# Mean Absolute Deviation - Why be MAD?

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## Objective

Students will be able to use mean absolute deviation to determine variation and consistency in data sets.

#### Big Idea

Mean absolute what?! Students will use MAD to look at variation in sets of data.

## Launch

10 minutes

Opener: The opener is a mixture of previously learned questions, and students should work individually, and then as table groups to discuss the methods for solving the questions.  After approximately 5 minutes, I will call on students to go to the board and solve the opener questions.  As with all openers, I will take volunteers to go to the board – the volunteer is expected to explain their reasoning, and other students are expected to follow along with the work and ask questions/make suggestions as necessary.  By having a student explain their reasoning while others listen and provide feedback, mathematical practice 3 – construct viable arguments and critique the reasoning of others – becomes a natural part of class.

Learning Target: After completion of the opener, I will address the day’s learning targets to the students.  In today’s lesson, the intended target is, “I can compare the variations of two data sets using mean absolute deviation, and draw conclusions regarding the consistency of the data.”  Students will jot the learning targets down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

## Explore

40 minutes

Guided Notes: The instructional portion of this lesson will begin with a discussion on MAD – what is it? What does it stand for? What does it tell us?  Then, we will move into practice problems on calculating MAD.  Explaining the steps to students can be cumbersome, as they will look at you like you are crazy – so I find it is best to just put the steps on the board and walk through them using an example problem.  Many students learn by doing – not by hearing! Throughout the process, attention to precision will be key, as slight missteps could throw off the final value - thus leading to incorrect comparisons in data later on, mathematical practice 6. I will allow students to use calculators for this process, mathematical practice 5, if they feel that it will help ease the process.  The importance right now is the process.  When calculating MAD, some students will be able to determine that when data points on the same they would not have to calculate their distance each time, thus being able to develop shortcuts - mathematical practice 7.

I will walk through two examples with the students, and then I will ask that they complete the last two examples with their tables.  Though the concept is relatively new for them, it is important that students are given time to grapple with the mathematics, and persevere to complete problems without my assistance, mathematical practice 1. They now need time to make sure they can do it without my assistance.  I will take volunteers (with a buddy if they choose) to go to the board to explain and show their work.

Problem Cards: After the example problems, the students will engage in a jigsaw activity.  Since I have 8 tables of students, I will use two different problems for this activity – four tables will receive one problem, four another problem.  Students will work with their tables to answer the question and make comparisons on the variations of the data sets. Students will be able to accurately make comparisons on real world data, making connections on how MAD can be used in the real world and its importance, mathematical practices 2 and 4.  After approximately 5-7 minutes, I will have students at each table letter off A, B, C, D.  For tables with problem 1, I will send all the A’s to table 1, B’s to table 2, C’s to table 3, and D’s to table 4.  For tables with problem 2, I will send all the A’s to table 5, B’s to table 6, C’s to table 7 and D’s to table 8.  This arrangement will place one member of each original group with one member from every other group with the same problem.  At their new tables, students will represent their original table, sharing their work and conclusions, and after every one has shared tables will discuss the similarities and differences in the conclusions made regarding the problem.  To wrap up this activity, I will ask that each group share out one major discussion point that was made at their table.

10 minutes