Sending Text Messages
Lesson 5 of 14
Objective: SWBAT interpret data using a histogram. SWBAT represent data using a box plot. SWBAT identify similarities and differences of these representations.
I like the Texting by the Numbers task in today's lesson for two reasons:
- The subject matter about text messages and the differing number of texts sent by students and their parents (and peers) is relevant to most students and they seem to get excited by the discussion about text messaging.
- I like how students are asked to compare and contrast the way the same data is represented in a histogram and a box plot. Students will be pressed to list the advantages of each representation and this can be a nice way for them pull together some of what they have learned about representing data.
I begin class by trying to get students excited and interested in today's task. I start by asking students, "On average, how many text messages do you think you send per day?" I have students report out and I record their answers on the board (I might save this data for a project or homework assignment later. It's always nice to have student generated data to work with). Next, I might ask students how many texts they think their parent or guardian sends in a day? We have a brief discussion about the prevalence of texting, the potential difference between how much they send vs. their parents, and if they think a certain number of texts is too many to send. I try not to let discussion get too off topic here but I am interested in what students share and I do want them to be engaged in today's class.
Next, we read through Texting by the Numbers together. I project the histogram from the first section on the board and we have a whole group discussion about what the data shows. Students are usually quick to point out that the histogram likely shows the two groups of data (Rachel's and her mom's) almost separately. I introduce the term bimodal and ask students what they think that might mean. Usually, students are able to say right away that the higher mode likely represents Rachel's friend's data while the lower mode probably represents the mom's friends.
Next, students get to work creating a box plot from the same data. Students sometimes complain about the tediousness of ordering the data and then setting up the box plot. I actually find it useful for them to get a sense of the data by doing this work. From ordering the data, students might notice that there are some jumps in the average number of sent texts (from 36 to 70, from 85 to 110 and again to 130, and from 175 to 275). I might ask them to look back at the histogram and see how those gaps are represented.
Once students have generated box plots, the next question asks them to compare the advantages and disadvantages of the two representations. I have students spend some time writing about their observations before we have a discussion as a whole group. Because some students will take a while to create their box plots, I have the students who finish more quickly move on to Part II.
Once students are finished with at least the first two questions in Part II, I bring the whole class back together for a group discussion. We first discuss the advantages of each representation (histogram and box plot). The key points I want to elicit from students are:
- The histogram does a good job of showing the bimodal distribution of the data.
- The box plot does not show the two modes clearly, but does show the median number of texts sent and the quartile ranges.
- Both representation show the outlier of 275. Now is a good time to show students how an outlier can be represented on a box plot if they haven't seen it already.
In Part II of the assignment, students get confirmation that Rachel's friends account for most of the texts sent in the hundreds. We can talk again about the outlier who sends 275 texts per day (and maybe discuss how many that is per hour!) and the few outliers who send less than 100 texts per day.
If there's time in class, I might have students create two box plots on the same set of axes. One of Rachel's friends and one of the mom's friends to further examine the differences between the two groups.
Closing + Reflection
If students haven't already done so, they can spend the rest of class working on the Last Two Questions. Though students may have firm opinions about many texts Rachel should be allowed to send, I insist that they use the math to back up their answers, rather than just their own opinion. This is a good opportunity for students to focus on Standard for Mathematical Practice 3: Construct Viable Arguments and Critique the Reasoning of Others. I might collect students' finished work and share out their arguments at the start of the next lesson, looking for feedback on other student reasoning.
Texting by the Numbers is licensed by © 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.