Lesson 2

Getting to Know Room 204 a Little Better

Est. Class Sessions: 2

Developing the Lesson

Part 1: Describe Room 204 with Numerical Variables

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Some teachers choose to engage their students in the actual data collection from their own classroom before reviewing Room 204's data in the Student Guide. These teachers may discuss the sample data tables and graph of Room 204's data in the Student Guide to provide closure to the activity.

Compare Categorical and Numerical Variables. Read together the first page of the Getting to Know Room 204 a Little Better pages in the Student Guide. Compare the types of variables discussed in Lesson 1 (e.g., main interest, favorite holiday, eye color, hair color) to those mentioned here (e.g., height, number of brothers, number of sisters, number of pets, number of times moved). Those discussed in Lesson 1 are categorical variables. In this lesson we focus on numerical variables. Numerical variables have values that are numbers while categorical variables do not.

Read together the second page of the Getting to Know Room 204 a Little Better pages in the Student Guide. Discuss the order in which the data tables were recorded.

Ask:

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  • Which data table do you think was made first? (The raw data was collected in the long table that lists each student's distance from school.)
  • How was the second table put together? (First, all the possible distances were entered in the left-hand column. Second, the number of students was counted by tally marks at each distance. Third, the number of tallies was written in the right-hand column for each distance.)
  • Which value, or distance in blocks, shows up most often? (2 blocks from school shows up 7 times.)
  • What does that tell us about Room 204's data? (More students live 2 blocks from school than any other distance.)

Find the Mode. Explain to students that the value that appears most frequently in a data set is called the mode. Sometimes that number is used to represent the whole data set. It is a kind of average.

Ask:

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  • Do you think someone might say about Room 204 “Most of the kids in Room 204 live about 2 blocks from school”? (Yes)
  • What do you think about someone saying that? Is it reasonable? (Answers may vary. It would be reasonable because 2 blocks appears the most times.)

Students will learn about another kind of average, the median, in Lesson 3.

Choose a Variable to Study. Refer back to the Variables and Possible Values Data Table students generated in Lesson 1. See Figure 1 in Lesson 1. Some variables your class listed in Lesson 1 may be numerical variables. Title the third column, “Type of Variable” (categorical or numerical). Ask students to say whether each variable is categorical or numerical and add their responses to the third column of the data table. For example, height and hand length are numerical variables. Eye color and birthday month are categorical. Brainstorm a few more variables with the class to ensure they understand the difference between categorical and numerical variables.

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Distinguishing between numerical and categorical variables. Some students may have the misconception that eye color is a numerical variable because you can count the number of students with brown eyes. Help students understand this distinction by asking questions like the following:

  • If the variable is “weight,” give me a value. (75 pounds)
  • Do you think “weight,” is a categorical or a numerical variable? (numerical)
  • Why? (75 pounds is a number)
  • If the variable is “type of shoe,” give me a value. (flip-flop)
  • Do you think “type of shoe,” is a categorical or a numerical variable? (categorical)
  • Why? (Because flip-flop is not a number)
  • If the variable is “number of children in a family,” give me a value. (2 children)
  • Is “number of children in a family,” a categorical or numerical variable? (It is numerical because the value, 2 children, is a number.)

Numerical variables are generally graphed using numbers on the horizontal axis, whereas categorical variables are graphed using words on the horizontal axis.

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The discussion of Questions 1–10 provides further opportunity for you to note individual students' abilities to name variables and list values [E1] and to find information by reading a table or graph [E7]. Focus on those students you were not able to assess in Lesson 1.

The Workshop in Lesson 6 provides targeted practice with reading tables and graphs.

Students work in groups to generate more numerical variables for the table (Question 1). Have each group draw a two-column data table. Ask them to record numerical variables in the first column and values that correspond to each variable in the second column. Some common examples of numerical variables are number of family members, number of pets, height, and number of times moved. The values of these variables are numbers, e.g., the number of pets could be 0, 1, 2, 3, etc. After students have been given ample time to think of different numerical variables, pull the class together and add some of their ideas to the Variables and Possible Values Data Table from Lesson 1. See Figure 1 in Lesson 1.

Question 2 asks your class to choose a numerical variable to study. It is important that the variable you choose involves quick and easy data collection and is well defined. See the TIMS Tip.

Student Guide: 8 9 10
Answers
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