Math Background

Lesson: Choosing an Appropriate Graph
Developing the Concept

After studying several types of graphs, students must now decide on which type or types might be used for different sets of data.

Materials: chart paper and markers or chalkboard and chalk

Preparation: On chart paper, the chalkboard, or overhead transparencies, prepare data tables such as the following ones.

Library Books Checked Out
October 642
November 508
December 792
January 556
How Many Books
Did You Read Last Year?
Interval Tallies
0—9 5 tally marks 1 tally mark
10—19 5 tally marks 5 tally marks 1 tally mark 1 tally mark
20—29 5 tally marks 1 tally mark 1 tally mark 1 tally mark
30—39 5 tally marks 5 tally marks
40 or more 1 tally mark 1 tally mark
What is Your Favorite
Kind of Book?
  Boys Girls
Mystery 29 23
Adventure 35 28
Science Fiction 14 20
Biography 8 17
Other 5 3

Prerequisite Skills and Concepts: In this chapter students have made and interpreted bar graphs, double bar graphs, histograms, line plots, line graphs, and double line graphs. In the past they have worked with pictographs and circle graphs.

  • Ask: What kinds of graphs have you made? What kinds of data are these graphs suitable for?

    Lead students until they name the following:

    Bar graphs—suitable for make comparisons among data
    Double bar graphs—suitable for comparing two sets of data
    Line graphs—suitable for showing change over time
    Double line graphs—suitable for comparing two sets of data over time
    Histograms—suitable for showing data in equal intervals
    Circle graphs—suitable for showing data that are parts of a whole
    Pictographs—suitable for showing data that are multiples of a number
  • Ask: Show the charts one at a time and ask students to tell what types of graphs they could make for each set of data.
    Encourage students to explain their answers.

    Students should say that the data on library books checked out might be shown on a bar graph to compare the numbers of books or a line graph to show how the numbers changed over four months time. For the data on books read last year, students should say that a histogram is suitable because the data is presented in intervals of 10. For the data on favorite kinds of books, students may say that a bar graph would let them compare numbers; however, since data is given for both boys and girls, a double bar graph may be more suitable.

  • Assign students to six groups. Two groups should make graphs of the data for library books checked out. Two groups should make graphs of the data for books read last year, and two groups should make graphs of the data for favorite kinds of books.
  • Invite groups to present their graphs and to review why they chose the type of graph. Each group should also tell several things about their graph. Have the class check each graph and ask questions after each presentation. Probably there will be variations in the ways each two groups made their graphs; there are many ways of choosing scales for the numbers, and choices of horizontal and vertical formats for the bar graphs.

Wrap-Up and Assessment Hints
Have students review kinds of data for which different kinds of graphs are used.

Have students write answers to questions such as these:

  • What kind of graph might you use to show change over time? (line graph)
  • If you have data for fifth graders' and eighth graders' favorite colors, what kind of graph might you use? (double bar graph)
  • If you have data for people's ages such as 0-9, 10-19, 20-29, and 30-39, what kind of graph should you use? (histogram)
  • What kind of graph might you use for data that shows parts of a whole? (circle graph)

Let students explain the reasons for their answers.

Houghton Mifflin Math Grade 5