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# Size and scale of giant monsters

Objectives
Students will:
Learn algebraic-geometric patterns for how changes in size affects surface area, volume and mass.
Be able to do numerical calculations for such changes
See how real world materials (e.g. bone) stand up to changes in scale.

### Godzilla, King Kong, Pacific Rim and Cloverfield. We see beasts of incredible size and mass

The Beast from 20,000 Fathoms, 1953, Warner Brothers

### What real-world limiting factors will appear? These are questions of scaling.

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## Proportionality and the Value of Ratios

### (Volume Big Sphere)/ (Volume Small Sphere) = (4/3 p (2R)3) / ( 4/3 p R3) = 23= 8

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### This works for squares, spheres, frogs,gorillas (King Kong!), dinosaurs (Godzilla), etc.

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# Godzilla vs Scaling Laws of Physics

Adapted from “Godzilla Versus Scaling Laws of Physics,”
Thomas R. Tretter, University of Louisville, Louisville, KY
The Physics Teacher Vol.43, Nov. 2005

# Godzilla, 1998, with Matthew Broderick.

View scene at 10:15 – footprint

– – – – –

### Measure the circumference of an ankle, then find the cross sectional area of your two ankles together.

Dr. Noah Weiss and Cameron Drake
http://blog.drake.fm/blog/gifs/

### Estimate Godzilla’s weight.

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34:00 Post rampage scenes including a building with a huge hole through it

## Learning standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

Appendix VIII Value of Crosscutting Concepts and Nature of Science in Curricula

In grades 9–12, students can observe patterns in systems at different scales and cite patterns as empirical evidence for causality in supporting their explanations of phenomena. They recognize that classifications or explanations used at one scale may not be useful or need revision using a different scale, thus requiring improved investigations and experiments. They use mathematical representations to identify certain patterns and analyze patterns of performance in order to re-engineer and improve a designed system.

Next Gen Science Standards HS-PS2 Motion and Stability

Crosscutting Concepts: Different patterns may be observed at each of the scales at which a system is studied and can provide evidence for causality in explanations of phenomena. (HS-PS2-4)

A Framework for K-12 Science Education

Scale, proportion, and quantity. In considering phenomena, it is critical to recognize what is relevant at different measures of size, time, and energy and to recognize how changes in scale, proportion, or quantity affect a system’s structure or performance….

The understanding of relative magnitude is only a starting point. As noted in Benchmarks for Science Literacy, “The large idea is that the way in which things work may change with scale. Different aspects of nature change at different rates with changes in scale, and so the relationships among them change, too” [4]. Appropriate understanding of scale relationships is critical as well to engineering—no structure could be conceived, much less constructed, without the engineer’s precise sense of scale.

• Dimension 2, Crosscutting Concepts, A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

## Film clips

Antman

Antman Thomas The Tank Engine fight scene

Cloverfield – bomb the creature

Fantastic Voyage | #TBT Trailer | 20th Century FOX

Them! 1954 movie

Pacific Rim – opening

Pacific Rim – scene girl in street

Pacific rim – Kaiju baby

Ghostbusters – The Stay Puft Marshmallow Man

Ghostbusters 2 Stature of Liberty

Godzilla 2014 – out of the water

Godzilla – all sightings analysis

(1964) Godzilla, Rodan, Mothra vs Ghidrah

King Kong battles the T-rexes

King Kong battles T Rex – original version

2:12 / 3:53 Sky Captain and the World of Tomorrow clip

The Incredible Shrinking man

Transformers 1 Movie – Base Attack

## Megastructures

Extreme Engineering S1E09B Boston Big Dig

Boston Big Dig | Megastructures – National Geographic

Mega Structures – Burj Khalifa, Dubai [National Geographic]

Megastructures – Aldar HQ Abu Dhabi Worlds First Round Skyscraper Documentary National Geographic.

Deep Sea Drillers | Megastructures National Geographic Factories

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