##### Teaching Phase: How will the teacher present the concept or skill to students?

Preview for the lesson by watching the YouTube videos. (You could preview with all three videos together or break the lesson into segments by using the videos strategically in the lesson.)

- Understand, construct and interpret two way tables - Lesson 1 of 3

http://www.youtube.com/watch?v=TFzLXThqVNQ
- Two-Way Tables Corbettmaths

http://www.youtube.com/watch?v=U785Y-QI-K8
- Frequency and Relative Frequency Distributions

http://www.youtube.com/watch?v=bzvHqVB-40A

I DO Phase: 1^{st} day/one class period - Teacher is demonstrating and giving students time to repeat the steps throughout the process.

**Formulate a Statistical Question**

**Ask:**

- Have ever flipped a coin to make a decision of what to do.
- What type of coin did you flip?
- What were the results?
- Why did you flip that coin?
- What do you expect to get when you flip a coin? Can you count on getting the same results every time you flip the coin? Why or why not?

The statistical question is, "When flipping a coin, will the results be the same no matter what type of coin you toss?"

**Collect Appropriate Data**

- Have one student demonstrate how he/she flips a coin. Ask whether other students have different strategies for how they flip the coin, allowing demonstration of a few. Have students discuss the pros and cons of the best strategies to decide what method will be used to collect data.
- Hand out the data collection sheet to each student.

SEE ATTACHMENTS:

- Data Collection Chart for Two-Way Table Lesson
- Data Collection Chart for Two-Way Table Lesson with Sample Data for teacher

Your students should check what type coin they will be flipping first. (Penny, Nickel, Dime, or Quarter) Students should record the data on the data collection sheet in the appropriate column by making a tally mark under the "Heads" column or under the "Tails" column for each of 50 coin flips. Tally marks should be totaled under each column after completing all 50 trials.

After recording data for one coin, students should repeat the process for the other three types of coins.

**Analyze the Data**

- Explain: one way to help analyze the data is to organize the data into a table. Determine which answers to record from the data collection sheets. On the board, display a data collection sheet.
- SEE ATTACHMENTS- Sample Tables For Instruction During Lesson

Explain to your students that their frequency table can be displayed in a different way, called a two-way table. A two-way table organizes data about two categorical variables with rows labeled with the categories of one variable and the columns labeled with the categories of the other variable. In this investigation, the rows of the table are labeled with Heads and Tails. The columns are labeled with the type of coin.

Draw and label a the two-way table. Note that the two-way format is useful when investigating whether there is an association between two categorical variables. Refer to the vocabulary sheet to be sure to discuss the vocabulary as you progress through the lesson.

SEE ATTACHMENT: Vocabulary for Working With Two-Way Tables

**Demonstrate:** Label the quarter section of the table with the letters "a" and "b" in the cells beneath Quarter. There are "a+b" events for quarters. The total for the column is reached by adding the numbers in both cells so that a+b= t

Ask your students to fill in the frequency counts for the possibilities for quarters based on their recording sheet. Students can plug in their frequency count data for the quarter into their own table.

The teacher should walk around the room checking for errors. Once each student has been checked for comprehension, they can be allowed to proceed with entering the data for their other coins.

Demonstrate how to total the "Heads" row and allow students to proceed with calculating the total for the "Tails" row.

Discuss joint frequency and marginal frequency vocabulary. (Refer to the "Vocabulary for Working With Two-Way Tables" sheet and the sample table sheet)

Ask your students to use the data from their table to answer the following questions. As students answer each question, have them point to the appropriate cell.

- How many total coin flips took place?
- How many "Heads" did you get when you flipped the quarter?
- How many "Heads" did you get when you flipped the Dime? Nickel? Penny?
- Were those answers all the same?
- How many "Tails" did you get when you flipped the quarter?
- How many "Tails" did you get when you flipped the Dime? Nickel? Penny?
- Were those answers all the same?

Have students make predictions for the probability of flipping Heads or Tails for each coin? How would we calculate that?

SEE ATTACHMENT

**Explain : **probability is a comparison of the number of times a result occurs as compared to the total number of trials. This can be calculated in columns, rows, or the entire table. Discuss vocabulary of conditional frequency.

Have students make a copy of their table, but this time they fill the cells with the relative frequency (percentage). ***Teacher will need to discuss the concept of rounding (precision) when using percentages.

Ask students to interpret the data in the relative frequency chart by making statements that compare the results. Discuss the statements.

Return to the initial question, "Did the size of the coin flipped make a difference in the probability of "Heads" or "Tails" occurring as the result of the flip?

Review the vocabulary using the vocabulary sheet.