Using Triangulation to Measure Mountain Ranges on Mars: A look at Stereopsis & Computer Vision
Grade Level:
Duration:
Grade 9/10
Minutes 120
Subject: Geometry
Prepared By: Mike Borowczak
Materials Needed
Req: Inclinometer (see Survey Engineering Inclinometer), Graphometer|Alidade (instructions included)
Analyze Learners
Overview & Purpose (STEMcinnati theme)
Students will gain/enhance & apply knowledge of trigonometry, unit
conversion and area & volume calculations to measure distant
objects. Students will discover how we are able to apply these skills
to measure features on Mars
Applications:
Surveying, Computer Graphics, 3-D Technologies
Careers:
Civil Engineers, Surveyors, Computer Engineers, Computer Scientists, Visual
Media Professionals
Society:
Fundamental Understanding of things we cannot physically measure (easily).
Entertainment & Communication (visual)
Science:
Technology:
Education Standards Addressed
Measurement Standard
Benchmark C. Apply indirect measurement
techniques, tools and formulas, as appropriate, to find
perimeter, circumference and area of circles, triangles,
quadrilaterals and composite shapes, and to find
volume of prisms, cylinders, and pyramids.
Benchmark D. Use proportional reasoning and apply
indirect measurement techniques, including right
triangle trigonometry and properties of similar
triangles, to solve problems involving measurements
and rates.
Benchmark E. Estimate and compute various
attributes, including length, angle measure, area,
surface area and volume, to a specified level of
precision.
Engineering:
Mathematics:
Geometry and Spatial Sense Standard
Benchmark I. Use right triangle trigonometric relationships
to determine lengths and angle measures.
Benchmark A. Use trigonometric relationships to verify
and determine solutions in problem situations. (11th grade)
Data Analysis & Probability Standard
Benchmark K. Make predictions based on theoretical
probabilities and experimental results.
Goals & Objectives
Goals and
Objectives
(Specify
skills/information that
will be learned.)
Teacher Guide
Student Guide
Goals:
Understand
1. The relationship between various broad
mathematical concepts (Trig/SA,Vol, Units) in
our everyday lives/society.
2. How knowledge of these impacts our ability to
understand foreign locations without having to be
there.
3. How we use these interactions to create and
deliver unique entertainment mediums.
Objectives:
1. Students will be able to assess whether they
have enough information to find the dimensions
of a distant object.
2. Students will describe triangulation and why it is
useful.
3. Students will compute the Surface Area and/or
Volume of a solid given limited information from
two known locations.
4. Students will construct a
Graphometer|Alidade|Surveyors Compass.
5. Students will justify the accuracy of their
measurement of nearby objects, and predict
what occurs, as objects are geospatially further
apart.
Assessment
1. Do you have enough
information to find the length of
side x in each of the following
problems?
2. Describe how you would go
about measuring the height of
a mountain that was on the
other side of an impassible
canyon.
3. Given the following
measurements for x,y,z and w,
compute the Surface Area OR
Volume of the following:
a. [VOL] Building with
height y, width z, and
depth w/x.
b. [SA] Side of Mountain
with base x and height
w.
4. Discuss why triangulation
using planar geometry
becomes less accurate the
further we are from another
object on our planet.
Select Instructional
Strategies –
Information
(Catch, give and/or
demonstrate necessary
information,
misconceptions, etc…)
Utilize Technology
Day 1
Pre-assessment (10 minutes)
 Questions to the right
Catch (n = 10 min)
 Have students close one eye and
illustrate depth perception
 MarsP1.ppt
o Show students pictures of
objections with no reference
point
o Showing Need to Depth /
Measurement Capabilities
Lesson (n = 20 min)
 Build to Measuring from a distance
o See part1.html
o See part2.html
Discussion (n = 5 min)
 Discuss Key Observations
Homework (n = 30-45 min)
 Using Worksheet, Build Alidade
 Compute Angles of Objects of
known width or distance away;
compute the missing variable
 Geogebra
(http://www.geogebra.org)
Catch
Students should notice that
the ability to measure
distance requires multiple
focal points.
Other Resources
(e.g. Web, books,
etc.)
Require Learner
Participation
Activity
(Describe the
independent activity to
reinforce this lesson)
Day 2
Review (n = 5 minutes)
 Handout Measure Me A Building Worksheet
 Students Paired
 Review Rules & Responsibilities
Activity (n = 30 minutes)
 Groups will be split in two, going to two consecutive sides of a
building (they will line up parallel to the building)
 Partners in a individual group will then have to stand such that the
angle between the building and their partner is acute
 Measurements will follow according to the worksheet
Evaluate
(Assessment)
Day 3
Reflection & Presentation
(Steps to check for
student understanding)
– See Objectives above
Standard Post-Assessment
Important Attachments:
1. Pre-Post Assessment
2. Worksheets
3. PowerPoint
4. Reflection after lesson
Additional Notes