Traffic Jam

Description of Unit

In this task, students will explore how leading researchers are using mathematics to understand the roots of complex problems such as “phantom traffic jams”—traffic congestion that suddenly appears on a roadway with no apparent cause (i.e., no observable accident, stalled vehicle, or other obstacle in a lane such as construction). Students investigate the connections between mathematics, science, and real-world problems in engineering and urban planning. At the conclusion of the task, students research a location in the community known for traffic congestion. Students identify the possible variables in the system such as the number of vehicles using the road during both high- and low-usage times, the types of vehicles, number of traffic signals and intersections, the timings and coordination of traffic signals, and the roadway’s carrying capacity. Students present their research findings using accurate mathematical vocabulary and suggest possible solutions for alleviating the traffic issues in the area studied.

This guide links the Traffic Jam unit to the Texas Essential Knowledge and Skills (TEKS) for high school students. Traffic Jam is a mathematics unit that allows students to study traffic patterns and analyze data using mathematical models. Traffic Jam also has interdisciplinary connections to science and social studies disciplines. For example, in order to conduct research in this task, the student must know and apply the laws governing motion in a variety of situations, as outlined in the Physics TEKS. Students also have opportunities to analyze the impact of technology and human modifications on the physical environment, as described in the Social Studies TEKS. The following document includes the applicable TEKS and the details of the Traffic Jam unit. The final section of this document presents the applicable Texas College and Career Readiness Standards adopted by the Texas Higher Education Coordinating Board (THECB) on January 24, 2008.

Phase I. Learning Experiences

Introduce students to the concept of using mathematics to model and explore problems in the real world. Read news articles and press releases highlighting research from leading mathematicians at MIT, Temple, and the University of Alberta who are using mathematics to investigate the causes for “phantom traffic jams”—jams that seem to occur without an obvious cause such as an accident, construction, or stalled vehicle. View the MIT article here: https://math.mit.edu/projects/traffic/
Discuss the article and introduce students to some of the mathematics concepts behind the research. How are mathematical tools used to study such phenomena? What are some of the intersections students observe between mathematics, engineering, and science?
Experiment with the equation in the article from Wired. Using data from area roads, what does the equation tell you about the amount of traffic density needed for a jam to occur?
Ask students to view the traffic wave simulations, charts, and graphics on the project’s web page at MIT (Note: to play many of these videos, the computer must be able to open .avi files in the DIXX format. The videos of cars driving on the circular road further down the page should play in any browser).
The researchers in the traffic project noticed the patterns of traffic jams were similar to the dynamics of explosions. What are some students’ hypotheses as to why this might be the case? Ask students to read this article and form small groups to examine the "backward traveling wave" in traffic jams. In what ways are the sudden occurrences of traffic snarls similar to the backwards-travelling wave in an explosion? What might be some ways to lessen the impact of these traveling waves of traffic?
Ask students to conduct Internet research on companies working to monitor, predict, and eventually lessen traffic congestion. For instance, students may wish to read an article about companies such as Inrix Inc. Inrix uses GPS devices, cellphone data, and sensors in highways to track vehicle usage of thousands of miles of roadways. The company can feed this data into algorithms, and send real-time information to navigational devices, news, web, and traffic reporting services. Visit the company’s web page to learn more.
Recently, the Texas A&M Transportation Institute (TTI) released the 2015 Urban Mobility Report, combining national research on traffic problems across the nation. TTI makes the data for 101 urban areas available as an Excel spreadsheet for other researchers. Ask students to use this information to analyze how much time they might spend in traffic making typical commutes in some of these urban areas. How much personal productivity would the student predict is lost in traffic snarls? Students should create graphs and charts to compare the worst cities. How do these data compare to information for the local area (if available)?
Read an article detailing work by Rutgers University-Camden mathematician, Benedetto Piccoli, who is using mathematics to study traffic problems. Near the end of the article, Piccoli talks about advances in “infomobility.” What are some possible examples he might be referring to? What sorts of future devices can you imagine that could help predict—or even better, prevent— the formation of traffic on roadways? For instance, how might “phantom traffic jams” become obsolete if robots did the driving?
In the MIT research, the mathematicians and scientists noticed similarities between traffic, water flow, and explosion patterns—what a casual observer might see as three seemingly unrelated phenomena. What might be some other situations you can observe in human-engineered scenarios or in nature that might mimic traffic jams (e.g., computer circuits, runners at the start of marathon races, ocean currents moving through undersea caverns)? Ask students to brainstorm examples and then narrow down choices to phenomena that scientists might be able to study using mathematics, physics, and technology. For an additional source on how scientists have thought about traffic, likening it to other types of phenomena, visit the Washington Post Archives for the article, Lab Studying Science Behind Traffic Patterns.

Phase II. Independent Research

A. Research process

Selecting a topic. Depending upon interests, students select one roadway or intersection in the local community on which to conduct an in-depth traffic analysis.
Depending upon the topic selected, students should develop 3-5 questions to guide their research proposals. Such questions might include:
- What is the capacity of this roadway?
- What is the density of vehicles when traffic begins to form?
- What municipalities or transit agencies oversee the maintenance of this roadway?
- What sort of usage fees—such as tolls— are there for this roadway?
- What obstacles, traffic signals, or chronic construction exist in the area that might inhibit traffic flow?
- Describe the geometry of the intersections on the roadway.
- What is the timing on the lights and in what ways are the signals coordinated with other traffic signals nearby?
- During what times of day do traffic jams occur in this area?
- What are some hypotheses about the causes of the traffic?
- In what ways might the traffic congestion be due to wave-like patterns as demonstrated in the MIT research? What might be some of the possible causes for slowdowns?
- How might traffic be alleviated during peak times?
Creating a research proposal. In the research proposal, the student should identify several key components such as:
- the location of the roadway or intersection
- the time of day they plan to conduct observations and gather data
- a list of possible secondary sources for background literature research
- a description of the type of data they plan to collect such as number of vehicles per minute, number of vehicles grouped by type (e.g., number of axles, or truck versus car bodies)
- a listing of names or position titles for candidates for interviews and/or focus groups
- a hypothesis explaining the student’s initial thoughts on the traffic problem at the location
- a research plan including a timeline, an explanation of the student’s proposed data gathering methods, a technology/materials list (e.g., hand-tally counters, cameras, measuring tools, timers, GPS devices, compasses, graph paper), and (if applicable) a budget for materials and supplies.
Conducting the research. Students collaborate with local transportation officials, librarians, parents/guardians, and/or the teacher to conduct observations during both low-and high-traffic time periods. Students gather data from literature, previous traffic studies, as well as through observation and/or interviews and focus groups. Additionally, depending upon student interest, students may choose to make a model of the location either in 3-D (such as with cardboard or foamcore) or using technology.
Sharing findings. Students will present their research through multimedia presentations that include images, charts, graphics, and summaries of the quantitative and qualitative data. Students should describe their findings and make recommendations as if they were presenting the information to city transportation planners, area transportation commission members, and/or city council members.

B. The product

Each student will develop a multimedia presentation that

describes the problem roadway or intersection,
details the research the student conducted,
presents the student’s analysis of both quantitative and qualitative data using accurate mathematical vocabulary terms, and
lists recommendations for the city or transportation planning board to implement to alleviate the problem.

C. Communication

Each student should present his/her findings using multimedia presentation software (e.g. Keynote, PowerPoint, Adobe PDF). The presentations should identify the problem, convey the research findings, and posit solutions in a manner that is of a professional-quality, visually cohesive, and compelling. Each presentation should allow time for an impromptu Q&A session. Students should accurately use mathematical vocabulary, standard units, signs, graphs, and equations.

D. A completed project consists of:

The research proposal
Research notes, photos and videos of the location, interview and/or focus group notes/recordings, models (if applicable), charts, graphs
Multimedia presentation file (e.g., PowerPoint, Keynote, Adobe Acrobat PDF)
A bibliography of cited sources
Video or audio of the presentation and Q&A session

Elicit

Lead the class in an informal discussion about traffic slowdowns and jams.

How many hours do you think you’ve lost this year to sitting in traffic (either while you were driving or riding as a passenger in a vehicle)?
Have you ever had the experience of sitting in a “phantom traffic jam”—a traffic jam that seems to have no obvious cause?
What is your emotional response when you encounter traffic?
Why do you feel this way and how do you react to these feelings?

Engage

Read news articles and press releases highlighting research from leading mathematicians at MIT, Temple, and the University of Alberta who are using mathematics to investigate the causes for “phantom traffic jams”—jams that seem to occur without an obvious cause such as an accident, construction, or stalled vehicle. One possible source is: https://math.mit.edu/projects/traffic/

Discuss the articles and introduce students to some of the mathematics concepts behind the research. How are mathematical tools used to study such phenomena? What are some of the intersections students observe between mathematics, engineering, and science?

Explore

Experiment with the equation in the article, Equation: Factors for Predicting Phantom Traffic Jams, from Wired. Using data from area roads, what does the equation tell you about the amount of traffic density needed for a jam to occur?

Ask students to view the traffic wave simulations, charts, and graphics on the project’s web page at MIT (Note: to play many of these videos, the computer must be able to open .avi files in the DIXX format. The videos of cars driving on the circular road further down the page should play in any browser).

The researchers in the MIT traffic project noticed the patterns of traffic jams were similar to the dynamics of explosions. What are some students’ hypotheses as to why this might be the case? Ask students to work in small groups to conduct this lab experiment and examine the patterns found from the “explosion.” In what ways are the sudden occurrences of traffic snarls similar to the backwards-travelling wave in an explosion? What might be some ways to lessen the impact of these traveling waves of traffic?

Explain

Small groups present their findings from the explosion experiment and suggest ways for lessening traffic based on their hypotheses and observations.

How does the backwards-travelling wave impact the amount of density at a given point on the roadway? How might this explain the formation of “phantom-traffic jams?”
What are some possible ways to alleviate these jams?
What other possible hypotheses might students develop related to the patterns found in traffic jams

Explore

Ask students to conduct Internet research on companies working to monitor, predict, and eventually lessen traffic congestion. For instance, students may wish to read an article about companies such as Inrix Inc. Inrix uses GPS devices, cellphone data, and sensors in highways to track vehicle usage of thousands of miles of roadways.

The company can feed this data into algorithms, and send real-time information to navigational devices, news, web, and traffic reporting services. Visit the company’s web page to learn more.

Recently, the Texas A&M Transportation Institute (TTI) released the 2015 Urban Mobility Report, combining national research on traffic problems across the nation. TTI makes the data for 101 urban areas available as an Excel spreadsheet for other researchers. Ask students to use this information to analyze how much time they might spend in traffic making typical commutes in some of these urban areas. How much personal productivity would the student predict is lost in traffic snarls? Students should create graphs and charts to compare the worst cities. How do these data compare to information for the local area (if available)?

Explain

Read an article detailing work by Rutgers University-Camden mathematician, Benedetto Piccoli, who is using mathematics to study traffic problems. Near the end of the article, Piccoli talks about advances in “infomobility.”

Discuss the article and the concept of “infomobility” in small groups.

What are some possible examples of “infomobility?”
What sorts of future devices can you imagine that could help predict— or even better, prevent— the formation of traffic on roadways? For instance, how might “phantom traffic jams” become obsolete if robots did the driving?
What sorts of devices, besides vehicles, might you design to solve this problem?
What might be your hypothesis concerning the degree to which human behavior (e.g., aggressive driving and road rage) contribute to the traffic problems? How might you design an experiment to investigate your hypothesis? How might these advances in “infomobility” impact the time lost during commutes for individuals in your area? Which geographic areas in the TTI study might see the greatest benefit? Which areas might you consider as pilot sites for testing the effects of your ideas?

Explore

In the MIT research, the mathematicians and scientists noticed similarities between traffic, water flow, and explosion patterns—what a casual observer might see as three seemingly unrelated phenomena. What might be some other situations you can observe in human-engineered scenarios or in nature that might mimic traffic jams (e.g., computer circuits, runners at the start of marathon races, ocean currents moving through undersea caverns)?

Ask students to brainstorm examples and then narrow down choices to phenomena that scientists might be able to study using mathematics, physics, and technology.

Elaborate (Phase II)

Research process

Selecting a topic. Depending upon interests, students select one roadway or intersection in the local community on which to conduct an in-depth traffic analysis.
Asking guiding questions. Depending upon the topic selected, students should develop 3-5 questions to guide their research proposals. Such questions might include:
- What is the capacity of this roadway?
- What is the density of vehicles when traffic begins to form?
- What municipalities or transit agencies oversee the maintenance of this roadway?
- What sort of usage fees—such as tolls—are there for this roadway?
- What obstacles, traffic signals, or chronic construction projects exist in the area that might inhibit traffic flow?
- Describe the geometry of the intersections on the roadway.
- What is the timing on the lights and in what ways are the signals coordinated with other traffic signals nearby?
- During what times of day do traffic jams occur?
- What are some hypotheses about the causes of the traffic?
- In what ways might the traffic congestion be due to wave-like patterns as demonstrated in the MIT research?
- What might be some of the possible causes for slowdowns?
- How might traffic be alleviated during peak times?
Creating a research proposal. In the research proposal, the student should identify several key components such as:
- the location of the roadway or intersection
- the time of day they plan to conduct observations and gather data
- a list of possible secondary sources for background literature research
- a description of the type of data they plan to collect such as number of vehicles per minute, number of vehicles grouped by type (e.g., number of axles, or truck versus car bodies)
- a listing of names or position titles for candidates for interviews and/or focus groups
- a hypothesis explaining the student’s initial thoughts on the traffic problem at the location
- a research plan including a timeline, an explanation of the student’s proposed data gathering methods, a technology/materials list (e.g., hand-tally counters, cameras, measuring tools, timers, GPS devices, compasses, graph paper), and (if applicable) a budget for materials and supplies.
Conducting the research. Students collaborate with local transportation officials, librarians, parents/guardians, and/or the teacher to conduct observations during both low- and high-traffic time periods. Students gather data from literature, previous traffic studies, as well as through observation and/or interviews and focus groups. Additionally, depending upon student interest, students may choose to make a model of the location either in 3-D (such as with cardboard or foamcore) or using technology.

Explain

Students will present their research through multimedia presentations that include images, charts, graphics, and summaries of the quantitative and qualitative data. Students should describe their findings and make recommendations as if they were presenting the information to city transportation planners, area transportation commission members, and/or city council members.

The product

Each student will develop a multimedia presentation that

describes the problem roadway or intersection,
details the research the student conducted,
presents the student’s analysis of both quantitative and qualitative data using accurate mathematical vocabulary terms, and
lists recommendations for the city or transportation planning board to implement to alleviate the problem.

Communication

Evaluate

Use the TPSP High School/Exit Level Rubric to assess each student’s learning. Additionally, you may wish to develop self- or peer-assessments based on the rubric that students could use to evaluate their products.

A completed project consists of:

The research proposal
Research notes, photos and videos of the location, interview and/or focus group notes/recordings, models (if applicable), charts, graphs
Multimedia presentation file (e.g., PowerPoint, Keynote, Adobe Acrobat PDF)
A bibliography of cited sources
Video or audio of the presentation and Q&A session

In what ways did the student:

Develop sophisticated, open-ended questions about the self-selected topic;
Use a variety of sources that access advanced content and include multiple perspectives;
Collect data using the tools of the discipline;
Analyze and interpret the data;
Capture and apply their analysis through an original product; and
Communicate his/her research findings, learning, and ideas to an audience using the language of the discipline.

Extend

Traffic Jam provides students with opportunities to study complex, real-world problems. Interdisciplinary extension activities include the following projects.

Science
Mathematical tools can help tease out other complex patterns in the physical and biological world. What patterns (if any) found in your study of traffic jams might cross over to study in biological systems, such as the cardiovascular system or the appearance of algal blooms in an ecosystem? Why might scientists be interested in applying mathematical concepts to study biophysical systems such as the beating of the human heart? Identify one real-world problem within a system in either the biological or physical sciences where you can use mathematics to observe patterns and trends in the system. Develop a hypothesis and design a small-scale experiment in order to collect data to support or refute your hypothesis. Capture and communicate your findings through an illustrated magazine article. Be sure to include charts, graphs, and other visuals.

Social Studies
How does the design of a city’s roadways contribute to or detract from the formation of traffic problems? What can cities with traffic issues do to solve the problem? What are the impacts of traffic on people’s psychological and emotional states? Research the psychological and sociological phenomena of road rage and design an awareness campaign for young drivers to help them understand their feelings, combat the stress related to traffic, and mitigate the damage traffic causes on the social fabric of a community. Develop your campaign into a coordinated set of advertisements or posters that will debut alongside a 30-second video for internet distribution.

English language arts
Create an anthology of stories that occurred when people were sitting in traffic. Develop a list of possible subjects to interview, create some research questions, and then collect people’s stories. Gather more stories than you need for your anthology. The final anthology might be presented in a text format, such as a research-based collection of personal narratives, or you may choose to disseminate your stories through audio podcasts.

Additional Resources

Students are encouraged to work with their teachers and parents/guardians to conduct the research necessary to support and enhance each task, following local district guidelines. Online resources like The Smithsonian Museum, The Library of Congress, The Texas State Archives, Texas State Historical Association, and National Geographic’s Kids offer information on a variety of topics and could serve as a good starting place.

This unit may address the following TEKS.

110.31, English Language Arts and Reading, English I

110.31(b)(1): Reading/Vocabulary Development. Students understand new vocabulary and use it when reading and writing.
110.31(b)(11): Reading/Comprehension of Informational Text/Procedural Texts. Students understand how to glean and use information in procedural texts and documents.
110.31(b)(15): Writing/Expository and Procedural Texts. Students write expository and procedural or work-related texts to communicate ideas and information to specific audiences for specific purposes.
110.31(b)(17): Oral and Written Conventions/Conventions. Students understand the function of and use the conventions of academic language when speaking and writing. Students will continue to apply earlier standards with greater complexity.
110.31(b)(20): Research/Research Plan. Students ask open-ended research questions and develop a plan for answering them.
110.31(b)(21): Research/Gathering Sources. Students determine, locate, and explore the full range of relevant sources addressing a research question and systematically record the information they gather.
110.31(b)(23): Research/Organizing and Presenting Ideas. Students organize and present their ideas and information according to the purpose of the research and their audience. Students are expected to synthesize the research into a written or an oral presentation that:
110.31(b)(24): Listening and Speaking/Listening. Students will use comprehension skills to listen attentively to others in formal and informal settings. Students will continue to apply earlier standards with greater complexity.
110.31(b)(25): Listening and Speaking/Speaking. Students speak clearly and to the point, using the conventions of language. Students will continue to apply earlier standards with greater complexity. Students are expected to give presentations using informal, formal, and technical language effectively to meet the needs of audience, purpose, and occasion, employing eye contact, speaking rate (e.g., pauses for effect), volume, enunciation, purposeful gestures, and conventions of language to communicate ideas effectively.

110.32, English Language Arts and Reading, English II

110.32(b)(1): Reading/Vocabulary Development. Students understand new vocabulary and use it when reading and writing.
110.32(b)(11): Reading/Comprehension of Informational Text/Procedural Texts. Students understand how to glean and use information in procedural texts and documents.
110.32(b)(15): Writing/Expository and Procedural Texts. Students write expository and procedural or work-related texts to communicate ideas and information to specific audiences for specific purposes.
110.32(b)(17): Oral and Written Conventions/Conventions. Students understand the function of and use the conventions of academic language when speaking and writing. Students will continue to apply earlier standards with greater complexity.
110.32(b)(20): Research/Research Plan. Students ask open-ended research questions and develop a plan for answering them.
110.32(b)(21): Research/Gathering Sources. Students determine, locate, and explore the full range of relevant sources addressing a research question and systematically record the information they gather.
110.32(b)(22): Research/Synthesizing Information. Students clarify research questions and evaluate and synthesize collected information.
110.32(b)(23): Research/Organizing and Presenting Ideas. Students organize and present their ideas and information according to the purpose of the research and their audience. Students are expected to synthesize the research into a written or an oral presentation that:
110.32(b)(24): Listening and Speaking/Listening. Students will use comprehension skills to listen attentively to others in formal and informal settings. Students will continue to apply earlier standards with greater complexity.
110.32(b)(25): Listening and Speaking/Speaking. Students speak clearly and to the point, using the conventions of language. Students will continue to apply earlier standards with greater complexity. Students are expected to advance a coherent argument that incorporates a clear thesis and a logical progression of valid evidence from reliable sources and that employs eye contact, speaking rate (e.g., pauses for effect), volume, enunciation, purposeful gestures, and conventions of language to communicate ideas effectively.

111.40., Algebra II

111.40(c)(1): Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
111.40(c)(3): Systems of equations and inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions.
111.40(c)(4): Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions.
111.40(c)(5): Exponential and logarithmic functions and equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.
111.40(c)(7): Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.

111.42, Precalculus

111.42(c)(1): Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
111.42(c)(2): Functions. The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
111.42(c)(4): Number and measure. The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.

111.43, Mathematical Models with Applications

111.43(c)(1): Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
111.43(c)(6): Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering.
111.43(c)(8): Mathematical modeling in social sciences. The student applies mathematical processes to determine the number of elements in a finite sample space and compute the probability of an event.
111.43(c)(10): Mathematical modeling in social sciences. The student applies mathematical processes to design a study and use graphical, numerical, and analytical techniques to communicate the results of the study.

111.44, Advanced Quantitative Reasoning

111.44(c)(1): Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
111.44(c)(2): Numeric reasoning. The student applies the process standards in mathematics to generate new understandings by extending existing knowledge. The student generates new mathematical understandings through problems involving numerical data that arise in everyday life, society, and the workplace. The student extends existing knowledge and skills to analyze real-world situations.
111.44(c)(3): Algebraic reasoning (expressions, equations, and generalized relationships). The student applies the process standards in mathematics to create and analyze mathematical models of everyday situations to make informed decisions related to earning, investing, spending, and borrowing money by appropriate, proficient, and efficient use of tools, including technology. The student uses mathematical relationships to make connections and predictions. The student judges the validity of a prediction and uses mathematical models to represent, analyze, and solve dynamic real-world problems.
111.44(c)(4): Probabilistic and statistical reasoning. The student uses the process standards in mathematics to generate new understandings of probability and statistics. The student analyzes statistical information and evaluates risk and return to connect mathematical ideas and make informed decisions. The student applies a problem-solving model and statistical methods to design and conduct a study that addresses one or more particular question(s). The student uses multiple representations to communicate effectively the results of student-generated statistical studies and the critical analysis of published statistical studies.

112.45., Physics (One Credit), Adopted 2020

112.45(c)(1): Scientific and engineering practices. The student, for at least 40% of instructional time, asks questions, identifies problems, and plans and safely conducts classroom, laboratory, and field investigations to answer questions, explain phenomena, or design solutions using appropriate tools and models. The student is expected to:
112.45(c)(3): Scientific and engineering practices. The student develops evidence-based explanations and communicates findings, conclusions, and proposed solutions. The student is expected to:
112.45(c)(5): Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to:
112.45(c)(6): Science concepts. The student knows the nature of forces in the physical world. The student is expected to:
112.45(c)(7): Science concepts. The student knows that changes occur within a physical system and applies the laws of conservation of energy and momentum. The student is expected to:
112.45(c)(8): Science concepts. The student knows the characteristics and behavior of waves. The student is expected to:

113.41, United States History Studies Since 1877

113.41(c)(14): Geography. The student understands the relationship between population growth and modernization on the physical environment.
113.41(c)(23): Citizenship. The student understands efforts to expand the democratic process.
113.41(c)(28): Science, technology, and society. The student understands the influence of scientific discoveries, technological innovations, and the free enterprise system on the standard of living in the United States.
113.41(c)(29): Social studies skills. The student applies critical-thinking skills to organize and use information acquired from a variety of valid sources, including electronic technology.
113.41(c)(30): Social studies skills. The student communicates in written, oral, and visual forms.
113.41(c)(31): Social studies skills. The student uses geographic tools to collect, analyze, and interpret data.
113.41(c)(32): Social studies skills. The student uses problem-solving and decision-making skills, working independently and with others, in a variety of settings.

113.42, World History Studies

113.42(c)(15): Geography. The student uses geographic skills and tools to collect, analyze, and interpret data.
113.42(c)(16): Geography. The student understands the impact of geographic factors on major historic events and processes.
113.42(c)(28): Science, technology, and society. The student understands how major scientific and mathematical discoveries and technological innovations have affected societies from 1750 to the present.
113.42(c)(30): Social studies skills. The student communicates in written, oral, and visual forms.
113.42(c)(31): Social studies skills. The student uses problem-solving and decision-making skills, working independently and with others, in a variety of settings.

113.47, Special Topics in Social Studies

113.47(c)(1): Social studies skills. The student uses problem-solving and decision-making skills, working independently and with others, in a variety of settings.
113.47(c)(2): Social studies skills. The student applies critical-thinking skills to organize and use information acquired from a variety of valid sources, including electronic technology.
113.47(c)(3): Social studies skills. The student creates written, oral, and visual presentations of social studies information.

113.48, Social Studies Research Methods

113.48(c)(1): Social studies skills. The student understands the need for an organizing framework to identify an area of interest and collect information.
113.48(c)(5): Social studies skills. The student creates a written and oral presentation of research and conclusions.
113.48(c)(6): Social studies skills. The student understands the principles and requirements of the scientific method.

Esta unidad puede abordar los siguientes TEKS.

110.31, English Language Arts and Reading, English I

110.31(b)(1): Desarrollo de lectura/vocabulario. Comprende vocabulario nuevo y lo utiliza al leer y al escribir.
110.31(b)(11): Lectura/comprensión de textos informativos/textos de instrucción. Comprende cómo recabar y usar información en textos de instrucción y en documentos.
110.31(b)(15): Escritura/Textos expositivos y de instrucción. Escribe textos expositivos y de instrucción, o textos relacionados con empleos para comunicar propósitos específicos, así como ideas e información a públicos específicos.
110.31(b)(17): Convenciones orales y escritas/Convenciones. Comprende la función y el uso de las convenciones del lenguaje académico al hablar y al escribir. Los estudiantes continúan aplicando estándares previos con mayor complejidad.
110.31(b)(20): Investigación/plan de investigación. Formula preguntas abiertas de investigación y desarrolla un plan para responderlas.
110.31(b)(21): Investigación/recolección de fuentes. Determina, localiza y explora todas las fuentes de información relevantes para responder a una pregunta de investigación y sistemáticamente registra la información recopilada.
110.31(b)(23): Investigación/organización y presentación de ideas. Organiza y presenta sus ideas y su información de acuerdo con el propósito de la investigación y de su público.
110.31(b)(24): Escuchar y hablar/escuchar. Usa destrezas de comprensión para escuchar con atención a los demás en ambientes formales e informales. Los estudiantes continuarán aplicando estándares previos con mayor complejidad.
110.31(b)(25): Escuchar y hablar/hablar. Habla claramente y de forma directa utilizando las convenciones del lenguaje. Los estudiantes continúan aplicando estándares previos con mayor complejidad. Se espera que los estudiantes den presentaciones usando lenguaje informal, formal y técnico de manera efectiva para atender las necesidades de audiencia, propósito y ocasión, empleando contacto visual, velocidad al hablar (p. ej., pausas para efectos específicos), volumen, enunciación, gesticulaciones intencionadas y convenciones del lenguaje para comunicar ideas de manera eficaz.

110.32, English Language Arts and Reading, English II

110.32(b)(1): Desarrollo de lectura/vocabulario. Comprende vocabulario nuevo y lo utiliza al leer y al escribir.
110.32(b)(11): Lectura/comprensión de textos informativos/textos de instrucción. Comprende cómo recabar y usar información en textos de instrucción y en documentos.
110.32(b)(15): Escritura/Textos expositivos y de instrucción. Escribe textos expositivos y de instrucción, o textos relacionados con empleos para comunicar propósitos específicos, así como ideas e información a públicos específicos.
110.32(b)(17): Convenciones orales y escritas/Convenciones. Comprende la función y el uso de las convenciones del lenguaje académico al hablar y al escribir. Los estudiantes continuarán aplicando estándares anteriores en textos de complejidad cada vez mayor.
110.32(b)(20): Investigación/plan de investigación. Formula preguntas abiertas de investigación y desarrolla un plan para responderlas.
110.32(b)(21): Investigación/recolección de fuentes. Determina, localiza y explora todas las fuentes de información relevantes para responder a una pregunta de investigación y sistemáticamente registra la información recopilada.
110.32(b)(22): Investigación/síntesis de información. Clarifica preguntas de investigación y evalúan y sintetizan la información recopilada.
110.32(b)(23): Investigación/organización y presentación de ideas. Organiza y presenta sus ideas y su información de acuerdo con el propósito de la investigación y de su público.
110.32(b)(24): Escuchar y hablar/escuchar. Usa destrezas de comprensión para escuchar con atención a los demás en ambientes formales e informales. Los estudiantes continúan aplicando estándares previos con mayor complejidad.
110.32(b)(25): Escuchar y hablar/hablar. Habla claramente y de forma directa utilizando las convenciones del lenguaje. Los estudiantes continuarán aplicando estándares anteriores en textos de complejidad cada vez mayor. Se espera que los estudiantes presenten primero un argumento coherente que incorpore una tesis clara y una progresión lógica de evidencias válidas de fuentes confiables y que empleen contacto visual, velocidad al hablar (p. ej., pausas para dar efecto deseado), volumen, pronunciación, gesticulaciones intencionadas y reglas del lenguaje para comunicar ideas de manera efectiva.

111.40., Algebra II

111.40(c)(1): Estándares de procesos matemáticos. El estudiante utiliza procesos matemáticos para adquirir y demostrar comprensión matemática.
111.40(c)(3): Systems of equations and inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions.
111.40(c)(4): Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions.
111.40(c)(5): Exponential and logarithmic functions and equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.
111.40(c)(7): Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.

111.42, Precalculus

111.42(c)(1): Estándares de procesos matemáticos. El estudiante utiliza procesos matemáticos para adquirir y demostrar comprensión matemática.
111.42(c)(2): Functions. The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
111.42(c)(4): Number and measure. The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.

111.43, Mathematical Models with Applications

111.43(c)(1): Estándares de procesos matemáticos. El estudiante utiliza procesos matemáticos para adquirir y demostrar comprensión matemática.
111.43(c)(6): Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering.
111.43(c)(8): Modelos matemáticos en estudios sociales. El estudiante aplica procesos matemáticos para determinar el número de elementos en un espacio muestral finito y calcular la probabilidad de un evento.
111.43(c)(10): Modelos matemáticos en estudios sociales. El estudiante aplica procesos matemáticos para diseñar un estudio y usar técnicas gráficas, numéricas y analíticas para comunicar los resultados del estudio.

111.44, Advanced Quantitative Reasoning

111.44(c)(1): Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
111.44(c)(2): Numeric reasoning. The student applies the process standards in mathematics to generate new understandings by extending existing knowledge. The student generates new mathematical understandings through problems involving numerical data that arise in everyday life, society, and the workplace. The student extends existing knowledge and skills to analyze real-world situations.
111.44(c)(3): Algebraic reasoning (expressions, equations, and generalized relationships). The student applies the process standards in mathematics to create and analyze mathematical models of everyday situations to make informed decisions related to earning, investing, spending, and borrowing money by appropriate, proficient, and efficient use of tools, including technology. The student uses mathematical relationships to make connections and predictions. The student judges the validity of a prediction and uses mathematical models to represent, analyze, and solve dynamic real-world problems.
111.44(c)(4): Probabilistic and statistical reasoning. The student uses the process standards in mathematics to generate new understandings of probability and statistics. The student analyzes statistical information and evaluates risk and return to connect mathematical ideas and make informed decisions. The student applies a problem-solving model and statistical methods to design and conduct a study that addresses one or more particular question(s). The student uses multiple representations to communicate effectively the results of student-generated statistical studies and the critical analysis of published statistical studies.

112.45., Physics (One Credit), Adopted 2020

112.45(c)(1): Scientific and engineering practices. The student, for at least 40% of instructional time, asks questions, identifies problems, and plans and safely conducts classroom, laboratory, and field investigations to answer questions, explain phenomena, or design solutions using appropriate tools and models. The student is expected to:
112.45(c)(3): Scientific and engineering practices. The student develops evidence-based explanations and communicates findings, conclusions, and proposed solutions. The student is expected to:
112.45(c)(5): Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to:
112.45(c)(6): Science concepts. The student knows the nature of forces in the physical world. The student is expected to:
112.45(c)(7): Science concepts. The student knows that changes occur within a physical system and applies the laws of conservation of energy and momentum. The student is expected to:
112.45(c)(8): Science concepts. The student knows the characteristics and behavior of waves. The student is expected to:

113.41, United States History Studies Since 1877

113.41(c)(14): Geography. The student understands the relationship between population growth and modernization on the physical environment.
113.41(c)(23): Citizenship. The student understands efforts to expand the democratic process.
113.41(c)(28): Science, technology, and society. The student understands the influence of scientific discoveries, technological innovations, and the free enterprise system on the standard of living in the United States.
113.41(c)(29): Destrezas de Estudios Sociales. El estudiante utiliza las habilidades del pensamiento crítico para organizar y usar la información que adquiere de una variedad de fuentes válidas, incluyendo la tecnología electrónica.
113.41(c)(30): Destrezas de estudios sociales. Se comunica en forma oral, visual y escrita.
113.41(c)(31): Destrezas de Estudios Sociales. El estudiante usa herramientas geográficas para recopilar, analizar e interpretar datos.
113.41(c)(32): Destrezas de Estudios Sociales. El estudiante utiliza habilidades para resolver problemas y tomar decisiones, en forma independiente y con otros, en diferentes ambientes.

113.42, World History Studies

113.42(c)(15): Geography. The student uses geographic skills and tools to collect, analyze, and interpret data.
113.42(c)(16): Geography. The student understands the impact of geographic factors on major historic events and processes.
113.42(c)(28): Ciencia, tecnología y sociedad. El estudiante comprende cómo los principales descubrimientos científicos y matemáticos e innovaciones tecnológicas han afectado a las sociedades de 1750 al presente.
113.42(c)(30): Destrezas de estudios sociales. Se comunica en forma oral, visual y escrita.
113.42(c)(31): Destrezas de estudios sociales. El estudiante utiliza habilidades para resolver problemas y tomar decisiones, en forma independiente y con otros, en diferentes ambientes.

113.47, Special Topics in Social Studies

113.47(c)(1): Social studies skills. The student uses problem-solving and decision-making skills, working independently and with others, in a variety of settings.
113.47(c)(2): Social studies skills. The student applies critical-thinking skills to organize and use information acquired from a variety of valid sources, including electronic technology.
113.47(c)(3): Social studies skills. The student creates written, oral, and visual presentations of social studies information.

113.48, Social Studies Research Methods

113.48(c)(1): Destrezas de Estudios Sociales. El estudiante comprende la necesidad de organizar el contexto para identificar un área de interés y reunir información.
113.48(c)(5): Destrezas de Estudios Sociales. Hará una presentación escrita y oral de la investigación y las conclusiones.
113.48(c)(6): Destrezas de Estudios Sociales. El estudiante comprende los principios y requisitos del método científico.

This unit may address the following Texas College and Career Readiness Standards.

Science:

S.I.A.2: Use creativity and insight to recognize and describe patterns in natural phenomena.
S.I.A.3: Formulate appropriate questions to test understanding of natural phenomena.
S.I.A.4: Rely on reproducible observations of empirical evidence when constructing, analyzing, and evaluating explanations of natural events and processes.
S.I.B.1: Design and conduct scientific investigations in which hypotheses are formulated and tested.
S.I.C.3: Demonstrate skill in the safe use of a wide variety of apparatuses, equipment, techniques, and procedures.
S.I.D.1: Demonstrate literacy in computer use.
S.I.D.2: Use computer models, applications, and simulations.
S.I.D.3: Demonstrate appropriate use of a wide variety of apparatuses, equipment, techniques, and procedures for collecting quantitative and qualitative data.
S.I.E.1: Use several modes of expression to describe or characterize natural patterns and phenomena. These modes of expression include narrative, numerical, graphical, pictorial, symbolic, and kinesthetic.
S.I.E.2: Use essential vocabulary of the discipline being studied.
S.II.A.4: Use proportional reasoning to solve problems.
S.II.A.5: Simplify algebraic expressions.
S.II.A.6: Estimate results to evaluate whether a calculated result is reasonable.
S.II.A.7: Use calculators, spreadsheets, computers, etc., in data analysis.
S.II.B.2: Represent natural events, processes, and relationships with algebraic expressions and algorithms.
S.II.E.1: Understand descriptive statistics.
S.II.F.1: Select and use appropriate Standard International (SI) units and prefixes to express measurements for real world problems.
S.III.C.1: Prepare and present scientific/technical information in appropriate formats for various audiences.
S.III.D.1: Use search engines, databases, and other digital electronic tools effectively to locate information.
S.IV.A.1: Recognize how scientific discoveries are connected to technological innovations.
S.IV.B.1: Understand how scientific research and technology have an impact on ethical and legal practices.
S.IV.C.2: Recognize the role of people in important contributions to scientific knowledge.
S.V.B.2: Know the processes of energy transfer.
S.V.C.1: Recognize patterns of change.
S.V.D.1: Understand that scientists categorize things according to similarities and differences.
S.V.E.1: Use models to make predictions.
S.V.E.2: Use scale to relate models and structures.
S.VIII.C.1: Understand the fundamental concepts of kinematics.
S.VIII.C.2: Understand forces and Newton’s Laws.
S.VIII.C.3: Understand the concept of momentum.
S.X.C.1: Recognize variations in population sizes, including human population and extinction, and describe mechanisms and conditions that produce these variations.
S.X.E.1: Describe the different uses for land (land management).

Social Studies:

SS.I.A.1: Use the tools and concepts of geography appropriately and accurately.
SS.I.A.2: Analyze the interaction between human communities and the environment.
SS.I.A.3: Analyze how physical and cultural processes have shaped human communities over time.
SS.I.A.4: Evaluate the causes and effects of human migration patterns over time.
SS.I.A.5: Analyze how various cultural regions have changed over time.
SS.I.A.6: Analyze the relationship between geography and the development of human communities.
SS.I.B.2: Identify and evaluate sources and patterns of change and continuity across time and place.
SS.IV.A.1: Identify and analyze the main idea(s) and point(s)-of-view in sources.
SS.IV.A.2: Situate an informational source in its appropriate contexts (contemporary, historical, cultural).
SS.IV.A.3: Evaluate sources from multiple perspectives.
SS.IV.A.6: Read research data critically.
SS.IV.B.1: Use established research methodologies.
SS.IV.B.3: Gather, organize, and display the results of data and research.
SS.IV.B.4: Identify and collect sources.
SS.IV.C.1: Understand and interpret presentations (e.g., speeches, lectures, informal presentations) critically.
SS.V.A.2: Use conventions of standard written English.
SS.V.B.1: Attribute ideas and information to source materials and authors.

Cross-Disciplinary Standards:

CDS.I.A.1: Engage in scholarly inquiry and dialogue.
CDS.I.C.1: Analyze a situation to identify a problem to be solved.
CDS.I.C.2: Develop and apply multiple strategies to solve a problem.
CDS.I.C.3: Collect evidence and data systematically and directly relate to solving a problem.
CDS.I.D.1: Self-monitor learning needs and seek assistance when needed.
CDS.I.D.2: Use study habits necessary to manage academic pursuits and requirements.
CDS.I.D.3: Strive for accuracy and precision.
CDS.I.D.4: Persevere to complete and master tasks.
CDS.I.E.1: Work independently.
CDS.I.E.2: Work collaboratively.
CDS.I.F.1: Attribute ideas and information to source materials and people.
CDS.I.F.2: Evaluate sources for quality of content, validity, credibility, and relevance.
CDS.II.A.3: Identify the intended purpose and audience of the text.
CDS.II.A.4: Identify the key information and supporting details.
CDS.II.A.5: Analyze textual information critically.
CDS.II.A.6: Annotate, summarize, paraphrase, and outline texts when appropriate.
CDS.II.C.1: Understand which topics or questions are to be investigated.
CDS.II.C.2: Explore a research topic.
CDS.II.C.3: Refine research topic based on preliminary research and devise a timeline for completing work.
CDS.II.C.4: Evaluate the validity and reliability of sources.
CDS.II.C.5: Synthesize and organize information effectively.
CDS.II.C.6: Design and present an effective product.
CDS.II.C.7: Integrate source material.
CDS.II.C.8: Present final product.
CDS.II.D.2: Use statistical and probabilistic skills necessary for planning an investigation and collecting, analyzing, and interpreting data
CDS.II.D.3: Present analyzed data and communicate findings in a variety of formats.
CDS.II.E.1: Use technology to gather information.
CDS.II.E.2: Use technology to organize, manage, and analyze information.
CDS.II.E.3: Use technology to communicate and display findings in a clear and coherent manner.
CDS.II.E.4: Use technology appropriately.

English Language Arts:

ELA.I.A.2: Generate ideas, gather information, and manage evidence relevant to the topic and purpose.
ELA.I.A.1: Determine effective approaches, genres, rhetorical techniques, and media that demonstrate understanding of the writer’s purpose and audience.
ELA.II.A.1: Use effective reading strategies to determine a written work’s purpose and intended audience.
ELA.II.A.2: Use text features to form an overview of content and to locate information.
ELA.III.A.5: Plan and deliver focused, coherent presentations that convey clear and distinct perspectives and demonstrate sound reasoning.
ELA.III.A.4: Adjust delivery, vocabulary, and length of message for particular audiences, purposes, and contexts.
ELA.III.A.2: Engage in reasoned dialogue, including with people who have different perspectives.
ELA.III.A.1: Participate actively, effectively, and respectfully in one-on-one oral communication as well as in group discussions.
ELA.III.A.3: Understand how style, register, and content of spoken language vary in different contexts and influence the listener’s understanding.
ELA.IV.A.5: Recognize fillers, intentional pauses, and placeholders in speech (e.g., um) and make inferences in context.
ELA.IV.A.4: Comprehend detailed instructions, explanations, and directions in a range of contexts (e.g., specialized contexts such as workplace procedures and operating instructions).
ELA.IV.A.3: Develop an awareness of rhetorical and stylistic choices used to convey a message.
ELA.V.A.3: Devise a plan for completing work on time.
ELA.V.A.1: Articulate and investigate research questions.
ELA.V.A.2: Explore and refine a research topic.
ELA.V.C.1: Integrate and organize material effectively.
ELA.V.C.3: Follow relevant rules governing attribution.
ELA.V.C.2: Use and attribute source material ethically.
ELA.V.B.3: Assess the relevance and credibility of sources.
ELA.V.B.1: Explore and collect a range of potential sources.
ELA.V.B.2: Distinguish between and among primary and secondary sources.

Mathematics:

M.I.C.1: Select or use the appropriate type of method, unit, and tool for the attribute being measured.
M.I.C.2: Convert units within and between systems of measurement.
M.I.B.1: Use estimation to check for errors and reasonableness of solutions.
M.I.A.1: Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
M.I.A.2: Perform computations with rational and irrational numbers.
M.I.B.2: Interpret the relationships between the different representations of numbers.
M.II.D.2: Convert among multiple representations of equations, inequalities, and relationships.
M.II.D.1: Interpret multiple representations of equations, inequalities, and relationships.
M.IV.C: Measurement involving probability
M.IV.C.1: Use probability to make informed decisions.
M.V.A.1: Formulate a statistical question, plan an investigation, and collect data.
M.V.B.3: Compute and describe the study data with measures of center and basic notions of spread.
M.V.B.2: Construct appropriate visual representations of data.
M.V.B.1: Classify types of data.
M.V.C.4: Identify and explain misleading uses of data.
M.V.C.3: Make predictions using summary statistics.
M.V.C.2: Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
M.V.C.1: Analyze data sets using graphs and summary statistics.
M.VI.C.1: Apply known functions to model real-world situations.
M.VI.C.2: Develop a function to model a situation.
M.VI.B.1: Understand and analyze features of a functions.
M.VI.A.1: Recognize if a relation is a function.
M.VI.A.2: Recognize and distinguish between different types of functions.
M.VI.B.2: Algebraically construct and analyze new functions.
M.VII.C: Logical reasoning
M.VII.C.2: Understand attributes and relationships with inductive and deductive reasoning.
M.VII.A.2: Formulate a plan or strategy.
M.VII.A.5: Evaluate the problem-solving process.
M.VII.A.3: Determine a solution.
M.VII.B.1: Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
M.VII.A.4: Justify the solution.
M.VII.D: Real-world problem solving
M.VII.D.1: Interpret results of the mathematical problem in terms of the original real-world situation.
M.VII.D.2: Evaluate the problem-solving process.
M.VIII.C.2: ate and use representations to organize, record, and communicate mathematical ideas.
M.VIII.C.3: Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
M.VIII.C.1: Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
M.VIII.B.1: Model and interpret mathematical ideas and concepts using multiple representations.
M.VIII.A.1: Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
M.VIII.A.2: Use mathematical language to represent and communicate the mathematical concepts in a problem.
M.VIII.A.3: Use mathematical language for reasoning, problem solving, making connections, and generalizing.
M.VIII.B.2: Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
M.IX.B.3: Know and understand the use of mathematics in a variety of careers and professions.
M.IX.B.2: Understand and use appropriate mathematical models in the natural, physical, and social sciences.
M.IX.B.1: Use multiple representations to demonstrate links between mathematical and real-world situations.
M.IX.A.1: Connect and use multiple key concepts of mathematics in situations and problems.
M.IX.A.2: Connect mathematics to the study of other disciplines.

Esta unidad puede abordar los siguientes estándares de Texas College and Career Readiness.

Science:

S.I.A.2: Usa la creatividad y el conocimiento para reconocer y describir patrones en fenómenos naturales.
S.I.A.3: Formula preguntas apropiadas para poner a prueba la comprensión de fenómenos naturales.
S.I.A.4: Confía en observaciones reproducibles de evidencias empíricas cuando desarrolla, analiza y evalúa explicaciones de eventos y procesos naturales.
S.I.B.1: Diseña y hace investigaciones científicas en las cuales se formulan y se ponen a prueba hipótesis.
S.I.C.3: Demuestra destrezas para usar con seguridad una amplia variedad de aparatos, equipos, técnicas y procedimientos.
S.I.D.1: Demuestra conocimiento del uso de la computadora.
S.I.D.2: Usa modelos, aplicaciones y simuladores por computadora.
S.I.D.3: Hace uso apropiado de una amplia variedad de aparatos, equipos, técnicas y procedimientos para reunir datos cuantitativos y cualitativos.
S.I.E.1: Usa varios modos de expresión para describir o caracterizar patrones y fenómenos naturales. Estos modos de expresión incluyen descripción escrita, numérica, gráfica, pictórica, simbólica y con lenguaje corporal.
S.I.E.2: Usa vocabulario esencial de la disciplina que se está estudiando.
S.II.A.4: Usa razonamiento proporcional para resolver problemas.
S.II.A.5: Simplify algebraic expressions.
S.II.A.6: Estima resultados para evaluar si un resultado calculado es razonable.
S.II.A.7: Usa calculadoras, hojas de cálculo, computadoras, etc., para analizar datos.
S.II.B.2: Represent natural events, processes, and relationships with algebraic expressions and algorithms.
S.II.E.1: Comprende la estadística descriptiva
S.II.F.1: Select and use appropriate Standard International (SI) units and prefixes to express measurements for real world problems.
S.III.C.1: Prepara y presenta información científica/técnica en formatos apropiados para varios públicos.
S.III.D.1: Usa de manera efectiva motores de búsqueda, bases de datos y otras herramientas digitales para localizar información.
S.IV.A.1: Reconoce cómo los descubrimientos científicos se relacionan con los inventos tecnológicos.
S.IV.B.1: Comprende cómo la investigación científica y tecnológica tiene un impacto en las prácticas éticas y legales.
S.IV.C.2: Reconoce el papel de las personas en las contribuciones importantes del conocimiento científico.
S.V.B.2: Conoce los procesos de transferencia de energía.
S.V.C.1: Reconoce patrones de cambio.
S.V.D.1: Comprende que los científicos clasifican las cosas de acuerdo con semejanzas y diferencias.
S.V.E.1: Usa modelos para hacer predicciones.
S.V.E.2: Usa escalas para relacionar modelos y estructuras.
S.VIII.C.1: Entiende los conceptos básicos de la cinemática.
S.VIII.C.2: Entiende las fuerzas y las leyes de Newton.
S.VIII.C.3: Entiende el concepto de cantidad de movimiento.
S.X.C.1: Reconoce las variaciones en el tamaño de las poblaciones, incluyendo crecimiento y extinción de las poblaciones de seres humanos, y describe mecanismos y condiciones que producen estas variaciones.
S.X.E.1: Describe los diferentes usos del terreno

Social Studies:

SS.I.A.1: Usa las herramientas y conceptos de geografía de manera apropiada y precisa.
SS.I.A.2: Analiza la interacción entre las comunidades humanas y el medio ambiente.
SS.I.A.3: Analiza cómo los procesos físicos y culturales han configurado las comunidades humanas a través del tiempo.
SS.I.A.4: Evalúa las causas y efectos de los patrones de migración humana a través del tiempo.
SS.I.A.5: Analiza cómo han cambiado varias regiones culturales a lo largo del tiempo.
SS.I.A.6: Analiza la relación entre la geografía y el desarrollo de las comunidades humanas.
SS.I.B.2: Identifica y evalúa las fuentes y patrones de cambio y continuidad a través del tiempo y del espacio.
SS.IV.A.1: Identifica y analiza las ideas principales y los puntos de vista en las fuentes.
SS.IV.A.2: Ubica una fuente informativa en su contexto apropiado.
SS.IV.A.3: Evalúa fuentes desde múltiples perspectivas.
SS.IV.A.6: Lee críticamente datos de investigación.
SS.IV.B.1: Usa metodologías de investigación establecidas.
SS.IV.B.3: Reúne, organiza y muestra los resultados de los datos y la investigación.
SS.IV.B.4: Identifica y reúne fuentes.
SS.IV.C.1: Comprende e interpreta críticamente presentaciones.
SS.V.A.2: Usa las reglas convencionales de la lengua inglesa escrita.
SS.V.B.1: Acredita las ideas y la información a los materiales de referencia y a los autores.

Cross-Disciplinary Standards:

CDS.I.A.1: Participa en el diálogo y la investigación académica.
CDS.I.C.1: Analiza una situación para identificar un problema a resolver.
CDS.I.C.2: Desarrolla y aplica múltiples estrategias para resolver un problema.
CDS.I.C.3: Reúne sistemáticamente evidencias y datos y los relaciona directamente para resolver un problema.
CDS.I.D.1: Autoevalúa sus necesidades de aprendizaje y busca ayuda cuando es necesario.
CDS.I.D.2: Usa hábitos de estudio necesarios para cumplir metas y requisitos académicos.
CDS.I.D.3: Se esfuerza por ser exacto y preciso.
CDS.I.D.4: Persevera hasta completar y dominar las tareas.
CDS.I.E.1: Trabaja de forma independiente.
CDS.I.E.2: Trabaja de manera colaborativa.
CDS.I.F.1: Acredita ideas e información a las fuentes de referencia y a las personas.
CDS.I.F.2: Evalúa las fuentes en función de la calidad de su contenido, validez, credibilidad y relevancia.
CDS.II.A.3: Identifica el propósito del texto y el público al que se dirige.
CDS.II.A.4: Identifica la información principal y los detalles de apoyo.
CDS.II.A.5: Analiza críticamente la información textual.
CDS.II.A.6: Comenta, resume, parafrasea y describe textos cuando sea apropiado.
CDS.II.C.1: Entiende cuáles temas o preguntas deben investigarse.
CDS.II.C.2: Explora un tema de investigación.
CDS.II.C.3: Afina el tema de investigación con base en una investigación preliminar y establece un calendario para terminar el trabajo.
CDS.II.C.4: Evalúa la validez y confiabilidad de las fuentes.
CDS.II.C.5: Sintetiza y organiza la información de manera efectiva.
CDS.II.C.6: Diseña y presenta un producto efectivo.
CDS.II.C.7: Integra las referencias.
CDS.II.C.8: Presenta un producto final.
CDS.II.D.2: Usa destrezas estadísticas y probabilísticas necesarias para planear una investigación y recaba, analiza e interpreta datos.
CDS.II.D.3: Presenta datos analizados y comunica los hallazgos en una variedad de formatos.
CDS.II.E.1: Usa tecnología para reunir información.
CDS.II.E.2: Usa tecnología para organizar, manejar y analizar información.
CDS.II.E.3: Usa tecnología para comunicar y mostrar hallazgos de una manera clara y coherente.
CDS.II.E.4: Usa la tecnología apropiadamente.

English Language Arts:

ELA.I.A.2: Generate ideas, gather information, and manage evidence relevant to the topic and purpose.
ELA.I.A.1: Determine effective approaches, genres, rhetorical techniques, and media that demonstrate understanding of the writer’s purpose and audience.
ELA.II.A.1: Use effective reading strategies to determine a written work’s purpose and intended audience.
ELA.II.A.2: Use text features to form an overview of content and to locate information.
ELA.III.A.5: Plan and deliver focused, coherent presentations that convey clear and distinct perspectives and demonstrate sound reasoning.
ELA.III.A.4: Adjust delivery, vocabulary, and length of message for particular audiences, purposes, and contexts.
ELA.III.A.2: Engage in reasoned dialogue, including with people who have different perspectives.
ELA.III.A.1: Participate actively, effectively, and respectfully in one-on-one oral communication as well as in group discussions.
ELA.III.A.3: Understand how style, register, and content of spoken language vary in different contexts and influence the listener’s understanding.
ELA.IV.A.5: Recognize fillers, intentional pauses, and placeholders in speech (e.g., um) and make inferences in context.
ELA.IV.A.4: Comprehend detailed instructions, explanations, and directions in a range of contexts (e.g., specialized contexts such as workplace procedures and operating instructions).
ELA.IV.A.3: Develop an awareness of rhetorical and stylistic choices used to convey a message.
ELA.V.A.3: Devise a plan for completing work on time.
ELA.V.A.1: Articulate and investigate research questions.
ELA.V.A.2: Explore and refine a research topic.
ELA.V.C.1: Integrate and organize material effectively.
ELA.V.C.3: Follow relevant rules governing attribution.
ELA.V.C.2: Use and attribute source material ethically.
ELA.V.B.3: Assess the relevance and credibility of sources.
ELA.V.B.1: Explore and collect a range of potential sources.
ELA.V.B.2: Distinguish between and among primary and secondary sources.

Mathematics:

M.I.C.1: Select or use the appropriate type of method, unit, and tool for the attribute being measured.
M.I.C.2: Convert units within and between systems of measurement.
M.I.B.1: Use estimation to check for errors and reasonableness of solutions.
M.I.A.1: Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
M.I.A.2: Perform computations with rational and irrational numbers.
M.I.B.2: Interpret the relationships between the different representations of numbers.
M.II.D.2: Convert among multiple representations of equations, inequalities, and relationships.
M.II.D.1: Interpret multiple representations of equations, inequalities, and relationships.
M.IV.C: Measurement involving probability
M.IV.C.1: Use probability to make informed decisions.
M.V.A.1: Formulate a statistical question, plan an investigation, and collect data.
M.V.B.3: Compute and describe the study data with measures of center and basic notions of spread.
M.V.B.2: Construct appropriate visual representations of data.
M.V.B.1: Classify types of data.
M.V.C.4: Identify and explain misleading uses of data.
M.V.C.3: Make predictions using summary statistics.
M.V.C.2: Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
M.V.C.1: Analyze data sets using graphs and summary statistics.
M.VI.C.1: Apply known functions to model real-world situations.
M.VI.C.2: Develop a function to model a situation.
M.VI.B.1: Understand and analyze features of a functions.
M.VI.A.1: Recognize if a relation is a function.
M.VI.A.2: Recognize and distinguish between different types of functions.
M.VI.B.2: Algebraically construct and analyze new functions.
M.VII.C: Logical reasoning
M.VII.C.2: Understand attributes and relationships with inductive and deductive reasoning.
M.VII.A.2: Formulate a plan or strategy.
M.VII.A.5: Evaluate the problem-solving process.
M.VII.A.3: Determine a solution.
M.VII.B.1: Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
M.VII.A.4: Justify the solution.
M.VII.D: Real-world problem solving
M.VII.D.1: Interpret results of the mathematical problem in terms of the original real-world situation.
M.VII.D.2: Evaluate the problem-solving process.
M.VIII.C.2: ate and use representations to organize, record, and communicate mathematical ideas.
M.VIII.C.3: Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
M.VIII.C.1: Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
M.VIII.B.1: Model and interpret mathematical ideas and concepts using multiple representations.
M.VIII.A.1: Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
M.VIII.A.2: Use mathematical language to represent and communicate the mathematical concepts in a problem.
M.VIII.A.3: Use mathematical language for reasoning, problem solving, making connections, and generalizing.
M.VIII.B.2: Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
M.IX.B.3: Know and understand the use of mathematics in a variety of careers and professions.
M.IX.B.2: Understand and use appropriate mathematical models in the natural, physical, and social sciences.
M.IX.B.1: Use multiple representations to demonstrate links between mathematical and real-world situations.
M.IX.A.1: Connect and use multiple key concepts of mathematics in situations and problems.
M.IX.A.2: Connect mathematics to the study of other disciplines.