Modeling & Simulation: Nodes and Graphs

Learning Resource Type

Classroom Resource

Subject Area

Mathematics
Digital Literacy and Computer Science

Grade(s)

9, 10, 11, 12

Overview

Introduce students to nodes and graph theory and their use in operations research. Show how Dijkstra’s Algorithm can be used to find the shortest or quickest route between nodes in a network.

Digital Literacy and Computer Science (2018) Grade(s): 09-12

DLCS18.HS.37

Evaluate the ability of models and simulations to test and support the refinement of hypotheses.

UP:DLCS18.HS.37

Vocabulary

  • model
  • simulations
  • hypotheses
  • phenomena
  • target system

Knowledge

Students know:
  • how to explain the use of models and simulations to generate new knowledge and understanding related to the phenomena or target system that is being studied.
  • how to explain the ability of models and simulations to test and support the refinement of hypotheses related to phenomena under consideration.
a.
  • that modeling and simulations are way to extrapolate and interpolate unrest situation and scenarios to help formulate, test and refine hypotheses.
b.
  • how to form a hypothesis.
  • how to test a hypothesis.
  • how to create a model or simulation.
c.
  • that simulations or models can be created to test a hypothesis but not provide the information expected or intended.
  • that it is vital to verify the data being generated by a model or simulation.

Skills

Students are able to:
  • use a diagram or program to represent a model to express key properties of a phenomena or target system.
  • research existing models and simulations and how they are used to test and refine hypotheses.
  • explain how existing models and simulations are used to test and support the refinement of hypotheses.
a.
  • create a model or simulation to formulate, test, and refine a hypothesis.
  • utilize a model or simulation to formulate, test, and refine a hypothesis.
b.
  • form a model of a hypothesis.
  • test the hypothesis by collecting and analyzing data from a simulation.
c.
  • examine a model or simulation to determine the correctness of the generated data.
  • examine a flawed model or simulation and identify areas in which it is providing incorrect data.

Understanding

Students understand that:
  • a simulation is based on a model and enables observation of the system as key properties change.
  • the accuracy of models and simulations are limited by the level of detail and quality of information used and the software and hardware used.
  • models and simulations are an effective and cost efficient way to understand phenomena and test and refine hypotheses.
a.
  • models and simulations are way to extrapolate and interpolate unrest situation and scenarios to help formulate, test and refine hypotheses.
  • models and simulations can be the only cost- ot time-effective way to test a hypothesis.
b.
  • Models and simulations can save money, are safer, usually requires less time, and do not have the environmental impact that a full experiment or operational test may induce.
c.
  • while a process may operate without errors, that does not guarantee that the process is providing accurate data to meet your needs.
Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.2

Use units as a way to understand problems and to guide the solution of multi-step problems.

UP:MA19.GDA.2

Vocabulary

  • Units
  • Scales
  • Descriptive modeling
  • Justify
  • Interpret
  • Identify
  • Quantities
  • Dimensional analysis
  • Formulas
  • Scale
  • Consistency
  • Precise
  • Accuracy
  • Margin of error
  • Perimeter
  • Volume
  • Area
  • Direct measurement

Knowledge

Students know:
  • Techniques for dimensional analysis,
  • Uses of technology in producing graphs of data.
  • Criteria for selecting different displays for data (e.g., knowing how to select the window on a graphing calculator to be able to see the important parts of the graph.
  • Descriptive models .
  • Attributes of measurements including precision and accuracy and techniques for determining each.

Skills

Students are able to:
  • Choose the appropriate known conversions to perform dimensional analysis to convert units.
  • Correctly use graphing window and other technology features to precisely determine features of interest in a graph.
  • Determine when a descriptive model accurately portrays the phenomenon it was chosen to model.
  • Justify their selection of model and choice of quantities in the context of the situation modeled and critique the arguments of others concerning the same situation.
  • Determine and distinguish the accuracy and precision of measurements.

Understanding

Students understand that:
  • The relationships of units to each other and how using a chain of conversions allows one to reach a desired unit or rate.
  • Different models reveal different features of the phenomenon that is being modeled.
  • Calculations involving measurements can't produce results more accurate than the least accuracy in the original measurements.
  • The margin of error in a measurement, (often expressed as a tolerance limit), varies according to the measurement, tool used, and problem context.
Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.7

Use mathematical and statistical reasoning with quantitative data, both univariate data (set of values) and bivariate data (set of pairs of values) that suggest a linear association, in order to draw conclusions and assess risk.

UP:MA19.GDA.7

Vocabulary

  • Mathematical reasoning
  • Statistical reasoning
  • Univariate data
  • bivariate data
  • quantitative data
  • linear association
  • Scatter plots
  • linear model
  • Slope
  • bar graphs, Pie graphs, Histograms
  • Mean, median, mode
  • Standard deviation

Knowledge

Students know:
  • Patterns found on scatter plots of bivariate data.
  • Strategies for determining slope and intercepts of a linear model.
  • Strategies for informally fitting straight lines to bivariate data with a linear relationship.
  • Methods for finding the distance between two points on a coordinate plane and between a point and a line.

Skills

Students are able to:
  • Construct a scatter plot to represent a set of bivariate data.
  • Use mathematical vocabulary to describe and interpret patterns in bivariate data.
  • Use logical reasoning and appropriate strategies to draw a straight line to fit data that suggest a linear association.
  • Use mathematical vocabulary, logical reasoning, and closeness of data points to a line to judge the fit of the line to the data.
  • Find a central value using mean, median and mode.
  • Find how spread out the univariate data is using range, quartiles and standard deviation.
  • Make plots like Bar Graphs, Pie Charts and Histograms.

Understanding

Students understand that:
  • Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated,
  • When visual examination of a scatter plot suggests a linear association in the data, fitting a straight line to the data can aid in interpretation and prediction.
  • Modeling bivariate data with scatter plots and fitting a straight line to the data can aid in interpretation of the data and predictions about unobserved data.
  • A set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
  • Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated.
  • Statistical measures of center and variability that describe data sets can be used to compare data sets and answer questions.
Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.29

Find patterns and relationships in figures including lines, triangles, quadrilaterals, and circles, using technology and other tools.

UP:MA19.GDA.29

Vocabulary

  • Conjectures
  • Construct
  • Congruent
  • Compass
  • Straightedge

Knowledge

Students know:
  • Use technology and other tools to discover patterns and relationships in figures.
  • Use patterns. relationships and properties to construct figures.

Understanding

Students understand that:
  • Many of the constructions build on the relationships among the objects and are justified by the properties used during the construction. Technology can be used as a means to explain the properties and definitions by developing procedures to carry out the construction.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

Public Domain
https://aptv.pbslearningmedia.org/resource/510631fa-4d5f-4b60-8f1a-ee0ca24ad6be…

Accessibility

Video resources: includes closed captioning or subtitles

Approved Date

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