Stage 3 - data – interpreting information in a table

Strategy

Students can:

  • organise information into columns and rows using a variety of tables
  • collect suitable tables from books or the internet on a variety of topics
  • locate and interpret information presented in two-way tables
  • calculate mean

Activities to support the strategy

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 presented 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.

Activity 1

1. Collect a variety of weather and sport reports where the term 'average' has been used.

In small groups students discuss:

  • What is meant by the term 'average'?
  • How did the newspaper calculate the average maximum and average minimum temperatures/sports scores?
  • What is another word for average?

Brainstorm some other ways the term 'average' (mean) is used,

  • e.g. average number of students in each class,
  • average rainfall in a month.

2. Pose this problem for students to solve. Ask them to underline the key words they need to solve the problem:

A baseball team scored the following runs during the first round of competition: 7, 10, 8, 7, 10, 8, 6, and 8.

  • What was the average number of runs scored per game?
  • Students explain how they solved the problem by identifying each step, e.g.

To calculate the average (mean)

Step 1: Find the total number of runs

(7 + 10 + 8 + 7 + 10 + 8 + 6 + 8 = 64)

Step 2: Divide the total number of runs by the total number of games

(64 ÷ 8 = 8)

3. Present students with other problems which involve calculating the average.

Activity 2 – geography

When teaching students how to identify and interpret information from tables, it is important that teachers guide students to determine the context of the table using probing questions such as:

  • What is the title?
  • What is the heading for each column?
  • What is the heading for each row?
  • Is it a simple or two-way table?
  • How does this affect the organisation and analysis of the information?
  • How does this help to sort the information?
  • Can we present this information in a different way, as a graph?
  • Which type of graph would be the most suitable?

Students justify their answers.

This will give students clues as to what the table is about and the focus of the information to:

  • identify the units of measurement or types of data used in the table
  • consider the date and source of the data to determine reliability
  • read data and find information within the table
  • use mathematical methods, such as calculating maximum, minimum, total, range, rank and averages.

Discuss with the class the validity of each type of calculation in light of the data presented.

Students complete calculations where appropriate.

Activity 3

In this activity students will identify, interpret and match data to make calculations and provide information about tourists visiting Australia. Give students a copy of the table Tourists to Australia (2006). Ask students some of the questions listed in Activity 2.

Tourists to Australia (2006)
Country of origin of visitorsNumber of visitorsAverage length of stay (nights)
Italy5173742
China30845248
United States of America45608424
United Kingdom73424434
Canada10984342
New Zealand107579714

Source: adapted from visitor profile statistics available for each country listed in the Markets section of the Tourism Australia website.

  • View/print (PDF 236.94KB)

Remind students to look at the title, column headings and row headings for clues.

Ask students to:

  • write a statement about the information contained in the table
  • identify the different types of data present
  • discuss the relevance of the data as being recent and/or reliable
  • make judgements about the reliability of the source and justify their decisions.

Activity 4

Revise terminology relating to calculations such as average, total, etc.

Test for understanding of the information contained within the table by asking questions and modelling answers such as:

  • From which country did the most number of visitors originate?
  • From which country did the least number of visitors originate?
  • Italy and which other country had visitors staying for the same average length of stay?
  • What was the average length of stay of the visitors to Australia in 2006?
  • What was the average number of visitors from the countries listed?
  • What was the difference between the numbers of visitors from China compared to the number of visitors from the USA?
  • What was the total number of visitors to Australia from these countries in 2006?

Students work in pairs to devise questions about the information in the table. Ask students to write the answers to their questions and then swap questions with another pair to answer.

Upon completion of these questions students could write a brief report outlining where tourists to Australia in 2006 originated, as well as providing a comparison of how long the visitors stayed.

These activities can be further extended by:

  • visiting the Tourism Australia website and adding data from other countries to the table
  • accessing the data from more recent years to make comparisons and identify possible reasons.

References

Australian curriculum reference: ACMSP119

Construct displays, including column graphs, dot plots and tables, appropriate for data; type, with and without the use of digital; technologies

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

Teacher resources

Lesson Plans and Activities

Student resources

Other resources

Nrich enriching mathematics website

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