Measure a Tree

Topic: Measuring a Tree

NCSCS: Sixth Grade
Mathematics Objectives: 2:11 Convert measures of length, area, capacity, weight and time expressed in a given unit to other units in the same measurement system. 2:12 Estimate solutions to problems involving geometry and measurement. Determine when estimates are sufficient for the measurement system.

Interdisciplinary Connections:
Science/Communication/Social Studies

Differentiation/Accommodation/Student Voice/Choice:

  • Small groups - students choose 4 classmates they would like to work with (at least one of their choices will be in their group-this strategy not only lets a unique learner have a choice, but also lets the teacher keep within his or her unique learner's discipline plan). Verbal and Auditory Opportunities/ Collaboration and Cooperation Opportunities

Materials:

Procedures:

  • Students will take a walk on Joyce Kilmer trail. As they walk they will look closely at the trees. They will notice the assortment of sizes, shapes, colors and textures. An experienced arborist may be able to judge the age of a tree simply by looking at its diameter and location. The growth rate of trees depends on the species and environmental conditions.
  • One of the largest old growth preserve in the eastern United States is Joyce Kilmer Memorial Forest. A walk through Joyce Kilmer Memorial Forest is a journey back in time through a forest with towering trees as old as 400 years. Some enormous yellow-poplars are over 20 feet in circumference and stand 100 feet tall.
  • Foresters measure trees to plan harvesting and to make other forest management decisions. To determine the approximate timber yield of a stand of trees, foresters do a "timber cruise" in which they calculate the volume of lumber in a given area, examine the health of the forest, and survey the species found there. Volume of wood can be measured in board feet [a piece of lumber 12 inches square (77 sq. cm and 1 inch (2.5 cm) thick], cords (a stack of logs 4 ft. x 4 ft. x 8 ft. or 1.2 m x 1.2 m x 2.4 m), cubic feet or cubic meters.
  • Select trees students should measure.
  • Tell students about a time when you measured your dinning room table in order to buy fabric to make a table cloth. Ask them to think of a time when they measured something. Have them think about what they measured, how they measured it, and what they learned from measuring it. Have the students share their thoughts with the other members of their group.
  • Explain to the students that people in early times used their own bodies (hand spans, for instance) to measure things. Have each group to measure identical objects in the classroom (like desks, length of the room, whiteboard, etc.) using different parts of their bodies: foot, hand span, arm span, length of finger, or walking paces. Have them record their findings on their recording sheets.
  • Talk with students about the accuracy of each type of measurement. Why did each group get different measurements? Have them to compare the different sizes of their hands, feet, fingers, and arms with members of their group.
  • Ask students why a person might want to measure a tree. Share with them why foresters measure trees.
  • Take students to measure the trees in Joyce Kilmer.
  • Ask students to estimate the circumference of the tree's trunk (inches or centimeters) and then measure it in arm spans (wrapping arms around the trunk) or hand spans (for small trunks). Record their estimates on recording sheet. Then have students measure the circumference using a piece of string and tape measure. Foresters always measure the diameter of a tree at 4.5 feet (1.4 m) above the ground. This measurement is called "Diameter at Breast Height" (DHBH). To see why this is an important measurement standard have students measure the circumference of the tree at 1 foot (.3 m), 2 feet (.6 m), and 4.5 feet (1.4 m) to see how size differ (trees usually get wider toward the base). Ask students what would happen if everyone measured the circumference of a tree at a different height (everyone would get different results).
  • Have students compare their actual measurement to their estimates, and the standard measurement to their personal measurement (arm and hand span).

    Have students determine the height of the tree by measuring the length of its shadow. Students must first measure their own height and the length of their shadow at the same time of day. Show students how to use a ratio comparison to determine the height of the tree:

  • Tree's Height = Student's Height
    Tree's Shadow Student's Shadow

    OR

    Tree's Height =
    Student's Height x Tree's Shadow
    ............................Student's Shadow

    AND

    Have one student stand at the base of the tree to be measured. Have another student hold a ruler at arm's length and walk backward, keeping arm stiff, until the top and bottom of the ruler line up with the top and bottom of the tree. Note where the top of the partner's head appears on the ruler (for example, at 2 inches or 5 cm). Divide the length of the ruler (12 inches or 30 cm by this figure. For example, 12" divided by 2" = 6 or 30 cm divided by 5 cm = 6 cm. Measure the partner's actual height and multiply it by the previous result. For example if the student's height was 55" or 1.4 m, then the height of the tree would be 55" x 6 = 330" (27.5 feet) or 1.4 m x 6 = 8.4 m.

    Ask students to compare their calculations. What might explain any differences?

    AND

    Have students measure the height of the tree like some Indian tribes did. Hold on to your ankles and walk away form the tree until you can see the top of the tree through your legs. Turn around and measure the number of meters or feet back to the tree.

    Lesson adapted from Project Leaning Tree and Aims Activity Guides

Assessment:

  • Students' recording sheets

Timeframe for Lesson:

  • Two 50 minutes class periods

 

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Page Author: Bobbie Burchfield
10/13/02