Lesson plan
Design your Dragon: A STEM Challenge thru Dimensional Analysis Inspired by "How to Train your Dragon"
The purpose of this lesson is to allow students to explore the wingspan vs wing area of multiple real-life flying organisms / objects to develop a basis for what can fly and what can not. Then, using dimensional analysis and scaling law, students will design a dragon (inspired by Toothless from How to Train Your Dragon) that should be able to fly.
Overview
Students ask whether a dragon like Toothless from How to Train Your Dragon could fly, starting with a film clip and a discussion of the forces acting on a flying creature. They compare wing data for a bald eagle, bat, pterosaur, and small glider, learn the square-cube scaling law, and estimate wing area for a dragon of about 1,000 kg. They then convert square meters to square feet and compare the estimate with aircraft wing data. In the culminating Engineering Design Process challenge, students calculate wing dimensions, produce a blueprint, revise it after peer feedback, and present a pitch, documenting the work in an Engineering Design Journal. The plan spans six days of instruction, each planned for 45-60 minutes.
Lesson Objectives
- Science Objectives
- Explain the physical forces (such as lift, gravity, and drag) acting on a flying object and how they affect the ability of a large creature like Toothless to fly.
- Apply the square-cube scaling law to calculate the estimated wing area required for a dragon weighing approximately 1,000 kg to achieve flight.
- Compare wing sizes and masses of various flying animals (bald eagle, bat, pterosaur, glider) and analyze which model best fits the flight requirements of Toothless. Mathematics Objectives
- Use ratios, proportions, and exponents to solve problems related to the scaling of wing area relative to body mass.
- Convert measurements between square meters and square feet to relate scientific data to real-world units. Engineering Objectives
- Design a scientifically plausible wing blueprint for a flying dragon using the Engineering Design Process, incorporating wing size calculations and aerodynamic principles.
- Evaluate and revise their dragon wing designs based on peer feedback and engineering criteria. English Language Arts Objectives
- Analyze a narrative passage describing flight from How to Train Your Dragon to identify descriptive language and emotional tone.
- Write a journal entry from the perspective of Hiccup explaining, with scientific reasoning, how he would help Toothless fly again, using accurate math and engineering concepts integrated into a coherent narrative. 10.Engage effectively in paired and group discussions, articulating ideas clearly and building on peers’ contributions related to flight challenges and design solutions. Key Vocabulary: mass, weight, lift, drag, thrust, area, volume, scaling law, dimensional analysis 4 Design your Dragon: A STEM Challenge thru Dimensional Analysis
Standards
NGSS · 8
- MS-PS2-2Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object.
- MS-PS3-1Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object.
- MS-ETS1-1Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution.
- MS-ETS1-2Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.
- MS-ETS1-3Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution. 2 Design your Dragon: A STEM Challenge thru Dimensional Analysis High School (Grades 9-12)
- HS-PS2-1Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among net force, mass, and acceleration.
- HS-PS3-2Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles or energy stored in fields.
- HS-ETS1-3Evaluate a solution to a complex problem based on prioritized criteria and trade-offs.
CCSS Math · 8
- 6.RP.A.3Use ratio and rate reasoning to solve real-world and mathematical problems.
- 7.RP.A.2Recognize and represent proportional relationships between quantities.
- 7.EE.B.4Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems.
- HSA-CED.A.2Create equations in two or more variables to represent relationships between quantities.
- HSA-REI.B.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
- HSA-SSE.A.1Interpret expressions that represent a quantity in terms of its context.
- HSF-LE.A.2Construct linear and exponential functions, including arithmetic and geometric sequences.
- HSN-Q.A.1Use units as a way to understand problems and guide solution strategies; choose and interpret units consistently in formulas.
CCSS ELA · 4
- W.6.3Write narratives to develop real or imagined experiences or events using effective techniques, relevant descriptive details, and clear event sequences.
- SL.6.1Engage effectively in a range of collaborative discussions (one-on-one, in groups, teacher-led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing their own clearly.
- W.9-10.3Write narratives to develop real or imagined experiences or events using effective techniques, well-chosen details, and well-structured event sequences.
- SL.9-10.1Initiate and participate effectively in a range of collaborative discussions on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. 3 Design your Dragon: A STEM Challenge thru Dimensional Analysis