Earthquake Magnitude: Designing a Logarithmic Scale
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we design a logarithmic scale to effectively measure and compare the magnitudes of earthquakes, considering its accuracy, usability, and real-world applications?Essential Questions
Supporting questions that break down major concepts.- How are logarithms used to measure quantities that vary greatly?
- How can we represent a wide range of earthquake magnitudes on a manageable scale?
- What are the mathematical properties of logarithms and how do they relate to earthquake intensity?
- How does the design of a logarithmic scale impact its accuracy and usability?
- How can we compare and contrast different earthquake magnitude scales?
- What are the real-world applications of logarithmic scales beyond measuring earthquakes?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Understand and apply the concept of logarithms to design an earthquake magnitude scale.
- Justify the design choices of the logarithmic scale based on mathematical principles and real-world applications.
- Analyze and compare different earthquake magnitude scales.
- Apply mathematical properties of logarithms to earthquake intensity measurements.
- Evaluate the accuracy and usability of the designed logarithmic scale.
- Relate the use of logarithmic scales to other real-world applications
Entry Events
Events that will be used to introduce the project to studentsClassroom Earthquake Simulation
Simulate an earthquake in the classroom using a shake table or online simulation. Students experience varying intensities and discuss how to quantify the differences, leading to the need for a logarithmic scale.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Earthquake Scale Investigator
Students will investigate existing earthquake magnitude scales (e.g., Richter scale, moment magnitude scale) and analyze their logarithmic bases and scaling factors. They will explore the mathematical principles behind these scales and how they relate to the energy released by earthquakes.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA comparative report analyzing different earthquake magnitude scales, including their logarithmic bases, scaling factors, and the rationale behind their design choices.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Justify the design choices of the logarithmic scale based on mathematical principles and real-world applications.Magnitude Calculation Challenge
Students will use real earthquake data to calculate magnitudes based on a chosen logarithmic scale. They will practice converting between earthquake intensity and magnitude using logarithmic formulas and apply the mathematical properties of logarithms to simplify calculations and solve problems related to earthquake measurements.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA problem set where students calculate earthquake magnitudes from given intensity data using logarithmic formulas and demonstrate their understanding of the mathematical properties of logarithms in simplifying calculations.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Apply mathematical properties of logarithms to earthquake intensity measurements.Scale Design Architect
Students will design their own logarithmic scale for measuring earthquake magnitudes, specifying the logarithmic base, scaling factor, and range of measurable magnitudes. They will justify their design choices based on mathematical principles, accuracy, usability, and real-world considerations.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA proposal for a new earthquake magnitude scale, including a detailed explanation of the design choices, mathematical justification, and a discussion of its potential advantages and limitations compared to existing scales.Alignment
How this activity aligns with the learning objectives & standardsLearning Goals: Evaluate the accuracy and usability of the designed logarithmic scale. Relate the use of logarithmic scales to other real-world applications.Logarithm Essentials Unveiled
Students will learn the basics of logarithms and their properties, focusing on how logarithms can be used to compress large ranges of numbers into a more manageable scale. They will explore the relationship between earthquake intensity and magnitude.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA presentation explaining the definition of a logarithm, its properties, and examples of how it simplifies the representation of large numbers, particularly in the context of earthquake measurement.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Understand and apply the concept of logarithms to design an earthquake magnitude scale.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioEarthquake Magnitude Scale Design Rubric
Scale Design and Justification
Focuses on the student's ability to design a logarithmic scale for measuring earthquake magnitudes, justifying their design choices based on mathematical principles, accuracy, usability, and real-world considerations.Logarithmic Application
Depth of understanding and application of logarithmic concepts.
Exemplary
4 PointsDemonstrates a sophisticated and nuanced understanding of logarithmic concepts and applies them innovatively to justify scale design.
Proficient
3 PointsDemonstrates a thorough understanding of logarithmic concepts and applies them effectively to justify scale design.
Developing
2 PointsShows an emerging understanding of logarithmic concepts and applies them inconsistently to justify scale design.
Beginning
1 PointsShows a beginning understanding of logarithmic concepts and struggles to apply them to justify scale design.
Design Justification
Clarity and justification of design choices based on mathematical principles and real-world applications.
Exemplary
4 PointsProvides an exceptionally clear and well-reasoned justification of design choices, demonstrating a deep understanding of mathematical principles and real-world applications.
Proficient
3 PointsProvides a clear and well-reasoned justification of design choices, demonstrating a good understanding of mathematical principles and real-world applications.
Developing
2 PointsProvides a partially clear justification of design choices, demonstrating a basic understanding of mathematical principles and real-world applications.
Beginning
1 PointsProvides a vague or unclear justification of design choices, demonstrating a limited understanding of mathematical principles and real-world applications.
Scale Accuracy and Usability
Accuracy and usability of the designed logarithmic scale.
Exemplary
4 PointsDesigns a scale that is exceptionally accurate, usable, and innovative, demonstrating a comprehensive understanding of real-world considerations.
Proficient
3 PointsDesigns a scale that is accurate and usable, demonstrating a good understanding of real-world considerations.
Developing
2 PointsDesigns a scale that has some accuracy and usability issues, demonstrating a basic understanding of real-world considerations.
Beginning
1 PointsDesigns a scale that has significant accuracy and usability issues, demonstrating a limited understanding of real-world considerations.
Proposal Quality
Quality and clarity of the proposal, including discussion of advantages and limitations compared to existing scales.
Exemplary
4 PointsPresents a proposal of outstanding quality and clarity, with a comprehensive discussion of the scale's advantages and limitations compared to existing scales.
Proficient
3 PointsPresents a proposal of high quality and clarity, with a clear discussion of the scale's advantages and limitations compared to existing scales.
Developing
2 PointsPresents a proposal of moderate quality and clarity, with a basic discussion of the scale's advantages and limitations compared to existing scales.
Beginning
1 PointsPresents a proposal of low quality and clarity, with a limited or unclear discussion of the scale's advantages and limitations compared to existing scales.