## Search form

How Does Your Tree Measure Up?

## Subjects

• Mathematics: Algebra
• Mathematics: Applied Math
• Mathematics: Arithmetic
• Mathematics: Measurement
• Mathematics: Statistics
• Science: Agriculture
• Science: Life Sciences: Botany
• Science: Physical Science: Environmental

• 3-5
• 6-8
• 9-12

## Brief Description

Complete the chart that shows locations and sizes of some of the biggest trees in the United States.

## Objectives

Students will

• work with partners or in small groups.
• measure accurately.
• accurately calculate data about a tree.

## Keywords

Calculate, data, tree, measure, circumference, transpiration, calculator, height, Arbor Day, spring

## Materials Needed

• ruler
• stick or dowel, about 4 feet in length
• 8 small sticks (ice pop sticks will work well) per team/group
• roll of string
• plastic bag (optional)

## Lesson Plan

In this lesson, students work in pairs or small groups to gather data about a tree. Each group might gather data about a different tree; all groups might collect data about the same tree; or two teams might gather data about each tree and compare their results.

Measuring the Height of a Tree
Explain to students that they can measure the height of a tree in the following ways:

• Stand at the base of the tree, and hold a ruler straight out in front of you in a vertical position. Close one eye and back away from the tree until you reach the point at which the ruler and the tree appear to be the same size. Stop and have a partner measure the distance between the tree and the ruler. That is the approximate height of the tree.
• One of the simplest ways to measure a tree's height requires a sunny day. Pound a stick or dowel into the ground. Measure the length of the stick above the ground, then measure its shadow. (For example, the stick might be 3 feet tall; its shadow might be 2 feet long.) Now you know that a 3-foot stick casts a 2-foot shadow. Measure the shadow cast by the tree. If the tree's shadow is 10 feet long, you can use a little algebra to figure out the height of the tree: If 2/3 = 10/x, then 2x =10 X 3 or 2x = 30, so x = 15; the tree is approximately 15 feet high.
• Students in the upper elementary grades and above can figure out the height of the tree by making an inclinometer and using it to calculate the tree's height.
• For additional tree-measuring methods, see Following Fall: Measuring Tree Height, How to Measure a Big Tree, or Measuring Guide.

Measuring the Tree's Canopy (Leaf Cover)
Provide students with 8 small sticks (ice pop sticks or small dowels work well), and explain that they should visualize the tree's leaf cover as a clock. Have students place sticks in the ground at the edge of the leaf cover at 12:00, 6:00, 3:00, and 9:00. Then have them place sticks halfway between each of those four sticks. When all eight sticks are inserted into the ground, students use string to create a large circle around all the sticks, and then measure the length of the string. The length of the string is the circumference of the tree canopy.

Estimating the Number of Leaves on the Tree
Have students count as accurately as possible the number of leaves on a small twig from the tree. Then have them count the number of twigs on an average branch, and calculate the approximate number of leaves on a branch. Then have them count the number of branches on the tree, and multiply the number of leaves on a branch by the number of branches on the tree. (Students might use calculators to complete this activity.) Have each student in the group calculate the number of leaves on the tree; the group then uses the average of its members' counts as its official "leaf census" number. Older students should produce a more accurate count than younger students.

Estimating the Age of the Tree
The approximate age of some trees can be estimated by measuring the distance around the trunk of the tree at a point five feet off the ground. If the tree's girth at that point measures 24 inches, the tree is approximately 24 years old. This method is not accurate for all trees. Contact a local tree expert or your university's extension service for additional information.

Calculating the Average Size of a Leaf
Students select four leaves of varying sizes from a tree. They use the square centimeter sheet to approximate the size of each leaf. That can be done by tracing the leaf on the centimeter sheet and counting how many squares (square centimeters) the leaf covers. Alternatively, you might provide students with the square centimeter sheets photocopied onto transparencies. Have students place a transparency over the leaf, color in the blocks that cover the leaf, then count the blocks.

Extension Activity: Determining a Tree's Transpiration
Older students can figure the amount of transpiration (water released) by a tree. (A mature tree can transpire more than 200 gallons per day!) In one method of determining the amount of transpiration, students tie a plastic bag over a group of leaves and measure the amount of water. For another more detailed method, see Determining the amount of transpiration from a schoolyard tree.

## Assessment

Students share how they arrived at each of their calculations. You might have students write in their journals explanations of the math processes they used.

Education World

Gary Hopkins

## National Standards

LANGUAGE ARTS: English

NL-ENG.K-12.12 Applying Language Skills

MATHEMATICS: Number and Operations

NM-NUM.3-5.3 Compute Fluently and Make Reasonable Estimates

NM-NUM.6-8.3 Compute Fluently and Make Reasonable Estimates

NM-NUM.9-12.3 Compute Fluently and Make Reasonable Estimates

MATHEMATICS: Algebra

NM-ALG.6-8.3 Use Mathematical Models to Represent and Understand Quantitative Relationships

NM-ALG.9-12.3 Use Mathematical Models to Represent and Understand Quantitative Relationships

MATHEMATICS: Measurement

NM-MEA.3-5.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement
NM-MEA.3-5.2 Apply Appropriate Techniques, Tools, and Formulas to Determine Measurements

NM-MEA.6-8.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement
NM-MEA.6-8.2 Apply Appropriate Techniques, Tools, and Formulas to Determine Measurements

NM-MEA.9-12.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement
NM-MEA.9-12.2 Apply Appropriate Techniques, Tools, and Formulas to Determine Measurements

MATHEMATICS: Problem Solving

NM-PROB.PK-12.2 Solve Problems That Arise in Mathematics and in Other Contexts
NM-PROB.PK-12.3 Apply and Adapt a Variety of Appropriate Strategies to Solve Problems
NM-PROB.PK-12.4 Monitor and Reflect on the Process of Mathematical Problem Solving

MATHEMATICS: Communications
NM-COMM.PK-12.2 Communicate Their Mathematical Thinking Coherently and Clearly to Peers, Teachers, and Others

MATHEMATICS: Connections
NM-CONN.PK-12.3 Recognize and Apply Mathematics in Contexts Outside of Mathematics

SCIENCE
NS.K-4.3 Life Science
NS.K-4.4 Earth and Space Science