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:
- Meter ruler or
yardstick
- Large ball of string
- Measuring tape
for each group
- Recording
sheet
- Scissors
- Pencils
- Related Web sites:
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
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