By Judith Albanese and Sarah B. Bush, Posted April 27, 2015 –  

In the December 2014/January 2015 issue of Mathematics Teaching in the Middle School, “The Oldest Person You’ve Known” explored ways to engage students in statistics using a Super Bowl commercial as a catalyst. Students recreated the commercial’s dot plot by polling themselves, their parents, and their grandparents on the question, “How old is the oldest person you’ve known?” They answered questions about their compiled data set and three subsets that addressed such concepts as measures of central tendency, shape of the data distribution, interquartile range, and absolute mean deviation. The article provided a frame for recreating this activity in your own classroom and included a student activity sheet. In this post, we suggest two additional tasks for “The Oldest Person You’ve Known.”

In the article, we suggested creating the wall-size graph (axes and labels) beforehand to ensure that there were enough frequencies and space for each dot and to save valuable class time. However, allowing students to make the graph could provide a learning opportunity for students in which you address the concepts of determining the scale, intervals, labeling, and the importance of attending to precision (Common Core State Standard (CCSSM) mathematical practice 6). By allowing students to create the graph, you can engage them in meaningful discourse about why scales and labels are important and why attending to precision is necessary. We recommend that before discussing the scale of the graph, students should examine and organize the class-collected data. Students can use a frequency table to determine the x-axis and y-axis. A frequency table will allow students to see the youngest and oldest ages and determine the age range for the x-axis and the frequencies needed for the y-axis. Working with students to troubleshoot potential issues with the graph can be a meaningful mathematics task.

Also found in the article was information about students’ examining three subsets of data (student, parent, and grandparent) and making informal comparative inferences among the populations (CCSSM 7.SP.3 and 7.SP.4). As an extension, students created three box plots representing the three subsets of data. As an additional task, students could use their collected data to create three different histograms representing the three subsets of data. CCSSM standard 6.SP.4 requires students to “Display numerical data in plots on a number line, including dot plots, histograms, and box plots.” See figure 1 and figure 2 for sample student histograms.

Fig. 1 Student histogram with 5-year age ranges

Fig. 2 Student histogram with 10-year age ranges

In addition to a meaningful task that aligns with CCSSM, having students make a histogram for each subset of data allows them to make connections and see the data through different data displays. Having students create three items—a dot plot, a box plot, and a histogram—provide unique opportunities to ask good thinking questions such as these:

• Which data display best describes the data? Justify your response.

• In addition to companies involved in retirement planning, what other jobs or businesses collect this type of data? Why?

• What other real-life data can you collect that would be best displayed by a dot plot? Box plot? Histogram? Justify your response.

Tasks that involve creating and discussing the scale and labels of a graph and creating a histogram are just two of many possible additions to “The Oldest Person You’ve Known” project. We advocate using meaningful activities when working with data and statistics that call for students to ask questions, collect data, analyze data, and interpret results, as recommended in the 2005 GAISE report. Teaching in this way aligns with the Mathematics Teaching Practices outlined in NCTM’s Principles to Actions, which include “Implement Tasks That Promote Reasoning and Problem Solving.”

Judith Albanese, jalbanese@stleonardlouisville.org, is a middle-grades mathematics teacher at St. Leonard School in Louisville, Kentucky. She seeks to develop her students’ conceptual understanding of mathematics by implementing instruction and activities that are engaging and relevant to her students.

Sarah B. Bush, sbush@bellarmine.edu, is an assistant professor of mathematics education at Bellarmine University in Louisville, Kentucky. She is a former middle-grades mathematics teacher who is interested in interdisciplinary, relevant, and engaging math activities.