SWBAT compare two treatments statistically using percentages and quartiles.

They look different, but can you prove it? Statistics will help you win the day!

5 minutes

*Your students will all need their copies of the Student Data Chart generated in the lesson "Categorically Quantified". In lieu of that you can either have them collect data at the beginning of class, or you can provide your students with "canned" data. I prefer to have my students generate their own data because it gives them a greater investment in the mathematics I ask them to explore. *I begin this lesson by asking all my students to take out their copy of the Student Data Chart. For students who have lost theirs, I provide a blank copy to fill in. I explain that today we will be looking for connections between some of the data sets. As an example I remind my students of a statement posted the first day of this unit about rock and classical music. I then challenge them to pair-share with a partner to come up with at least two sets of data to compare so that we have lots of options to choose from and so they have to stretch themselves beyond one simple answer. As my students talk, I walk around observing and making note of particularly interesting combinations.** (MP2, MP4) **After a few minutes I ask for one member of each pair to share their suggestions with the class. *Either I write the ideas on the board or I have a student "scribe" write them, without editing but avoiding duplications.* When everyone has shared I ask my students to individually review the list and determine if all of the combinations are viable. I ask for possible eliminations and encourage students to speak in defense of any combinations they think should remain. **(MP3)** The final list usually has some gender comparisons (Do boys own more shoes than girls? Do girls like different colors than boys?) and some other comparisons. (Do tall people have fewer shoes than short people? Do older students prefer different colors than younger students?) Some of these sets require additional definitions so I ask my students to clarify the terms "older", "younger", "taller" and "shorter". When we've completed this process I tell them they should now choose two combinations they want to individually work with and write them down.

45 minutes

**Class Discussion ***8 min***:** I ask my students to reflect on all the different methods for summarizing data we've talked about then invite them to come to the board to write any they remember. *I have my students come to the board and/or share with the class frequently to provide a more active learning environment, especially since they sit in more traditional classes most of the day! I'm anticipating that they will list mean, median, mode, range, bar graphs, pie charts, stem-and-leaf plots, and maybe a linear equation/model. *Generally as some students post, others remember additional methods until we have several charting methods listed as well as measures of center and spread. **(MP4, MP5)** *If no one lists certain methods like boxplot or 5-number summary I add those myself or quietly suggest it to a student to post so that we have the full spectrum of options posted. * When we're done, I ask them to consider which methods might work for comparing the data sets we've chosen. *As an example, if we are looking at whether tall or short people own more shoes, we might look at the measures of center and spread for each group or we could look at back-to-back stem-and-leaf plots, dotplots or boxplots. *I ask whether there is a clear advantage to using one of the methods given and most of the responses focus on the ease of use rather than mathematical appropriateness. Rather than simply tell my students which method to use for each comparison they've chosen, I suggest that they apply all the methods they reasonably can and determine which give a better representation of the data when they're done. **(MP1, MP5)** *This allows my students to build on their understanding of the appropriateness of different mathematical approaches.*

**Independent Work ***25 min***:** I have my students work independently for this activity because it helps build their mathematical confidence and competence. Each student will be using their own copy of the Student Survey Data Chart *(I've included a copy in my resources) *as they work through this activity. I tell them that they will be creating multiple mathematical comparisons of the two data sets they've chosen to work with. In addition I ask that they use a separate piece of paper for each of the two comparisons so that we can post them. **(MP1, MP4) ** *My stated expectations are that each student will compare two different data sets as selected at the beginning of class and will utilize as many methods for comparison as possible. I try to state my expectations as I have here at the beginning and end of my directions, so that my students have ample opportunity to understand.* As they work I walk around providing encouragement and redirecting as necessary.

I divide my whiteboard into sections representing the possible combinations generated in the first part of this lesson in preparation for student postings. I advise them when there are only 5 minutes left so they can prepare to share their work and encourage any who are done to post their two papers in the appropriate spots on the board.

**Student Sharing*** 8 min***: **As everyone finishes and posts his/her work on the board I ask my

students to review all the posts and look for work that differs from theirs. I tell them they will have five minutes to talk with at least one other person about what they posted and why. **(MP3) ** At the end of five minutes, I give each student a notecard and ask them to briefly explain which method of comparing gave the best results and why they think so. *This section is a formative assessment that gives both my students and me insight into what aspects of summarizing data they understand and what we still need to work on.*

10 minutes