| Lab Name |
Analyzing Relationship of the Variables Involved in Airplane Routes
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| Subject Area |
Mathematics
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| Grade |
6 - 12
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| Topic |
- Pythagorean Theorem
- D = RxT
- Law of Cosines
- Correlation
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| Experiment Title |
Airplane Route Analysis
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| Hardware |
- COSMOS Toolkit: Computer Node
- Software Defined Radio (i.e., ADALM Pluto SDR, RTL-SDR)
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| Software |
- COSMOS Toolkit: Framework
- DUMP1090 Software
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| Number of Sessions to teach the topic |
3 - 4
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| Educational standards to be addressed |
- 6.EE.9
Use variables to represent two quantities in a real-world problem that change in relationship to
one another; write an equation to express one quantity, thought of as the dependent variable, in
terms of the other quantity, thought of as the independent variable.
Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
- 7.RP.2
Recognize and represent proportional relationships between quantities.
- Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
- Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
- 7.EE.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational
numbers in any form (whole numbers, fractions, and decimals), using tools strategically.
Apply properties of operations to calculate with numbers in any form; convert between forms as
appropriate; and assess the reasonableness of answers using mental computation and
estimation strategies.
- 8.G.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
- 8.EE.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
- 8.EE.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
- G-SRT.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
- A-REI.6 59
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- F-IF.6 71
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Build a function that models a relationship between two quantities
- F-BF.1 40
Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
- S-ID.6 62
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
- G-SRT.11
Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
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| COSMOS concepts to be used for the lab |
Using the COSMOS Toolkit, you can open a terminal and run:
- cd ~/Desktop/cosmos-toolkit-framework/dump1090; ./dump1090 --net --interactive --write-json ~/Desktop/cosmos-toolkit-framework/dump1090/stats/
You can also open a browser page to the following page:
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| K12 Educational Goals (How the educational goals are achieved through teaching using the experiment, how the topic is connected to the COSMOS concepts used) |
Using the webpage and the terminal, the students will analyze the trend and the airplane routes in JFK or La Guardia airport and apply the different concepts of Pythagorean Theorem, Law of Sines & Cosines, D=RxT and percentages in this real-life scenario integrated.
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| Short Description and Walk-through of the experiment |
Students will study the different airplane routes of the two different/same airports and find out the percentages and trends of the flights for a specific period of time. Then they can measure the angle of elevation and depression of a given airplane at the current location and compute the distance for the line of sight or use a triangulation technique and use the Pythagorean Theorem to find the missing side. They can have a project extension by group through creating their own investigation and analyzing trends of other airlines.
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| Testbed mapping of the experiment |
This experiment will be run on the terminal of the COSMOS Toolkit and at the same time opening the local host on a web browser to observe the Airplane Routes from any of the NYC airports - JFK or La Guardia and students will:
- describe the relationship of distance, time and rate of a certain airplane flight and analyze these variables in terms of proportionality.
- use these variables to go deeper into the application of the Pythagorean Theorem, Law of Sines and Cosines in the real-world of wireless technology.
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