Measure a Tree, by John Cowens

Measure even the tallest trees with planning, teamwork and math skills. No ladders required!

What's the tallest object your students can measure with a meter stick? A fence? The ceiling? If they work as a team, your students can measure the height of any object, no matter how tall, by using mathematical problem solving, data sets with one variable and employing ratios to compare similar triangles.

The Line Sighter needs to position himself to line up the top of the Math Magician's head with the top of the tree.

About this activity
This lesson easily conforms to the NCTM Standards. For grades 6-8, data analysis is utilized as students collect, organize and represent data sets that have one variable and identify relationships of the data collected. Students will know various forms of display of data sets.

Data gathered in this activity will ultimately be displayed on a Height Data Table (the format for the table appears at the end of the article). The intent of recording the data on the table is to encourage students to explore the design of a mathematical plan to solve a problem (often students are often more concerned with getting the "right answer" and avoiding embarrassment).

Have teams discuss their methods before posting data on the Height Data Table. There may be interesting mathematical plans that gave results that didn't make sense. Be sure to praise good analysis of why a method didn't work as well as any teams who got the right answer.

Choosing teams
Teams of four are suggested to fully involve students of different learning styles in the different roles this activity requires. If possible, choose team members that represent "Kinesthetic" (perfect for the role of Meter Stick Master), "Spatial" (Line Sighter), "Quantitative/ Mathematical" (Math Magician) and "Verbal/Literal" (Inspector/Recorder).

The Math Magician stands between the measuring being done and the object to be measured, holding the end of a string on the top of his or her head.

The Line Sighter "sights" using a string to line up the top of the Math Magician's head with the object to be measured. If students are having trouble with this concept, which involves aligning two objects so they seem superimposed, try using two pencils held with the erasers on top, one close to the eye and one at arm's length. Have the students align the two erasers with a distant object. Or, if a mirror is available, have students align the pencils by looking at themselves in the mirror where they see their eyes as well as the reflected pencils.

The Meter Stick Master must be able to make successive measurements of a long distance with one or two meter sticks by going end to end and keeping track. This student must also be able to measure decimal portions of meters and express the final measurement in one number that includes decimals. For example, the student measures five full meter sticks and an additional 40 centimeters, which would be 5.40 meters.

The Inspector/Recorder reads directions, inspects work that's being done and records data from the Meter Stick Master. The student in this role also gets equipment and brings a pencil and the Height Data Table to the field with a clipboard.

Activity: Measuring a tree
Materials:

• pencil, paper and clipboard (or equivalent)

• long piece of string (long enough to stretch from the Line Sighter to the top of the Math Magician's head)

• meter stick (two per team if possible)

Procedure:

1. The Inspector/Recorder chooses a place from which to measure the tree. It should be a place where the Line Sighter can lie on his or her stomach and have a clear view of the tree.

2. The Math Magician chooses a place to stand and holds the end of a long string on top of his or her head.

3. The Line Sighter takes the other end of the string and moves to a place where he or she can lie face down and still see the top of the Math Magician's head in such a way that it is lined up with the top of the tree. The Line Sighter uses the string pulled tight to "sight" the tree and the Math Magician's head and line them up. The Line Sighter may have to move several times.

4. The Meter Stick Master now measures the distance on the ground (not the string) between the Line Sighter's eye and the feet of the Math Magician. Without moving the meter stick, the Meter Stick Master reads the measurement and tells the Inspector/ Recorder what it is (it should be a number that has decimals for the small parts of a meter measure). Do not remove the meter stick!

5. The Meter Stick Master continues measuring until the tree is reached. He or she reads the measurement and tells the Inspector/Recorder the total distance between the Line Sighter's eye and the base of the tree.

6. The Meter Stick Master measures the height of the Math Magician and the Inspector/Recorder writes it down.

7. The Math Magician leads the team in the analysis of the data collected and designs a mathematical plan to compute the height of the tree.

Suggestions: Draw the experiment as seen by someone watching from the side. Show the position of each person and draw lines to show what the Line Sighter was looking at.

8. What is a ratio? Can it help solve this problem? On their drawing, students should write the data they collected, write out a mathematical plan (equation) and fill in the data numbers. Students then compute the height of the tree using their plan. Does the answer make sense or does the height seem too short or too tall?

9. If a team wants to try again, that's fine. They can ask another team for help, but be sure they bring their work with them so the new team knows what they were thinking about. Put the teams' computed answers for the height of the tree on the Height Data Table (shown below). Compare the answers.

You can make a copy of the Height Data Table for every group of students.

Extension: Do research on the manner in which astronomers measure the distances of newly discovered planets, stars, galaxies and other objects found in space.

For more information check out PlanetQuest and for additional NASA educational materials you can visit the NASA website.

This lesson is from NASA's Planet Quest – The Search for Another Earth (Activities for Students Grades 4 and up. Educational Product EB-2002-07-023-JPL). Permission is given by NASA Jet Propulsion Laboratory to duplicate this publication for educational purposes.

John Cowens has taught for 26 years. He currently teaches sixth grade at Fleming Middle School in Grants Pass, OR.