December 60

2. Students are given the tourist bus table picture graph template (PDF 77.88KB) to graph the bus arrivals during the year. They use the key because there are a large number of buses to record on the graph. Students draw half a bus for numbers like 15, 25, 35 and 45.

Each symbol drawn on the graph represents 10 buses. Half a symbol represents 5 buses

When students finish their graph, they:

• work in pairs and discuss some facts that can be obtained from the graph
• write three questions that could be answered using the information presented in the picture graph.

### Activity 3 – column graphs

This table records the predicted weather in each of the capital cities on one day in February.

Capital city weather
City Conditions Maximum degrees (Celcius)
Adelaide Fine, sunny 29
Brisbane Rain at times 28
Canberra Showers 17
Darwin Few showers 31
Hobart Fine 20
Melbourne Fine 26
Perth Fine 30
Sydney Rain 22

1. Students use the information in the table and complete a column graph showing the predicted weather in each of the cities, You can great your own or use the predicted weather in capital cities table and column graph template (PDF 126.26KB)

Discuss:

• What information is along the horizontal axis? (name of each capital city)
• What label could be written to match this information? (Capital city)
• What information is along the vertical axis? (temperature)
• What label could be written to match this information? (Temperature oC)
• What is the difference between each number on the vertical axis? (5)

The markers on the vertical axis are 5 numbers apart.

The temperature scale on the vertical axis is marked in 5°C intervals

2. Students use the information in the table to complete the column graph by drawing the missing columns, giving the graph a title and labelling the axes. As the maximum temperature for some of the capital cities lies between the intervals on the temperature scale, students will have to measure the height of the columns carefully.

### Activity 4 – drawing graphs

Students will use information in a table to present a graph, of their choice. The table shows data from the 2012 Olympic Games medal tally and ranks the top 20 medal-winning countries.

#### The 20 most successful nations at the 2012 London Olympic Games

Ranked by Gold Country Gold Silver Bronze Total
1 United States of America 46 29 29 104
2 People's Republic of China 38 27 23 88
3 Great Britain 29 17 19 65
4 Russian Federation 24 26 32 82
5 Republic of Korea 13 8 7 28
6 Germany 11  19 14 44
7 France 11  11 12 34
8 Italy 9 11 28
9 Hungary  4 5 17
10 Australia 16 12 35
11 Japan 14 17 38
12 Kazakhstan 7 1 5 13
13 Netherlands 6 6 8 20
14 Ukraine 6 5 9 20
15 New Zealand 6 2 5 13
16 Cuba 5 3 6 14
17 Islamic Republic of Iran 4 5 3 12
18 Jamaica 4 4 4 12
19 Czech Republic 4 3 3 10
20 Democratic People's Republic of Korea 4 0 2 6

View/Print 20 most successful nations at 2012 London Olympics (PDF 258.16KB)

Students work in pairs and discuss how they will present their information as a graph. Brainstorm some of the decisions that will need to be made. The following points could be used to stimulate discussion:

• select the category of data that you wish to graph. You could choose gold medals, silver medals, bronze medals or the total medals. (They may choose more than one category to graph.)
• decide on the type of graph you are going to present – picture graph, column graph or another type of graph.
• choose an appropriate scale, symbol and key. for example, a picture of a medal represents 5 medals
.
• give your graph a title.
• decide whether you will draw it or use a computer program.

Students construct their graphs either on paper or on computer and print a copy.

When their graph is complete they could present it to the class using these questions as a guide.

• What is the title of your graph?
• Have you labelled your graph?
• What key did you use?
• How did you determine the key or scale?

Graphs are useful because they present information clearly and simply. After they have presented their graph, each student writes 3 -4 facts that their graph provides.

### Activity 5 – interpreting a graph

Introduce this activity to the class by saying:

This activity requires your detective skills to analyse the information provided in a graph and do some clever problem solving. Your assignment is to work out what this graph could be about because some vital information is missing.

To carry out this investigation use the column graph which displays some 'Mystery Data'. Mystery data graph (PDF 136.08KB)

By studying the graph you can see:

• the vertical axis (the left edge of the graph) is marked in centimetres.
• the horizontal axis (the bottom edge of the graph) is labelled 'a' to 'm'.
• there is no title for this graph. At present it is just called "Mystery Data".

Think...

• What could this graph be about?
• What could be that long? Or tall?
• Why are there so many columns?

After carefully analysing the graph, students decide what the title for this graph could be and record their suggestions and reasons.

They may like to share their ideas with a partner.

I think the title of this graph should be ____________________

because____________________________________________

Students answer these questions

What scale has been used on the vertical axis? _________________________________

What strategies did you use to decide the title ___________________________________

What extra information do you need to interpret the graph correctly? __________________

### Activity 6 – graphing data

This activity can be used as an assessment task.)

#### Prior learning

Students have had experiences reading and interpreting different forms of data representation. They have constructed and labelled a variety of graphs to represent information. Students have discussed how a scale is used and have constructed and answered questions based on the observations and analysis of information provided in graph form.

#### Description of activity

Students are given the results of a school survey and asked to:

1. Write the missing features, such as labels, on the graph.
2. Explain the information presented in the graph, including how many students were surveyed.
3. Represent the information in different ways.

### Activity 7 – graphing data

Students can survey the class on other suitable topics and present their graphs on computer using Excel. They can use symbols from the Internet or clip art to represent their data.

View/ print graphing data example (PDF 84.56KB)