Shadow Secrets Slides SHADOW SECRETS
The Power of Indirect Measurement
Similarity & Proportions
The Tall Problem
How do you measure something that is too tall to reach?
No giant ladders
No drones with rulers
Just a meter stick and the Sun
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📏
Mathematical Similarity
The Rules
1
Corresponding Angles must be identical.
2
Corresponding Sides must be in the same ratio.
Original
Scaled x2
Scale Factor: 2
"Shadow Reckoning"
Over 2,500 years ago, Thales of Miletus measured the Great Pyramid of Giza.
"Wait for the moment when your shadow is exactly your own height. At that instant, the pyramid's shadow will be exactly its height."
Pyramid
Meter Stick
The Secret Ratio
Height OBJ
Shadow OBJ
=
Height STICK
Shadow STICK
1. Measure
The Building Shadow
2. Measure
Stick height & shadow
3. Solve
Calculate for X!
Shadow Sketcher Worksheet SHADOW SKETCHER
Similarity & Indirect Measurement
NAME:
DATE:
The Method
When the Sun hits two objects at the same angle, they form similar right triangles. Use this proportion to find the missing height:
\[ \frac{\text{Height of Object}}{\text{Shadow of Object}} = \frac{\text{Height of Stick}}{\text{Shadow of Stick}} \]
1
The School Flagpole
A student stands a 1.5 meter tall measuring stick vertically. The stick casts a shadow 0.6 meters long. At the same time, the flagpole casts a shadow 4.2 meters long.
How tall is the flagpole?
A. Set up the proportion:
x
_______
=
_______
_______
Show Calculations Below
2
The Neighborhood Oak
Examine the diagram. Using the measurements provided, calculate the height of the tree.
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SHADOW: 8.5 METERS
SHADOW: 1.2 M
Height: 1 M
Calculation Zone
Final Tree Height
3
The Lighthouse Challenge
A lighthouse casts a 50-meter shadow. A 2-meter fence nearby casts a 2.5-meter shadow. However, the ground near the lighthouse slopes down, making its shadow appear 10% longer than it actually is on level ground.
Step 1: Strategic Adjustment (Explain your logic)
True Height
Shadow Scouting Guide Shadow Scouting Guide
Teacher Implementation & Field Study Notes
Lesson Objective
Students will transition from theoretical similarity to real-world application. The primary goal is for students to successfully perform an indirect measurement of a structure on campus using the shadow method, preparing them for the scale model project.
Key Vocabulary
• Indirect Measurement
• Shadow Reckoning
• Scale Factor
• Thales' Theorem
Required Tools
• Meter Sticks (1 per group)
• Tape Measures (Long)
• Clipboards
• Level Ground (Outdoor)
Pro-Tips
Timing: Shadows are shortest at solar noon. Aim for 9:00–10:30 AM or 2:00–3:30 PM for maximum length and accuracy.
Cloudy Days: Use high-powered flashlights or "work lights" in the gym to cast sharp, measurable shadows.
Field Facilitation
1
Site Selection
Choose structures with clear shadows on flat pavement. Avoid uneven grass or gravel.
2
Simultaneity
The stick and object must be measured at the exact same moment. One marks, one measures.
3
Precision
Ensure the stick is perfectly vertical. A slight tilt will ruin the proportion calculations.
Deep Dive Discussion
"How does the height of the Sun affect the length of our shadows, but not our final calculation?"
"If we measured a building on a 10% slope, would our height result be too high or too low?"
"Why can't we use this method with streetlights? Hint: think about parallel rays of light."
"Explain why Thales waiting for his shadow to equal his height was a 'mathematical shortcut'."
Field Observation Notes / Misconception Log
Scale Scout Project Guide SCALE SCOUT PROJECT
Indirect Measurement & Model Engineering
The Mission
Document a local landmark using Shadow Reckoning and build a precision 3D scale model for the museum archives. Accuracy is your primary directive.
Target Scale
1 : 50
Phase 1: Field Recon
Measure three (3) shadows at different times.
Average your results for the "Master Height."
Field Data Log (Heights/Times)
Phase 2: Blueprinting
Calculate model dimensions using 1:50 scale.
Draw a scaled 2D profile on your Build Log.
Phase 3: The Build
Construct the frame using scaled measurements.
Prepare a "Data Plaque" for final display.
Architectural Standard
Accuracy is non-negotiable. Ensure every measurement on your final model matches your 1:50 scale calculations within 5% error. Clean joints and stable framing are required.
Submission Deadline ________________
Selected Structure ________________
Project Ref: ARCH-SCALE-01
Model Master Rubric MODEL MASTER RUBRIC
Evaluation Criteria: Scale Scout Project
Final Score
/ 100
Criteria Exemplary (25) Proficient (15) Developing (5) Field Data & Math
Accuracy of measurements and proportions.
| Error-free math; multiple time trials documented clearly. | Shadow trials recorded; minor math errors only. | Incomplete trials or significant calculation errors. |
|
Scale Accuracy
Consistency of 1:50 scale across dimensions.
| All model dimensions perfectly match scale factor. | Main dimensions accurate; minor detail inconsistencies. | Scale applied incorrectly or inconsistently. |
|
Craftsmanship
Stability, material use, and polish.
| Sturdy, professional construction; creative materials. | Stable build; minor visible glue or rough cuts. | Fragile or sloppy build; messy material use. |
|
Presentation
Quality of Exhibit Plaque and Log.
| Professional plaque; blueprint included; log is pristine. | Readable plaque with basic data; log is complete. | Plaque/Log missing, messy, or lacks key data. |
Instructor Feedback
Letter Grade
Evaluated by: _______________________
Document Ref: SCALE-SCOUT-RUBRIC
Build Blueprint Log BUILD BLUEPRINT LOG
Architectural Records & Scale Conversions
ARCHITECT:
STRUCTURE:
Phase 1: Field Measurements
Trial Stick H (m) Stick Shadow (m) Obj. Shadow (m) Calc. Height (m) 01
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| 02 |
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Average Building Height:
Phase 2: Scale
Scale Ratio: 1 :
50
Conversion Math
Model Height (cm):
Drafting
Scaled Profile Sketch
Phase 3: Build Strategy
Materials Checklist:
Stability Solutions:
