Sal explains what it means to simplify a rational expression and why we would want to do that. Just don't forget the excluded values! [15:22]

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The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily. [6:42]

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Module 2 builds on students' previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

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

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.

(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.

Polynomial identities are equations that are true for all possible values of the variable. This introduction video gives more examples of identities and discusses how we prove an equation is an identity. [4:56]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

The polynomial remainder theorem says that for a polynomial p(x) and a number a, the remainder on division by (x-a) is p(a). This might not be very clear right now, but you will understand this much better after watching these examples. [5:31]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Sal finds the remainder of (-3x^3-4x^2+10x-7) divided by (x-2) using the PRT (Polynomial Remainder Theorem). [3:31]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial's graph. We will also see that they are directly related to the factors of the polynomial. [5:08]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

When we are given the graph of a polynomial, we can deduce what its zeros are, which helps us determine a few factors the polynomial's equation must include. [3:00]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

See worked examples for using exponent properties to multiply and divide when there are integer exponents. [4:23]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This site from Richland Community College provides lecture notes to a class on Algebra. It covers a wide array of topics including functions, quadratic equations, inequalities, and much more.

Students are able to have an on line quiz where the score and time elapsed is recorded on various level of solving equation problems.

This video demonstrates how to take the formula for the area of a triangle and rewrite it in terms of height. [2:29]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Video introducing the concept of even and odd functions by first looking at visual examples and then the formal definitions. Includes link to additional practice at the top of the video. [12:25]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Explains how to solve two different quadratic equations using the completing the square method. [14:06]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Sal introduces the concept of "range" of a function and gives examples for functions and their ranges. [6:38]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Linear equations can be solved and graphed using this interactive site. This site allows the user to enter any linear equation in standard form and the y-intercept will be found through a step-by-step process. Systems of inequalities can also be explored here. Related sections of the site, accessed through tabs along the top, provide many practice problems, lessons, videos, and in-depth explanations of concepts.

In this game activity students practice comparing shapes and naming something that is alike or different about them.

Commercial fishing nets often trap "unprofitable" animals in the process of catching target species. In this activity, students experience the difficulty that fishermen experience while trying to isolate a target species when a variety of sea animals are found in the area of interest. Then the class discusses the large magnitude of this problem. Students practice data acquisition and analysis skills by collecting data and processing it to deduce trends on target species distribution. They conclude by discussing how bycatch impacts their lives and whether or not it is an important environmental issue that needs attention. As an extension, students use their creativity and innovative skills to design nets or other methods, theoretically and/or through hands-on prototyping, that fisherman could use to help avoid bycatch.