## Heights of Students in Our Class

• Lesson
3-5
1

In this activity students collect height data and then construct a box‑and‑whisker plot to display the results. The activity sheet presents a sequence for setting up a box‑and‑whisker plot.

To begin the lesson, ask students to identify objects which are approximately one centimeter in size. Students may respond by saying:

• the width of a small fingernail
• the width of a black key on a piano

Next, ask students to identify objects which are approximately one meter in length or height. Students may respond by saying:

• height of a doorknob (the distance from the doorknob to the floor
• the distance from a person's waist to the floor (for a typical adult)

If students have never measured using a meter stick, you may wish to give them time to practice measuring items in the classroom.

At the start of the measuring activity, each student should be placed into pairs. Each person in the pair should measure the other's height (in centemeters) using a meter stick. Since students will need to use their height data to complete the activity, tell students to write down their heights on index cards.

Prior to measuring, you may wish to ask students if they already know their heights. Some students may know their heights, but they may respond in feet and inches. Cuation students to measure their heights in centimeters.

Distribute the Heights of Students in Our Class activity sheet to each student.

 Heights of Students in Our Class Activity Sheet

Have the students record the heights of ten other students and themselves on the activity sheet.

Have the students order the heights from smallest to largest by plotting them on the number line at the bottom of the second page of the activity sheet. Have them plot each height with an x.

Ask the students to determine the middle height of the eleven heights plotted. Ask why the middle heights is the sixth height. Explain that the middle height is called the median.

If students are not familiar with the mathematical term median, lead a discussion which explains its meaning.

Ask the students to determine where the third and ninth heights fall. Indicate that these points represent the first and third quartiles, respectively. Ask the students to explain why this result is so. Have the students draw a box above the area delineated by the third to ninth heights. Then have them draw a vertical line segment inside the box denoting the sixth height.

Ask the students to draw a line segment from each edge of the box to the smallest and largest heights. These lines represent the "whiskers" of a box‑and‑whisker plot. Ask the student why they think these line segments are called whiskers.

Have the students complete items 7 through 9 on the activity sheet. These questions help the students understand how to interpret the box‑and‑whisker plot. Discuss the responses to these items with the class.

Students may also complete the box plot using the NCTM Box Plotter tool. Directions for using the tool can be found on the website.

 Box Plotter

Students can plot the data recorded on their activity sheet and compare their hand-drawn box-and-whisker plots to the computer-generated version.

Extensions

1. Consider having the students arrange their height data using a stem-and-leaf plot. Use the tens and hundreds digits as the stem.
2. Have students determine the mean and mode for the heights.

Questions for Students

1. Compare your box-and-whisker plot to a classmate's. How are they similar? How are they different?
2. How would your box-and-whisker plot have changed had you included all of the heights in your class?
3. When you drew a line segment from each edge of the box to the smallest and largest heights, what mathematical concept did you identify? What was the range for your set of data?

Teacher Reflection

• Which students were able to create the box-and-whisker plot with minimum supervision?
• Which students could identify the measures of central tendency with understanding?
• How can I extend this instructional experience? What will I do differently the next time that I teach this lesson?

### Learning Objectives

Students will:
• Measure heights of classmates
• Display and interpret data using a box‑and‑whisker plot