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**MEASUREMENT**

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**PRE-TRIP
CLASSROOM ACTIVITIES**

Students will prepare for measuring things which they
cannot reach, using concepts of measurement, geometry, and proportion.

The teacher will read aloud *The Librarian Who
Measured the Earth*, by Kathryn
Lasky, and students will have access to other reading materials such as *Sir
Cumference and the First Round Table*,
and other books related to measurement, geometry, and proportion.

**Circumference/Diameter/pi Activity**

Students participate in a discovery activity which
demonstrates the relationship between diameter and circumference. Students are provided with a collection
of cylinders of different sizes (e.g., cardboard tubes of different sizes from
toilet paper, paper towels, wrapping paper; lids or plastic containers,
etc.).

1.
Pairs of students are
asked to measure the diameter of one cylinder, marking its length on a string
with a pen.

2.
Next, the student team
measures around the cylinder with the diameter-marked string, making a mark at
each unit of diameter length.

2.
Students write down how
many diameter lengths make up the circumference.

3.
Students do this for
each cylinder in their kit.

4.
Students will discover
that regardless of the size of the cylinder, its circumference will be a little
bit more than three times its diameter.

*Variation:*

Students can actually measure the diameters and
circumferences using a cm or inch tape measure, and calculate a more exact
relationship for each cylinder, recording them on a data sheet. Results should demonstrate a close
proximity to pi for each cylinder.

In subsequent group discussions, students devise a
formula to represent the relationship they discovered, with Õ representing the repeating factor they discovered in
their cylinder activity. The
formula should look something like:

C=d×Õ

Students can confirm their findings by referring to
math text explanations of pi, and practice circumference/diameter problems from
the text using pi.

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**Height Measurement**

Students practice both methods of height measurement
(see description of methods under Field Site Activites, below) on the school
site, beginning with structures of known height and working toward objects of
unknown height. Students compare
their results using both methods.

In class discussions, students discuss both methods,
the benefits of having two or more methods to confirm a particular measurement
(no answer key in life!!), and conjecture about the circumstances that would
lead one to select one method over another if both were not possible.

**MATERIALS
AND RESOURCES**

** ***The Librarian Who Measured the Earth**°**,* Kathryn Lasky

*Sir
Cumference and the First Round Table, *

Math
textbook

Yard
or meter sticks

Tape
measure

**EVALUATION**

Students will be evaluated on their participation in
the pi discovery activity and subsequent discussions. Data sheets and circumference math problems confirm the
student¹s ability to measure, to discern patterns, and to understand the
relationship between pi, diameter, and circumference.

__ __

**FIELD TRIP ACTIVITIES**

Students pairs measure the size of a tree by
measuring its trunk, crown (broadest width of tree including branches), and
height. Students record their data
on a data sheet at the site.
Before the field trip, students will have:

·
learned vocabulary
words __horizontal__, __vertical__, __measure__, __crown__, __trunk__,
__circumference__, __diameter__, __round__ (math), __straight__, __opposite__,
__length,__ __base__, and __height__

·
read and understood
activity instructions

·
studied the
relationship between circumference and diameter (d×p = C)

·
practiced the height
measurement method.

**Student Instructions:**

Instructions
for measuring the trunk:

1. Measure from the ground to 4 1/2 feet high on the
trunk.

2. At that height, measure the trunk's __circumference__. Use a string around the trunk and
measure the length of the string.

3. __Round__ to the nearest inch. Record the number
as the __circumference__. Make
sure you and your partner agree on the results.

4. Using a calculator, calculate the tree¹s __diameter__
(__circumference__ ¸ p), __round__ to the nearest tenth of an inch, and
record. Make sure you and your
partner agree on the results.

Instructions
for measuring the crown:

1. Find the tree's five longest branches.

2. Put markers on the ground beneath the tip of the
longest branch.

3. Find a branch that is __opposite__ it and mark its
tip on the ground.

4. Measure along the ground from first marker to the
second marker.

5. Record the number and label as __crown__. Make sure both you and your partner
agree on the results.

Instructions for measuring the height - Method I:

1. Have your partner stand at the __base__
of the tree.

2. Back
away from the tree, holding your ruler in front of you in a __vertical__
position. Keep your arm __straight__. Stop when the tree and the ruler appear
to be the same size. (Close one eye to help you line it up.)

3. Turn
your wrist so that the ruler looks level to the ground and is in a __horizontal__
position. Keep your arm straight.

4. Have your partner walk to the spot that you see as the top of the ruler. Be sure the base of the ruler is kept at the base of the tree.

5. Measure
how many feet he or she walked.
That is the tree's __height__.
__Round__ to the nearest foot and record your answer as the __height__.

6. Switch
roles with your partner and repeat Steps 1-5. If you and your partner obtain completely different results,
measure the __height__ again until you agree on an accurate measurement.

Instructions for measuring height Method 2 (best done close to midday when shadows are shortest):

1. Measure
the __length__ of the shadow of a tree.

2. Measure
the length of the shadow of an object of known __height__ (e.g., the
student)

3. Have
students establish an equation representing equivalent proportions between
shadow __length__ and __height__.

a. tree
__height__ ÷ tree shadow __length__ = student __height__ ÷ student
shadow __length__

4. Have
students solve for tree __height__ (use calculator)

a. tree
__height__ = tree shadow __length__ x student __height__ ÷ student
shadow __length__

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**Materials and resources:**

String,
12-inch ruler, paper, pencil, data sheet, yard stick or tape measure,
calculators, tree

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**Evaluation:**

If
possible, allow time for pairs in each group to compare answers and then
remeasure the tree if needed. When
independently derived answers are in agreement, students will make the
assumption their measurements are correct. If numbers do not agree, and time does not allow, students
should be able to hypothesize some reasons for differences. Student product for formal evaluation: data sheets.

**POST-TRIP
CLASSROOM ACTIVITIES**

** **

Students discuss their
experiences of measuring the tree¹s circumference, diameter, height, and
crown. In a class discussion, they
compare and analyze their results, and suggest possible reasons for variations
or error. Students relate their
experiences to the more general topic of measurement, discussing issues
relating to accuracy (ballpark v. pinpoint accuracy), methodology,
practicality, etc., and relate these issues to other kinds of measurement in
the world.

A guest speaker (e.g.,
forestry resource manager) comes to the classroom to talk about how trees are
measured (for purposes of resource management, dendrochronology, fire
prevention) in real-life applications.
The speaker relates the kinds of measurements the students made with
these real applications. The
speaker also introduces students to possible career paths in forestry and
resource management.

**MATERIALS
AND RESOURCES**

Speaker
(contact local environmental education resources, USDA Forestry Dept., state
and county forestry resources, private timber companies who employ resource
managers, etc.)

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**EVALUATION**

Informal
evaluation is based on student participation in discussions and speaking
events.

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