Overview

Students manually create a frequency chart and circle graph using the zodiac signs of their classmates.

Objective

Students will be able to accurately calculate fractions, percentages and central angles; measure and construct angles using a protractor; and construct a circle graph by hand.

Standards Addressed

Mathematics — Data Analysis

Grade 5

Data Collection, Benchmark A

01. Read, construct and interpret frequency tables, circle graphs and line graphs.

 

Grade 6

Data Collection, Benchmark A

01. Read, construct and interpret line graphs, circle graphs and histograms.

Statistical Methods, Benchmark B

05. Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data, level of symmetry, outliers.

Data Collection, Benchmark E

02. Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph.

 

Grade 7

Data Collection, Benchmark E

02. Analyze how decisions about graphing affect the graphical representation; e.g. scale, size of classes in a histogram, number of categories in a circle graph.

 

Materials

• Protractors

• Calculators

• Compasses

• Overheads or pictures of circle graphs from magazines, newspapers, etc.

• Zodiac table

Procedure

1. 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.

2. Use an overhead projector or Web images to present examples of circle graphs and to briefly discuss these items:

   What is represented in each graph.

   The message that the creator of the graph is trying to convey to the audience.

   The details such as labels, legends, choice of color, etc.

   Explain to the students that the examples were probably created using computer software. Creating graphs by hand, however, gives a deeper understanding of the concepts underlying circle graphs.

3. Tally the students’ zodiac signs of the classroom. Have a zodiac chart handy for reference in case students don’t know their zodiac sign.

4. Use this information to make a frequency chart. Calculate the fraction of the class in each category. If, for example, 12 students out of 24 are Capricorns, then the fraction of the class that is a Capricorn is one-half (1⁄2). Write this number in a separate column in your table.

5. Next calculate the percentage of the class in each category (for the above example, 50 percent of the students are Capricorns) and write this number on yet another column.

6. Use the percentage in each category to calculate the measurement of the central angle for each sector of your circle graph by multiplying the percentage by 360. Make this another column in the frequency table.

7. Use a compass to construct a circle on the blackboard and a protractor to measure the opening of the desired angle.



8. Repeat this procedure until all the categories from your survey have been represented on your graph. Make sure to use conventional symbols and labels.

9. Model how to check your calculations by making sure that the sum of all your categories is 100 percent and the sum of all your angles is 360 degrees.

10. Technology Extension: Students can use their data to create circle graphs using the child-friendly Web site http://nces.ed.gov/nceskids/createagraph. Compare the two and draw conclusions about which method of creating graphs is more efficient.

11. Extension: To develop their understanding further, students should independently create their own circle graph using the percentages from the nutrition facts label from their favorite foods. Or they can bring in their favorite recipe, work out the percentages from each ingredient and create a circle graph manually. They can check their work on the computer.

Evaluation

Category	4	3	2	1
Fractions	Understand, solve and explain problems involving simple fractions. Calculations are done correctly. Works independently.	Student is able to add fractions with simple denominators. Calculations are made with few errors. Student works independently but sometimes needs assistance.	Student is able to identify the numerator and denominator, and calculations are attempted. Student requires assistance.	Student is unable to understand fractions and is unable to identify numerator and denominator. No calculations are made. Student requires assistance.
Percentages	Student understands, calculates and describes percent using appropriate terminology. Student works independently.	Student is able to calculate simple percentages. The mathematical concepts of finding percentages are understood. Calculations are made with few errors. Student works independently but sometimes needs assistance.	Student is able to identify the concepts involved in calculating percentages. Calculations are attempted, but many errors are made. Student requires assistance.	Student is unable to understand percentages and to make calculations. Student requires assistance.
Angles	Student understands and demonstrates congruence of figures by measuring angles and sides, matching corresponding parts. Student is able to use mathematical terms and calculate the central angle with no errors, and works independently.	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.	Student is able to use a protractor and understands concepts concerning angles. Calculations of central angles are attempted, but many errors are made. Student requires assistance.	Student is unable to understand the concepts concerning angles (i.e. measurements and calculations of central angle etc.). Calculations aren’t attempted. Student requires assistance.
Constructed Circle Graphs	All circle graphs are correctly labeled and well-presented. Student works independently.	Most circle graphs are complete. Works independently; needs little assistance.	Some circle graphs are incomplete or inaccurate drawn. Assistance is necessary.	Circle graphs are incorrect (missing titles, legends, labels or angles incorrectly drawn). Student requires assistance.