The goal of this discussion is for students to think about how to construct and interpret data. Here is a sample table displaying made-up data for a class. 

Discuss students’ understanding of using a table to interpret data, and ask questions about the data points that are not addressed in the questions. Here are sample questions to promote a class discussion:

• “What is the difference between a table and a two-way table?” (Two-way tables are a specific type of table that can be used to organize data into two categories at once.)
• “What strategies did you use to answer questions about specific categories?” (I was sure to circle the entire column or row that the question asked about so that I could narrow down the focus on the table and have a more clear idea of what was being asked of me.)
• “What does the number 6 mean in the table?” (6 is the total number of students who prefer laptops.)
• “What does the number in the bottom right of the table represent?” (It is the total number of students who were surveyed in the class.)
• “How many students prefer baseball?” (12)
• “How many students prefer baseball and tablets?” (9)
• “How many students prefer basketball and laptops?” (4)

The goal of this discussion is for students to explain how they completed and interpreted the two-way table.

Direct students’ attention to the reference created using Collect and Display. Ask students to share how they filled in the table. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases. For example, the display may have “I filled in the boxes” already on it and can be updated with the phrase “I added the values in the cells in a row or column to calculate the total.”

Discuss how students interpret the table. Here are questions to promote class discussion:

• “How can you tell which number represents the total number of students who were surveyed?” (I look for the part of the table with the total that includes the numbers from all of the categories.)
• “What do you find challenging about interpreting a two-way table?” (Having multiple categories can make the data difficult to interpret.)
• “What are some advantages of organizing data with a two-way table?” (It can make categorical data easier to organize, sort, and interpret.)