# Comparing Populations - What are center, shape and spread?

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## Objective

Students will be able to compare data using center, shape, and spread.

#### Big Idea

Center, shape, and spread â a new way to do hair? No! We are talking stats in this lesson!

## Launch

10 minutes

Opener: As students enter the room, they will immediately begin working on the 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 populations using center, shape, and spread.” 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).  In order to activate their prior knowledge, I will conduct a class discussion on the mean absolute deviation – and how it was used in the previous lesson to make inferences about the data.

40 minutes

## Summarize

10 minutes

Comparing Populations Summary Cards: To summarize this lesson, I am going to give each table a scenario, and ask that they assign each member of their table a roll: center, shape, spread or conclusion.  Each student will work on their portion of the problem on their own paper, and then each person in the group will paste their portion of the work on a small poster, along with the graphical display of the problem that I gave them to begin with.  This activity will allow me to get a good sense of which students/tables are struggling with the concept of comparing populations using center, shape, and spread.

This summary activity gives students a chance to persevere with their own problem, while critiquing the reasoning of other members of their groups, mathematical practices 1 and 3.  The problems I chose represent real world scenarios - students will have to reason abstractly and quantitatively use the real world models, mathematical practices 2 and 4.  With any problems dealing with MAD, attention to precision, mathematical practice 6, will be very imporant - as students are using MAD to draw conclusions about real world problems, and a misstep in calculation could lead a student to draw the wrong conclusion. When working with the box and whisker plots, some students will be able to draw conclusions without actually calculating the interquartile range, as they will be able to draw connections between the size of the box and the IQR, mathematical practices 7, 8.