Shadow Seekers Mission Guide Shadow Seekers
Field Mission Guide: Indirect Measurement
Name: ____________________________________
Date: _____________________________________
The Mission
Use the sun's rays and similar triangles to calculate the heights of tall objects on campus that you cannot measure directly.
The Logic
\[ \frac{\text{Ht. Obj.}}{\text{Sh. Obj.}} = \frac{\text{Ht. Ref.}}{\text{Sh. Ref.}} \]
Field Rules
Measure height to the top of the reference's head.
Measure shadows from the absolute base of the object.
Take all measurements quickly while the sun is steady.
Phase 1: Field Data
Measurement Type Data Value (Include Units: cm or in) Height of Reference Person Shadow of Reference Person Target Object 1: _________________ Shadow of Object 1 Target Object 2: _________________ Shadow of Object 2
Phase 2: Mathematical Analysis
Analysis: Object 1
Final Calculated Height (X): _________________
Analysis: Object 2
Final Calculated Height (X): _________________
Mission Debrief
1. Why is it important that all measurements are taken within a very short window of time?
2. What was the most challenging part of getting an accurate measurement outdoors?
Shadow Seekers Presentation Shadow Seekers
The Geometry of Indirect Measurement
The Challenge
How do you measure the height of a flagpole, a tree, or the school building without a giant ladder?
"We measure the unreachable by using what is reachable."
Tall = Unmeasurable?
The Solar Secret
Because the Sun is 93 million miles away, its rays are virtually parallel when they hit Earth.
This means the angle of the sun is the same for every object in your immediate area.
Same Angle = Similar Triangles
The Power of Proportions
Tall Object
\[ \frac{\text{Height (X)}}{\text{Shadow}} \]
=
You (Reference)
\[ \frac{\text{Height}}{\text{Shadow}} \]
Cross-Multiply and Solve!
Field Simulation
1
Reference Height: 160 cm
2
Reference Shadow: 40 cm
3
Flagpole Shadow: 200 cm
Set up the Proportion:
\[ \frac{X}{200} = \frac{160}{40} \]
X = 800 cm
(The flagpole is 8 meters tall!)
Your Mission
Head outside with your Mission Guide and tape measure.
Identify two tall objects to measure.
Record your data quickly (the sun moves!).
Perform your calculations in your guide.
GO EXPLORE!
Shadow Seekers Teacher Guide Teacher Facilitation Guide
Project: Shadow Seekers
Level
7-8
Learning Objectives
Apply the AA (Angle-Angle) similarity criterion to real-world scenarios.
Set up and solve proportions involving similar right triangles.
Practice precise measurement in a field environment.
Understand the concept of indirect measurement.
Pacing (60-75 mins)
Introduction & Slides 15 mins
Field Data Collection 25 mins
Calculations & Analysis 15 mins
Debrief & Closing 10 mins
Equipment
Tape Measures (25ft+)
Clipboards
Mission Guides
A Sunny Day (Required!)
Instructional Strategies
The "Reference" Setup
Groups of 3 work best. One student is the "Reference Person." Measure their height to the top of their head. Remind students that they must stand up perfectly straight for an accurate triangle!
Shadow Integrity
Ensure students measure the shadow from the base of the object (e.g., where the flagpole hits the ground) to the very tip of the shadow. For buildings, watch out for shadows that wrap around corners or fall on uneven ground.
Timing is Everything
The sun's angle changes constantly. Groups should measure the reference shadow and the target shadow within 1-2 minutes of each other. If they wait 20 minutes between measurements, their proportions will be inaccurate.
Common Misconceptions
Mixing Units
Students often mix inches and feet or cm and meters. Encourage them to convert everything to a single unit (total inches or total cm) before setting up the proportion.
Inverted Proportions
Stay consistent: \[ \frac{\text{Height 1}}{\text{Shadow 1}} = \frac{\text{Height 2}}{\text{Shadow 2}} \] Avoid mixing numerator/denominator logic between objects.
Grading Checklist
Criteria Evidence of Proficiency Data Precision Measurements are recorded with units; values are realistic for the environment. Proportion Setup Equation correctly aligns heights and shadows of the corresponding objects. Mathematical Accuracy Cross-multiplication and division are performed correctly with appropriate rounding. Analytical Reflection
Shadow Seekers Answer Key Answer Key & Samples
Shadow Seekers Mission Guide
Teacher Reference
Sample Field Data
Measurement Type Sample Data (Example Group) Height of Reference Person 165 cm Shadow of Reference Person 110 cm Target Object 1: Flagpole Targeting Height (X) Shadow of Object 1 600 cm
Sample Proportion Logic
Step 1: Set up the ratio
\[ \frac{\text{Height of Flagpole (X)}}{\text{Shadow of Flagpole}} = \frac{\text{Height of Reference}}{\text{Shadow of Reference}} \]
Step 2: Plug in values
\[ \frac{X}{600} = \frac{165}{110} \]
Step 3: Solve for X
\( 110X = 99,000 \quad \rightarrow \quad X = 900 \text{ cm (9 meters)} \)
Sample Reflection Responses
1. Why is it important that all measurements are taken within a short window?
"As the sun moves, the angle of its rays changes. This directly alters the ratio of height to shadow length. If you measure the reference person at 10:00 AM and the flagpole at 10:45 AM, the triangles are no longer similar because the sun's altitude has shifted."
2. What are potential sources of error in this field mission?
Uneven Ground: If the ground slopes, the shadow length won't reflect the true geometry of a right triangle.Measurement Point: Identifying the exact tip of a blurry shadow or measuring from the wrong base point.Posture: The reference person leaning even slightly creates an incorrect angle. 
