Math Background

Lesson: Keeping Track of and Displaying Data
Developing the Concept

Once students feel comfortable with keeping track of data using tally marks, introduce them to a way to visualize and organize their results. You may wish to create a bar graph or a line plot with the results. Encourage students to share their thoughts and strategies as the lesson progresses.

Materials: paper for each student, carpenter's tape measure

Preparation: none

Prerequisite Skills and Concepts: Students should have basic measuring and counting skills. Students should be able to make tally marks and interpret data.

Distribute a sheet of paper to each student. Have them fold the paper to make an airplane.

  • Say: Today we will learn how to collect data and show it as a line plot. We will fly our paper airplanes and record the distance flown. Then we will tally the results in a tally chart. Finally, from our tally chart, we will make a line plot of the results.
    Have students line up to fly their paper airplanes. One at a time, have students fly their planes. Then record each distance with a tape measure. (You may want to round to the nearest foot.) Have a volunteer record the distances on the board. Announce the furthest distance flown.
  • Ask: How can we show these distances on a tally chart without writing each distance?
    Lead students to realize that the distances can be grouped into ranges. Possible choices might be the following: under 5 feet, 5 to 7 feet, 7 to 9 feet, 9 to 11 feet, and over 11 feet.
  • Say: I need a few volunteers to help arrange these distances.
    Assign 3 or 4 distances to each volunteer. Have the volunteers decide which category the distances belong in.
  • Say: Now we can make the tally chart.
    Write the distance categories on the board. Ask the previous volunteers to make a tally mark next to each appropriate category. Have the class check each tally as it is written. For example, “6 feet” belongs in the category of “5 to 7 feet.”
  • Ask: How many planes flew between 7 and 9 feet? How many planes flew more than 9 feet? How do you know?
    Students should be able to skip-count the appropriate tallies on the board in order to obtain accurate answers.
  • Say: Now we are ready to make a line plot. A line plot is a type of graph that gives a picture of the tally chart. It will show us the number of flights within each distance category. I need a few volunteers to help me.
    Draw a long line on the board. At even intervals below the line, write each distance category used in your tally chart. Above the first category, instruct a volunteer to make an X for each tally in that category of the tally chart. Repeat with the other categories. Write a title for the line plot.
  • Ask: Look at our line plot. What conclusions can you make?
    Students should realize that the same conclusions made for the tally chart also hold for the line plot.
  • Ask: How are the chart and line plot alike?
    Students should recognize that the same information or data is shown in both the chart and the line plot.
  • Ask: How are the chart and line plot different?
    Students should recognize that the information is presented in a different way. The tally chart might allow faster counting, while the line plot offers a more visual representation. Lead children to understand that each method of organizing has its own benefits.

Wrap-Up and Assessment Hints
In pairs, have students organize and represent other data in a tally chart and a line plot. Remind students to give appropriate titles and labels as needed. Be sure they check the tallies in each category against the X's of their line plot. As you assess each student, check if he or she has a clear understanding of the tally marks and can interpret the tally chart and line plot meaningfully.

Houghton Mifflin Math Grade 3