Getting Started

The student does not understand how to construct a two-way frequency table.

The student:

• Determines cell entries incorrectly (e.g., writing the total number of “yes” and “no” answers for each category (“Sports” and “Instruments”), without regard to the relationship between them.
  
  
     
   
• Significantly miscounts the raw data.
  
  
     
   
• Displays the data in some way other than a two-way table (e.g., as a table with one column or in a Venn Diagram).
  
  
  
   

What are the two variables in this survey? 

What do the letters in the table mean? Do you see any patterns in the values in the table?

What is a two-way frequency table? What does this kind of table look like?

What were the students who were surveyed asked?

Provide instruction on the structure of two-way frequency tables. Emphasize that the structure of the table must allow for all possible combinations of the levels of the variables to be represented. Assist the student in identifying the two variables described in the context (e.g., playing a sport and playing an instrument) and the number of levels of each variable (e.g., “yes” or “no”). Assist the student in developing the structure of the table. Then ask the student to tally the number of individuals described by each cell. Ask the student to calculate the row and column totals and explain that row and column totals should sum to the total number of students surveyed.

Provide additional opportunities to create two-way frequency tables from raw data.

Making Progress

The student omits a necessary component from the two-way frequency table.

The student has the correct basic structure of the table but makes a minor error. The student:

• Miscounts one or two of the data points.
  
  
  
   
• Neglects to include row and/or column totals.
  
  
  
   
• Miscounts row and/or column totals.
• Does not include appropriate labels and/or title.

Can you verify you have included all the data in your table?

What labels and title should be used for this table?

What are the totals for each column and row? What does this number (20) represent?

Provide feedback to the student regarding any error made and allow the student to revise his or her table. Then ask the student to interpret cell entries in context to check for further understanding.

Introduce the student to the concept of a relative frequency. Ask the student to convert the entries in the table to relative frequencies. Consider implementing the MFAS task Two-Way Relative Frequency Table (8.SP.1.4).

Got It

The student provides complete and correct responses to all components of the task.

The student correctly constructs a two-way frequency table with appropriate title, labels, cell values, and totals.

   

What does the cell value of eight represent, in this context?

How could you change the cell values to relative frequencies?

Are there any patterns of association between the two variables?

Introduce the student to the concept of a relative frequency. Ask the student to convert the entries in the table to relative frequencies. Have the student determine if there are any associations between playing or not playing sports and playing or not playing an instrument in the data from this survey.

Consider implementing the MFAS task Two-Way Relative Frequency Table (8.SP.1.4).

Provide opportunities for the student to practice interpreting data from a two-way table by implementing the MFAS tasks School Start Time and Siblings and Pets (8.SP.1.4).