Getting to Know Room 204 a Little Better

Est. Class Sessions: 2

Developing the Lesson

Part 2: Collecting, Organizing, and Graphing the Data

Collect and Organize Data. Before collecting the raw data on the variable your class has chosen, create a class data table on large paper or several displays of the Three-Column Data Table. In the first column, list students' names. In the heading of the second column, list the name of the variable you are studying. Then, record each student's individual data beside his or her name. See Figure 1 for an example of raw data.

Next, your class needs to organize the data by creating a new table like that in Figure 2. Make another three-column data table. Label the three headings as follows: the name of the variable you are studying, Tally, and Number of Students.

Ask a volunteer to list all of the values that appeared in your raw data table in numerical order in the first column. Then, using the raw data, have students tally the number of students that have the same value for the variable. Once all the data has been tallied, the marks are counted and the total for each row is recorded in the third column. The total number of all of the tally marks should equal the number of students in the class. The organized data can then be graphed.

Improve the Graphs. Before students begin to draw their graphs, use displays of the Bar Graphs I and II: How Would You Improve It? Masters to continue the class discussion from Lesson 1 about correct and effective graph making. These masters show bar graphs of the Room 204 data but do not organize the data as well as they could.

Ask students these questions after they study Bar Graph I:

How well does Bar Graph I organize Room 204's data about the number of blocks they live from school?
What do you notice about this graph compared to the one in your Student Guide? What are some ways the data might be organized better? (Because a bar is graphed for each individual's data, this graph does not organize that data any better than the raw data table. Also, the two variables we want to graph are not name and number of blocks but rather number of students and number of blocks.)

Choosing a Good Variable to Study. Have the class think through the expected values of a variable before they choose it. For example, if you choose number of pencils in your desk as the numerical variable you can easily ask each student to count his or her pencils and tell you the number. A numerical variable such as number of pets may be a good choice for your classroom to study. However, the number of pets may not vary much in some classrooms. (Many students might not have any pets or they may have only 1 or 2.) Choosing height, hand area, or the number of windows in students' homes would require more time since students would need to gather data.

The numerical variable you select must be well defined. If you collect data on family size, you will need to define this variable. A student's definition of family could include members outside the immediate family, especially if relatives such as a grandmother or an uncle reside in the home. Decide upon a definition such as the following: As long as the person lives in the student's home full-time, he or she could be considered part of the family. Number of pets is another variable that may need some definition. Does a student who has an aquarium count all the fish in the tank or do fish count as one pet?

Ask students these questions after they study Bar Graph II:

How well does Bar Graph II organize Room 204's data about the number of blocks they live from school?
What do you notice about this graph compared to the one in your Student Guide? How might the data in this graph be organized better? (The horizontal axis does not list the values in order. The graph does not include a place-holder to show that no students live 6 blocks from school.)

Graph Your Data. Use a display of Centimeter Graph Paper to demonstrate setting up a bar graph as shown in Figure 3. Be sure to discuss the following before students create their own graphs: giving the graph a title, labeling and scaling axes, and drawing the bars. Discuss which variable will go on the horizontal axis.

Ask students to look back at Room 204's graph in the Student Guide.

Which variable did the students in Room 204 put on the horizontal axis? (The number of blocks)
Which variable did they put on the vertical axis? (The number of students)
Why do you think they put the number of blocks on the horizontal axis? (Responses will vary. It is similar to the graph in which the variable was “main interest.”)
Why is it like “main interest,” which is a categorical variable? (You want to be able to see how many students are at each value.)

Students are now ready to graph the data they have collected. While students graph the data on Centimeter Graph Paper, have one student create a class graph of the data to display for the class. This class graph will serve as a reference for class discussion.

Read Graphs to Find Information. Use Questions 3–6 to start a discussion about what you have learned about your class.

Questions 7–10 ask similar questions about Room 204's data. Question 8 asks about the reasonability of the graph when the numbers (numerical values) are not in order. The shape of Room 204's graph in the Student Guide tells us more when the numbers are in order. Question 9 helps students recognize the graph's story. See Figure 4. The story that the tall bars at the beginning of the graph tell us is that the majority of the students in Room 204 live near school—3 blocks or closer. The short bars in the middle tell us that not as many students live between 5 and 7 blocks away. Then, the final bar shows that several students live quite far. These students might get to school by bus.

Student Guide: 11

Answers