## Pacing a Gunther Chain

### Jacqueline RobertsBay District Schools

#### Description

In this activity, students learn to pace a Gunther Chain, which is a unit of measurement used by foresters to determine distance and area.

#### 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.

Relates the concepts of measurement to similarity and proportionality in real-world situations.

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.

Determines the level of accuracy and precision, including absolute and relative errors or tolerance, required in real-world measurement situations.

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

#### Materials

-Area to do the activities
-10 feet or longer tape measure
-Calculator (optional)
-Stakes
-Handouts located in Associated File (One per student)

-Florida Division of Forestry - Educational Department
715 W Hwy 15th Street
Panama City, Florida
850-872-4175
-[Introduction to Forestry in Florida], Florida Department of Agriculture and Consumer Services, Division of Forestry Service, Tallahassee, Florida.
-[Florida's Forest Facts] pamphlet, Florida Division of Forestry
-Website [Florida Forests Forever] (See WebLinks)
-Website [Florida Division of Forestry] (See WebLinks)

#### Preparations

1. Make copies of the pacing information and rubrics for each student. (See Associated File)
2. Identify either a wooded area on campus for the activity OR various sites on campus with the following shapes: square, rectangle and triangle.

Be prepared to:
1. Review definition of pace.
2. Review definition of Gunther Chain.
3. Demonstrate “what a pace should look like.”
4. Demonstrate how to use a tape measure.
5. Review data sheets.
6. Review formulas for perimeter of square, rectangle and triangle.
7. Review formulas for area of square, rectangle and triangle.
8. Assign student partners or allow students to select their own partners.

#### Procedures

Prior to beginning the class discussion, share the Oral Presentation Rubric and the Lab Assessment Rubric with students. (See Associated File) Explain to students how they will be formatively assessed both through observations and the use of the rubrics. Make sure students understand the process before beginning the discussion.

(Note: Be sure to utilize the vocabulary from the unit's attached files throughout your discussion with students. (see Weblinks) As students are being tested on the information, they should have a working knowledge of the vocabulary. Modeling will act as a necessary review and illustration of the vocabulary.)

Review information from the previous lesson, Wanted Dead or Alive...How Big Is It?

Ask students the essential questions from the unit. Allow them to share what they have learned so far concerning measuring timber. Discuss the following and allow students to make comments or ask questions. Demonstrate pacing as you discuss these. Make sure students have an:

1. Understanding that “in the field,” a forester surveys distance and area by pacing.

2. Understanding that a pace is equal to two normal and relaxed steps.

3. Understanding that a pace is individualized and varies dependent upon age, gender and the amount of relaxation achieved in the step.

4. Understanding that to determine an accurate measurement of pace, the student must practice their stride pace, record and repeat this several times to get an average pace.

5. Understanding that foresters convert paces into a standard unit of measurement known as a Gunther Chain.

6. Understanding that a Gunther Chain is a rough survey equal to sixty-six feet on a flat surface.

7. Understanding that to be accurate when “in the field” the Gunther Chain pace must be practiced occasionally.

8. Understanding that ten square chains equal one acre.

9. Understanding perimeter measurement of square, rectangle and triangle.

10. Understanding area measurement of square, rectangle and triangle.

At this point, ask students when they might need to use a Gunther Chain and how using a Gunther Chain might be helpful in determining the value of timber. Prior to beginning the next section, be sure students are shown and understand the rubrics by which they will be assessed.

PARTNER ACTIVITY (Review the following with students.)
ACTIVITY I: WALKING A PACE
1. Student walks in relaxed manner two normal steps. (See Pacing Attachment #1 in Associated File)

2. Student, with the help of a partner, measures the length of his/her pace (two normal, relaxed steps).

3. Student records pace measurement on data sheet. (See Pacing Attachment #2 in Associated File)

4. Student repeats activity twice.

5. Students average the recorded data to determine the “pace factor.”

6. Activity 1 through 5 is repeated for partner.

7. Students demonstrate their gained knowledge through oral presentation assessed by a rubric. (See Pacing Attachment #6 in Associated File)

ACTIVITY 2: GUNTHER CHAIN
1. Students measure a Gunther Chain (sixty-six feet) on a flat surface and stake it out.

2. Students clearly mark a starting point and an ending point of the chain.

3. Students pace in a relaxed manner the “staked” or pre-measured Gunther Chain.

4. Student and partner count the number of paces needed to accomplish the distance of a Gunther Chain.

5. Students record the number of paces necessary to complete a Gunther Chain. (See Pacing Attachment #3 in Associated File)

6. Students repeat and record this activity 2 more times.

7. Students average the recorded data to determine the “pace per chain” for a Gunther Chain.

8. Procedures 3-7 are repeated for the second student.

9. Students demonstrate their gained knowledge through oral presentation assessed by a rubric. (See Pacing Attachment #6 in Associated File)

Prior to students beginning the application section, make sure that students understand the activity by reviewing with them Pacing Attachments #4 and #5. (See Associated File)

ACTIVITY 3: APPLICATION - PERIMETER (IDENTIFY VARIOUS SITES ON CAMPUS WITH THE FOLLOWING SHAPES: SQUARE, RECTANGLE AND TRIANGLE, OR TAKE A FIELD TRIP TO A WOODED AREA.) If necessary, review the formulas needed and give examples prior to students going outside.

As students are participating in the application, be sure to actively observe them at work and correct misconceptions as they occur. The continual process of teaching and feedback will help students achieve mastery of the selected standards.
1. Student with partner selects a shape to measure.

2. Student with partner selects a site to measure.

3. Student identifies site and records shape of site on data sheet. (See Pacing Attachment #4 in Associated File)

4. Student records correct perimeter formula for selected site on data sheet.

5. Student estimates perimeter of site and records on data sheet.

6. Student paces perimeter according to requirements of formula and records on data sheet.

7. Student uses correct formula to determine perimeter of site and records on data sheet.

8. Student converts total number of paces to chains and records on data sheet.

9. Student uses tape measure to determine perimeter of site and record on data sheet.

10. Students compare actual measurement to their personal measurements and record on data sheet.

11. Partner selects a site and numbers 2 through 7 are repeated and recorded on data sheet.

12. Students explain on data sheet why it might be advantageous to use pacing and Gunther Chain rather than actual measurement.

ACTIVITY 4: APPLICATION - AREA (SUGGEST STUDENTS USE INFORMATION FROM ACTIVITY 3 TO COMPLETE ACTIVITY 4)
1. Student identifies site and records shape of site on data sheet. (See Pacing Attachment #5 in Associated File)

2. Student records correct area formula for selected site on data sheet.

3. Student estimates area of site and records on data sheet.

4. Student uses correct formula to determine area and records square chains on data sheet.

5. Student converts square chains (divide by 10) to area.

6. Student records data.

7. Partner repeats activity 1 through 6 and records information on data sheet.

8. Students explain on data sheet why it might be advantageous to use pacing and the Gunther Chain to determine the area of a site rather than actual measurement.

#### Assessments

Formative Assessments occur as student orally present or explain and then apply what they've learned outside.

1. Use the Oral Presentation Rubric, which assesses students' knowledge of the information contained in activities 1 and 2. (See Pacing Attachment #6 in Associated File)

2. Use the Laboratory Assessment Rubric, which assesses students'knowledge of the application of the knowledge contained in activities 3 and 4. (See Pacing Attachment #7 in Associated File)

Students need feedback and guidance since these skills are also summatively assessed at the end of the 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).