Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 129901
Investigating Relationships With Two-Way Frequency
Tables
In this lesson, students are introduced to two-way frequency tables. They will calculate joint, marginal, and relative frequencies and draw
conclusions about the relationship between two categorical variables.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Interactive Whiteboard,
Basic Calculators
Instructional Time: 50 Minute(s)
Keywords: two-way frequency tables, categorical variables, joint frequencies, marginal frequencies, relative
frequencies
Resource Collection: FCR-STEMLearn Algebra
ATTACHMENTS
GuidedPracticewithKey.docx
IndependentInvestigation.docx
SummativeAssessmentandKey.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to:
Create a two-way frequency table using data collected on two categorical variables.
Read and interpret data displayed in a two-way frequency table.
Calculate relative frequencies in each of three different ways.
Use a two-way frequency table to clearly describe relationships between two categorical variables and provide supporting evidence.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should:
1. Understand the distinction between categorical and quantitative data.
2. Know how to display one-variable data in a one-way frequency table.
3. Be able to calculate decimals and percents.
Guiding Questions: What are the guiding questions for this lesson?
How can the relationship between two categorical variables be analyzed?
Teaching Phase: How will the teacher present the concept or skill to students?
To begin the lesson, the teacher should put a copy of the first frequency table from the Independent Investigation sheet on the board. The teacher can have students
page 1 of 3 add a tally mark in the appropriate cell of the table as they enter the class. As an alternative, the teacher can ask each student to indicate a preference by a show of
hands in a whole-class setting and record counts in the displayed table. This table will be used later for the Independent Investigation.
The teacher should use this opportunity to review the structure of a two-way frequency table. Make explicit that there are two categorical variables represented in the
table (gender and music type) and that there are two levels of each variable (male and female; hip-hop and rap). Clearly explain what the values in each cell
represent. Introduce the terms joint frequencies and marginal frequencies and illustrate these terms using entries from the table.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The teacher should then transition to the Guided Practice. A Guided Practice worksheet is provided and intended to be used as an integral part of the lesson. The
teacher will facilitate the completion of this worksheet.
Display the two-way frequency table for gender and ice cream flavor preference. Guide students to complete the marginal frequencies and then engage them in a
discussion of possible interpretations of the table.
Next, guide students to complete the relative frequency tables in each of three different ways (using the grand total, column totals, and row totals as the
denominator). Engage students in a discussion of the differences in what each table conveys. Then ask students to answer the question, "Is there a relationship
between gender and ice cream preference?" Circulate through the class and provide assistance and feedback, as needed. Next, engage the class in a whole-group
discussion of their responses to the question. Model how to clearly write a response that includes supporting evidence drawn from one or more of the tables.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
After the guided practice, students are challenged to interpret the data on music preference and gender collected at the start of class. An Independent Investigation
worksheet is provided which should be distributed to each student.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Eventually, reconvene the class to discuss responses to the Independent Investigation, review the main points of the lesson, and transition to the summative
assessment. Collect all written work; provide written feedback and return papers the next day.
Before transitioning to the summative assessment, review the main points of the lesson:
Frequency tables are used to examine the relationships between two categorical variables.
Frequency tables can contain frequency counts or relative frequencies.
There are three ways that relative frequencies can be calculated. Each conveys different information.
Summative Assessment
After the guided practice portion of the lesson and the Independent Investigation, students will complete the Summative Assessment worksheet. This can be
completed in class or as homework, depending on time constraints.
Formative Assessment
The teacher will have the opportunity to monitor student progress and provide feedback throughout the lesson. Analysis of responses on the Independent Investigation
worksheet can provide additional opportunities to uncover and address any misconceptions students might hold.
Feedback to Students
Throughout the lesson, the teacher will have the opportunity to circulate through the room to monitor student progress and provide feedback. Additionally, written
student work will be collected, evaluated, and returned with comments.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students can be paired with each other to provide assistance and mutual support.
Calculators can be used to find percents.
Extensions:
Introducing conditional relative frequencies is a natural extension of this lesson.
Suggested Technology: Interactive Whiteboard, Basic Calculators
Further Recommendations:
Answer keys for the Guided Practice and Summative Assessment are included in each document.
Additional Information/Instructions
By Author/Submitter
Math Practices:
Construct viable arguments and critique the reasoning of others.
Reason abstractly and quantitatively.
SOURCE AND ACCESS INFORMATION
Contributed by: Terry Crawford
Name of Author/Source: Terry Crawford
District/Organization of Contributor(s): Hendry
page 2 of 3 Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.S-ID.2.5:
Description
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the
context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and
trends in the data. ★
page 3 of 3