Lab Name Proportionality and Rate of Change Using the Experiment on Bandwidth & Data Rate.
Subject Area Mathematics
Grade 6 - 8
Topic Ratio, Rate, Proportionality & Rate of Change.
Experiment Title Finding Ratio, Rate, Proportionality & Rate of Change by observing different bandwidth with their amount of data flow at a given time.
Hardware
  • COSMOS Toolkit: Computer Node
  • COSMOS Toolkit: Mobile Node
  • COSMOS Toolkit: IoT Nodes with sensors (i.e., temperature, humidity, polluting dust, luminocity, CO2)
Software
  • COSMOS Toolkit: Framework
  • GNU Radio Companion
  • Chronograf
Number of Sessions to teach the topic 5 - 6
Educational standards to be addressed
  • CCSS.MATH.CONTENT.6.RP.A.1
    Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
  • CCSS.MATH.CONTENT.6.RP.A.2
    Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
  • CCSS.MATH.CONTENT.6.RP.A.3
    Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • CCSS.MATH.CONTENT.7.RP.A.1
    Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
  • CCSS.MATH.CONTENT.7.RP.A.2
    Recognize and represent proportional relationships between quantities.
  • CCSS.MATH.CONTENT.7.RP.A.2.A
    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.
  • CCSS.MATH.CONTENT.7.RP.A.2.B
    Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  • CCSS.MATH.CONTENT.7.RP.A.2.C
    Represent proportional relationships by equations.
  • CCSS.MATH.CONTENT.8.F.A.1
    Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
  • CCSS.MATH.CONTENT.8.F.A.2
    Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
  • CCSS.MATH.CONTENT.8.F.A.3
    Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
COSMOS concepts to be used for the lab Frequency, voltage, noise, decibel (dB), transmitter amplitude, noise amplitude, environmental noise, health hazards, noise path, receiver, noise source, bandwidth, data rate, signal bandwidth, modulation.
K12 Educational Goals (How the educational goals are achieved through teaching using the experiment, how the topic is connected to the COSMOS concepts used) Students will be using word problems regarding hose with different diameters/radius and the rate of the water flow per hose. Using the rate of each hose, they will be computing the amount of water accumulated given let's say 10 minutes. They will compare the different volume of water in the tank. This will be used as an analogy to the COSMOS experiment on bandwidth and data rate in the wireless network.
Short Description and Walk-through of the experiment 5 - 6 sessions:
  1. Day 1: Hose of different sizes and rate of water flowing through each. They will solve the problem by determining the amount of water gathered in a tank given the same amount of time. They will see how the diameter of the hose determines the volume of water.
  2. Day 2: In the same manner, they will investigate how the size of the bandwidth affects the rate of information which is passed over the air. They observe that the greater the capacity of the bandwidth, the greater the capacity of the transmission.
  3. Day 3: They will use this idea studying traffic flow or the amount of vehicles on certain huge highways with 6-8 lanes compared to small/narrow roads. They will research on the amount of pollution/carbon dioxide, level of noise and heat in areas like this.
  4. Project ( assigned for 2 - 3 weeks ):
    • Day 4: Students will investigate this phenomenon on day 3 using the carbon dioxide, noise and temperature sensor.
    • Day 5: They will analyze the data gathered in these different real-world scenarios and discuss similarities & differences.
  5. Students will present their discussions on Google Classroom with their powerpoint presentations of their analysis, findings and conclusions & even questions.
Testbed mapping of the experiment The experiment can be extended by executing this on a Testbed like ORBIT(Rutgers) and WItest(NYU). Teachers/Students will have to make reservations before running the experiment. Once given the approval, they will log in to them over the internet and run the experiment on them via remote access. In the experiment, they will send information using signals with different bandwidth, and see how long it takes to send a fixed amount of data.

Experiment Execution

Select the bandwidth you prefer (1 is the smallest, 6 is the highest) and the appropriate function of the node (Transmitter or Receiver), and press START to begin the experiment. In order to terminate the experiment press STOP.
Transmitter Receiver
1 2 3
4 5 6


To collect environmental measurements from nearby IoT nodes press START button. In order to terminate the experiment press STOP button.

Experiment Material

NGSS Lesson Plan
Worksheet
Other

© 2018 COSMOS Project. Created by Juditha Capa Damiao, Joseph F. Lamb School