
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 identify associations and trends in a teacher provided twoway frequency table.
 Students will construct a twoway frequency table when given a topic and guidelines to follow.
 Students will calculate relative frequencies for data in twoway frequency tables.
 Students will identify associations and trends in the data set they created.
 Students will interpret and compare relative frequencies to decide whether different data sets have associations and trends.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should already know how to create twoway frequency tables and calculate relative frequencies.

Guiding Questions: What are the guiding questions for this lesson?
Do male and female students differ in their preferences for food and/or interests?

Teaching Phase: How will the teacher present the concept or skill to students?
The teacher will begin class with the Warm Up worksheet (see attached) that asks students several questions. These questions will be collected, separated by question, and used as data for a later activity. The data will be separate by gender as well, using two shades of colored paper may assist in this. The teacher will ask the following questions.
 How do we categorize and display date that we collect?
 In a data set, are there different associations depending on which conditional relative frequencies we use (i.e., row vs. column)?
 Is it possible to display the data in a way that will mislead viewers?
Since the creation of a twoway frequency tables is review, teacher will ask students to explain what a twoway frequency table looks like and what type of information would be presented in one. Teachers are looking for an answer such as: a statistical table that shows the observed number (frequency) of data for two variables (i.e., bivariate catagorical data), the rows would indicate one category and the columns indicating the other category. For example, there are 500 students in the 9^{th} grade class and two students were running for class president, Ben and Alexis. The table can be used to display the results of the vote by gender.
Voting Results

Ben

Alexis

Total

Male




Female




Total



500

The teacher should make note of students who do not seem comfortable with the topic and provide these students with a sheet to fill in as the teacher is reviewing Examples 1 and 2 from the Examples of TwoWay Frequency Tables worksheet described in the Guided Practice section.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Whole class: Students will be given a couple of completed twoway frequency tables to examine (see attached Examples of TwoWay Frequency Tables worksheet). (The teacher will either project the tables or give handouts to the class). If needed, teacher should explain that each type of relative frequency table makes a different contribution to understanding the relationship between gender and curfew time. The teacher may need to remind the students that a conditional relative frequency compares a frequency count to the marginal total. Students and teacher will interpret what they see in the tables in Example 1 on the worksheet. For example, "Relative Frequency for Rows" table most clearly shows the probability that each gender will prefer a particular leisure activity. For instance, it is easy to see that the probability that a man will prefer dance is 10%; the probability that a woman will prefer dance is 53%; the probability that a man will prefer sports is 50%; and so on. Students should be able to answer questions such as: How many males participated in the survey? How many females participated in the survey? How many students had a curfew? How many female students did not have a curfew? Teacher should have the class discuss the change in the relative frequencies from one table to the next (e.g., the relative frequency of females with a curfew is 30%, but given the student was female the conditional relative frequency is 66.7%). What would the frequencies equal if there was no association between the data, (i.e., if the data was independent)? (22.5% of both males and females would have a curfew and 27.5% of both genders would not have a curfew.) The teacher should lead the student in drawing conclusions and developing a summary of their finding. For example, among 9^{th} graders, there seems to be an association between being male and not having a curfew, as well as being a female and having a curfew. 70% of the 50 males surveyed did not have a curfew and 60% of the 50 females surveyed did have a curfew While the association could be stronger, if asked if a male 9^{th} grader had a curfew, I would predict that he doesn't. If asked if a female 9^{th} grader has a curfew, I would predict that she did.
Students and teacher will calculate relative frequencies and conditional relative frequencies for the data in the tables and compare their findings in Example 2. Students should be able to answer questions such as: What percentage of those surveyed are female? What is the relative frequency of females who had a curfew? Was there a higher percentage of males or females who did not have a curfew? Students and teacher will identify associations and practice writing a paragraph to summarize their findings. An association exists between two categorical variables if there is a significant different between the conditional relative frequencies of the rows or columns of the table. The bigger the differences in the conditional relative frequencies, the stronger the association between the variables. If there is not a difference in the conditional relative frequencies, there may not be an association between the variables, (i.e., if there is not association between male and female voters in the election, that would mean that 28% of male and 26% of female students would vote for Ben and 24% of the male and 22% of the female students would vote for Alexis. The teacher should make note of students who do not seem comfortable with the topic.
Group work: The teacher will introduce Red, Yellow, and Green Cue Cards (see attached) and explain how each group will use them. (The purpose of the colored cards are described in the Formative Assessment section.) The Teacher will give directions for what each group will be expected to do. Each student will be creating their own frequency table using the Student worksheet: TwoWay Frequency table classwork (see attached). Each group member will use the same data within their group. Groups will create four tables for their data: a twoway frequency table, a relative frequency table and two conditional relative frequency tables (row and column). Groups will discuss the data and compare their findings. Groups will write a summary of their data findings, including identifying associations and trends in the data. Suggested answers are attached (sample_Answers). The teacher will ask the following questions and tell students to keep these in mind while doing their work.
 How do we categorize and display data that we collect?
 In a data set, are there different associations depending at which conditional relative frequencies we look? (row vs. column)
 Is it possible to display the data in a way that will mislead viewers?
Once the directions are given, students will be broken up into 4 groups for the activity. The teacher will group students who are knowledgeable with students who seemed to struggle with the topic. Each group will randomly choose a topic for their twoway frequency table from the Group Topic Cards (see attached) as the teacher passes out a ziplock bag with Student Role Cards (see attached). Groups will agree on roles for their members and place the role card on the corresponding desks for the members in their group. Roles are as follows: Materials Manager, Female Student Tally Counter, Male Student Tally Counter, Procedural Technician/Time Keeper (keeps group on task), Resource Person (in charge of the Red/Yellow/Green cue cards for the group), and Recorder. If the group has less than 6 students, some students will have to take on multiple roles. [While students are deciding on roles, teacher should be cutting up questions 1  4 from the Warm up worksheet given at the beginning of class and grouping each question by gender. [If the teacher decides to have more than 4 groups, the teacher would cut out all 6 questions from the Warm up worksheet.] Once students have decided who will be the Materials Manager, the teacher can have that student go up and take a marker board, dry erase marker, eraser, Student worksheet: TwoWay Frequency table for their group (1 per person at this time), rulers, and one paper clipped stack Cue Cards.] By the time each group has completed the above, the teacher should have cut and separated the questions by topic and gender. (The teacher may consider using one color paper for male students' surveys and a second color for female students' surveys to make sorting easier). The teacher will give each group the responses to the survey topic they selected. The Male and Female Student Tally Counter will tally the responses for their table. The recorder will display the data for the group. Each student will use his or her own Student worksheet: TwoWay Frequency table and construct his or her own twoway frequency table to represent the data. Students will do their own calculations and complete the relative frequency tables and then compare with the group. The recorder will be responsible for writing the final calculations on the marker board for class presentation. Students will discuss their data, interpret and compare relative frequencies to conclude if the data sets have any associations and trends. Each student will write their own paragraph explaining their findings. Each group will present their data to their classmates. (See Rubric attachment) Students will answer the following questions:
 How do we categorize and display data that we collect?
 In a data set, are there different associations depending at which conditional relative frequencies we look? (row vs. column)
 Is it possible to display the data in a way that will mislead viewers?

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
For homework, students will collect 40 more pieces of data regarding the same topic from people outside of their class and add it to their collection of data from class. Students will recreate the twoway frequency table constructed in class to represent the new totals within each category. Students will complete the worksheet, calculating relative frequencies and conditional relative frequencies for the data in their new table, identify associations and trends found in their new data. Students will draw conclusions based on the relative frequencies and write a summary of their findings when the 40 new pieces of data were added. In their summary, students need to include a comparison of original associations and new associations, or lack there of. The teacher will pass out the TwoWay Frequency Table_homework document for students to take home to complete their homework.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Teacher will discuss the data collected in class today. How could we display the data if we worked for Apple vs. Samsung? Do you think companies use this technique when advertising? The teacher will discuss how adding more data could affect the current associations that were found in class today and make conjectures about what will happen when we collect more data.

Summative Assessment
Each group will present their data, findings, and summaries. The class will discuss the associations found by each group and give any interpretation they may have found that the presenters did not discuss. Individually, students will be expected to gather more data, update the tables made in class, calculate relative frequencies and create a new summary interpreting, comparing, and explaining associations found at home to those found in class. The teacher will check student work and read summaries to check for student understanding.

Formative Assessment
Since students should have prior knowledge of creating twoway frequency tables, the teacher will ask students to explain/review what they know about creating and reading twoway frequency tables. The teacher can have students raise their hands or stand up when they agree with their classmates' explanation. The teacher will make note of students who seem uneasy about the topic and be sure to place them in groups later with students who have explained and seem capable of completing their tables.
(If most of the class does not participate in explaining twoway frequency tables, see Accommodations.) The teacher will have a discussion with the class, calculate relative frequencies, identify associations, trends, and practice writing a paragraph explaining any associations found in the given twoway frequency table. (If the class created one together, they would discuss that table and then move to the example given with this lesson.)
During group work, groups will use cue cards to indicate their status with the activity. Students have red, yellow, and green cards that they place on their desk that describes their comfort level or status during the activity. They will place the red card on top if their groups is stuck or not able to move forward, yellow on top if they need support soon or have a question that nobody in the group can answer or on which that they don't agree, and they place green on top if they are good to go! The teacher will utilize this strategy to access student understanding during the group activity and target support for the group(s) with red cards first, then move to the group(s) with yellow cards, and finally check with the group(s) with the green cards to ensure the level of understanding of these students as well. Groups should change their colors as needed to describe their status.

Feedback to Students
The teacher will circulate the classroom and give positive reinforcement to groups and answer questions/clarify misunderstandings during the activity as needed. Students will have an opportunity to use the feedback from the teacher during class discussion, during their group work, and on their homework assignments.