Kinesthetic Astronomy
Space Foundation Summer Course
June 14th -18th , 2010
Lyons Township High School
Chicago, Illinois
Lesson Plan
Laura A. Broadnax
McClure Junior High School
Altitude: What does it mean and how can we calculate it?
Objectives
1. Students will learn the meaning of the word altitude as well as connect it to
other words following the same linguistic pattern.
2. Students will be able to use an altitude tracker to calculate the height of an
object in preparation for designing and measuring rockets.
Suggested Grade Level
6-10
(Written for a seventh grade classroom)
Subject Areas
Science, Physics
Language Arts
Time line
Two 42 minute class periods, with extra time needed if students’ math skills need
reinforcement.
Standards
Science
NS.K-12.1 Science as Inquiry
 Abilities necessary to do scientific inquiry
NS.K-12.5 Science and Technology
 Abilities of technological design
Language Arts
NL-ENG.K-12.6 Applying Knowledge
 Students apply knowledge of language structure, language conventions (e.g.,
spelling and punctuation), media techniques, figurative language, and genre to
create, critique, and discuss print and non-print texts.
NL-ENG.K-12.8 Developing Research Skills
 Students use a variety of technological and information resources (e.g., libraries,
databases, computer networks, video) to gather and synthesize information and to
create and communicate knowledge.
Background
Altitude can be defined simply as the height of an object or place above the sea. Altitudes
can me measured in several ways, so context must be given when describing an altitude.
Within the aviation world altitude is generally expressed in feet, and typically uses either
the using either Mean Sea Level (MSL) or local ground level (Above Ground Level, or AGL as
a reference point.
Because the angles of a right triangle always add up to 180°, the trigonometric function
tangent can be used to find the height of and object if the distance to the base of the object
and the angle to the top of the object are known.
If an observer measures angle A then the measure of side a
is the tangent of angle A times the measure of side b.
The use of Greek and Latin root words as a decoding strategy in reading is an important
skill for developing readers. Many online resources can provide lists of root words, many
of which play a large role in scientific terminology.
Vocabulary
Altitude, theta, tangent
Materials
Internet access, or student friendly dictionaries
Student worksheets
Scientific calculators
Metersticks, measuring tapes, or hedometers.
Altitude tracker template(Can be found at www.fmalive.com)
Lesson
1. Ask students if they have heard the word “altitude” before, and if so, can they define
it. Ask when in science might we need or want to know the altitude of an object?
Accept all reasonable responses.
2. Hand out the altitude vocabulary worksheet and have students use a dictionary such
as the online Longman Dictionary and Dictionary.com to complete the worksheet.
3. Conclude the activity with a review of the worksheet and the following extension
questions:
a. Were there other words that you thought of that either fit or did not fit the
linguistic pattern of “altitude”?
b. Ask when in science might we need or want to know the altitude of an
object?
4. Explain to students that now they will be learning to calculate the altitude of an
object.
5. Pass out the altitude tracker templates, and have students assemble the trackers.
6. Have students practice sighting through the tracker and measuring the angle of an
object such as a overhead projector or spot high on a wall. Ensure that each student
knows how to hold, sight and measure the angle using the tracker.
7. Once all students are comfortable with the trackers, small groups of 2-4 students
should answer the questions on page 1 of the Calculating Altitude worksheet. As a
group they should brainstorm solutions to the design flaw given in the example.
8. For the rest of the calculations packet, the teacher may wish to separate the class
into groups of students as determined by their independent math skills. Some
students may be able to read the packet independently and then practice the skill,
while other students will need the teacher to read through the instructions and
examples, providing extra explanation.
9. The class will then go outside (providing the weather is not inclement) or to the
gymnasium to practice calculating the altitude of tall objects. Teachers may wish to
complete the calculations for nearby objects before the lesson so that answers can
be checked and errors spotted more easily.
Extensions
Students should research how the altitude measurement would be altered if an object, like
a rocket, was not traveling straight up. Have the students research and propose ways to
obtain a more accurate altitude reading.
Evaluation
At the end of the lesson, collect the practice sheets and check the results found. If altitude
found is more than 10% in error, students may need more practice or reinforcement of the
skill before moving on to the rocket design project.
Resources
FMA Live website. Teachers need to set up a free account to access lesson plans, although
searching for FMA Live and altitude tracker will yield the .pdf file in Google.
http://fmalive.com/teacher/home.php
Longman English Dictionary Online
http://www.ldoceonline.com/
Dictionary.com
www.dictionary.com
Wikipedia, “Altitude”
http://en.wikipedia.org/wiki/Altitude
Wikipedia, “Trigonometry”
http://en.wikipedia.org/wiki/Trigonometry
AltiMeaning/
Definition:
+
-tude
Suffix used to
make Latin words
into new nouns
= altitude
The height of an object
or place above the sea
Synonyms: ____elevation, height_____ Antonyms:_________depth__________
Connection to your life or a drawing:
Students could write or draw about going up in an airplane or climbing
something like a hill or stairs.
Words that follow the same rule as altitude with the suffix of –tude turning Latin adjectives or
participles into nouns.
Fill in the meaning of the words and their roots below.
Magnitude: _____the great size or importance of something________
(in Latin magnus means ___great or size____)
Certitude: ___ the state of being or feeling certain about something__
(in Latin certus means _____sure_______)
Latitude: __distance north or south from equator, or freedom to
choose what you do or say _
(in Latin latitudo means ______breadth or width_______)
Longitude: ______distance east or west on the earth’s surface
measured from the prime meridian______
(in Latin longitudo means _____length______)
Words that do not follow the same pattern, but do end in –tude
Attitude: means manner, disposition, feeling, position etc. with
regard to a person or thing. Look up Attitude in a dictionary to
determine why it does not follow this pattern.
The beginning of Att- does not mean anything on its own; the whole
word comes from French meaning aptitude.
Example: Mrs. Broadnax measured the height of the school building
using the following measurements:
39 degree angle

3.6m
If she were trying to measure the height of the entire wall, why
would this measurement not give her an accurate answer?
She is measuring the angle to the top of the wall while standing,
which makes the angle measurement lower. She would be missing
the amount of her height from the result.
What suggestions do you have to solve this problem? Feel free to
diagram your answer similar to the example above.
Students should suggest ways to obtain a more accurate angle
reading (i.e. sitting or laying down), and/or adding in the height of
the observer to the final answer, whether they are sitting or
standing.
45 degree angle

3.6m
To get a more accurate angle measurement, Mrs. Broadnax sat
down. While seated her eyes were approximately .75 meters off the
ground.
Calculating the height of the building:
Trigonometry can be used to find the sides and angles of a
right triangle when some measurements are known. In this case we
know that the building and the ground make a right angle. We also
know that the angle (named theta, ,a Greek letter) measures 45
degrees. We also know that the bottom of the triangle in this case is
3.6 meters long.
The tangent of an angle is equal to the length of the side
opposite of the angle dived by the length of the side adjacent to the
angle.
Tan  = Opposite length
Adjacent length
This side is
OPPOSITE
of angle 

This side is
ADJACENT
to angle 
So using what we know, let’s calculate the height of the building.
First we rearrange the equation…
Opposite length = tan  x adjacent length
Then we fill in the numbers that we know…
Opposite = tan __45°__ x ___3.6_____ meters =
3.6 m tall
Finally, we need to add on the height of Mrs. Broadnax’s eyes from
the ground.
Mrs. B is ___.75___m tall when sitting + _____3.6__m
= total height of the building is ___4.3_______ m!
Now use this same method to diagram and calculate the
altitude of other objectsaround the school grounds. Suggestions
include the flagpole or trees. Remember that you must be able to
get to the bottom of the object so you can measure your distance
from it along the ground.
Diagram
Practice #1: Object________________________
Horizontal distance to object _______________
Angle measured _________________
Height of observer’s eye _______________
Calculations: (show all work and labels!)
Practice #1: Object________________________
Horizontal distance to object _______________
Angle measured _________________
Height of observer’s eye _______________
Calculations: (show all work and labels!)