In this activity students apply direct measurement of angles and length to determine height. They will use the tangent ratio and a clinometer, an easy-to-make instrument that allows one to estimate the height of an object such as a building, tree, or flag pole by using the properties of a right triangle. This is one of a series of activities that will help students understand how the Northern Lights work, what causes them, and how to observe them. Educational levels: High school, Middle school

Susan Higley

English

Digital Library for Earth System Education

IMAGE      Exploring the Northern Lights 1
THE NORTHERN
LIGHTS
A Grade 7-8 guide to understanding the Aurora Borealis
through math, geometry and reading activities.
IMAGE      Exploring the Northern Lights 2
This series of activities will help students understand how the
Northern Lights work, what causes them, and how to observe them.
Through a series of math and reading activities, students will learn:
How aurora are described by scientists and by other students
(Reading)
The geographic locations of aurora based on satellite data
(Geography)
How aurora appear in the sky at different geographic
latitudes (Geometry)
The height of aurora above the ground (Geometry - parallax)
How to predict when they will appear (Mathematics)
What Norse Mythology had to say about aurora (symbolic
code translation)
This booklet was created by the NASA,
IMAGE satellite program's Education and
Public Outreach Project.
Writers:
Dr. Sten Odenwald (NASA/IMAGE)
Ms. Susan Higley (Cherry Hill School)
Mr. Bill Pine (Chaffey High School)
Students:
Emily Clermont (Holy Redeemer School)
Denali Foldager (Seward Elementary School)
Sonta Hamilton (Mt. Edgecumbe High School)
The cover shows a view from the NPOESS satellite looking down at an aurora over Greenland.
(http://npoesslib.ipo.noaa.gov/S_sess.htm). Viking rune inscription
(http://www.commersen.se/vikingar/vardag/runor.html). The three smaller images at the bottom of the
page are: (Left) an aurora borealis viewed from the Space Shuttle; (middle) portion of the auroral
oval over North America viewed by the DMSP satellite showing city lights; (right) the auroral oval
viewed over the Arctic region on July 15, 2000 by the IMAGE satellite.
For more classroom activities about
aurora and space weather, visit the
IMAGE website at:
http://image.gsfc.nasa.gov/poetry
IMAGE      Exploring the Northern Lights 3
Objectives:
Students will read essays to
be informed about auroral activity
and describe the information given.
Materials:
Essays
Student Page
Procedure:
1) Discuss the student's prior
knowledge about aurora.
2) Allow sufficient time for the
students to read the three
essays.
3) Students will answer
questions 1 through 5.
Encourage the students to
refer to the article as needed.
4) Discuss the student
responses.
Conclusion:
Students will learn about
the aurora phenomenon and
how scientists have studied it
over the last few centuries. They
will learn how older ideas have
been replaced by newer
explanations.
Activity 4 Estimating Heights with a Clinometer
A clinometer is a simple-to-make instrument which lets you estimate the height of
an object (building, tree, flag pole) by using the properties of a right-triangle.
Objectives:
Students will apply direct
measurement of angles and length to
determine height using the tangent
ratio and the clinometer (a measuring
tool).
Materials for the lesson:
Rulers or yardsticks
An object to hang
A big X to hang under the object
Clinometers
Calculators – degree mode
Tangent table (optional if calculator is
not available)
Graph paper or drawing paper
Student worksheet
Student Clinometer Activity Sheet
Teacher Demonstration Examples
(Transparency)
Teachers scaled drawing
Ladder for the teacher
Roll of yarn
Scissors
Station marking items (paper taped to
the floor indicating use this point here)
Ducked Tape
Benchmarks:
6-8 Models are often used to think
about processes that happen too slowly, too
quickly or on too small a scale to observe
directly, or that are too vast to be changed
deliberately.
9-12 Find answers to problems by
substituting numerical values in simple
algebraic form las.
9-12 Make and interpret sc le
drawings
Procedure:
Step 1: Hang an object high from the c nter of the classroom. A big X can be taped
to the floor so that th object anging from it is directly under it. Based on the
number of students in the class, locate enough stations so that each group will make
at least two measurements from opposite sides of the room. Students will measure
the distance o t from the point ight under the object, or the teacher could have
already located the corresponding points. This is teacher discretion. In either case,
vary the le gth of the distance for each station from where the student will stand to
measure with the clinomet r and the object. For instance, Station 1 is located five
feet out from the point directly under the object while Station 3 is located 3.5 feet
away from the point benea h the hanging object.
See the following figure for an example of the station set up. Note: groups may share
a station since they could be on opposite sides of the room measuring.
Extension: Have students measure the height of a tree or flagpole using the
clinometer.
IMAGE      Exploring the Northern Lights 4
Students completing Station 1 need to measure out five feet in both
directions from the hanging object towards opposite sides of the room. The
teacher may opt to tape yarn in lines through the point directly under the
hanging object. This will provide the students with a direction guide.
Students will need to measure the distance to a point designated a
certain distance from the location under the object. Reminder, a big X can
be taped to the floor so that the object hanging from it is directly under it.
Therefore, the triangle for Station 1 would be drawn as follows:
Hanging
object
Station 1
5 ft
Station 1
5 ft
Station 2
4 ft
Station 2
4 ft
Station 3
3.5 ft
Station 3
3.5 ft
object
X
Station 1
5 ft from the
point X
Station 1
5 ft from the
point X
Measured
distance
Measured
distance
Students would have to determine the appropriate scale based on the
individual classrooms.
Step 2: The teacher will have to prepare a scale drawing for one of the
stations to use for discussion purposes in Step 8. Use the above
diagram as a model based on your classroom.
IMAGE      Exploring the Northern Lights 5
Step 3: Using the Clinometer Instructions, students construct the clinometer. Another option
is for the teachers to have the clinometers already constructed or to use store bought
clinometers. The actual construction provides a hands on component prior to the actual
measuring activity.
Step 4: Teacher guides the students through the teacher directed activity (see Teacher
Demonstration Examples and Student Worksheet). This provides students with exposure to
the process they will perform when determining the height of the object in the room. Teacher
may opt to demonstrate location and clinometer as a visual model while completing the
examples.
Step 5: Assign student groups to the stations that they will measure. Provide time for the
students to complete their measurements, calculate the height, and check for
reasonableness of their answer. Students record their answers on the Student Clinometer
Activity Sheet. Teacher monitors measurements and calculations.
Step 6: The whole group discusses the possible answer as to how high the object is hanging
and a what a possible scale diagram might look like from one of the stations.
Average the answers from each station.
Step 7: Select a station to be used as an example. The students from the group that used
that station will be the helpers. Students use the yarn to go from the opposite endpoints of
the station to each other to construct the base of the triangle. Students hold the endpoints.
Another student gives the teacher, who is up on the ladder, two separate pieces of yarn
while the students at the endpoints are given the other ends. Students duct tape the yarn to
the floor. As a final step, the teacher uses another piece of string to construct the height of
the triangle. The teacher duct tapes the yarn to the object, climbs down the ladder, removes
the ladder, and duct tapes the other end of the 'height' yarn to the floor. What this step is
doing, essentially, is to construct a visual model of the triangle that they will draw. (See
diagram)
Endpoint for
a station
Endpoint for
a station
object
X
Parallax angle
The teacher holds the yarn up near the object and the student groups hold the other ends
in opposite endpoints of a station.. The triangle should be evident. The teacher can then
extend the ends of the yarn to demonstrate the Parallax angle, and the property of
vertical angles in a visible format.
Step 8: Using a piece of graph paper, students construct a scale drawing of the stations
that they used to determine the height of the hanging object. Refer to Step 9 on the
Student Clinometer Activity Sheet.
Step 9: Students share their scaled drawings.
Step 10: Teacher leads students in a discussion about how the scientists would use this
method to determine the height of an aurora.
This is how the yarn
should appear to the
students when the
teacher is on the
ladder and students
are holding the base
vertices of the
triangle.
IMAGE      Exploring the Northern Lights 6
Materials to build a clinometer
(one for each group of students):
Copy of the clinometer diagram
Straw
Scissors
Tape
13 centimeters of string
coin or weight
tagboard or cardboard
one hole punch
Instructions:
1. Mount a copy of the clinometer onto tagboard or cardboard. Cut
out the clinometer.
2. Use a one hole punch or a push pin to poke a hole in the small
circle in the upper right hand corner of the clinometer.
3. Put the piece of string through the hole in the clinometer. Allow
about two or three centimeters of string on the backside of the
clinometer. Tape the string securely to the back of the
clinometer. Let the string on the other side dangle freely.
4. Tape a penny, nickel, or other coin to the end of the freely
swinging piece of string. This will serve as a weight and act as
a plumb line.
5. Lay the straw across the top of the clinometer. Cut off the
excess straw. Tape the straw securely to the clinometer.
When using the clinometer, sight the top of the object through the
straw. The plumb line remains perpendicular to the ground, and able
to move freely, as the clinometer is moved to sight the object. The
angle can be determined based on the string’s location.
CLINOMETER INSTRUCTIONS
90o
80o
70o
60o
50o
40o
30o
20o
10o 0o
Clinometer
Tape Straw Here
IMAGE      Exploring the Northern Lights 7
90o
80o
70o
60o
50o
40o
30o
20o
10o 0o
Clinometer
Tape Straw Here
Sight from this end
IMAGE      Exploring the Northern Lights 8
Teacher Demonstration Examples
(Transparencies)
X
LOCATION 1 LOCATION 2
OBJECT
Student One is
standing at
Location 1
Student Two is
standing at
Location 2.
The goal is to
determine how
high the object
is above the X.
A diagram is
provided.
Student One
uses a
clinometer and
measures the
angle to be 53
degrees. He
measures the
length from
Location 1 to
the X to be 5
feet. How high
is the object
based on his
measurements?
X
LOCATION 1 LOCATION 2
OBJECT
53
5 feet
Tan 53 = X / 5
(Tan 53) * 5 = X
6.64 feet = X
This is not the height. In order to finish calculating the height, it is
necessary to add in the student's line of sight. The student measures
his height from the floor to eye level and adds that amount back in to the
height.
Student Ones’ eye height is 4 feet.
The height is 6.64 feet + 4 feet = 10.64 feet.
What is 0.64 of a foot?
0.64 * 12 = 7.68 inches
Therefore, the height is approximately 10 feet 8 inches.
PROBLEM 1:
IMAGE      Exploring the Northern Lights 9
Student Two measures the distance from Location 2 to the X as 5 feet.
Using the clinometer, she estimates the angle is 54 degrees. She is 4 and a half feet
tall to her line of sight. How high is the object?
X
LOCATION1 LOCATION2
OBJECT
54
5feet
Tan54=X/ 5
(Tan54) *5feet=X
6.88=X
Convert .88to inchesbyusing
.88*12=10.56 inches
Nowaddthetwovalues togetherplusherheight
for the final height of theobject.
6 feet +10.5 inches+4feet 5 inches=10feet and
15.5 inches
This simplifies to11 feet 3and half inches.
AVERAGE THE TWO ESTIMATED ANSWERS.
10 FEET 8 INCHES + 11 FEET 3.5 INCHES = 21 FEET 11.5 INCHES
= 263.5 INCHES
263.5 INCHES / 2 = 131.75 INCHES
= 10.97 FEET
= 10 FEET 11.6 INCHES
PROBLEM 2:
IMAGE      Exploring the Northern Lights 10
Problem 1:
Student One uses a clinometer and measures the angle to be 53 degrees. He measures the
length from Location 1 to the X to be 5 feet. How high is the object based on his
measurements?
Showthe calculations below.
X
LOCATION 1 LOCATION 2
OBJECT
53
5 feet
Problem 2
Student Two measures the distance from Location 2 to the X as 5 feet. Using the
clinometer, she estimates the angle is 54 degrees. She is 4 and a half feet tall to her line
of sight. How high is the object?
X
LOCATION1 LOCATION2
OBJECT
54
5 feet
Show the calculations below.
Average the two answers to obtain a closer estimate.
Name _______________________________________ Date _____________
Student Worksheet
IMAGE      Exploring the Northern Lights 11
Student Clinometer Activity Sheet
SIGHTER________________________
RECORDER______________________
MEASURER______________________
CALCULATOR___________________
STEP 1: Decide which person will perform each of the above tasks.
STEP 2: Locate one of the station numbers that you were assigned.
STEP 3:Measure the distance in feet from the X to your station. Record the measurement in
the table below.
STEP 4:Measure the eye level of the sighter from the floor to eye level. Record the data in
the table below.
STEP 5: Use the clinometer to locate the top of the object. The measurer will need to
determine the angle reading on the clinometer. Record the angle reading in the table.
STEP 6: Repeat the process above at the second assigned station recording the results in the
table below.
STEP 7: Use the tangent ratio and the previous examples that were completed with teacher
assistance to determine the height of the object.
Station
Number
Clinometer
Reading
Length to
the X ( in
feet)
Sighting
Students eye
height
For each station fill in the following measurements for your calculations.
TAN (angle measure) = (the missing height) / (the length to the X)
TAN ( ) = ( the missing height) / ( )
TAN ( ) ( ) = (missing height)
Next add in the height of the sighter.
(missing height) + (height of the sighter) = (total height of the object)
The estimated total height of the object is ______________________ feet.
STEP 8: Average the results from all of the stations to obtain a closer estimate of the height
of the hanging object.
STEP 9: Using a piece of graph paper, make a scale drawing of the two stations and the
object.
IMAGE      Exploring the Northern Lights 12
Useful Web Resources
Exploratorium "Auroras:Paintings in the Sky"
http://www.exploratorium.edu/learning_studio/auroras/
Archive of aurora photos by Jan Curtis:
http://www.geo.mtu.edu/weather/aurora/images/aurora/jan.curtis/
Archive of aurora photos by Dick Hutchinson:
http://www.ptialaska.net/~hutch/aurora.html
Space Weather Today:
http://www.spaceweather.com/
IMAGE real-time aurora images from space:
http://image.gsfc.nasa.gov/poetry/today/intro.html
http://www.sec.noaa.gov/IMAGE/
http://sprg.ssl.berkeley.edu/image/
NOAA Auroral Activity monitor:
http://www.sec.noaa.gov/pmap/index.html
CANOPUS real-time auroral monitor:
http://www.dan.sp-agency.ca/www/rtoval.htm#TOPOFPAGE
Current solar activity report:
http://www.dxlc.com/solar/
Alaska Science Aurora page for kids:
http://www.alaskascience.com/aurora.htm
Human Impacts of Space Weather:
http://image.gsfc.nasa.gov/poetry/weather01.html
Ask the Space Scientist:
http://image.gsfc.nasa.gov/poetry/ask/askmag.html
More classroom activities:
http://image.gsfc.nasa.gov/poetry/activities.html
The Northern Lights Essay Competition:
http://image.gsfc.nasa.gov/poetry/alaska/alaska.html


The Northern Lights: Estimating Heights with a Clinometer

http://image.gsfc.nasa.gov/poetry/activity/nl4.pdf

The Northern Lights: Estimating Heights with a Clinometer

Abstract

Similar works

Full text

Available Versions

Digital Library for Earth System Education