Which Graph?

Purpose

In this unit students explore how bar graphs and pie graphs can show different aspects of a data set. Bar graphs show the number differences between data categories and pie graphs can be used to clearly show proportional differences between data categories.

Specific Learning Outcomes
  • Interpret information from graphs
  • Make statements based on data shown on graphs
  • Identify the most suitable graph to show survey results
Description of Mathematics

There are many different types of graphs. In this unit we look at how category data can be shown on bar graph and a pie graph. We explore how bar graphs can clearly show the number of items in a category or the differences between categories. We explore how pie graphs can show the proportions, for example, nearly half the class picked honey as their favourite breakfast spread.    Students construct bar and pie graphs from the same data set, use the graphs to answer questions about the data, and identify the most suitable graph to illustrate statements about the data.

Required Resource Materials
Copymaster 3: Graphs of spread survey

Copymaster 4: Lucky dip cards

Copymaster 5: Pie graph with divisions

Copymaster 6: Favourite graph

Copymaster 2: Outline for pie graph

Copymaster 7: Graphs and statements

Copymaster 1: Bar graph

Chart paper, scissors, sellotape

Key Vocabulary

bar graph, pie graph, strip graph, categories, proportions, percentage, true, false.

Activity

Getting Started

In this session students explore how the same data can be shown on a bar graph and a pie graph. They take a bar graph and rearrange it to make a strip graph and then turn it into a pie graph.  At the end of the session the students will have 3 graphs of the same data.

  1. Provide students with 2 copies of Copymaster 1. Copymaster 1 is a bar graph showing the data from a survey of 32 children. Ask them to take one copy of the graph and cut up the bars. Using sellotape students stick the bars end to end to form a strip graph.
  2. Discuss with the students the two graphs. For example, questions that highlight that the same data is shown on both graphs.
  3. Ask students to take the strip graph and put it on its edge around the circumference of the circle in Copymaster 2. By drawing a line from the circumference where the colour changes on the strip graph to the centre of the circle students will mark the sections of the pie graph. Students should then colour the sections of the pie chart to match the colours of the strip graph. 
  4. Discuss with the students that the 3 graphs all show the same data.

Exploring

Choose a graph

Activity 1

Refer to the bar and pie graph that students constructed in the exploring session.
Ask the students questions and ask which graph they used to answer the question:
For example: How many children walk to school?
What percentage of children travel by car?
The school thinks about a third of the children come by bike. Is this true?
How many more children come by bus than by car?

Discuss with the students why bar graphs are useful for showing the number of items and why pie graphs show proportions well.

Activity 2

Show students the two graphs in  Copymaster 3 of a school survey about  favourite spreads.
Ask the students which type of graph they would use if they want to show:
15% of the children in the survey like jam.
Over a third of the children picked nutella.
10% more children like honey than like jam.
The most popular spread is nutella.
 

Lucky Dip

  1. Organise the students into groups of 4. Cut out the lucky dip cards in Copymaster 4 and have the students take turns at selecting a card from a container. Use all the cards. 
  2. Students work together to construct a bar graph and a pie graph. Use Copymaster 5 for the pie chart.  Colour the categories the same colour of each graph, e.g. red for lollipops.
  3. Students discuss and decide which graph is best for answering the following questions about the data.
    1. How many bouncy ball prizes are there?
    2. Which prize is about a third of all the prizes?
    3. Are there more bouncy balls or pencil prizes?
    4. What prize is 25% of all the prizes?
    5. How many more lollypop prizes are there than yoyo?
  4. Students are likely to have answered questions a, c and e using the bar graph, and questions b and d using the pie graph.
  5. Ask students to use the questions and answers to write appropriate statements about the data under each of the graphs. 

Writing and evaluating statements

  1. Provide the students with the favourite graphs. Copymaster 6
  2. Ask the students to complete the graphs by choosing the categories. Remembering that the categories need to correspond to the same percentage values on both graphs.
  3. Ask students to write statements under each graph. Remind students that the graph should clearly illustrate their statement.
  4. Ask students to exchange their work with a buddy and check that the statement is true and is clearly shown by the graph.

Reflecting

In this final session students evaluate if statements are true about a graph and if the graph clearly illustrates the statement.

  1. Give the students a copy of Copymaster 7.
  2. Ask them to complete the Statements Table in Copymaster 7.
  3. After working by themselves students compare their answers with a classmate.

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