SYNOPSIS: In this lesson, students use algebra to calculate the number of wind turbines needed to power a local community.

SCIENTIST NOTES: This lesson has students determine the energy generated from a wind turbine. They would be able to analyze the number of units needed for a household, a community, or a small town and share with their community the pros and cons of investing in wind power. All materials were thoroughly reviewed, and this lesson has passed the credibility review process.

POSITIVES:
-Students use their algebra skills in a real-world application.
-The calculations are relevant to students because they estimate the number of wind turbines needed for their own city.
-Students practice supporting their ideas with evidence, which is a skill that is applicable across all disciplines.

ADDITIONAL PREREQUISITES:
-This is lesson 3 of 5 in the 6th-8th grade Renewable Energy Algebra unit.
-Students will need calculators.
-Teachers may need to provide the population of their city to students for question 5 on the Student Document.
-One-to-one technology is ideal. If this is not possible, omit questions 9 and 10 on the Student Document or complete these questions as a class.

DIFFERENTIATION:
-Teachers can have students work in pairs or small groups to complete the calculations instead of individually.
-The discussion at the end of the lesson could be done as a whole group instead of first in pairs.
-Teachers can complete the first few questions with students to get them started before letting them work individually.

In this stage students practice using the Design Recipe to write functions which solve for word problems. Towards the end of the lesson students should be ready to begin using the Design Recipe on problems from your own math curriculum.

Differential Equations and Linear Algebra is a free and open textbook introducing the basics of differential equations and linear algebra to undergraduate students. Students should have taken courses in Differential and Integral Calculus before using this textbook. This book is a combination of 3 open educational resources: 1. Elementary Differential Equations by William F. Trench, licensed under CC BY-NC-SA 3.0. 2. Differential Equations for Engineers by Jiří Lebl, licensed under CC BY-NC-SA 3.0. 3. A First Course in Linear Algebra (an open text) by Lyryx Learning – based on original text by Ken Kuttler, licensed under CC BY.

The topics for this course vary each semester. This semester, the course aims to introduce techniques for studying intersection theory on moduli spaces. In particular, it covers the geometry of homogeneous varieties, the Deligne-Mumford moduli spaces of stable curves and the Kontsevich moduli spaces of stable maps using intersection theory.

(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 módulos anteriores, los estudiantes analizan el proceso de resolver ecuaciones y desarrollar fluidez en la escritura, interpretación y traducción entre varias formas de ecuaciones lineales (Módulo 1) y funciones lineales y exponenciales (Módulo 3). Estas experiencias combinadas con el modelado con datos (Módulo 2), preparan el escenario para el módulo 4. Aquí los estudiantes continúan interpretando expresiones, crean ecuaciones, reescriben ecuaciones y funciones en formas diferentes pero equivalentes, y gráficos e interpretan funciones, pero esta vez utilizando polinomial funciones y funciones más específicamente cuadráticas, así como funciones de raíz de raíz cuadrada y de cubos.

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

English Description:
In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.

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

This is an activity that uses basic algebra to assess the costs and savings of electric vehicles. It uses math to measure the trade-offs of buying electric versus gas-powered car models.

(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.)

Los estudiantes crean una comprensión formal de la probabilidad, considerando eventos complejos como sindicatos, intersecciones y complementos, así como el concepto de independencia y probabilidad condicional. La idea de usar una curva suave para modelar una distribución de datos se introduce junto con el uso de tablas y tecnología para encontrar áreas bajo una curva normal. Los estudiantes hacen inferencias y justifican conclusiones de encuestas de muestra, experimentos y estudios de observación. Los datos se usan de muestras aleatorias para estimar una media o proporción de población. Los estudiantes calculan el margen de error y lo interpretan en contexto. Dados los datos de un experimento estadístico, los estudiantes usan la simulación para crear una distribución de aleatorización y lo usan para determinar si hay una diferencia significativa entre dos tratamientos.

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

English Description:
Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability.  The idea of using a smooth curve to model a data distribution is introduced along with using tables and technology to find areas under a normal curve.  Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.  Data is used from random samples to estimate a population mean or proportion.  Students calculate margin of error and interpret it in context.  Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.

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

SYNOPSIS: In this lesson, students complete real-world calculations related to residential solar energy use, including the number of solar panels needed to power the average house and how many solar panels could fit on their own home or a local building.

SCIENTIST NOTES: This lesson lets students evaluate the impact of solar energy in addressing the energy crisis and energy inequities, especially in low-income communities. It would build their analytic skills in calculating the amount of energy a solar panel can produce per hour, which is important information for houseowners to choose the size of solar panels to build. All materials embedded in the lesson are illustrative and were fact-checked thoroughly. On that account, this lesson has passed our science credibility process and is recommended for teaching.

POSITIVES:
-Students are able to use algebra skills in real-world applications.
-The lesson is engaging for students because it is personalized to each student's actual home or local building.

ADDITIONAL PREREQUISITES:
-This lesson is 2 of 5 in our 6-8th Grade Renewable Energy Algebra unit.
-If teachers did not complete lesson 1, omit questions 1, 3, and 5 on the Student Document and use this video to introduce solar energy and its connections to climate change.
-Slides 14-16 are vocabulary words from the first lesson that teachers may wish to review with students again or introduce if teachers skipped lesson 1.
-Students need access to computers and calculators for this lesson.

DIFFERENTIATION:
-Students can work individually or in groups.
-If students do not feel comfortable using their actual address, they can select a random nearby address to use.
-Teachers can walk students through certain calculations as a class. Teachers can also pull small groups to work through any areas with the most needs.

Gallery OverviewAllow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.Gallery DescriptionsMatch InequalitiesStudents match inequalities to their solutions.Product Between One-Half and OneStudents find a range of values for an inequality situation.Inequalities about NumbersStudents write inequalities to solve problems about the sums of three consecutive numbers.School DanceStudents use equations and an inequality to model the costs and revenues of holding a school dance.What Could My Number Be?Students use inequalities to identify possibilities for a number given certain conditions.Batting AverageStudents use an inequality to find the number of hits needed to get a desired batting average.