Summary
Throughout this activity and lesson, the teacher will help facilitate and guide student connections between prior knowledge of mathematical concepts and new knowledge. This lesson will activate student prior knowledge and elicit students to begin creating their own questions about box and whisker plots.
Essential Question(s)
How and for what types of data might a box and whisker plot be useful when displaying data? What data points are unclear when using a box and whisker plots?
Snapshot
Engage
Students use their birthdays and a number line to construct a human dot plot by applying previous knowledge and then discuss other ways they could display their data from the dot plot.
Explore
Students learn how to transform data sets (their dot plot) into a new type of graph by applying knowledge of dot plots, minimum value, maximum value, and median. Students discover the fundamentals of box and whisker plots through their active participation in creating a human box and whisker plot. Student then draw and record the final result in their notebooks.
Explain
Students explain how the data is dispersed within the plot/graph. Also, students describe how to construct box and whisker plots from a set of data.
Extend
Students construct their own box and whisker plots from different data sources (either provided by the teacher or researched by the student). Some extra extensions are included to modify for 7th and 8th graders.
Evaluate
Students reflect and detail the key components of constructing a box and whisker plot. They also describe how data is displayed (quartiles) and what information can be easily gathered from a box and whisker plot (medians, minimum/maximum value, spread of the data, etc.).
Materials
Sticky notes to create a number line, evenly spaced and numbered from 0–31
Five mini flags or another item to visually indicate five specific points on the Human Box and Whisker Plot
Bubble wrap (or any other wide material, like butcher paper). Length is dependent upon the group size and spacing on the number line.
Two calculator tape rolls (or any other thin material like yarn or ribbon). Length is dependent upon the group size and spacing on the number line.
Student notebooks for drawing graphs and record keeping
Pencils (one for each student)
Excel spreadsheet or TI-nSprire calculator
Paper
Rulers
Colored pencils or markers
Engage
Begin by asking students to recall their birthday. They can even share their birthday with their neighbor.
Ask students to find the sticky note along the wall that corresponds to the day of the month on which they were born (1-31). There's no need to worry about the month or year.
Now that everyone has found a space on the number line, it is time to do some statistical reasoning! Share with students that by lining up in front of the number line they have created something in statistics called a "dot plot."
Next, students will engage with their peers to answer some simple questions about the dot plot. Pose the following questions to the whole class (who are still lined up on their sticky notes):
1. "What do you notice about our dot plot?" Ask students to think for a moment about the way their data is displayed. Next, have them talk to a peer about what they notice. Then, solicit a few responses from the class.
2. "What other ways could you imagine displaying our birthday data?" Again, ask students to think about their response independently for a moment, then pair up with a neighbor, and solicit a few responses from the class.
Explore
First, share with students that together they are going to construct a box and whiskers plot using statistical terminology. They are going to do so as a whole class, but you will help guide them.
In a similar fashion as in the Engage section above, ask students to think about the following terms: maximum, minimum, median, and quartile. Ask students to pair up and discuss what they think each term means. Solicit responses from the class and help students clarify misconceptions they may have.
Based on the definitions created for the terms above, ask students to determine what they believe are the minimum and maximum values for their dot plot. Hand the student(s) standing on the maximum and minimum values a flag to mark these. (Note: These will be the least and greatest values, if students are having a difficult time articulating them.)
Next, ask students to think about what they believe is the median value for their dot plot and how they would go about finding it. Once students think for a minute, have them pair with a partner to discuss their answer. Solicit a few responses from the class and go about finding the median value based on their suggestions. You may want to try a couple of different ways to show multiple solutions, assuming time permits.
Mark the median value with another flag. The median marks the 2nd quartile and will help us determine the other quartiles. Ask students to think about how they may go about finding the four quartiles now that they know the median.
Use student responses to determine all four quartiles. Here's a brief overview of how to do it in order to help guide students:
After you identify the median of the whole data set, use this value as the minimum of the upper half of your data set. Find the median of the upper half of the data set.
Find the median of the lower half of the data set. The median of the entire data set will serve as the maximum for this calculation.
Label the four points (quartiles) you have: Q1—the median of the lower half; Q2—the median of entire data; Q3—the median of the upper half; and Q4—the maximum of data set.
Mark Q1 and Q3 with flags. Now you should have five marked data points:
Minimum
Q1
Median (Q2)
Q3
Maximum (Q4)
Finally, to complete the box and whisker plot, we'll need to use bubble wrap (or any other wide material, such as butcher paper) and calculator tape. Use the bubble wrap to designate the distance between Q1 and Q3. Ask the person standing at Q1 to hold the end of the bubble wrap and unravel it until you get to Q3. Ask the person standing at Q3 to hold their end. The calculator table will extend in two places: From the minimum to Q1 and also from Q3 to the maximum.
Ask students to set their materials down, step in front of the box and whisker plot that has been created, and note what they see.
Explain
Have students return to their desks and distribute the "Explaining Box and Whisker Plots" handout.
Working with a partner, ask students to share their observations about the box and whisker plot they helped create in the class. Ask students to identify and define the terms as directed in the handout: quartiles, median, maximum, minimum, box, and whiskers.
Extend
In the Extend section, students will further explore different data sets. To do this, distribute the attached Extend Handout to each pair of students. Each Extend Handout is tailored to the grade level indicated in the file name. The instructions at the top of the handout indicate that students will either be generating a data set of their own or they will be given one. This is completely up to your discretion as a teacher. If you choose to have students create their own, some ideas are listed below. If you would like to use some that are already made, you can find a Google Sheet with prepared data sets here and attached. The full URL for the link is listed in the resources below.
For constructing graphs in the Extend exercises, you can have students use Excel, a TI-nSpire calculator, or they can do so by hand. If using Excel or TI-nSpire, be sure to practice in advance so that you are prepared to help resolve any challenges students may encounter. If you are asking students to create their graphs by hand, make sure they have rulers, paper, and bright color options to make their creations artistic, informational, and accurate. Both methods, digital and manual, have many positives, and students can easily display their work for others to see.
Evaluate
For the lesson evaluation, guide students in a Gallery Walk instructional strategy.
Distribute extra-large sticky notes, butcher paper, or poster paper to each pair of students.
Explain to students that they need to create a visual representation of their findings, such as a graph or other visual image that accurately and adequately expresses their data.
Give students 10–15 minutes to create their poster, then have them attach it to a wall and stand near it.
Distribute three or four sticky notes to each student. Explain to students that they can use these to write down questions and comments to place on their peers' posters.
Have students freely move about the room to explore other students' work. As they do, they will leave their sticky note comments, questions, or suggestions on the other posters. After everyone has completed the Gallery Walk, students may return to their own poster and read the comments that were left.
Resources
K20 Center. (n.d.). Gallery walk / carousel. Strategies. Retrieved from https://learn.k20center.ou.edu/strategy/d9908066f654727934df7bf4f505a54d
K20 Center. (2019). Human Box Plot Data Sets. Retrieved from https://docs.google.com/spreadsheets/d/1Q_-l4gzXR4rOHq712WS6jrSo2vxZJ1MJVeYHnTaSv6I/edit#gid=0