
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 know how to create and interpret frequency tables and will be able to draw conclusions by describing possible associations and trends in the data.

Prior Knowledge: What prior knowledge should students have for this lesson?
MAFS.8.SP.1.4  Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies and relative frequencies in a twoway table.
The students should be able to construct and interpret a twoway frequency table by summarizing the data of two categorical variables. The students should also be able to use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Guiding Questions: What are the guiding questions for this lesson?
Does gender play a role in the beverages, music, sports, theme parks, subjects, travel locations, and food that high school students prefer?

Teaching Phase: How will the teacher present the concept or skill to students?
As the students walk into the classroom, the teacher will have the students indicate his or her sneaker preference in a tally chart drawn on the board. The tally chart can be drawn similar to the chart on the student worksheet with rows representing sneaker brands (i.e., Jordan, Nike, Sketchers) and columns indicating gender (i.e., girls and boys). Pose the question, "Do you believe there is an association between gender and sneaker preference?" To further engage the students, the teacher can ask them to justify why they believe there is, or isn't, an association. Distribute the Teaching Phase worksheet (see attached) to to the students. Have the students transfer the information from the board onto their frequency table. (If time is limited, the teacher may use the fabricated data available in the key.)
After the tally chart on the board is complete, the teacher will begin by asking the students to discuss the following questions with a partner, or group.
 What is a twoway frequency table?
 What are joint and marginal frequencies?
 What are conditional frequencies and how are they calculated?
Based on student conversations and questioning, the teacher may need to review the following information.
Understanding TwoWay Frequency Tables:
A twoway frequency table is a table that compares the frequency of two categorical variables. Relative frequency is the number of times an event occurs out of the total number of events. It can be expressed as a ratio, decimal or percent. The cells that join one variable from the row with one variable from the column in a relative frequency table are called the joint relative frequencies. Joint relative frequency is the ratio of the frequency in a particular category out of the total number of data values. The sum of the joint relative frequencies over the total number of data values is the marginal relative frequency, which is located in the margin, or right and bottom edge, of the table. Conditional relative frequency is the ratio of a joint relative frequency and the related marginal relative frequency. Conditional relative frequencies are used to investigate possible associations between bivariate categorical data. The greater the differences in the conditional relative frequencies, the stronger the association between the variables. The teacher should stress to the students that an association between two variables, regardless of how strong, does not necessarily mean causation.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
The teacher will have the students transfer the data from the Tally Chart (Part 1) to the Frequency Table (Part 2) of the Teaching Phase worksheet (see attached). If needed, the teacher may want to remind the students how to create a twoway frequency table from a tally chart. Have the students respond to the questions in Part 2 on the worksheet. The teacher should monitor student responses and provide feedback as needed.
The teacher should provide the answers to Part 2 of the Teaching Phase worksheet (see included key) and address any questions or misconceptions the students may have at this point. Guide the students to understand that in order to look for an association between gender and sneaker preference, they will need to compare the conditional relative frequencies for the category of interest. The students should use same twoway frequency table but will need to calculate the conditional relative frequencies that would be most helpful in determining whether or not there is an association between gender and sneaker brand. Encourage the students to recognize that the category of interest is gender and that they should therefore calculate the conditional relative frequencies by columns.
Students will then use this twoway frequency table to create a conditional relative frequency table by columns (Part 3). The students should look for associations or trends within the data. Have the students discuss what they observe with a partner or in groups. The students should analyze the twoway frequency table to investigate possible associations between gender and sneaker preference. The students should then answer the questions in Part 3. Student responses should be used to determine the students' understanding of the lesson objectives. The teacher should provide the answers to Part 3 of the Teaching Phase worksheet (see included key) and address any questions or misconceptions the students may have at this point.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Prior to the lesson, the teacher will place the students in groups and give each group a topic for their survey. Each group member will survey twenty (20) people as a home learning assignment and record the data in a tally chart. The data collected by each student will be used during the activity.
The teacher should distribute the Distribution of Duties list (included in the Activity worksheet attached) and one copy of the Activity worksheet (see attached) to each member of the group. If there are not 5 members in the group, some duties may be shared.
The following duties below should be either selected by or assigned to the students in the group.
 Data Collector  This student will compile all the data from each group member into a single frequency table. The table will then be used by each group member to create his or her twoway frequency table.
 Data Check (1)  This student will lead the group in comparing the joint and marginal frequencies of each member's twoway frequency table. He or she will guide the discussion regarding the correction of any mistakes. If all members of the group do not agree with a specific value or understand how the frequency was calculated, this student will notify the teacher of the unresolved question in the group.
 Data Check (2)  This student will lead the group in comparing the relative joint and marginal frequencies of each member's conditional relative twoway frequency table. He or she will guide the discussion regarding the correction of any mistakes. If all members of the group do not agree with a specific value or understand how the frequency was calculated, this student will notify the teacher of the unresolved question in the group. This student will select the table that will be presented to the class under the projector.
 Data Analysis  This student will lead the group in comparing the statistical question, any observations, and any associations in the data made by each group member and compiling it into one for the presentation.
 Presenter  This student will present the findings (e.g., the statistical question, an accurate conditional relative twoway frequency table, any observations from the data, and any associations between the two categorical variables) to the class.
Students should sit with their group and compile the data that was previously collected.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Class discussion based on the presentations.
Students will have a homework assignment where they will go around the school and collect data on how students come to school. The categories mode of of transportation (e.g., school bus, metro bus, walking, parent drop off, driving, biking) and the grade level of the student (e.g., 9^{th} , 10^{th} , 11^{th}, 12^{th}). The assignment should include a statistical question, an accurate conditional relative twoway frequency table, any observations from the data, and any associations between the two categorical variables.

Summative Assessment
The summative assessment will be the presentations made by each group. The students have an opportunity to receive teacher and peer feedback prior to their presentation.

Formative Assessment
As the students are recording the data in their frequency table (Part 1 of the Teaching Phase worksheet attached) and discussing the questions posed at the beginning of the period, the teacher should monitor their work and conversations to access prior knowledge and identify gaps and misconceptions. If students are unable to correctly complete the tally chart or answer the questions, the teacher should spend more time reviewing the vocabulary (Teaching Phase) with the class. If needed, the teacher can also demonstrate how to create a twofrequency table using the data they collected.
The teacher will walk around the classroom during the Guided and Independent Practice as each student or group of students work(s) on generating the twoway frequency table. The teacher may decide to pull students that are still struggling after the Guided Practice and assist them as they work on the Independent Practice. The teacher could also group these students together and provide the group members with fabricated data for one of the survey topics. This would allow the students to work together on the same data set as the teacher provides assistance.
At the end of the activity (lesson), the teacher will ask each group to present any associations or trends they observed in the data and to justify their response using the twoway frequency table, explaining their interpretation of joint, marginal and conditional relative frequencies. The teacher should use this opportunity to address any questions or misconceptions the students may have.

Feedback to Students
The teacher should provide feedback during both the Guided and Independent Practice. The teacher will also provide the students with the answers to Part 2 of the Teaching Phase worksheet. At this time, the students should adjust their responses as guided by the teacher.
Each student will calculate the conditional relative frequency for the data in their group. The students should compare their results and provide feedback to each other regarding differences in their responses.
Each group will have the chance to present their statistical question, their twoway frequency table with their findings regarding an association between the bivariate categorical data. Students will receive feedback from the teacher during their presentations. They will also have the opportunity to receive feedback from their peers.