Unit 2: Mashing it up: physical models of deformation and strain
These materials have been reviewed for their alignment with the Next Generation Science Standards as detailed below. Visit InTeGrate and the NGSS to learn more.
OverviewStudents utlize physical models to qualitatively and quantitatively describe deformation and strain. They use algebra and vectors to illustrate and describe strain in physical models.
Science and Engineering Practices
Using Mathematics and Computational Thinking: Use mathematical, computational, and/or algorithmic representations of phenomena or design solutions to describe and/or support claims and/or explanations. HS-P5.2:
Using Mathematics and Computational Thinking: Apply techniques of algebra and functions to represent and solve scientific and engineering problems. HS-P5.3:
Developing and Using Models: Develop a complex model that allows for manipulation and testing of a proposed process or system. HS-P2.5:
Cross Cutting Concepts
Systems and System Models: Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales. HS-C4.3:
Stability and Change: Change and rates of change can be quantified and modeled over very short or very long periods of time. Some system changes are irreversible. HS-C7.2:
Scale, Proportion and Quantity: Using the concept of orders of magnitude allows one to understand how a model at one scale relates to a model at another scale. HS-C3.4:
Patterns: Mathematical representations are needed to identify some patterns HS-C1.4:
Disciplinary Core Ideas
Natural Hazards: Natural hazards and other geologic events have shaped the course of human history; [they] have significantly altered the sizes of human populations and have driven human migrations. HS-ESS3.B1:
Information Technologies and Instrumentation: Multiple technologies based on the understanding of waves and their interactions with matter are part of everyday experiences in the modern world (e.g., medical imaging, communications, scanners) and in scientific research. They are essential tools for producing, transmitting, and capturing signals and for storing and interpreting the information contained in them HS-PS4.C1:
Earth and Human Activity: Construct an explanation based on evidence for how the availability of natural resources, occurrence of natural hazards, and changes in climate have influenced human activity. HS-ESS3-1:
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This page first made public: Dec 9, 2016
Unit 2 Learning Outcomes
- Students will be able to use physical models to illustrate different types of deformation and strain.
- Students will be able to mathematically calculate 1-D extension.
- Students will be able to correctly analyze and depict how a triangle of GPS stations and inscribed circle move or deform during translation, rotation, dilation, contraction, or distortion.
Unit 2 Teaching Objectives
- Cognitive: Facilitate students' ability to make calculations and depictions related to extension, deformation, and strain.
- Behavioral: Provide an opportunity for students to connect physical models to principles of deformation and strain.
Context for Use
This module was designed for structural geology courses but may also be used successfully in geophysics, tectonics, or geohazards courses or possibly even a physics or engineering course seeking practical applications. It can be done at almost any point during the term. The module assumes that students have had a basic physical geology introduction to plate tectonics, faults, and earthquakes. Unit 2 gives students an opportunity to develop an intuitive, as well as mathematical, understanding of deformation and strain. Unit 2 (particularly the extended version) could be done as a successful lab activity without any other part of this module. Although later units could be done without Unit 2, some other introduction to the terms extension, translation, rotation, etc. would be necessary. As an alternative to a single lab exercise, it is also possible to do one or two physical model activities included over a series of class periods as a break from regular class lecture or lab. We strongly suggest doing at least the Basic version of the physical models exercise prior to Units 3–6. The opportunity to interact physically with the concepts does help a wide range of different learners.
Also included in Unit 2 materials are a range of supporting mathematical materials that can be used to build student skills and knowledge of vectors, matrices, and strain analysis algorithms.
Description and Teaching Materials
Basic version physical models:
The basic version of the unit has the students using just rubber bands and stretchy fabric to practice making measurements and descriptions of different types of extension and deformation. This provides an efficient way for students to learn about the mathematical and structural geology concepts that underpin the GPS station "triangles" in inscribed strain ellipse. They practice identifying how rotation, translation, extension, compression, etc. affect GPS velocity vectors. We have included a reading about strain and a few PowerPoint slides about extension that could be given before or after the physical models exercise. Often it works well to have the students explore the physical models first. The reading may not be necessary in courses with a text or lectures that cover strain in depth.
- Unit 2 Introduction to Basic Physical Models of Deformation (PowerPoint 2007 (.pptx) 6MB Dec5 16)
- Unit 2 Basic physical models instructor notes (Microsoft Word 2007 (.docx) 4.4MB Dec19 17)
- Unit 2 Introduction to Strain Student Reading (Microsoft Word 2007 (.docx) 4.1MB Dec19 17)
Unit 2 Introduction to Strain Student Reading PDF (Acrobat (PDF) 4.9MB Dec19 17)
- Unit 2 Basic physical models exercise for students (Microsoft Word 2007 (.docx) 4.3MB Dec19 17)
Unit 2 Basic physical models exercise for students PDF (Acrobat (PDF) 5.7MB Dec19 17)
- GPS triangle and strain ellipse images (Microsoft Word 2007 (.docx) 1.7MB Sep23 15)
- Simple diagrams of the different components of strain
Extended version physical models:
Physical models can be tremendously helpful for students to gain a fuller intuitive understanding of deformation. In this extended exercise, students explore strain and deformation in a variety of media and more broadly focused than just the concepts to support GPS and infinitesimal strain. Instructors could choose to: (1) add one or two additional models to the Basic version of the exercise, (2) have a full lab period devoted to exploring all the different models in both the Basic and Extended versions, or (3) weave one or two models at a time into the course over days or weeks so students have a chance to return to and review different concepts. The extended version also includes a model using bungee cords that could be used instead of the rubber bands in the Basic version.
- Unit 2 Extended physical models exercise instructor notes (Microsoft Word 2007 (.docx) 4.6MB Dec19 17)
- Unit 2 Extended physical models exercise for students (Microsoft Word 2007 (.docx) 1.6MB Dec19 17)
Unit 2 Extended physical models exercise for students PDF (Acrobat (PDF) 2.1MB Dec19 17)
These math materials are not directly related to the physical models activities. They are designed for instructors interested in addressing the quantitative analysis component of GPS and infinitesimal strain more thoroughly. This is particularly useful for instructors who want the "GPS Strain Calculator" (introduced in Unit 4) to be less of a black box. In order for students to understand the underlying math, they need to know about vectors, matrices, and strain analysis. It is generally good to start introducing this well before getting to Unit 4. For instance, a short lecture on vectors and/or matrices could be given on the same day as the Basic Physical Models exercise. The Infinitesimal Strain Analysis reading takes some time to digest. If it is going to be assigned as a reading, giving it out some time in advance of Unit 4 would be best. It may also be helpful background reading for instructors who want to brush up on their understanding of infinitesimal strain.
- Vector reading (Microsoft Word 2007 (.docx) 4.2MB Dec6 16)
- Vector worksheet for students (Microsoft Word 2007 (.docx) 201kB Dec6 16)
- Matrix and dot product reading (Microsoft Word 484kB Dec7 16)
- Matrix and dot product worksheet for students (Microsoft Word 2007 (.docx) 251kB Dec6 16)
- Orthogonal coordinate transfer reading (Microsoft Word 2007 (.docx) 633kB Dec7 16)
- Infinitesimal Strain Analysis in 1, 2, and 3-D reading (Microsoft Word 2007 (.docx) 1.1MB Dec6 16)
Teaching Notes and Tips
- This unit may be split in half and combined with Units 1 and 3 for instructors teaching in 75-minute blocks.
- These activities may be used as a sort of think-pair-share activity where students complete key steps and then discuss as a class. Discussion points could include (1) after steps 1–5 of the rubber band model, (2) after step 6 of the rubber band model, (3) after the first t-shirt model, (4) after the last t-shirt model (general deformation).
- Instructors may want to end the class by having students interpret deformation from displacements, a skill they will use in Unit 4.
Observation of student activity and conversations, individual questioning, and group discussion are excellent ways to conduct formative assessment as the students complete this exercise.
The student exercise is the summative assessment for this unit. Most of the questions have definite right or wrong answers. To receive full credit, students must show their work, where appropriate. Where an open-ended answer is required, students are assessed based on a simple 2-point system.
2 points = correct answer with thorough supporting evidence and/or complete description
1 point = answer not completely correct or lacking thorough supporting evidence or description
0 points = incorrect answer
References and Resources
- More ideas about fun physical models to try can be found at Vince Cronin's Physical Models webpage
- Video on how to make Physical model of strain ellipses in stretching and shortening