# Which graph?

Purpose

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

Achievement Objectives
S3-1: Conduct investigations using the statistical enquiry cycle: gathering, sorting, and displaying multivariate category and wholenumber data and simple time-series data to answer questions; identifying patterns and trends in context, within and between data sets;communicating findings, using data displays.
S3-2: Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.
Specific Learning Outcomes
• Interpret information from graphs
• Make statements based on data shown on graphs
• Identify the most suitable graph to show survey results
• Construct graphs using digital tools (e.g. Microsoft Excel, Google Sheets)
Description of Mathematics
There are many different types of graphs. In this unit we look at how category data (i.e. data that can be organised into distinctive groups - such as eye colours) can be shown on a 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.

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

• providing partner support, explicit modelling, and/or video tutorials, for students unfamiliar with Microsoft Excel or Google Sheets
• providing sentence starters or examples to help students make statements about data shown from each type of graph
• encouraging sharing and discussion of students’ thinking
• using collaborative grouping so students can support each other and experience both tuakana and teina roles
• encouraging mahi tahi (collaboration) among students.

The contexts for this unit can be adapted to suit the interests and cultural backgrounds of your students. Capitalise on the interests of your students. Food, sports, hobbies, and entertainment are appealing to most students.

Te reo Māori vocabulary terms such as kauwhata (graph), kauwhata pou (bar graph), raraunga whakarōpū (category data) and kauwhata porowhita (pie graph) could be introduced in this unit and used throughout other mathematical learning.

Required Resource Materials
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 use it to draw a pie graph.  At the end of the session the students will have 3 graphs of the same data.

1. As a class, decide on a simple, meaningful topic to collect data about as a class. Try to frame this in response to the current learning interests or events that are a part of your students’ lives (e.g. a school camp, Polyfest). Examples could include favourite sports, method of transport to school, or food usually eaten for breakfast.
2. As a class, come up with a survey question to ask to the class (e.g. what activities are our class members most looking forward to on school camp?) Explain to the class that we are looking to find categorical data - meaning data that looks at different groups or categories, and describes the quality of something. For this question, the different camp activities would be the quality measured.
3. Conduct a survey as a class. Model collecting this data in an organised and logical manner. You could use a paper template, or Google Sheet to do this.
4. Model how to enter this data into Microsoft Excel or Google Sheets. You will need to add the categories (e.g. the activities on school camp) to one column - with one option in each cell. In the column to the right, record the numbers of students that preferred each activity.
• If you are using Microsoft Excel, select all of the data in both columns, choose the Insert tab, click the column graph icon () and choose the top left option (clustered column graph). Using the chart design tab you can change the format and appearance of the graph.
• If using Google sheets, select all of the data in both columns and click insert → chart from the menu bar. A pie graph will appear. Using the chart editor, you can change the format and appearance of the graph.
5. Support students to create their own bar graph - individually or in pairs. Ensure that they add a title and axis labels. If your students are ready to be extended, they could come up with a new question to investigate.
6. Print two copies of the bar graph you created with the class.
7. Ask the students 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.
8. Discuss the two graphs with the students. For example, ensure that they recognise that that the same data is shown on both graphs.
9. Ask students to take the strip graph, put it on its edge, and join the two ends to make a circle. By drawing a line from the circumference where the colour changes on the strip graph to the centre of the circle students can mark the sections of a pie graph. Students should then colour the sections of the pie graph to match the colours of the strip graph.
10. Discuss with the students that the 3 graphs all show the same data.

#### Choose a graph

Activity 1

Refer to the bar and pie graph that students constructed in the previous session.
For example: How many children walk to school? Which graph shows this best?
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

Students are to make a bar graph and a pie graph for favourite spreads using the percentages given in the table below.

 Spread Percentage Nutella 40 Honey 25 Peanut butter 20 jam 15

Check that they include titles on both graphs and labels on the axes of the bar graph.

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 1 and have the students take turns at selecting a card from a container. Use all the cards.
2. Have students construct a bar graph and a pie graph of the data using Excel or Sheets.
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 lollipop prizes are there than yoyo?
Students are likely to have answered questions a, c and e using the bar graph, and questions b and d using the pie graph.
4. 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. Students complete a bar and a pie graph by choosing their own topic and categories. As a class, brainstorm a list of topics and categories that students could explore.
2. Ask students to write statements under each graph. Remind students that the graph should clearly illustrate their statement.
3. 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. Using the data in the table below, students construct a bar graph and a pie graph of "Favourite things to do in the school holidays".

 Favourite thing to do in the school holidays Percentage Holiday with family 40 Playing computer games 15 Going to holiday programmes 20 Playing with friends 25
2. Ask them to complete the Statements Table on Copymaster 2.
3. After working by themselves students compare their answers with a classmate.
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