
Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
1. Students will be able to interpret relative (joint, marginal, and conditional) frequencies presented in the given table.
2. Students will be able to identify any relationships between the variables within a twoway table.
3. Students will be able to provide a verbal and written justification of the associations, or lack thereof, in a twoway frequency table.

Prior Knowledge: What prior knowledge should students have for this lesson?
1. Students should be able to define bivariate data.
 The teacher can have students copy the definition into their math notebook.
2. Students should be able to construct a twoway frequency table from a data set.
 The warmup will review this information.
3. Students should be able to calculate relative frequencies.
 The warmup will review this information.

Guiding Questions: What are the guiding questions for this lesson?
Is there a factor that can be associated with the number of dropouts?

Teaching Phase: How will the teacher present the concept or skill to students?
WarmUp (10 minutes)
1. Students will complete the Job/Car Handout, Warm Up Part 1 (see attached). On a sheet of paper (or on the attached handout), students will construct a twoway table and calculate the relative frequencies. Students should be allowed to compare their answers to other students in close proximity to their assigned seat. Students that understand Part 1 clearly should begin Warm Up Part 2.
2. After eight minutes, the teacher will provide the answer to both warm ups by eliciting responses from the students. At this time, the teacher should ensure that the majority of the students are comfortable with moving forward with the lesson.
Lesson (15 minutes)
1. The teacher will begin the lesson by discussing the relative frequencies from Warm Up Part 2 (see attached). The teacher should define and identify for the students: joint, marginal, and conditional frequencies. Remind the students that relative frequency and conditional relative frequencies can be expressed as a ratio or a percent.
 Relative Frequency  the ratio of the number of times an event occurs to the total number of events.
 Joint Frequency  the ratio of the frequency in a particular category divided by the total number of data values.
 Marginal Frequency  the sum of the joint relative frequencies in a row or column of a twoway table.
 Conditional Frequency  compares a frequency count to the marginal total that represents the condition of the ratio of a joint relative frequency to a related marginal relative frequency in a twoway table.
2. The teacher should also include in the discussion how associations and trends are found in the data. Associations/Trends are suggested when there are significant differences in the conditional relative frequencies. The bigger the difference the more likely there is an association (i.e., the variables are dependent) . A smaller difference between relative conditional frequencies would suggest that there may not be an association between the categorical variables (i.e., the variables are independent).
 The teacher should also mention that association of categorical data does not lead to causation. It is simply a correlation of the variables.
The teacher should refer back to the warm up and have students discuss the associations in the table.
 There appears to be no association between seniors having a job and owning or not owning a car.
 There appears to be a strong association between seniors who do not have a job and do not own a car.
 There is a strong association of seniors who own a car and have a job.
 There is a moderate association of seniors who do not own a car and do not have a job.
3. The teacher should pass out the "Dropping Out or Staying In" handout (see attached) or project the handout on the board to facilitate a short discussion on the reasons why students drop out of high school and why others choose to complete high school. See Dropping Out or Staying In Answer Key for possible responses.
 The guided practice and the independent practice activities follow this theme.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
In pairs or in small groups and under the direction of the teacher, students will complete the Guided Practice handout (see attached; 10 minutes). The handout will give the students an opportunity to practice the following:
 Calculate and compare the conditional frequencies.
 Identify any associations.
 Write a justification for an association or no association and an explanation of what this means in context.
During this portion of the lesson, the teacher will model how to correctly answer a written response question. The response should include all three bullets listed above (see Guided Practice Answer Key handout attached).

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will individually or in pairs complete the Independent Practice handout (see attached; 10 minutes). As the students complete this handout, the teacher should walk around the room and observe the students as well as monitor their written responses. This assignment should be reviewed in class prior to dismissal as the final opportunity for feedback prior to assigning the summative assessment.
The student should:
 Calculate and compare the conditional frequencies.
 Identify any associations.
 Write a justification for an association or no association and an explanation of what this means in the context of the problem.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
On a sticky note, note card, or sheet of paper, the students will provide an answer to one, two, or all three of the following questions (5 minutes). The responses should be collected before the students are released from class.
1. How can a twoway frequency table be useful in identifying associations and trends in the data?
Answer: An association exists if the conditional frequencies of two categorical variables for the row or column are different. The bigger the difference the stronger the relationship. The smaller the difference the more likely there is no association.
2. Is it necessary to calculate all of the relative frequencies when analyzing a twoway table?
Answer: The math question determines which relative frequency you need to calculate. If you are looking for associations, it is necessary to calculate the conditional relative frequencies.
3. Explain how correlation and causation relates to association found in a twoway frequency table.
Answer: Associations do not imply cause and effect relationships between categorical variables. They do, however, imply such a relationship if there is a correlation between the categorical variables within a twoway frequency table.

Summative Assessment
Students will complete a five question assessment that can be used as a quiz or homework assignment.
 The assessment will evaluate the student's ability to interpret, analyze, and explain any associations within the variables represented in a twoway table.
The student should:
 Calculate and compare the conditional frequencies.
 Identify any associations.
 Write a justification for an association or no association and an explanation of what this means in the context of the problem.

Formative Assessment
1. During the warmup activity (Warm Up Part 1 and Warm Up Part 2 attached), students will be given categorical data to summarize in a table format and asked to calculate the relative frequencies. This activity will inform the teacher if the students have the prior knowledge needed to proceed with the lesson. If needed, work with students that need additional assistance with Warm Up Part 1 as the remaining students begin on Warm Up Part 2.
2. The guided and independent practice activities will offer another opportunity for the teacher to assess if the students are able to analyze the relative frequencies in a twoway table and write a justifiable response to the presence of associations or no association.
Frequency distributions are constructed for these reasons:
 Large data sets can be summarized,
 we can gain some insight into the nature of data, and
 we have a basis for constructing important graphs (such as histograms, introduced in the next section).

Feedback to Students
1. The students will receive feedback while the teacher reviews the student responses to the warmup activity. This will give the students immediate feedback regarding their prior knowledge. This will also inform the teacher if the class is ready to move on to the lesson, or if there is a need to provide the class a minilesson on constructing and calculating twoway frequency tables.
2. The students will also receive feedback while completing the guided practice and after the independent practice activities.