| Lab Name |
Models Representing the Speed of the Data and Time it Takes to Upload or Download Over different communication mediums.
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| Subject Area |
Mathematics
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| Grade |
6 - 12
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| Topic |
Regression Analysis, Functions, Proportionality.
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| Experiment Title |
Determine the Regression model of the data flow along the communication line in order to transmit and receive data over different communication mediums.
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| Hardware |
- COSMOS Toolkit: Computer Node
- Graphing calculator
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| Software |
- COSMOS Toolkit: Framework
- GNU Radio Companion
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| Number of Sessions to teach the topic |
2 - 3 sessions or longer for classes that needs differentiation.
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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 the 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.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 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.
- F-IF.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
- F-IF.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate
- F-IF.6
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.
- F-IF.8
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- F-IF.9
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
- A-REI.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- F-BF.1
Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context.
- S-ID.6
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.
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| COSMOS concepts to be used for the lab |
Network services that are involved in end-to-end communication, understanding the network protocols and how they are organized in layers and run a prepared activity to see how addresses are used at each layer in an end-to-end communication.
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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) |
Apply the concept of regression analysis and give students the opportunity to analyze the regression model that fits the relationship between the two quantities compared in the given situation.
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| Short Description and Walk-through of the experiment |
Students will send a message/text/email to the other someone and find out how fast the data travelled over the network before it arrived to the receiver. They will compare this phenomenon with the data sent via wireless network versus using cable wires versus optical.
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| Testbed mapping of the experiment |
As the packet moves between layers, a header is added with information regarding the specific layer between the interconnected hosts. At any given layer, the endpoints involved in a communication must agree on how a given service will be provided - a set of rules for how that service will work known as protocols.
With the toolkit, the students could see how fast a data packet moved through different medium like wireless( satellite, wifi, cellular) verus wired medium (such as cable/dsl) versus optical (fiber) and record the speed and the time it takes from Host A to Host B. Having gathered the data of speed and time, with the size of the data sent-students will find out the trend. They will find out what regression model fits the given phenomenon.
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