Primary Type: Formative Assessment
Status: Published
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Resource ID#: 69381
Two-Way Relative Frequency Table
Students are asked to convert raw data to relative frequencies by both rows and columns given a two-way frequency table.
Subject(s): Mathematics
Grade Level(s): 8
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, association, variables, bivariate data, two-way table, relative frequencies, percentages
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_TwoWayRelativeFrequencyTable_Worksheet.docx
MFAS_TwoWayRelativeFrequencyTable_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Two-Way Relative Frequency Table worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not have a complete understanding of the construction of a relative frequency table.
Examples of Student Work at this Level
The student:
Rewrites frequencies into the relative frequency table.
page 1 of 4 Provides two versions of the same table.
Does not differentiate between relative frequency tables by “row” or “column” totals.
Questions Eliciting Thinking
What are the two variables summarized in the table?
What does the entry 80 represent?
What is the total number of students who preferred math?
What is the total number of students who preferred team sports?
Instructional Implications
Explain the meaning of a relative frequency and the various ways they can be represented (e.g., as fractions, decimals, or percents). Guide the student to calculate the
column and row totals and to use the totals to complete each table. Assist the student in understanding the difference between relative frequencies calculated using
column totals and those calculated using row totals.
Provide additional opportunities to create two-way frequency tables and two-way relative frequency tables.
Consider implementing the MFAS task Music and Sports (8.SP.1.4) to assess the student’s understanding of creating a two­way frequency table.
Making Progress
Misconception/Error
The student makes a calculation error.
Examples of Student Work at this Level
The student calculates column and row totals and uses the appropriate total to calculate the relative frequencies. However, the student:
Rounds incorrectly.
Makes an error calculating a relative frequency.
Calculates a total incorrectly, therefore using the wrong value to calculate the relative frequencies.
page 2 of 4 Questions Eliciting Thinking
What is the correct way to round a number? Can you check the way you rounded each value?
What total did you use when you calculated each relative frequency? Can you check your work?
Can you review your calculations of the totals? What is each row/column total?
Instructional Implications
Provide feedback to the student regarding any error made and allow the student to revise his or her work. Ask the student to explain what each value represents in
context.
Ask the student to explain the difference in meaning between the relative frequencies calculated by rows and the relative frequencies calculated by columns.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly converts the raw data to relative frequencies by using fraction, decimal, or percent values.
Questions Eliciting Thinking
What does the cell value of 67% represent, in this context?
Are there any patterns of association between the two variables?
Which table, the frequency or relative frequency, is better to use when looking for patterns of association?
Instructional Implications
Ask the student to look for and describe any patterns of association between the two variables.
Consider implementing the MFAS tasks School Start Time and Siblings and Pets (8.SP.1.4) to assess interpreting patterns of association.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Two-Way Relative Frequency Table worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
page 3 of 4 Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.8.SP.1.4:
Description
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and
relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical
variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible
association between the two variables. For example, collect data from students in your class on whether or not they
have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those
who have a curfew also tend to have chores?
page 4 of 4