Bridges
Grade 4, Interdisciplinary
Description of Unit
This interdisciplinary unit includes math, science, technology, English language arts, and reading content. Additional ties could be made to drafting and architectural design. To engage fourth-grade students in the topic, the teacher will introduce relevant books—such as Iggy Peck, Architect by Andrea Beaty and Monsters Under Bridges by Rachel Roellke Coddington. Classroom discussion, video clips, or articles about architecture and bridge design will be shared to engage students, activate prior knowledge, and assist students in choosing a bridge type. Individually or in small groups, students will research various types of bridges, explore structural considerations, and design a bridge incorporating specific mathematical concepts. Using their designs, students will construct their bridge, present their research findings on the bridge type and model bridge to peers, hypothesize the architectural soundness of their bridge design prior to conducting a weight test using appropriate mediums, and have the opportunity to redesign and retest. Finally, students will give a presentation that includes information about their bridge design, construction and weight test, their weight test data, and approaches for the redesign and retest.
This guide links the Bridges unit to the Texas Essential Knowledge and Skills (TEKS) for fourth-grade students. Bridges is an interdisciplinary unit designed to foster an interest in STEM (science, technology, engineering, and math), the architectural process, and creative problem solving. In a world that depends heavily on the exchange of goods and transportation of people in the most efficient manner possible, bridges have become increasingly important to today’s society. According to the National Science Foundation:
In the 21st century, scientific and technological innovations have become increasingly important as we face the benefits and challenges of both globalization and a knowledge-based economy. To succeed in this new information-based and highly technological society, students need to develop their capabilities in STEM to levels much beyond what was considered acceptable in the past.
The following document includes the applicable TEKS and the details of the Bridges 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.
Descripción de la unidad
Esta unidad interdisciplinaria incluye matemáticas, ciencias, tecnología, artes del lenguaje en inglés y contenido de lectura. Se podrían hacer conexiones adicionales con el dibujo y el diseño arquitectónico. Para motivar a los estudiantes de cuarto grado sobre el tema, el maestro introducirá libros relevantes—como Iggy Peck, Arquitect (Pedro Perfecto Arquitecto) por Andrea Beaty y Monsters Under Bridges (Monstruos debajo de los puentes) por Rachel Roellke Coddington. Se realizarán discusiones en clase, se compartirán videos o artículos sobre arquitectura y diseño de puentes para motivar a los estudiantes, activar el conocimiento previo y ayudar a los estudiantes a escoger un tipo de puente. Individualmente o en grupos pequeños, los estudiantes investigarán varios tipos de puentes, explorarán las consideraciones estructurales y diseñarán un puente incorporando conceptos específicos de matemáticas. Usando sus diseños, los estudiantes construirán sus puentes, presentarán a sus compañeros sus hallazgos de la investigación sobre tipos y modelos de puentes, harán una hipótesis de la solidez arquitectónica del diseño de su puente antes de conducir una prueba de peso usando los medios apropiados y tendrán la oportunidad de rediseñar y volver a probar. Finalmente, los estudiantes darán una presentación que incluye información sobre el diseño de su puente, construcción y prueba de peso, la información de la prueba de peso y los enfoques para rediseñar y repetir la prueba.
Esta guía conecta la unidad Puentes con los Conocimientos y destrezas esenciales de Texas (TEKS) para los estudiantes de cuarto grado. Puentes es una unidad interdisciplinaria diseñada para fomentar el interés en STEM (por sus siglas en inglés; ciencias, tecnología, ingeniería y matemáticas), el proceso arquitectural y la resolución creativa de problemas. En un mundo que depende mucho del intercambio de bienes y la transportación de personas en la manera más eficiente posible, los puentes se han convertido en algo cada vez más importante en la sociedad de hoy. De acuerdo con la Fundación Nacional de Ciencias:
En el siglo 21, las innovaciones científicas y tecnológicas se han vuelto cada vez más importantes a medida que enfrentamos los beneficios y los retos tanto de la globalización como de una economía basada en el conocimiento. Para tener éxito en esta nueva sociedad basada en la información y altamente tecnológica, los estudiantes necesitan desarrollar sus capacidades en STEM a niveles mucho más allá de lo que fue considerado aceptable en el pasado.
El siguiente documento incluye los TEKS correspondientes y los detalles de la unidad Puentes: La última sección de este documento presenta los Estándares de Preparación para la Universidad, Carreras Técnicas y el Mundo Laboral de Texas (Texas College and Career Readiness Standards) adoptados por la Mesa Directiva Coordinadora de la Educación Superior en Texas (Texas Higher Education Coordinating Board -THECB) el 24 de enero de 2008.
Phase I. Learning Experiences
Students will develop deeper understanding of the various types of bridges, their purposes, and their construction. The teacher will share books—such as Iggy Peck, Architect by Andrea Beaty and Monsters Under Bridges by Rachel Roellke Coddington—video clips, and articles to engage the students and guide them through a discussion regarding the types, purposes, and construction of bridges. See the recommended websites in the Internet Resources section.
Possible guiding questions for classroom discussion might include the following:
- What do you know about bridges?
- Why do we need bridges?
- What defines a structure as a bridge?
- What characteristics do bridges have?
- Where might bridges be found or used?
- What types of bridges are there?
The teacher may also need to teach the students about the various types of bridges and preteach relevant vocabulary. This website is a resource for explaining different types of bridges including the following: http://www.historyofbridges.com/facts-about-bridges/types-of-bridges/
- Arch bridge
- Beam bridge
- Truss bridge
- Cantilever bridge
- Tiered-arch bridge
- Suspension bridge
- Cable-stayed bridge
- Pedestrian bridge
The teacher will provide students with pictures of several bridges using Google Images or another search engine of choice, as well as those pictures included in Monsters Under Bridges, and have them identify the mathematical features in each. Possible concepts might include the following:
- Angles
- Lines
- Line segments
- Parallel and perpendicular lines
- Lines of symmetry within a two-dimensional figure
- Acute, right, and obtuse triangles
During this time, the teacher can also lead a discussion about using a protractor to measure angles found in bridges and other aspects of bridges that can be measured. Depending on student understanding of these concepts, the teacher may need to provide additional instructional support of these math concepts.
Possible questions for classroom discussion and to guide student research might include the following:- What do you know about bridges?
- Why do we need bridges?
- What shapes and angles are present in bridge design?
- Is symmetry important in bridge construction? Why or why not?
- What mathematical concepts are included in bridge design?
- What role do angle measurements play in bridge design?
- Depending on bridge type, are certain shapes favorable over others?
- What is the optimal length of a bridge?
- How do you determine how long to make a bridge?
- To develop understanding of the components of an effective weight test, students will be placed
in small groups to conduct an experiment on how the length and strength of a bridge are
related.
Equipment:- Two books of the same thickness
- A small paper cup
- Approximately 50 pennies
- 4¼-inch-wide strips of paper with lengths of 5, 6, 8, 9, and 11 inches
- Make paper bridges from the strips. For each strip, fold up 1 inch on each of the long sides.
- Make a hypothesis about which bridge will hold the most pennies.
- Start with the 5-inch bridge. Suspend the bridge between two surfaces with the two books holding down opposite ends. The bridge should overlap each book by about 1 inch. Place the paper cup in the center of the bridge.
- Put pennies into the cup one at a time until the bridge collapses.
- Record the number of pennies added to the cup. This number is the breaking weight of the bridge.
- Repeat the experiment to find the breaking weights for the remaining lengths of bridges.
- Predict the breaking weight of a 3-inch bridge and a 14-inch bridge. Explain your reasoning in your science journal.
Have students consider the following questions:
- What made this test effective?
- Which variable was tested?
- Was your hypothesis correct?
- What are the characteristics of an effective weight test?
Phase II. Independent Research
A. Research process
- Selecting a topic. Students will choose a bridge type to research. Students will continue to develop their understanding and knowledge of bridges that were introduced in Phase I through further research using credible Internet sources, books, video clips, or other types of media.
- Guiding questions. The questions below may be used to guide students through their
individual or small-group research.
- How do you think the idea for fabricated bridges came about?
- What purposes do bridges serve?
- What factors influence what type of bridge is used in a particular region or location?
- What materials are used in bridge construction?
- Are all bridges made from the same materials? Why or why not?
- Why would a bridge be made out of a specific set of materials?
- What shapes are best for bridge strength?
- What steps are needed to construct a bridge?
- What types of careers are associated with bridge design and construction?
- Would plate tectonics or other environmental factors affect the types, placement, or materials used in bridge construction for a specific location?
- How has bridge construction changed over time?
- Are there any instances where soil composition would factor into bridge construction? What considerations must be taken into account when determining the type of bridge needed in a specific location?
- What happens when a bridge fails?
- What can be done to improve a bridge if it fails?
Students may generate their own questions in their science journal as well.
- Designing a research proposal. Students will develop a plan and construct a model bridge
based on knowledge and information gained through their research. Students will
determine the appropriate construction material for their bridge. They may utilize drafting
and design programs, other technology resources, or paper and pencil. Their design needs
to be drawn to scale and include specific information about their bridge, including the
following:
- Type of bridge
- Materials needed
- Types and measurements of angles and shapes found in their design
- All dimensions needed to construct and replicate the design
- Given name
- Conducting research. Students will construct a model of the designed bridge. Model bridges must meet these requirements:
- Minimum of 10 pounds supported when tested
- Minimum length of 12 inches
- Maximum amount of 8 ounces of liquid glue
- Maximum amount of one of the following:
- 200 popsicle sticks (standard size)
- 500 toothpicks
- 300 cotton swabs
B. The product
Students will demonstrate what they have learned about bridges through the construction of a
model bridge. The model will be constructed from a scaled drawing.
After presentations of the various bridges, students will individually generate hypotheses as to
how much weight each bridge will support and which bridge type will support the most weight.
They will record their hypotheses in their science journal.
Students will then conduct a weight test on their own bridge.
To test, weight (e.g., washers, books, bags of sugar, beans or weights) will be suspended from
the center of the bridge using either bungee cords or rope and a standard five-gallon bucket.
Students should take into consideration the weight of the bungee cords, rope, and bucket when
calculating the amount of weight their bridge supports.
An integral part of the engineer design process is redesigning and retesting. Therefore, if the students’ bridge fails the test or the students wants to try and make their bridge stronger, they will be allowed to redesign and retest.
C. Communication
Communication will be done in two stages.
- Stage I: Throughout the scientific process, students will communicate to their peers the bridge type, purpose, mathematical concepts, and any additional information the students discovered while building the bridge. Students will then conduct a weight test on the bridge to support their hypothesis on the bridge’s strength and stability.
- Stage II: Students will conclude the project with a final presentation through an avenue of their choice. Possible means include posters, digital presentations, brochures, or oral presentations. The presentation will include an overview of their bridge design and construction, weight-test guidelines and data, and if applicable, approaches taken for the redesign and retest. The presentation audience may include outside guests, such as parents, school staff, or other professionals. The audience will be given time to ask impromptu questions to reflect student learning.
D. A completed project consists of:
- Research
- A design of a model bridge
- A constructed model bridge
- A research and design presentation
- A weight test and data collection
- A redesign and retest (if needed)
- A final presentation
Fase I. Experiencias de aprendizaje
- Los estudiantes desarrollarán un entendimiento más profundo acerca de los diferentes tipos de puentes, sus propósitos y su construcción.
El maestro compartirá libros - como Iggy Peck, Architect (Pedro Perfecto Arquitecto) por Andrea Beaty y Monsters Under Bridges (Monstruos debajo de los puentes) por Rachel Roellke Coddington- videos y artículos para motivar a los estudiantes y guiarlos a través de una discusión acerca de los tipos, propósitos y construcción de puentes. Ver los sitios web recomendados en la sección Recursos de la Internet
Las posibles preguntas guía para una discusión en el salón de clases pueden incluir las siguientes:- ¿Qué sabes acerca de los puentes?
- ¿Por qué necesitamos puentes?
- ¿Qué define una estructura como un puente?
- ¿Qué características tiene un puente?
- ¿Dónde se encuentran o se usan los puentes?
- ¿Qué tipos de puentes hay?
El maestro también podría necesitar enseñarles a los estudiantes acerca de los diferentes tipos de puentes y enseñar previamente vocabulario relevante. Este sitio web es una fuente para explicar los diferentes tipos de puentes incluyendo los siguientes: http://www.historyofbridges.com/facts-about-bridges/types-of-bridges/
- Puente de arco
- Puente de viga
- Puente de acero
- Puente voladizo
- Puente en arco atirantado
- Puente colgante
- Puente atirantado
- Puente peatonal
El maestro proveerá a los estudiantes fotos de algunos puentes usando Google Images o algún otro navegador de su elección, así como las fotos incluidas en Monsters Under Bridges (Monstruos debajo de los puentes) para que identifiquen las características matemáticas en cada una. Posibles conceptos podrían incluir los siguientes:
- Ángulos
- Líneas
- Segmentos de recta
- Líneas paralelas y perpendiculares
- Líneas de simetría en una figura de dos dimensiones
- Triángulos agudos, rectos y obtusos
Durante este tiempo, el maestro puede también dirigir una discusión sobre el uso de un transportador para medir los ángulos encontrados en los puentes y otros aspectos que se pueden medir en los puentes. Dependiendo del entendimiento del estudiante sobre estos conceptos, el maestro puede necesitar proveer educación adicional para apoyar estos conceptos matemáticos.
Las posibles preguntas para la discusión en el salón de clases y para guiar la investigación del estudiante podrían incluir las siguientes:
- ¿Qué sabes acerca de los puentes?
- ¿Por qué necesitamos puentes?
- ¿Qué figuras y ángulos están presentes en un diseño de un puente?
- ¿La simetría es importante en la construcción de un puente? ¿Por qué sí o por qué no?
- ¿Qué conceptos matemáticos están incluidos en el diseño de un puente?
- ¿Qué papel juegan las medidas de un ángulo en el diseño de un puente?
- Dependiendo del tipo de puente, ¿hay ciertas figuras más favorables que otras?
- ¿Cuál es la longitud óptima de un puente?
- ¿Cómo determinas cuán largo hacer un puente?
- Para desarrollar un entendimiento de los componentes de una prueba de peso efectiva, los estudiantes se colocarán en grupos pequeños para llevar a cabo un experimento acerca de cómo se relacionan la longitud y la fuerza de un puente.
- Dos libros del mismo grosor
- Un vaso pequeño desechable
- Aproximadamente 50 monedas de un centavo
- Tiras de papel de 4¼ pulgadas de ancho con longitudes de 5, 6, 8, 9 y 11 pulgadas
- Hacer puentes con las tiras de papel. Para cada tira, doblar 1 pulgada de cada extremo.
- Hacer una hipótesis sobre cuál puente aguantará más monedas de un centavo.
- Comenzar con un puente de 5 pulgadas. Colgar el puente entre dos superficies con los dos libros sujetando los extremos opuestos. El puente debería solapar cada libro por aproximadamente 1 pulgada. Colocar el vaso desechable en el centro del puente.
- Colocar las monedas de un centavo en el vaso una a la vez hasta que el puente colapse.
- Anotar el número de monedas de un centavo añadidas al vaso. Este número es el peso máximo que el puente puede sostener.
- Repetir el experimento para encontrar el peso máximo para las longitudes restantes de los puentes.
- Predecir el peso máximo de un puente de 3 pulgadas y un puente de 14 pulgadas. Explicar tu razonamiento en tu cuaderno de ciencias.
- ¿Qué hizo que esta prueba fuera efectiva?
- ¿Qué variable fue probada?
- ¿Fue correcta tu hipótesis?
- ¿Cuáles son las características de una prueba efectiva de peso?
Equipo:
Instrucciones:
Pida a los estudiantes que consideren las siguientes preguntas:
Fase II. Investigación independiente
A. Proceso de investigación
- Seleccionando un tema. Los estudiantes escogerán un tipo de puente para investigar. Los estudiantes continuarán desarrollando su comprensión y conocimiento acerca de los puentes que fueron introducidos en la fase I, investigando más a través de fuentes confiables de la Internet, libros, videos u otros tipos de medios de comunicación.
- Preguntas guía. Las siguientes preguntas pueden usarse para guiar a los estudiantes en su investigación individual o en grupos pequeños.
- ¿Cómo crees que surgió la idea de construir puentes?
- ¿Para qué sirven los puentes?
- ¿Cuáles factores influencian qué tipo de puente se usa en una región o lugar en particular?
- ¿Qué materiales se usan en la construcción de un puente?
- ¿Todos los puentes están hechos con los mismos materiales? ¿Por qué sí o por qué no?
- ¿Por qué un puente se construiría con un conjunto específico de materiales?
- ¿Cuáles figuras son mejores para la fuerza de un puente?
- ¿Qué pasos se necesitan para construir un puente?
- ¿Cuáles tipos de carreras profesionales están asociadas con el diseño y la construcción de puentes?
- ¿Las placas tectónicas u otros factores ambientales afectarían los tipos de puentes, la colocación o los materiales usados en la construcción de un puente para un lugar en específico?
- ¿Cómo ha cambiado con el paso del tiempo la construcción de puentes?
- ¿Hay algunas ocasiones en las que la composición del suelo afectaría la construcción de un puente?
- ¿Qué consideraciones se deben tomar en cuenta al determinar el tipo de puente necesario en un lugar en específico?
- ¿Qué ocurre cuando un puente falla?
- ¿Qué se puede hacer para mejorar un puente si este falla?
Los estudiantes también pueden generar sus propias preguntas en su cuaderno de ciencias.
- Diseñando una propuesta de investigación. Los estudiantes desarrollarán un plan y construirán un modelo de un puente basado en el conocimiento e información obtenida a través de su investigación. Los estudiantes determinarán los materiales de construcción apropiados para su puente. Pueden utilizar programas de dibujo y diseño, otros recursos tecnológicos, o papel y lápiz. Sus diseños deben ser dibujados a escala e incluir información específica sobre su puente, incluyendo lo siguiente:
- Tipo de puente
- Materiales necesarios
- Tipos y medidas de ángulos y figuras encontradas en sus diseños
- Todas las dimensiones necesarias para construir y reproducir el diseño
- Nombre dado
- Realizando la investigación. Los estudiantes construirán un modelo del puente diseñado. Los modelos de los puentes deben cumplir con estos requisitos:
- Soportar un mínimo de 10 libras cuando se ponen a prueba
- Una longitud mínima de 12 pulgadas
- Un máximo de 8 onzas de pegamento líquido
- Cantidad máxima de uno de los siguientes:
- 200 palitos de paletas (tamaño estándar)
- 500 palillos de dientes
- 300 hisopos de algodón
B. El producto
Los estudiantes demostrarán lo que han aprendido sobre los puentes mediante la construcción de un modelo de un puente. El modelo se construirá de un dibujo a escala.
Luego de la presentación de varios puentes, los estudiantes generarán individualmente hipótesis de cuánto peso soporta cada puente y cuál tipo de puente soportaría el mayor peso. Registrarán sus hipótesis en sus cuadernos de ciencias.
Los estudiantes luego realizarán una prueba de peso en sus propios puentes.
Para la prueba, el peso (por ej., arandelas, libros, bolsas de azúcar, frijoles o pesas) será suspendido del centro del puente usando cuerdas flexibles o una cuerda y una cubeta estándar de cinco galones. Los estudiantes deben tomar en consideración el peso de las cuerdas flexibles, la cuerda y la cubeta cuando calculen la cantidad de peso que sus puentes soportan.
Una parte integral del proceso de diseño de ingeniería es volver a diseñar y volver a probar. Por lo tanto, si el puente del estudiante falla la prueba o el estudiante quiere intentar hacer su puente más fuerte, se le permitirá rediseñar y repetir la prueba.
C. Comunicación
La comunicación será en dos etapas.
- Etapa I: A través de proceso científico, los estudiantes comunicarán a sus compañeros el tipo de puente, propósito, conceptos matemáticos y cualquier información adicional que los estudiantes descubrieron mientras construían el puente. Luego, los estudiantes realizarán una prueba de peso en el puente para apoyar su hipótesis de la fuerza y estabilidad del puente.
- Etapa II: Los estudiantes concluirán el proyecto con una presentación final a través del medio que ellos escojan. Los posibles medios incluyen carteles, presentaciones digitales, folletos o presentaciones orales. La presentación incluirá un resumen del diseño y construcción del puente, las reglas e información de la prueba de peso y, si aplica, los enfoques tomados en el rediseño y repetición de la prueba. La audiencia de la presentación puede incluir invitados especiales, como padres de familia, empleados de la escuela u otros profesionales. Se le dará tiempo a la audiencia para hacer preguntas improvisadas que reflejen el aprendizaje del estudiante.
D. Un proyecto completo consiste de:
- Investigación
- El diseño de un modelo de puente
- La construcción del modelo de un puente
- La presentación de la investigación y el diseño
- La prueba de peso y la información recopilada
- El rediseño y la repetición de la prueba (de ser necesario)
- Una presentación final
This unit may address the following TEKS.
110.6., English Language Arts and Reading, Grade 4, Adopted 2017
- 110.6(b)(4)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--fluency. The student reads grade-level text with fluency and comprehension. The student is expected to use appropriate fluency (rate, accuracy, and prosody) when reading grade-level text.
- 110.6(b)(1)(D)
- work collaboratively with others to develop a plan of shared responsibilities.
- 110.6(b)(6)(H)
- synthesize information to create new understanding
- 110.6(b)(6)(C)
- make, correct, or confirm predictions using text features, characteristics of genre, and structures;
- 110.6(b)(7)(F)
- respond using newly acquired vocabulary as appropriate
- 110.6(b)(7)(G)
- discuss specific ideas in the text that are important to the meaning.
- 110.6(b)(9)(F)
- recognize characteristics of multimodal and digital texts.
- 110.6(b)(9)(D)
- recognize characteristics and structures of informational text, including:
- 110.6(b)(13)(H)
- use an appropriate mode of delivery, whether written, oral, or multimodal, to present results.
- 110.6(b)(3)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--vocabulary. The student uses newly acquired vocabulary expressively.
- 110.6(b)(5)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--self-sustained reading. The student reads grade-appropriate texts independently. The student is expected to self-select text and read independently for a sustained period of time.
- 110.6(b)(10)
- Author's purpose and craft: listening, speaking, reading, writing, and thinking using multiple texts. The student uses critical inquiry to analyze the authors' choices and how they influence and communicate meaning within a variety of texts. The student analyzes and applies author's craft purposefully in order to develop his or her own products and performances.
- 110.6(b)(11)
- Composition: listening, speaking, reading, writing, and thinking using multiple texts--writing process. The student uses the writing process recursively to compose multiple texts that are legible and uses appropriate conventions.
- 110.6(b)(12)
- Composition: listening, speaking, reading, writing, and thinking using multiple texts--genres. The student uses genre characteristics and craft to compose multiple texts that are meaningful.
- 110.6(b)(13)
- Inquiry and research: listening, speaking, reading, writing, and thinking using multiple texts. The student engages in both short-term and sustained recursive inquiry processes for a variety of purposes.
- 110.6(b)(1)
- Developing and sustaining foundational language skills: listening, speaking, discussion, and thinking--oral language. The student develops oral language through listening, speaking, and discussion.
111.6, Mathematics, Grade 4
- 111.6(b)(1)
- Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
- 111.6(b)(1)(A)
- apply mathematics to problems arising in everyday life, society, and the workplace;
- 111.6(b)(1)(B)
- use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
- 111.6(b)(1)(C)
- select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
- 111.6(b)(1)(D)
- communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
- 111.6(b)(1)(E)
- create and use representations to organize, record, and communicate mathematical ideas;
- 111.6(b)(1)(F)
- analyze mathematical relationships to connect and communicate mathematical ideas;
- 111.6(b)(1)(G)
- display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
- 111.6(b)(6)
- Geometry and measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties.
- 111.6(b)(6)(A)
- identify points, lines, line segments, rays, angles, and perpendicular and parallel lines;
- 111.6(b)(6)(B)
- identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure;
- 111.6(b)(6)(C)
- apply knowledge of right angles to identify acute, right, and obtuse triangles;
- 111.6(b)(6)(D)
- classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size.
- 111.6(b)(7)
- Geometry and measurement. The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees.
- 111.6(b)(7)(C)
- determine the approximate measures of angles in degrees to the nearest whole number using a protractor;
- 111.6(b)(8)
- Geometry and measurement. The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement.
- 111.6(b)(8)(C)
- solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.
- 111.6(b)(10)
- Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security.
- 111.6(b)(10)(A)
- distinguish between fixed and variable expenses;
- 111.6(b)(10)(B)
- calculate profit in a given situation;
112.15, Science, Grade 4
- 112.15(b)(1)
- Scientific investigation and reasoning. The student conducts classroom and outdoor investigations, following home and school safety procedures and environmentally appropriate and ethical practices.
- 112.15(b)(2)
- Scientific investigation and reasoning. The student uses scientific inquiry methods during laboratory and outdoor investigations.
- 112.15(b)(3)
- Scientific investigation and reasoning. The student uses critical thinking and scientific problem solving to make informed decisions.
- 112.15(b)(4)
- Scientific investigation and reasoning. The student knows how to use a variety of tools, materials, equipment, and models to conduct science inquiry.
128.6., Spanish Language Arts and Reading, Grade 4, Adopted 2017
- 128.6(b)(4)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--fluency. The student reads grade-level text with fluency and comprehension. The student is expected to use appropriate fluency (rate, accuracy, and prosody) when reading grade-level text.
- 128.6(b)(1)(D)
- work collaboratively with others to develop a plan of shared responsibilities.
- 128.6(b)(6)(H)
- synthesize information to create new understanding
- 128.6(b)(6)(C)
- make, correct, or confirm predictions using text features, characteristics of genre, and structures;
- 128.6(b)(7)(F)
- respond using newly acquired vocabulary as appropriate
- 128.6(b)(7)(G)
- discuss specific ideas in the text that are important to the meaning.
- 128.6(b)(9)(D)(i)
- the central idea with supporting evidence;
- 128.6(b)(9)(F)
- recognize characteristics of multimodal and digital texts.
- 128.6(b)(13)(H)
- use an appropriate mode of delivery, whether written, oral, or multimodal, to present results.
- 128.6(b)(3)(B)
- use context within and beyond a sentence to determine the relevant meaning of unfamiliar words or multiple-meaning words;
- 128.6(b)(3)(C)
- identify the meaning of and use base words with affixes, including mono-, sobre-, sub-, inter-, poli-, -able, -ante, -eza, -ancia, and -ura, and roots, including auto, bio, grafía, metro, fono, and tele;
- 128.6(b)(5)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--self-sustained reading. The student reads grade appropriate texts independently. The student is expected to self-select text and read independently for a sustained period of time.
- 128.6(b)(10)
- Author's purpose and craft: listening, speaking, reading, writing, and thinking using multiple texts. The student uses critical inquiry to analyze the authors' choices and how they influence and communicate meaning within a variety of texts. The student analyzes and applies author's craft purposefully in order to develop his or her own products and performances.
- 128.6(b)(11)(D)
- edit drafts using standard Spanish conventions, including:
- 128.6(b)(11)(D)(vii)
- pronouns, including personal, possessive, objective, reflexive, and prepositional;
- 128.6(b)(11)(D)(v)
- adverbs that convey frequency and adverbs that convey degree;
- 128.6(b)(11)(D)(ii)
- irregular verbs;
- 128.6(b)(11)(D)(iii)
- singular, plural, common, and proper nouns, including gender-specific articles;
- 128.6(b)(11)(D)(iv)
- adjectives, including their comparative and superlative forms;
- 128.6(b)(11)(D)(vi)
- prepositions and prepositional phrases;
- 128.6(b)(12)(D)
- compose correspondence that requests information.
- 128.6(b)(12)(B)
- compose informational texts, including brief compositions that convey information about a topic, using a clear central idea and genre characteristics and craft;
- 128.6(b)(11)(D)(xi)
- correct spelling of words with grade-appropriate orthographic patterns and rules
- 128.6(b)(13)
- Inquiry and research: listening, speaking, reading, writing, and thinking using multiple texts. The student engages in both short-term and sustained recursive inquiry processes for a variety of purposes.
- 128.6(b)(13)(F)
- recognize the difference between paraphrasing and plagiarism when using source materials;
- 128.6(b)(13)(G)
- develop a bibliography
- 128.6(b)(13)(A)
- generate and clarify questions on a topic for formal and informal inquiry;
- 128.6(b)(13)(B)
- develop and follow a research plan with adult assistance;
- 128.6(b)(13)(C)
- identify and gather relevant information from a variety of sources;
- 128.6(b)(1)
- Developing and sustaining foundational language skills: listening, speaking, discussion, and thinking--oral language. The student develops oral language through listening, speaking, and discussion.
- 128.6(b)(1)(C)
- express an opinion supported by accurate information, employing eye contact, speaking rate, volume, enunciation, and the conventions of language to communicate ideas effectively
- 128.6(b)(1)(B)
- follow, restate, and give oral instructions that involve a series of related sequences of action;
- 128.6(b)(1)(A)
- listen actively, ask relevant questions to clarify information, and make pertinent comments;
Esta unidad puede abordar los siguientes TEKS.
110.6., English Language Arts and Reading, Grade 4, Adopted 2017
- 110.6(b)(4)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--fluency. The student reads grade-level text with fluency and comprehension. The student is expected to use appropriate fluency (rate, accuracy, and prosody) when reading grade-level text.
- 110.6(b)(1)(D)
- work collaboratively with others to develop a plan of shared responsibilities.
- 110.6(b)(6)(H)
- synthesize information to create new understanding
- 110.6(b)(6)(C)
- make, correct, or confirm predictions using text features, characteristics of genre, and structures;
- 110.6(b)(7)(F)
- respond using newly acquired vocabulary as appropriate
- 110.6(b)(7)(G)
- discuss specific ideas in the text that are important to the meaning.
- 110.6(b)(9)(F)
- recognize characteristics of multimodal and digital texts.
- 110.6(b)(9)(D)
- recognize characteristics and structures of informational text, including:
- 110.6(b)(13)(H)
- use an appropriate mode of delivery, whether written, oral, or multimodal, to present results.
- 110.6(b)(3)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--vocabulary. The student uses newly acquired vocabulary expressively.
- 110.6(b)(5)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--self-sustained reading. The student reads grade-appropriate texts independently. The student is expected to self-select text and read independently for a sustained period of time.
- 110.6(b)(10)
- Author's purpose and craft: listening, speaking, reading, writing, and thinking using multiple texts. The student uses critical inquiry to analyze the authors' choices and how they influence and communicate meaning within a variety of texts. The student analyzes and applies author's craft purposefully in order to develop his or her own products and performances.
- 110.6(b)(11)
- Composition: listening, speaking, reading, writing, and thinking using multiple texts--writing process. The student uses the writing process recursively to compose multiple texts that are legible and uses appropriate conventions.
- 110.6(b)(12)
- Composition: listening, speaking, reading, writing, and thinking using multiple texts--genres. The student uses genre characteristics and craft to compose multiple texts that are meaningful.
- 110.6(b)(13)
- Inquiry and research: listening, speaking, reading, writing, and thinking using multiple texts. The student engages in both short-term and sustained recursive inquiry processes for a variety of purposes.
- 110.6(b)(1)
- Developing and sustaining foundational language skills: listening, speaking, discussion, and thinking--oral language. The student develops oral language through listening, speaking, and discussion.
111.6, Mathematics, Grade 4
- 111.6(b)(1)
- Estándares de procesos matemáticos. El estudiante utiliza procesos matemáticos para adquirir y demostrar comprensión matemática.
- 111.6(b)(1)(A)
- aplique las matemáticas a los problemas que surgen en la vida diaria, la sociedad y el trabajo;
- 111.6(b)(1)(B)
- utilice un modelo de resolución de problemas que incorpora el análisis de información dada, la formulación de un plan o estrategia, la determinación de una solución, la justificación de la solución y la evaluación del proceso de resolución de problemas, así como lo razonable de la solución;
- 111.6(b)(1)(C)
- seleccione herramientas cuando sean apropiadas, incluyendo objetos reales, manipulativos, papel y lápiz, y tecnología, además de técnicas cuando sean apropiadas, incluyendo el cálculo mental, la estimación y el sentido numérico, para resolver problemas;
- 111.6(b)(1)(D)
- comunique ideas matemáticas, su razonamiento y sus implicaciones utilizando múltiples representaciones cuando sean apropiadas, incluyendo símbolos, diagramas, gráficas y el lenguaje común;
- 111.6(b)(1)(E)
- genere y utilice representaciones para organizar, anotar y comunicar ideas matemáticas;
- 111.6(b)(1)(F)
- analice relaciones matemáticas para conectar y comunicar ideas matemáticas;
- 111.6(b)(1)(G)
- muestre, explique y justifique ideas y argumentos matemáticos utilizando lenguaje matemático preciso en forma verbal o escrita.
- 111.6(b)(6)
- Geometría y medición. El estudiante aplica los estándares de procesos matemáticos para analizar atributos geométricos que le permitan desarrollar generalizaciones de sus propiedades.
- 111.6(b)(6)(A)
- identifique puntos, líneas, segmentos de recta, rayos, ángulos y líneas perpendiculares y paralelas;
- 111.6(b)(6)(B)
- identifique y dibuje uno o más ejes de simetría, si los hubiera, en una figura de dos dimensiones;
- 111.6(b)(6)(C)
- utilice el conocimiento de ángulos rectos para identificar triángulos agudos, rectos y obtusos;
- 111.6(b)(6)(D)
- clasifique figuras de dos dimensiones basadas en la presencia o ausencia de líneas paralelas o perpendiculares, o en la presencia o ausencia de ángulos de un tamaño específico.
- 111.6(b)(7)
- Geometría y medición. El estudiante aplica los estándares de procesos matemáticos para resolver problemas que involucran ángulos menores que o iguales a 180 grados.
- 111.6(b)(7)(C)
- determine las medidas aproximadas de ángulos en grados al número entero más cercano utilizando un transportador;
- 111.6(b)(8)
- Geometría y medición. El estudiante aplica los estándares de procesos matemáticos para seleccionar apropiadamente unidades del sistema inglés (usuales) y métricas, estrategias y herramientas que le permitan resolver problemas de medición.
- 111.6(b)(8)(C)
- resuelva problemas sobre medidas de longitud, intervalos de tiempo, volumen líquido, masa y dinero utilizando la suma, la resta, la multiplicación o la división según sea apropiado.
- 111.6(b)(10)
- Comprensión de finanzas personales. El estudiante aplica los estándares de procesos matemáticos para manejar eficazmente sus propios recursos financieros para lograr una seguridad financiera de por vida.
- 111.6(b)(10)(A)
- distinga entre gastos fijos y variables;
- 111.6(b)(10)(B)
- calcule las ganancias en una situación dada;
112.15, Science, Grade 4
- 112.15(b)(1)
- Investigación y razonamiento científicos. El estudiante lleva a cabo investigaciones dentro y fuera del salón de clases siguiendo procedimientos de seguridad de la escuela y del hogar, y prácticas ambientales adecuadas y éticas.
- 112.15(b)(2)
- Investigación y razonamiento científicos. El estudiante usa el método de investigación científica en el laboratorio y al aire libre.
- 112.15(b)(3)
- Investigación y razonamiento científicos. El estudiante usa el razonamiento crítico y la resolución científica de problemas para tomar decisiones informadas.
- 112.15(b)(4)
- Investigación y razonamiento científicos. El estudiante entiende cómo usar una variedad de herramientas, materiales, equipos y modelos para realizar investigaciones científicas.
128.6., Spanish Language Arts and Reading, Grade 4, Adopted 2017
- 128.6(b)(4)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--fluency. The student reads grade-level text with fluency and comprehension. The student is expected to use appropriate fluency (rate, accuracy, and prosody) when reading grade-level text.
- 128.6(b)(1)(D)
- work collaboratively with others to develop a plan of shared responsibilities.
- 128.6(b)(6)(H)
- synthesize information to create new understanding
- 128.6(b)(6)(C)
- make, correct, or confirm predictions using text features, characteristics of genre, and structures;
- 128.6(b)(7)(F)
- respond using newly acquired vocabulary as appropriate
- 128.6(b)(7)(G)
- discuss specific ideas in the text that are important to the meaning.
- 128.6(b)(9)(D)(i)
- the central idea with supporting evidence;
- 128.6(b)(9)(F)
- recognize characteristics of multimodal and digital texts.
- 128.6(b)(13)(H)
- use an appropriate mode of delivery, whether written, oral, or multimodal, to present results.
- 128.6(b)(3)(B)
- use context within and beyond a sentence to determine the relevant meaning of unfamiliar words or multiple-meaning words;
- 128.6(b)(3)(C)
- identify the meaning of and use base words with affixes, including mono-, sobre-, sub-, inter-, poli-, -able, -ante, -eza, -ancia, and -ura, and roots, including auto, bio, grafía, metro, fono, and tele;
- 128.6(b)(5)
- Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--self-sustained reading. The student reads grade appropriate texts independently. The student is expected to self-select text and read independently for a sustained period of time.
- 128.6(b)(10)
- Author's purpose and craft: listening, speaking, reading, writing, and thinking using multiple texts. The student uses critical inquiry to analyze the authors' choices and how they influence and communicate meaning within a variety of texts. The student analyzes and applies author's craft purposefully in order to develop his or her own products and performances.
- 128.6(b)(11)(D)
- edit drafts using standard Spanish conventions, including:
- 128.6(b)(11)(D)(vii)
- pronouns, including personal, possessive, objective, reflexive, and prepositional;
- 128.6(b)(11)(D)(v)
- adverbs that convey frequency and adverbs that convey degree;
- 128.6(b)(11)(D)(ii)
- irregular verbs;
- 128.6(b)(11)(D)(iii)
- singular, plural, common, and proper nouns, including gender-specific articles;
- 128.6(b)(11)(D)(iv)
- adjectives, including their comparative and superlative forms;
- 128.6(b)(11)(D)(vi)
- prepositions and prepositional phrases;
- 128.6(b)(12)(D)
- compose correspondence that requests information.
- 128.6(b)(12)(B)
- compose informational texts, including brief compositions that convey information about a topic, using a clear central idea and genre characteristics and craft;
- 128.6(b)(11)(D)(xi)
- correct spelling of words with grade-appropriate orthographic patterns and rules
- 128.6(b)(13)
- Inquiry and research: listening, speaking, reading, writing, and thinking using multiple texts. The student engages in both short-term and sustained recursive inquiry processes for a variety of purposes.
- 128.6(b)(13)(F)
- recognize the difference between paraphrasing and plagiarism when using source materials;
- 128.6(b)(13)(G)
- develop a bibliography
- 128.6(b)(13)(A)
- generate and clarify questions on a topic for formal and informal inquiry;
- 128.6(b)(13)(B)
- develop and follow a research plan with adult assistance;
- 128.6(b)(13)(C)
- identify and gather relevant information from a variety of sources;
- 128.6(b)(1)
- Developing and sustaining foundational language skills: listening, speaking, discussion, and thinking--oral language. The student develops oral language through listening, speaking, and discussion.
- 128.6(b)(1)(C)
- express an opinion supported by accurate information, employing eye contact, speaking rate, volume, enunciation, and the conventions of language to communicate ideas effectively
- 128.6(b)(1)(B)
- follow, restate, and give oral instructions that involve a series of related sequences of action;
- 128.6(b)(1)(A)
- listen actively, ask relevant questions to clarify information, and make pertinent comments;
This unit may address the following Texas College and Career Readiness Standards.
Cross-Disciplinary Standards:
- CDS.I.B.3
- Gather evidence to support arguments, findings, or lines of reasoning.
- CDS.I.B.4
- Support or modify claims based on the results of an inquiry.
- CDS.I.C.3
- Collect evidence and data systematically and directly relate to solving a problem.
- CDS.II.C.2
- Explore a research topic.
- 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.
Science:
- S.I.A.1
- Utilize skepticism, logic, and professional ethics in science.
- S.I.B.1
- Design and conduct scientific investigations in which hypotheses are formulated and tested.
- S.I.E.2
- Use essential vocabulary of the discipline being studied.
- S.III.B.1
- Read technical and scientific articles to gain understanding of interpretations, apparatuses, techniques or procedures, and data.
- S.III.B.2
- Set up apparatuses, carry out procedures, and collect specified data from a given set of appropriate instructions.
- S.III.B.3
- Recognize scientific and technical vocabulary in the field of study and use this vocabulary to enhance clarity of communication.
- 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.III.D.2
- Evaluate quality, accuracy, completeness, reliability, and currency of information from any source.
- S.V.E.1
- Use models to make predictions.
English Language Arts:
- ELA.I.A.2
- Generate ideas, gather information, and manage evidence relevant to the topic and purpose.
- ELA.I.A.3
- Evaluate relevance, quality, sufficiency, and depth of preliminary ideas and information; organize material generated; and formulate a thesis or purpose statement.
- ELA.I.A.4
- Review feedback and revise each draft by organizing it more logically and fluidly, refining key ideas, and using language more precisely and effectively.
- ELA.II.B.1
- Identify new words and concepts acquired through study of their relationships to other words and concepts.
- ELA.III.A.2
- Engage in reasoned dialogue, including with people who have different perspectives.
- ELA.III.A.3
- Understand how style, register, and content of spoken language vary in different contexts and influence the listener’s understanding.
- ELA.III.A.4
- Adjust delivery, vocabulary, and length of message for particular audiences, purposes, and contexts.
- ELA.III.A.5
- Plan and deliver focused, coherent presentations that convey clear and distinct perspectives and demonstrate sound reasoning.
- ELA.V.A.1
- Articulate and investigate research questions.
- ELA.V.A.2
- Explore and refine a research topic.
- ELA.V.A.3
- Devise a plan for completing work on time.
- ELA.V.B.1
- Explore and collect a range of potential sources.
- ELA.V.B.2
- Distinguish between and among primary and secondary sources.
- ELA.V.B.3
- Assess the relevance and credibility of sources.
- ELA.V.C.1
- Integrate and organize material effectively.
- ELA.V.C.2
- Use and attribute source material ethically.
- ELA.V.C.3
- Follow relevant rules governing attribution.
Mathematics:
- M.I.A.1
- Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
- M.III.A.1
- Recognize characteristics and dimensional changes of two- and three-dimensional figures.
- M.III.A.2
- Form and validate conjectures about one-, two-, and three-dimensional figures and their properties.
- M.III.A.3
- Recognize and apply right triangle relationships including basic trigonometry.
- 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.VIII.C.1
- Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
- 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.V.A.1
- Formulate a statistical question, plan an investigation, and collect data.
- M.V.B.2
- Construct appropriate visual representations of data.
- M.VII.A.1
- Analyze given information.
- M.VII.A.2
- Formulate a plan or strategy.
- M.VII.A.3
- Determine a solution.
- M.VII.A.4
- Justify the solution.
- M.VII.A.5
- Evaluate the problem-solving process.
- 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.C
- Logical reasoning
- M.VII.C.2
- Understand attributes and relationships with inductive and deductive reasoning.
- 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.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.
- M.IX.B.1
- Use multiple representations to demonstrate links between mathematical and real-world situations.
- 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.
Esta unidad puede abordar los siguientes estándares de Texas College and Career Readiness.
Cross-Disciplinary Standards:
- CDS.I.B.3
- Reúne evidencias para apoyar argumentos, hallazgos o líneas de razonamiento.
- CDS.I.B.4
- Apoya o clarifica aseveraciones basadas en los resultados de una investigación.
- CDS.I.C.3
- Reúne sistemáticamente evidencias y datos y los relaciona directamente para resolver un problema.
- CDS.II.C.2
- Explora un tema de investigación.
- 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.
Science:
- S.I.A.1
- Utiliza el escepticismo, la lógica y la ética profesional en las ciencias.
- S.I.B.1
- Diseña y hace investigaciones científicas en las cuales se formulan y se ponen a prueba hipótesis.
- S.I.E.2
- Usa vocabulario esencial de la disciplina que se está estudiando.
- S.III.B.1
- Lee artículos técnicos y científicos para comprender interpretaciones, aparatos, técnicas o procedimientos y datos.
- S.III.B.2
- Prepara aparatos, lleva a cabo procedimientos y reúne datos específicos de un conjunto dado de instrucciones apropiadas.
- S.III.B.3
- Reconoce el vocabulario científico y técnico en el campo de estudio y usa este vocabulario para que la comunicación sea más clara.
- 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.III.D.2
- Evalúa la calidad, exactitud, integridad, confiabilidad y actualidad de la información de cualquier fuente.
- S.V.E.1
- Usa modelos para hacer predicciones.
English Language Arts:
- ELA.I.A.2
- Generate ideas, gather information, and manage evidence relevant to the topic and purpose.
- ELA.I.A.3
- Evaluate relevance, quality, sufficiency, and depth of preliminary ideas and information; organize material generated; and formulate a thesis or purpose statement.
- ELA.I.A.4
- Review feedback and revise each draft by organizing it more logically and fluidly, refining key ideas, and using language more precisely and effectively.
- ELA.II.B.1
- Identify new words and concepts acquired through study of their relationships to other words and concepts.
- ELA.III.A.2
- Engage in reasoned dialogue, including with people who have different perspectives.
- ELA.III.A.3
- Understand how style, register, and content of spoken language vary in different contexts and influence the listener’s understanding.
- ELA.III.A.4
- Adjust delivery, vocabulary, and length of message for particular audiences, purposes, and contexts.
- ELA.III.A.5
- Plan and deliver focused, coherent presentations that convey clear and distinct perspectives and demonstrate sound reasoning.
- ELA.V.A.1
- Articulate and investigate research questions.
- ELA.V.A.2
- Explore and refine a research topic.
- ELA.V.A.3
- Devise a plan for completing work on time.
- ELA.V.B.1
- Explore and collect a range of potential sources.
- ELA.V.B.2
- Distinguish between and among primary and secondary sources.
- ELA.V.B.3
- Assess the relevance and credibility of sources.
- ELA.V.C.1
- Integrate and organize material effectively.
- ELA.V.C.2
- Use and attribute source material ethically.
- ELA.V.C.3
- Follow relevant rules governing attribution.
Mathematics:
- M.I.A.1
- Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
- M.III.A.1
- Recognize characteristics and dimensional changes of two- and three-dimensional figures.
- M.III.A.2
- Form and validate conjectures about one-, two-, and three-dimensional figures and their properties.
- M.III.A.3
- Recognize and apply right triangle relationships including basic trigonometry.
- 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.VIII.C.1
- Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
- 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.V.A.1
- Formulate a statistical question, plan an investigation, and collect data.
- M.V.B.2
- Construct appropriate visual representations of data.
- M.VII.A.1
- Analyze given information.
- M.VII.A.2
- Formulate a plan or strategy.
- M.VII.A.3
- Determine a solution.
- M.VII.A.4
- Justify the solution.
- M.VII.A.5
- Evaluate the problem-solving process.
- 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.C
- Logical reasoning
- M.VII.C.2
- Understand attributes and relationships with inductive and deductive reasoning.
- 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.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.
- M.IX.B.1
- Use multiple representations to demonstrate links between mathematical and real-world situations.
- 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.