Math Background

Lesson: Representing Data
Developing the Concept

Your students have had an opportunity to make a double bar graph with your help. It is now time for them to make one on their own with a little guidance from you.

Materials: graph paper, a ruler, and a pencil

Preparation: Make a poster with the following data on it:

table

Also set up a graph similar to the one below to show students how it should look.

graph

Prerequisite Skills and Background: Students should be able to read a table and make a bar graph from the information in it.

  • Say: Yesterday we reviewed what a bar graph and a line graph are, and you learned how to make a double bar graph. Who can tell me what kind of data is better represented by a bar graph than a line graph?
    Students should answer with data sets that are discrete. If they can't identify these, suggest several data sets that would best be represented by a bar graph—the heights of a group of students, for one.
  • Ask: What kind of data are better represented on a line graph?
    Students should suggest data that are continuous, such as the temperature at different times of the day or the distance you travel from home when you go for a walk. If students can't think of any examples, mention several examples so that they can see the difference between data in bar and line graphs.
    Show students the poster with the data collected from 10 boys and 10 girls about the kinds of vegetables they like.
  • Say: These data were collected from 10 boys and 10 girls. They were asked if they liked each of the vegetables listed. The data represent the number of boys and girls who liked a particular vegetable. What vegetable was liked best by both groups? (corn)
  • Say: I want you to make a double bar graph illustrating this information. But before you begin, I'd like to ask you a few questions to make sure you understand how to make the graph. What information do you think should be along the horizontal axis? Explain your answer. (Students should say that the names of the vegetables should be on the horizontal axis since they are the choices.) When you start to make your graph, be sure to give yourself enough room along the horizontal axis for two bars for each vegetable and a little space between each pair of bars.
  • Ask: What information should be along the vertical axis? Explain.
    Students should say the number of boys and girls who liked each vegetable.
    What scale should you use?
    Students should say at least 10, but you might want to suggest that they extend the scale a little.
  • Say: Be sure to label your axes and give your graph a title. Please get started. I'll come around the room to see how you are doing.
  • Say: It looks as if you have done a good job making the graph. Most of you have made a graph similar to mine.
    Show your bar graph and give students an opportunity to compare their graphs to yours.
  • Say: What do we need to do now to finish our graph? (Students should say that you need to graph the information from the table.) Good. How will I distinguish the information about the girls from the information about the boys?
    Students may suggest using one color for the bars representing boys, and another color for the bars representing girls.
  • Say: However you present your information, you will have to include a key so that someone reading your graph will be able to understand what the bars refer to.
    As students are finishing their graphs, walk around the room to see how they are progressing.

Wrap-Up and Assessment Hints
Assessing a graph created by a student is a complex process. You may want to develop a rubric, giving points when students successfully complete various aspects of the graph. One such rubric is given below.

Has selected an appropriate graph to display the information 2 points
Has clearly displayed the key information 2 points
Has labeled the horizontal and vertical axes correctly 1 point
Has named the graph correctly 1 point
Has provided a key for reading the graph, if necessary 1 point
Houghton Mifflin Math Grade 6