A collection of relevant lessons to supplement your units in Algebra I/II. Mix these lessons into your course to show students the algebraic reasoning behind social issues, public health, the environment, business, sports, and more.

"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."

In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

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

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.

(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 calificaciones anteriores, los estudiantes definen, evalúan y comparan las funciones y las usan para modelar las relaciones entre las cantidades. En este módulo, los estudiantes extienden su estudio de funciones para incluir la notación de la función y los conceptos de dominio y rango. Exploran muchos ejemplos de funciones y sus gráficos, centrándose en el contraste entre las funciones lineales y exponenciales. Interpretan funciones dadas gráfica, numérica, simbólica y verbalmente; traducir entre representaciones; y comprender las limitaciones de varias representaciones.

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

English Description:
In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

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 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 task is for instructional purposes only and builds on ``Building an explicit quadratic function.''

This is the first of a series of task aiming at understanding the quadratic formula in a geometric way in terms of the graph of a quadratic function.

This task is intended for instruction and to motivate "Building a general quadratic function.''

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: In this task we will explore the effect that changing the parameters in a sinusoidal function has on the graph of the function. A general sinusoidal fu...

This lesson unit is intended to help teachers assess how well students are able to: model a periodic situation, the height of a person on a Ferris wheel, using trigonometric functions; and interpret the constants a, b, c in the formula h = a + b cos ct in terms of the physical situation, where h is the height of the person above the ground and t is the elapsed time.

This lesson unit is intended to help teachers assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties with: choosing an appropriate, systematic way to collect and organize data; examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile; generalizing using numerical, geometrical or algebraic structure; and describing and explaining findings clearly and effectively.

In this task students use algebraic methods to determine whether each of the functions is odd, even, or neither.

This task has students explore the relationship between the three parameters a, b, and c in the equation f(x)=ax2+bx+c and the resulting graph. There are many possible approaches to solving each part of this problem, especially the first part. We outline some of them here (which overlap heavily in places), applied to the top left graph, and then only give the final answers in the solution provided.

This task has students explore the relationship between the three parameters a, h, and k in the equation f(x)=a(x−h)2+k and the resulting graph. There are many possible approaches to solving each part of this problem, especially the first part. We outline some of them here (which overlap heavily in places), applied to the top left graph, and then only give the final answers in the solution provided.

Interactive resources including videos and activities from the Mathematics Vision Project.  In these lessons students will review Families of Functions and then develop understanding of combining functions.Lessons were taken from the Mathematics Vision Project.

This task addresses the first part of standard F-BF.3: ŇIdentify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative).Ó Here, students are required to understand the effect of replacing x with x+k, but this task can also be modified to test or teach function-building skills involving f(x)+k, kf(x), and f(kx) in a similar manner.

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

Grade Level: Students taking Algebra 2Content: The curriculum being discussed is creating the vertex equation for a parabola from the parent equation.Previous Knowledge: Students should know how to transform a linear equation. That knowledge will aid when they are manipulating the quadratic equation.Students should know the basic quadratic equation information and how it affects the graph i.e. x-intercepts, vertex, axis of symmetry.Students should know that a basic (parent) quadratic equation is y = x².Objective: Be able to write an equation for a parabola in vertex form given multiple parameters. Will also use technology to aid in this discovery.IntroductionAfter reviewing the objectives for the day’s lesson, I have students open their notebooks. Then, I let students know that I want them to take notes as they watch a 2-minute video over quadratic functions and parabolas in the real world.After the video is complete, I ask students to complete the following Think-Pair-Share protocol:Think – 2 minutes to write down your thoughts and update your notes from watching the videosPair – 3-5 minutes to compare and contrast your ideas with a partnerShare – 5-10 minute class discussion of ideas answering the prompt “Describe different characteristics of quadratic functions and their graphs”VocabularyParabolaQuadratic EquationVertexAxis of SymmetryMinimumMaximumBody of LessonThe students will get into pairs to log in to the desmos website. They will be given approximately ten different scenarios of how to move their parabola. For instance, they will be given the parent equation of y = x² and told to move it five units to the left. The student will have to guess where to represent the five in the equation to make the entire graph move five units. The different scenarios could include moving the graph right or left, up or down, and stretching or compressing the parabola.After they have worked out the different scenarios, the students will work with their partners to create the formula for vertex form for a quadratic equation.Next, the students will then use the equation they just created to help them in graphing more parabolas.As part of the closure, we will discuss as a class how the actual vertex (h, k) relates to the equation.Accommodations/ ModificationsGo around the classroom and make sure all students understand what to doPair students with a compatible partner so they can teach each otherProvide extra time for students to finish assignment or assessmentsReduce independent practice to half of the problemsAllow students to use the textbook in their first language or use a Dictionary to help them translate words so that they understand what is being asked of them​​​​​​​AssessmentThe the students will be given a quiz over the concept of parabolas the next day.The students will be assessed over this concept at the end of the chapter on the chapter test.​​​​​​​MaterialsTextbookComputer with Internet ConnectionNotebookPencil​​​​​​​StandardsA-CED 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.F-IF 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.F-BF 3. Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.MA 11.2.1.g Analyze and graph quadratic functions (standard form, vertex form, finding zeros, symmetry, transformations, determine intercepts, and minimums or maximums)​​​​​​​