# Circle and bar graphs – Teachers notes

## Teacher’s notes

### Main focus

Students examine data from a variety of sources, use the data to construct different types of graphs, then interpret the graphs that have been created. By the end of the activity, they will be able to

• change fractions into decimal numbers and percentages
• use data to construct a circle graph
• interpret different types of graphs and evaluate the effectiveness of the choice of representation

### Specific outcomes

For Grade 7 Mathematics (Nova Scotia):

• read and make inferences for grouped and ungrouped data displays
• formulate statistical projects to explore current issues in mathematics, other subject areas, or the world of students
• illustrate, explain and express ratios, fractions, decimals and percentages in alternative forms
• demonstrate a number sense for percentages
• estimate and determine percentages when given the part and the whole
• interpolate and extrapolate number values from a given graph

### Assessment

Use a rubric to assess students individually for their understanding of the following concepts:

• organizing and interpreting data
• estimating parts of the whole, given the percentages
• making connections among fractions, decimals and percentages
• completing a task such as constructing a circle graph
• making decisions about how best to display data

### Communication

Have your students explain the following:

• how they estimated the number of students who own the different pets
• what types of information can be presented using the circle and bar graphs
• which graph they prefer
• whether the data they have chosen to display in their project are well served by the graph they have chosen to use

### Technology

• Students will need a calculator to help them change fractions to percentages.
• If computers are available, you can provide an electronic spreadsheet of the classCensus at School survey results.

### Materials

The Student worksheet consists of three pages. Present them to your class as follows:

• Show Page 1 to your class using an LCD projector or by making a transparency and using an overhead projector.
• Provide hard copies of Page 2 to your class.
• Show Page 3 to your class by projector or by handing out hard copies.

Access the Census at Schoolfile of the class survey results and provide each student with a hard copy or an electronic file. Keep a copy of these results for future use. You can use them to generate many interesting activities.

### Lesson notes

Page 1: Interpreting circle graphs (one to two classes)

Have your students look the circle graph and estimate how many students they think own each type of pet. Allow time for students to estimate individually and then share their results with a partner.

Teacher-led discussion: Allow all students in the class to share their initial observations, comparisons and justifications before refining their estimates. During the discussion, make comparisons using simple fractions and refine your estimates as more information becomes relevant.

For example, the portion of the graph representing those who do not own a pet appears to be slightly less than half the circle, or half of the 58 survey respondents. So some of your students may start by estimating that slightly fewer than 29 survey respondents do not own a pet. As they continue to estimate the size of each portion, some students will have ‘used up’ all of the 58 respondents before they get to considering the number who own a reptile. Then they will have to adjust their estimates.

Have a class discussion about ways of determining whether their estimates are reasonable. Ask your class why it is important to know that no student in the survey owns more than one pet.

Note: If your class is experiencing difficulty with the concept of fractions, you may choose to change the total number of students surveyed in the circle graph to 60 to make estimating easier.

Page 2: Creating circle graphs (one class)

Take some time to look at Table 1 with your students.

• Could these results have come from our school?
• What are some methods of transportation that could be included in the ‘other’ category?
• What kind of community might this school be in (e.g., rural, urban, suburban)?

Ask your students what kind of additional information is needed before they begin completing the table (i.e., the total number of students). Be sure that all students are working with the correct total.

Page 3: Comparing graphs(one class)

Give your students some time to formulate responses to Questions 1 to 5 individually.

Discuss the answers as a class, allowing students to share their observations. Students should understand that a circle graph visually shows the ‘parts of the whole’ better than a bar graph. However, it may be easier to compare categories using a bar graph.

Students may also want to discuss which graph requires less work to create. Encourage them to express their impressions of which graph they prefer, based on different factors: the visual impact and appeal of how categories are represented, the neatness of the graph, the ease in reading and comparing categories, and the calculations required to make the graph.

Page 3: Project (two classes)

It is important for your students to realize that not all of the data in the Census at School file are suitable for display as a circle or bar graph. Encourage your students to find a topic for their projects that both interests them and is structured in a way that the responses can be easily categorized.

Ask your students to think about why they chose a circle graph or a bar graph to display their data and to be prepared to explain their choice. While students work on their projects, circulate and speak to each student individually about this.

Have your students highlight comparisons and observations in their newspaper article. Encourage them to use simple fractions to make the comparisons more easily understood by the reader. Students can have fun and choose creative ways to display their results. Suggest that they come up with a ‘catchy’ headline for their newspaper article.

Contributed by Anna Spanik, Math teacher, WestHalifax High School, Nova Scotia

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