The purpose of this activity is not to construct a perfect two-way table, but to motivate the need for an efficient representation. Monitor for students who:

1. Go back to the original statements to answer each question from scratch.
2. Draw shapes to represent the students and group them into utensil and paper preferences.
3. Create a table to keep track of the information, complete the table, and then answer the questions.

The purpose of this discussion is for students to share the different ways they approached this problem and to introduce how to represent data using a two-way table.

Select previously identified students who used different solving methods in the order: 

1. Answering the question from scratch
2. Drawing shapes for groupings
3. Creating a table

Point out that a variable is a characteristic that can take on different values and a categorical variable represents data which can be divided into groups or categories. In this example, writing utensil preference and paper preference are two categorical variables.

If no students used a table to organize the information and answer the questions, demonstrate how to solve the questions by creating and completing a two-way table. 

Ask students:

• “Why is this table an effective method for solving this question?” (It is effective because it keeps track of all the information we know and don’t know in a way that is organized to show the relationship between each piece of information.)
• “Was using a table the only way to solve the questions?” (No, there are other methods to arrive at a good solution. Reasoning from the original statements, drawing a representation of the situation, or other similar methods are also good ways to approach the problem.)
• “What does the word ‘two’ in a two-way table refer to? How is it seen in the example from the task?” (It refers to the number of categorical variables, not the number of categories for each variable. In this example, the two variables are writing utensil preference and paper preference.)

Summarize by stating: “A two-way table can be used to organize data from two different categorical variables.”

The mathematical purpose of this activity is for students to interpret data in a two-way table. Students answer questions, such as the meaning of particular values or totals for a group, using information in a two-way table.

This activity gives students an opportunity to determine and request the information needed to understand the relationships among cells in a two-way table.  

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).