Creating Circles

Overview

This activity can be an introduction to circle graphs. The activity sheet included can be used to consolidate the concepts presented and/or assess students understanding of what was taught. During this activity a number of circle graphs are examined, data are calculated and circle graphs are constructed by hand. Evaluation suggestions and answers to the student activity sheets are also available.

Contributor: Irini Clelland, Statistics Canada Support Teacher.

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Objectives

As students progress through their education they need to meet the curriculum standards set by the government. Constructing circle graphs by hand is one of the skills students must master by the end of grade seven in Ontario. Being able to make inferences and convincing arguments that are based on data analysis is another reason students must learn to understand the concepts related to circle graphs.

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Suggested Grade Levels

Grade 6-7 Mathematics: Data Management

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Outcomes

Students will:

• calculate fractions, percentages and central angles
• measure and construct angles using a protractor
• construct circle graphs by hand
• make inferences that are based on data analysis

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Materials

1. Student worksheet
2. Protractors
3. Calculators
4. Writing and colouring utensils
5. Compasses
6. Overheads or pictures of circle graphs from magazines, newspapers etc.
7. Overhead projector
8. Students' math journals

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Classroom Instruction

Bring in different magazines or newspapers and allow some time for students to view the different ways companies and individuals present their information to the public.

Use an overhead projector to present a number of circle graphs that you have collected from different sources. Briefly discuss what is represented in each graph and the message that the creator of the graph is trying to convey to the audience. Draw students' attention to details such as labels, legends, choice of colour etc. Explain to students that all of those graphs were probably created using computer software. Creating graphs by hand, however, gives you a deeper understanding of the concepts underlying circle graphs.

To teach students how to create circle graphs (see Answers to Students' Activity Sheets for an example):

• Take a quick in-class survey such as colour of hair or favourite ice cream.
• Construct a table on the blackboard to record your data.
• Calculate the fraction of the class in each category. If for example, 12 students out of 24 in your class have brown hair, then the fraction of the class that has brown hair is one half (1/2). Write this number on a separate column in your table.
• Next calculate the percentage of the class in each category (for the above example, 50% of the students have brown hair) and write this number on yet another column.
• Use the percentage in each category to calculate the measurement of the central angle for each sector of your circle graph.
• Use a compass to construct a circle on the blackboard and a protractor to measure the opening of the desired angle

• Repeat this procedure until all the categories from your survey have been represented on your graph.
• Make sure to use conventional symbols and labels.
• Model how to check your calculations by making sure that the sum of all your categories is 100% and that the sum of all your angles is 360º.
• Use a number of colours to distinguish each category and to make it esthetically appealing to your audience.

Give students time to have their questions answered and present them with the activity sheet. Depending on your objectives and on the needs of your class you may decide to have students work in small groups or individually. Your role during this time will be that of a facilitator.

When students have completed their worksheets invite them to discuss what is represented in their graphs, difficulties they encountered producing the graphs and conclusions that can be made using these graphs.

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Evaluation

As with most lessons there are a number of ways you can evaluate the students' comprehension. Some of the things you should be looking for during your evaluation should be:

• calculations completed and verified
• graphs including appropriate labels, legends and titles
• the clear and esthetically appealing presentation of data
• compasses and protractors were used effectively in the construction of the circle graphs

Here is an unauthorized evaluation rubric for this activity:

Fractions

Level 1: No understanding of fractions. Unable to identify numerator and denominator. No calculations are made. Assistance is necessary.
Level 2: Able to identify the numerator and denominator and calculations are attempted. Assistance is necessary.
Level 3: Able to add fractions with simple denominators. Calculations are made with few errors. Works independently sometimes needs assistance.
Level 4: Understand, solve and explain problems involving simple fractions. Calculations are done correctly. Works independently.

Percentages

Level 1: No understanding of percentages. Unable to make calculations. Assistance is necessary.
Level 2:Able to identify the concepts involved in calculating percentages. Calculations are attempted, but many errors are made. Assistance is necessary.
Level 3: Able to calculate simple percentages. The mathematical concepts of finding percentages are understood. Calculations are made with few errors. Works independently sometimes needs assistance.
Level 4: Understands, calculates and describe percent using appropriate terminology. Works independently.

Angles

Level 1: Unable to understand the concepts concerning angles (i.e. measurements and calculations of central angle etc.). Calculations aren't attempted. Assistance is necessary.
Level 2: Able to use the protractor. Understands concepts concerning angles. Calculations of central angles are attempted, but many errors are made. Assistance is necessary.
Level 3: Able to estimate the size of angles within a reasonable range. Use mathematical language to describe geometric ideas. Calculations of the central angle are made with little error. Works independently needs little assistance.
Level 4: Understands and demonstrates congruence of figures by measuring angles and sides matching corresponding parts. Able to use mathematical terms and calculate the central angle with no errors. Works independently.

Constructed Circle Graphs

Level 1: Incorrect circle graphs (missing titles, legends, labels or angles incorrectly drawn). Assistance is necessary.
Level 2: Some circle graphs are incomplete or inaccurately drawn. Assistance is necessary.
Level 3: Most circle graphs are complete. Works independently needs little assistance.
Level 4: All circle graphs correctly labeled and well presented. Works independently.

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Enrichment

Invite students to use the data in their activity sheets to create circle graphs using computer software. Compare the two and draw conclusions about which method of creating circle graphs is more efficient.

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Please e-mail comments or examples of how you used this exercise in your class.