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

Background photo: © Inga Nielsen/iStockphoto.

About This Lesson Plan



Bars, Lines, & Pies!

Bars, Lines, and Pies

Looking Through Line Graphs

Photo: © Rubberball/Getty Images.
Photo: © Rubberball/Getty Images.

In this lesson and activity, students understand how to use and read line graphs.

Students will understand:

  • that line graphs show how two pieces of information are related and how data changes over time;
  • the dependent variable of a line graph typically appears on the Y-axis, and the independent variable appears on the X-axis;
  • that line graphs are used to analyze the nature of changes in quantities.

Reproducible Activity 3, rulers, colored pencils, calculators


  1. Reproducible Activity 3: Looking Through Line Graphs
  2. Bonus Activity 3: Tap the Math Facts Behind Bottled Water


  1. Draw and label an X-axis and a Y-axis on the board. Tell students that they will be learning about line graphs in this activity. Explain that a line graph uses points and lines to examine changes over time. Line graphs are often used when examining relationships between two types of information.
  2. Tell students that, like the bar graph, the line graph has an X- and a Y-axis. The dependent variable is plotted on the Y-axis and usually measures quantity (percentage, dollars, liters, etc.). The independent variable is plotted on the X-axis and usually measures time. Use the following data to complete your line graph on the board:
    • Y-axis: $0.50, $0.75, $1.00, $1.25
    • X-axis: year: 2005, 2006, 2007, 2008
  3. Write the title “Cost of Milk at School” above the graph. Ask students where the first point in the graph should go if the cost of milk was 50 cents in 2005. Mark this point on the graph. Have students point out where other points should be marked. When done, connect the points with a line.
  4. Distribute Reproducible Activity 3. Read the first paragraph as a class. When you are finished, point out the data group that students will be using to make their graph.
  5. Direct students to the “Line It Up” question on the reproducible. Instruct them to use the data from the table to create a line graph in the space provided. Tell students they will need to create a frequency scale on the Y-axis to illustrate the frequency of each group of data. Remind students to include a title and labels on their graph. Once students have finished their graphs, instruct them to move on to the questions on the reproducible.
  6. Once complete, review the answers to the reproducible as a class and invite students to share their line graphs with the class.
  7. Ask the class when a line graph would be chosen to illustrate a data set. Have a volunteer give an example of when percentages might be illustrated using a line graph rather than a pie chart.

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.)

Family Activities Welcome (PDF)
Family Activity 3: Energy Equations for the Future (PDF)

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