# 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, etc.

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 e.g.10 symbols can represent 100.

Draw one car on the whiteboard. One car = 10

Draw three more symbols.

What number would be represented now?

Change the number of symbols to 4, 8, 11, etc. 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.

e.g.

• 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?

2. Students are given this template of picture graph 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.

1. Students will use this information and the template below to complete a column graph, which will show the predicted weather in each of the cities.

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 GoldCountryGold SilverBronzeTotal
1United States of America462929104
2People's Republic of China38272388
3Great Britain29171965
4Russian Federation24263282
5Republic of Korea138728
6 Germany11  19 14 44
7 France11  11 12 34
8 Italy 9 11 28
9Hungary  4 5 17
10 Australia 16 12 35
11 Japan 141738
12Kazakhstan71513
13Netherlands66820
14Ukraine65920
15New Zealand62513
16Cuba53614
17Islamic Republic of Iran45312
18Jamaica44412
19Czech Republic43310
20Democratic People's Republic of Korea4026

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. e.g.
• 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 you need to look at the column graph below which displays some 'Mystery Data'.

By studying the graph you can see that:

• 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____________________________________________

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

(Activity 6 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.

## References

### Australian curriculum reference: ACMSP148

Interpret secondary data presented in digital media and elsewhere

### NSW syllabus reference: MA3-18SP

Uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two way tables.

### NSW literacy continuum reference: REAC11M4

Reading texts, Cluster 11, Marker 4: Manipulates multiple texts that include a variety of purposes and modes to locate information for a specific purpose.

### Other literacy continuum markers: COMC11M2

Comprehension, Cluster 11, Marker 2: Re-examines sections of texts for evidence to support interpretations and opinions.  WRIC11M6: Aspects of writing, Cluster 11, Marker 6: Uses topic sentences and appropriately organises main and subordinate ideas.

Links to other curriculum areas: Geography HSIE

## Teacher resources

Nrich website activities