A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.

What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk.

4-6

DURATION
45

UNIT PLAN
Bars, Lines, & Pies!

# Peering into Pie Charts

In this lesson and activity, students understand how to use and read pie charts.

OBJECTIVE
Students will understand:

• that a pie chart is used to represent a part-to-whole relationship;
• that the size of each segment represents the segment’s proportion to the whole set of data;
• how to critically read pie charts and use information to perform calculations and make predictions

MATERIALS
Reproducible Activity 1, rulers, protractors, colored pencils, calculators

REPRODUCIBLES

DIRECTIONS
Getting Started: In the 3 lessons of this program, students will create, apply, and analyze pie charts, bar graphs, and line graphs. The poster (PDF) provides a good discussion starter on the topic of graphs. Review the definition of a graph with students: a diagram that visually shows the relationship between numbers or amounts. Ask students what they think it means to show numbers. Where have they seen graphs before? What are the purposes of graphs?

1. On the board, draw a simple pie chart with eight sections. Ask students what the circular image looks like. Guide students to compare the circle to a pie, with each “slice” representing a portion of the whole pie. Tell students that pie charts (or circle graphs) are used to represent data as portions (or segments) of a whole. Explain that just as they would see a pizza pie cut up into pieces, a pie chart is divided into different pieces of data. Each portion represents a percentage of the pie; all portions add up to 100%. Explain that if a pie chart is divided evenly, each portion is the same. Show students how the pie chart on the board has eight even segments and that each segment represents 12.5% (100 ÷ 8 = 12.5).
2. Draw another circle on the board. Ask students to list five different percentages that add up to 100%. Write the percentages on the board. Show the students a rough estimation of how to divide the circle to match the provided percentages.
3. Explain to students that by using the total number of degrees of a circle (360º), they can calculate the degree of the angle for each segment. Write this simple formula on the board: 1% = 3.6º. Demonstrate how, with simple multiplication, the percentage of a data set can be converted into a degree figure. For example: 25% = 3.6º x 25 = 90º. Ask students for five other percentages that add up to 100%. Draw a new pie chart with these percentages, using the formula to generate the correct angles. Provide additional examples if needed.
4. Explain that once a pie chart is divided into segments, each segment should be colored and labeled with the percentage it represents. Point out that circle graph segments are ordered by size from smallest to largest in a clockwise direction (usually starting at “12 o’clock”) in order to help people more quickly compare the data.
5. Distribute Reproducible Activity 1. Read the introductory text and discuss the table. Instruct students to review the table and answer questions 1 and 2. Then direct them to the “Make a Pie” question and the location of the pie graph template. If necessary, provide guided practice by showing students how to compute the size of the first segment (percentage of old homework paper). Review method for determining segment sizes if needed. Point out the radius line that runs through the circle. Instruct students to use this line as a starting point for creating their segments.
6. Ask students to give examples of the type of data illustrated with a pie chart and have a volunteer describe how the segment sizes in a pie chart are calculated using a protractor.
7. Instruct students to answer the questions on the reproducible. When they are finished, review the answers as a class.

LESSON EXTENSION
Real-World Math:

1. Ask students to think of graphs that they have seen in the real world. For what purposes were they used? Have students hunt for examples in books, in magazines, on the Internet, in newspapers, and in business documents.
2. Review with students the definition of actuary on the poster. How can statistics help someone plan for the future? How might an actuary use graphs and math in the following real-world situations?

--Help a school principal plan a recycling program. How could math and graphs show what the school has used in the past, and how much could be saved in the future by recycling? (Use past data to figure out future data [extrapolate], and compare results in a graph.)
--Help the manager of a city plan for a second landfill. How much space would be needed for the new landfill? (Use past data from the first landfill, as well as data that reflects current use and extrapolate for future data. Display the findings in a graph.)
--Help the manager of a company figure out how much money could be saved by recycling over a period of 10 years. (A line graph would reflect the increase of money saved over a period of time.)

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