
Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
As a result of this lesson, students will understand and be able to:
 use given information and construct a twoway frequency table,
 complete all values within the frequency table,
 identify and explain the meaning of the marginal and joint frequencies,draw conclusions and state trends that are indicated by the data.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should have learned about oneway frequencies and be able to create and read them.

Guiding Questions: What are the guiding questions for this lesson?
 What strategies are useful in completing all the cells of a frequency table? (Answer: 1) Look for a row or column that is missing only one value. That value can be found by subtracting the known marginal frequencies of that row or column from the total of the row or column. Or, if only the total is missing, then add up the values in that row or column. 2) The totals of the rows and the total of the columns should add up to the same grand total.)
 What is the specific meaning of each joint frequency? (Answer: This varies depending on the categories. For example, the number of boys who like Legos, or the number of girls who like Legos. Each case is the intersection of a row and a column.)
 What is the specific meaning of each marginal frequency? (Answer: This also varies; it is based on the categories. For example: total number of respondents who preferred painting, or total number of boys.)
 What is the meaning of the total of each row? Of each column? (Answer: It tells the total number for that category.)

Teaching Phase: How will the teacher present the concept or skill to students?
The lesson and activities begin with the structure of a powerpoint presentation. The slides contain extensive notes for the teacher. The notes include answers to the questions and tips on common errors that may occur.
The teaching phase begins with a classic puzzle called a "Magic Square." This will engage the students and also provide the basis for an important strategy used in completing twoway frequency tables, which is to start by filling in a row or column that is only missing one value.
The next activity, "Rainy Day Fun", provides a step by step process for the students to complete as a guided practice, while being guided by the teacher and the powerpoint slides. Specific notes to the teacher, sample questions to ask the class, and desired responses are all included in the notes accompanying each slide.
 Students will be introduced to a twoway frequency table in the context of a survey about camp activities for a rainy day.
 The teacher will ask students to respond to questions about the categories, data points, marginal frequencies, and joint frequencies, both in writing and in class discussion.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
The students will complete the worksheet activity, "Lollipops, anyone?", which parallels the previous example. In addition, the following will occur:
 With teacher guidance, the students will complete a twoway frequency table that is only partially filled in.
 With teacher guidance, students will explain and discuss their methods of completing the table and checking their work.
 Students will be asked to explain the methods they used to complete the table.
In this activity, the students may work individually, in pairs, or small groups. Each group will be able to complete the frequency table given, and answer the accompanying questions.
Because all the answers are interrelated, it will be especially important for students to discuss their methodology and to practice checking their work.
After the students have completed the worksheet, then the answers can be checked as a class discussion/activity. An alternative is to prepare the original incomplete table on a flip chart or on the chalkboard and then call on students one at a time to complete ONE data point in the table. This will be a dynamic activity, since each student will have to depend on what the previous students have filled in, and to then determine what can be filled in next.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
The students will complete the worksheet activity, "What's for lunch?", which parallels the previous example. It has more categories, so the table is larger and contains more data points.
In this activity, the students may work individually or in pairs. They should be able to complete the frequency table given, and answer the accompanying questions.
Because all the answers are interrelated, it will be especially important for students to discuss their methodology and to practice checking their work.
After the students have completed the worksheet, then the answers can be checked as a class discussion/activity.
An alternative is to prepare the original incomplete table on a flip chart or on the chalkboard and then call on students one at a time to complete ONE data point in the table. This will be a dynamic activity, since each student will have to depend on what the previous students have filled in, and determine what can be filled in next. After the table is filled in, then the questions on the worksheet can be discussed, and students may be called on to share their answers.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
After the independent practice is completed and checked, the teacher can lead a quick review discussion by asking the students to volunteer the main ideas they have learned. The teacher can make a bulleted list on the board of what the students suggest. The list should include:
 To start to fill in a table, look for a row or column that is only missing one number.
 The right column and the bottom row should both have the same total.
 The Joint Frequencies in the middle of the table tell information involving both categories.
 The Marginal Frequencies are in the right column and the bottom row. They tell the totals for any given category.

Summative Assessment
The students will complete an example similar to the ones used in the guided and independent practice. This example is the document "Summer Fun". It will be the summative assessment, and involve using given data to construct a twoway frequency table, identifying the joint and marginal frequencies, describing the meaning of values within the frequency table, and using the data in the table to draw conclusions.
Because the summative assessment is very detailed, it will provide the teacher with accurate insight about the level of student learning that has been achieved.

Formative Assessment
Formative assessment occurs during the guided practice and the independent practice.
Throughout the lesson, the teacher will gather information about student understanding by posing questions, asking students to explain their thinking, and by circulating around the classroom and observing student work.
At each phase of the lesson, the teacher will be able to gauge to what extent students understand the concepts. If students comprehend well, then the teacher can proceed with the next step in the activity. If the teacher observes that the students do not thoroughly understand something and are not ready to proceed, then additional explanation, examples, or discussion is recommended. There are specific notes accompanying the powerpoint document that provide specific guidelines to the teacher concerning common misconceptions and errors that may occur.

Feedback to Students
Throughout the lesson the students will respond to questions and prompts that the teacher poses. During each example, sharing of answers, methods, and explanations will occur. The teacher will moderate these wholeclass discussions and provide reinforcement of correct work or correction of responses that are not accurate.
At each phase of the lesson, students will have the opportunity to make corrections or redo any part of the examples where appropriate.