SWBAT calculate relative frequencies to better understand two-way table data.

Becoming familiar with relative frequency sets groundwork for critical interpretaion of data.

10 minutes

As students enter I hand each an Entrance Slip to begin Part 2 of our lesson on Two-way Tables. Completing this table helps students to recall yesterday's lesson and helps us to begin moving into new content. After students complete the questions below the chart, I will call on volunteers to share their responses. My favorite part of this warmup follows. I extend the exercise by asking students to think of questions on their own, sharing them out loud for all to hear. When a student poses a question, I call on students that raise their hands to answer the student's prompt. So no one spoils the fun, I warn students not to shout answers out. For me, these questions and answers provide good insight into my students' current level of understanding.

15 minutes

In the New Information section of today's lesson I give a 10 minute lecture on **Relative Frequency** using a presentation. I project the presentation on the white board so that we can add details as I introduce material to the class. My primary is for my students to become comfortable with the mathematical meaning of relative frequency. Once Slide 3 is discussed, I let students know that relative frequency values can be written into a two-way table next to frequency values. But, they can also be recorded separately in a **relative frequency table**. To show them what I mean, I project these Example Tables . I point out two things here:

- These tables show horizontal or "row" relative frequencies, not columns.
- The sum of relative frequencies in each row must equal 1.

At this point in the lesson I want feedback from the students about their current level of understanding. I will use a non-verbal cue. I'll say, "I want to see how you are feeling about this material, hold up a hand with 1-to-5 fingers showing. Give me 5 five fingers if you 'Have got this and are ready to move on' or 4, 3, 2, or 1 finger(s) if you are Good, Okay, Confused or Lost." After I survey the class's responses, I will decide whether to move on, take questions, or share another example. When we are ready to move on, I will share the link to this Khan Academy resource with my students:

Two Way Relative Frequency Tables

I'll say, this is tough content, so don't be afraid to ask questions or make use of other resources to help you master it.

30 minutes

Now that I have introduced my students to relative frequency, I want to give them the opportunity to apply what we have learned. Each student should receive a copy of Application Relative Frequency. As I distribute the papers I will pair my students up, so they can work together. I will make sure that students are working with someone who can help them if needed.

Parts I through III of this activity help students learn how to calculate horizontal and vertical relative frequencies. Then, depending on the question asked, they must judge when to use one or the other. The thinking that students do in working on this task is always interesting. I listen in as much as possible and give students the opportunity to persevere. Waiting for students is a challenge (see **Reflection: Changing Culture**).

Part IV of the activity includes the most challenging questions where students must critically interpret the data to answer Questions 7 and 8. These will bring on much discussion and certainly reveal deeper understanding of two-way tables. ELL students will likely need some additional support with this Part of the activity. I will have made sure not to pair up two ELL students at the start of the task. Nonetheless, I will make extra efforts to coach these students as I wind around the groups.

5 minutes

Despite the fact that at this point in the lesson I have some idea of where students stand in being able to calculate read and interpret the data presented in our application section, I ask students for quick feedback on how they feel about each activity question. I will ask students to draw arrows pointing up, down, or sideways after each part of the Application sheet, according to how well they feel they understood the questions. I want to know which parts of the worksheet I should address again before our next lesson. There should be an arrow after each of the 8 questions on the Application sheet.

HOMEWORK 2way tables II provides practice with relative frequency tables. I expect it would take my students about 15 to 20 minutes.