This unit focuses on the diversity of life at Hartje School Forest and centers around NGSS Standards on Ecosystem Interactions, Energy and Dynamics. Field experiences in observing and recording the diversity of life, seed dispersal methods, plant pollination, and plant life cycles will support science disciplinary core ideas, cross-cutting concepts, and hands-on engineering practices.

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.

Students are introduced to measuring and identifying sources of air pollution, as well as how environmental engineers try to control and limit the amount of air pollution. In Part 1, students are introduced to nitrogen dioxide as an air pollutant and how it is quantified. Major sources are identified, using EPA bar graphs. Students identify major cities and determine their latitudes and longitudes. They estimate NO2 values from color maps showing monthly NO2 averages from two sources: a NASA satellite and the WSU forecast model AIRPACT. In Part 2, students continue to estimate NO2 values from color maps and use Excel to calculate differences and ratios to determine the model's performance. They gain experience working with very large numbers written in scientific notation, as well as spreadsheet application capabilities.

"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."

This unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus.

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.

AtomTouch is a molecular simulation app, created through a partnership between UW MRSEC and Field Day Lab. It allows learners to explore principles of thermodynamics and molecular dynamics in a tactile, exploratory way. The simulation was developed to help students understand the structures and attributes of particles at the molecular level, providing real-time feedback and responding to students’ actions.

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet.

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet.

In this Illuminations lesson plan students explore the use of variables as they solve for the weights of objects using information presented in pictures. Learners model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols. A student activity sheet is available and downloadable (pdf).

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.

Starting from atoms, see how many molecules you can build. Collect your molecules and see them in 3D!

Students first learn how the sound-symbol correspondence in letters and words work so that they better understand how text is used.

This Java applet activity allows students to explore the various situations described in "The Chairs Around the Table" lesson (cataloged separately). The user can select Exploration mode, in which the number of chairs needed for a particular arrangement of tables is displayed; or Guess, in which the user is able to construct an arrangement and then predict the number of chairs. There are two types of tables to choose from and two different table arrangements. Instructions and exploration question are provide.

MPS teacher designed resource adapted from the Illustrative Math Task: Choosing an Appropriate Growth Model.

Suney Park wants her students to know that what they learn in class is relevant to their lives and the world. In this introduction, she shows us how her students come up with a plan to recreate the Earth and its atmosphere and test their own hypotheses about rising CO2 levels.

Suney Park's hands-on activity has her students making the greenhouse effect happen in a model. Using a light bulb for the sun, they create different control groups that imitate Earth's atmosphere with the help of a soda bottle. This adds up to a meaningful experience that connects what students learn in class to real-world events.

After a month studying climate change, students create models of the earth and its atmosphere, and design experiments to test the variables involved in climate change. Students write their own driving questions, develop hypotheses, and build the models to use in their experiments.