# Central Tendency

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## Objective

SWBAT calculate mean, median, mode, and compare them as measures of central tendency.

#### Big Idea

students work independently and in pairs to calculate ans use measures of central tendency to describe distributions

## Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. The Do Now includes percent problems students must review as evidenced by the data from the Unit Test.  Students will also be provided with calculators since my goal is to focus on the procedures for solving problems like these. When I looked closely at students’ work on the Unit Test, I noticed many of them had no work and seemed to be guessing. I can’t be sure of the problem (is it conceptual or skill based?), thus I am utilizing the Do Now to assess.

As I walk around the room I am looking at students’ work, or lack of work, and forming strategic groups. Some students seem to understand the steps needed to solve. These students will be leading the review of the answers in the last five minutes of this section. I make sure to flag at least 5 different students. I also notice the students who seem to struggle to complete the problems or answer using the wrong strategies; these students will be sitting with me when it is time to review. Students selected to lead the review in each group will be given a review sheet to defend their correct answer. It is important to also select the students who are using the strategies taught in class (i.e. the formula for percent change and percent error).

After 5 minutes, I ask those 5 students I flagged to sit at booths and/or other empty tables in the room. Then I ask all students to form groups of 4 – 5 with these targeted students. I also announce that I will be pulling some students to work with me. While students are moving around the room, I tap the struggling students and ask them to sit with me.

A note about negative reactions: some students do not like to be told “you’re going work with me”. Any time that a student reacts negatively to me pulling them into my group, they will usually get the following response from me: “Please do not react negatively, I am trying to help you. If you do not want the help, please find a more appropriate way to let me know that. Do you think you can do that now?” If the student is so upset that they cannot, I ask them to sit out of this activity. If they DO find an appropriate way to respond, then I explain, “ok, you can go work with another group, however, I will be check back in with you at the end of class to make sure you understand how to do these problems. If you still do not understand, we will need to find a time to meet so that you can get the information you need”. This is an example of a situation where I stop to address character. Students are expected to communicate in an appropriate way and are held accountable for their choices. I usually come back to these students and we reflect on whether the choice was good or bad based on the data I pull from resulting work or exit tickets. This way, students are coached through making tough decisions which require prioritizing learning over friends.

## Class Notes

15 minutes

After about 2-3 minutes I ask for a student reader and we review the class notes, filling in the blanks and finding the mean, median and mode of the numbers.  I do not talk about range because it is a measure of variation. Many students group mean, median, mode, AND range as measures of center, making it difficult to correctly identify these measures in word problems. Keeping these topics apart will help with the distinction between measures of center and variation.

Many students know how to calculate the mean but do not understand its meaning as a measure of center. The question at the end of the notes aims to get students to think about the purpose of an average in a real world problem. The big idea is that measures of center describe the middle set of the data, the “average joe”. This information can be used to compare two or more sets of data.

20 minutes

In the last 5 minutes of this section, I will be asking students to write their answers on the board. We will be reviewing the answers at the end of class.

## Closing

10 minutes

Students who were able to put their work up on the board will be asked to explain the logic behind his steps. He/she may also choose to have me review the work for them.

Since students have calculators throughout this lesson, this is a great time to emphasize showing work neatly, linearly showing the numbers used for each step, as shown in the example below.

After reviewing each problem, students pack up and go to the next class.