This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: 127 is a number. Write it as a sum of 100's, 10's, and 1's. Write its name in words. Draw a picture to represent the number. Locate it on the number li...

A mathematics task that involves a multi-step word problem related to addition and subtraction situations. Students are expected to model with mathematics as they complete the task. Task relates to standard 2.OA. A.1

This task has students solve a multi-step addition and subtraction problem based on a given data chart. Students are solving a variety of problem types involving addition and subtraction. This task is related to evidence statement 3.D.2 and Common Core Standard 2.OA.A.1

This resource provides students with the opportunity to solve a multi-step contextual word problem with a degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills.

This resource provides students with the opportunity to solve a multi-step contextual word problem with a degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills.

This resource provides students with the opportunity to solve a multi-step contextual word problem with a degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills.

This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

"In this module, students synthesize and generalize what they have learned about a variety of function families.  They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4).  They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions.  They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3).  Students identify appropriate types of functions to model a situation.  They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit.  The description of modeling as, “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions,” is at the heart of this module.  In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics."

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

"En este módulo, los estudiantes sintetizan y generalizan lo que han aprendido sobre una variedad de familias de funciones. Extienden el dominio de las funciones exponenciales a toda la línea real (n-rn.a.1) y luego extienden su trabajo con estas funciones a incluir la resolución de ecuaciones exponenciales con logaritmos (F-le.a.4). Exploran (con herramientas apropiadas) los efectos de las transformaciones en gráficos de funciones exponenciales y logarítmicas. Notan que las transformaciones en un gráfico de una función logarítmica se relacionan con el Propiedades logarítmicas (F-BF.B.3). Los estudiantes identifican tipos apropiados de funciones para modelar una situación. Ajustan los parámetros para mejorar el modelo y comparan los modelos analizando la idoneidad del ajuste y las juicios sobre el dominio sobre el cual un modelo es un buen ajuste. La descripción del modelado como, el proceso de elegir y usar matemáticas y estadísticas para analizar situaciones empíricas, comprenderlas mejor y tomar decisiones, está en el corazón de este módulo. En particular, a través de oportunidades repetidas para trabajar a través del ciclo de modelado (consulte la página 61 del CCLS), los estudiantes adquieren la idea de que la misma estructura matemática o estadística a veces puede modelar situaciones aparentemente diferentes.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics ".

English Description:
"In this module, students synthesize and generalize what they have learned about a variety of function families.  They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4).  They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions.  They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3).  Students identify appropriate types of functions to model a situation.  They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit.  The description of modeling as, “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions,” is at the heart of this module.  In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics."

Explores how organizations can use system dynamics to achieve important goals. Student teams work with client managers to tackle the clients' most pressing issues. Students discuss experiences with their clients, and learn modeling and consulting skills they need to be effective. Focus on gaining practical insight from the system dynamics process. Projects are sponsored by diverse organizations from a range of industries and sizes from start-ups to the Fortune 500.

This is the second undergraduate architecture design studio, which introduces design logic and skills that enable design thinking, representation, and development. Through the lens of nano-scale machines, technologies, and phenomena, students are asked to explore techniques for describing form, space, and architecture. Exercises encourage various connotations of the "machine" and challenge students to translate conceptual strategies into more integrated design propositions through both digital and analog means.

This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

This course explores natural and electric lighting that integrates occupant comfort, energy efficiency and daylight availability in an architectural context. Students are asked to evaluate daylighting in real space and simulations, and also high dynamic range photography and physical model building.

" This course will guide graduate students through the process of using rapid prototyping and CAD/CAM devices in a studio environment. The class has a theoretical focus on machine use within the process of design. Each student is expected to have completed one graduate level of design computing with a full understanding of solid modeling in CAD. Students are also expected to have completed at least one graduate design studio."

This course provides a review of physical, chemical, ecological, and economic principles used to examine interactions between humans and the natural environment. Mass balance concepts are applied to ecology, chemical kinetics, hydrology, and transportation; energy balance concepts are applied to building design, ecology, and climate change; and economic and life cycle concepts are applied to resource evaluation and engineering design. Numerical models are used to integrate concepts and to assess environmental impacts of human activities. Problem sets involve development of MATLABĺ¨ models for particular engineering applications. Some experience with computer programming is helpful but not essential.