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

Lesson 3 of 10

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

## Big Idea: Center, shape, and spread – a new way to do hair? No! We are talking stats in this lesson!

*60 minutes*

#### Launch

*10 min*

**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.

#### Resources

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#### Summarize

*10 min*

**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.**

#### Resources

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- UNIT 1: Introduction to Mathematical Practices
- UNIT 2: Proportional Reasoning
- UNIT 3: Percents
- UNIT 4: Operations with Rational Numbers
- UNIT 5: Expressions
- UNIT 6: Equations
- UNIT 7: Geometric Figures
- UNIT 8: Geometric Measurement
- UNIT 9: Probability
- UNIT 10: Statistics
- UNIT 11: Culminating Unit: End of Grade Review

- LESSON 1: Interpreting Measures of Center - What does the mean, mean?
- LESSON 2: Mean Absolute Deviation - Why be MAD?
- LESSON 3: Comparing Populations - What are center, shape and spread?
- LESSON 4: Measures of Center and Variability Fluency Practice
- LESSON 5: Measures of Center and Variability Test
- LESSON 6: Random Sampling - How do you make sure your sample is random?
- LESSON 7: Biased versus Unbiased Samples - What does your sample represent?
- LESSON 8: Making Predictions - What do you do with the data from a random sampling activity?
- LESSON 9: Sampling and Predictions Review - Are you biased?
- LESSON 10: Sampling and Predictions - Time to Test!