students in pairs and pass out the following to each pair: a
protractor, a small weight or washer, a piece of string or dental floss
4–6 inches long, a drinking straw, and 2 or 3 short pieces of tape.
Explain that they will be measuring the height of a tall building, such
as the school building. Ask students to brainstorm how to measure
objects that are taller than a person using only the materials
provided. List the ideas on the board and discuss which ideas are
practical and reasonable ways to measure the building.
Draw an isosceles right triangle on the board with one leg
drawn on the bottom horizontally. Ask students questions to introduce
the properties of an isosceles right triangle. Here are some questions
you may choose to ask the class:
- What does "isosceles" mean?
[Two sides of the triangle are congruent.]
- What does "right" mean?
[One angle of the triangle has a measure of 90°.]
- Can you identify the congruent sides and right angle?
[Have a student volunteer label the appropriate parts of the triangle.]
- Do we know anything about the other angles of the triangle? Can we figure out their measures?
[They are both 45°.]
Relate these properties back to the challenge of measuring the
height of a building with the given materials, and ask for new or
revised ideas on how to accomplish the task. Finally, introduce the
idea of using a clinometer if it has not already been suggested. Pass
out one Building Height Activity Sheet to each pair of students. Read through the directions on
the first page and ensure that students understand how a clinometer
Building Height Activity Sheet
Help each pair of students create their clinometer. Direct them to follow the steps provided on the Clinometer Construction Overhead. Create a clinometer along with students, step-by-step, at the front of the room.
Clinometer Construction Overhead
Before going outside, read through the activity sheet again and
address any student questions. Once outside, direct students to a
specific area of the school building. Decide on a common definition of
“height of the school” for students to measure, which will vary
depending on the architecture of the building being measured. Allow
students to find the height of the building following the instructions
on the activity sheet. Once students are finished taking their
measurements, go back to the classroom and collect data from each team.
Each team should put their measurement for the height of the building
on the board, and then record the data from the board onto the chart on
page 2 of the activity sheet.
Lead a whole class discussion of the results, using the following questions as a guideline:
- Were the answers from the groups the same or different? Why do you think this is?
[There will most likely be variation among the answers from
different teams. Explanations for this will vary, but possible answers
could include accuracy in measurement, difficulty in reading the
clinometer accurately, or precision in measurement (such as rounding
- Does a person’s height affect the measurement of the building height?
[No, measuring eye-level height accounts for a possible
difference. A person 2 inches taller than another will stand 2 inches
closer to the building when taking the measurement.]
Direct teams to complete the Questions 3–5 on the activity sheet.
Circulate among the pairs and provide assistance as needed. You may
want to give hints for Questions 4 and 5, but do not provide direct
answers. Once most pairs have finished, ask volunteers to put up their
calculations for the mean, median, and mode, showing their work. Then
have a class discussion about Questions 4 and 5. Use the following as a
- What measure of central tendency (mean, median, or mode) best represents the "average" height? (Question 4)
[Answers will vary, but students should choose either the
mean or the median. If there is an outlier, median would be best. If
there are no outliers, mean would be the best value to report.]
- How could you improve the accuracy of the measurements? (Question 5)
[Answers will vary. Students may suggest standing still and using a more precise protractor.]
Maxwell, Sheryl A. 2006. Measuring tremendous trees: Discovery in action. Mathematics Teaching in the Middle School 12:132–41.