## Determining Mercantile Volume of a Pine Tree

### Lois WalshBay District Schools

#### Description

Students determine timber volumes as sawtimber or pulpwood like a forester would for market purposes.

#### Objectives

Uses concrete and graphic models to derive formulas for finding perimeter, area, surface area, circumference, and volume of two- and three- dimensional shapes including rectangular solids, cylinders, cones and pyramids.

Solves real-world and mathematical problems involving estimates of measurements including length, time, weight/mass, temperature, money, perimeter, area, volume, and estimates the effects of measurement errors on calculations.

Selects and uses appropriate instruments, technology, and techniques to measure quantities in order to achieve specified degrees of accuracy in a problem situation.

#### Materials

-Timber volume tables (2 - sawtimber and pulpwood) in Associated File
-Diameter and height of a tree, given or measured
-Clipboard
-Pen/pencil
-Calculators (optional)
-Handouts located in the Associated File (one per student)

#### Preparations

1. Collect the materials.
2. Determine the diameter and height of a tree (given or measured) to be used as an example.
3. Identify location of trees to be measured and travel time.
4. Make copies of handouts for students.

#### Procedures

Note: Be sure to review the vocabulary for the unit, which can be found in the unit's attached files. (See Weblinks)

Background: With diameter and merchantable height measurements in hand, the forester is able to determine timber volumes by referring to tree volume tables. There are two reference volume tables, one for sawtimber and one for pulpwood. (See associated file)

Teacher Directions:
Part 1
Review solving volume using concrete and graphic models from online lessons: Centimeter Slinkies, Measure This and Measurement Scavenger Hunt. (See unit WebLinks) Present how to solve the volume of a cord and board feet . See how to in student directions: Part I #3 a.& b. Allow practice time.
Each student then explains orally how to solve the volume of a cord and board feet before going to the field.

Part 2
Present how to use timber volume tables. See how to in student directions:Part I # 3c. Allow practice time. Each student then explains orally how to use timber volume tables before going to the field.

Note: You may want to have individual student rubrics to use during the presentation so as to mark students who demonstrate knowledge of these concepts.

Part 3
1. Distribute the Field Data Sheets, Rubrics and Volume Tables (see associated file.) Students take a field trip to the woods or find wooded area at school.
2. Paired students are assigned a tree to measure.
3. Students are given clipboards and calculators, if needed.
4. Each student should already have taken and recorded their own measurements of tree diameter and height and determined the type of merchantable wood. (from a previous lesson in this unit)
5. Students determine the volume of the tree and record on data sheets.
6. Students calculate the standard merchantable volumes and record on data sheets.

Student Directions:
Part 1 (In the Classroom)
1. Explain orally how to solve the volume of a cord and board feet.
2. Explain orally how to use timber volume tables. Distribute the Volume Tables and allow students to look at them as you demonstrate.
3. Students should be able to explain as follows. This is the same information that the teacher should explain and demonstrate at the beginning of class.
a- Volume of a cord:
Pulpwood is bought and sold on the basis of a cord. A cord of wood is a stack of round wood that measures 4 feet wide, 8 feet long, and 4 feet high. To calculate volume, the length, width and height are multiplied by each other. So 4ft x 8ft x 4ft = 128 cubic feet. However, the 128 cubic foot stack also includes empty air space and bark, so a cord is considered to have 90 cubic feet of solid wood. 90 cubic feet is the true merchantable volume of a cord. To determine Standard cords from the volume tables convert by dividing the cubic feet by 90.

b- Volume of board feet:
Sawtimber’s volume is based on board feet. A board foot is a piece of lumber that is 12 inches wide, 12 inches long and 1 inch thick (height). To calculate volume, the length, width and height, are multiplied by each other. So 12in x 12in x 1in = 144 cubic inches. However, the 144 cubic inches stack also includes bark and lost lumber to sawdust from cutting. So generally one cubic foot of wood will yield about 6 board feet of lumber. Sawtimber is bought and sold on the basis of one thousand board feet, MBF. MBF is the merchantable volume of board feet. To determine MBF from the volume tables convert by dividing the volume by 1000.

c- Use volume table:
To use the volume table, find the tree diameter along the left column and follow it to where it intersects with the tree’s merchantable height. This will give you the total merchantable volume. To calculate standard merchantable volumes see a or b above.

Part 2 (In the Field) Student Directions:
1. Be sure to take and record own measurements of tree diameter and height and determine the type of merchantable wood.
2. Determine the volume of the tree and record on data sheet.
3. Calculate the standard merchantable volumes and record on data sheet.
4. To do this:
a- Type of tree is determined by the diameter. In Florida =
Pulpwood (paper products) = 4 - 8 inches
Saw Timber (lumber) = 8 inches or more
b- Use volume table:
To use the volume table, find the tree diameter along the left column and follow it to where it intersects with the tree’s merchantable height. This will give you the total merchantable volume.
c- To calculate standard merchantable volumes:
To determine Standard cords from the volume tables convert by dividing the cubic feet by 90. To determine MBF from the volume tables convert by dividing the volume by 1000. (1000 board feet = 3 cords)

Following this lesson are two unit summatives. Students should be comfortable using the vocabulary and be ready to perform the unit summatives. Prior to administering them, it would be wise to have some sort of review for the students. By using a game show format like Who Wants to be a Millionaire or Jeopardy, students can glean important review information while having fun. For information about the Summative Assessment (performance) for this whole unit, see the extensions.

#### Assessments

Use the rubric in the associated file for criteria to assess student's presentation and Field Data Sheet. This is a formative assessment and students will need feedback and guidance as they work since these skills are covered on the summative assessment for this unit.

#### Extensions

a. The Beacon Unit Plan associated with this lesson can be viewed by clicking on the link located at the top of this page or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=2960. Once you select the unit’s link, scroll to the bottom of the unit plan page to find the section, “Associated Files.” This section contains links to the Unit Plan Overview, Diagnostic and Summative Assessments, and other associated files (if any).

Web supplement for Determining Mercantile Volume of a Pine Tree

Web supplement for Determining Mercantile Volume of a Pine Tree
Measure This

Web supplement for Determining Mercantile Volume of a Pine Tree
Measurement Scavenger Hunt

Obtain all unit information from this site, including lessons, files, assessments, etc.