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.

(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.

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.

This unit provides Common-Core aligned lessons based for Math 3, English 10, and Biology (NGSS Standards). The subjects are linked by a text on climate change, and they hit the standards of argumentation for English, comparing functions in Math 3, and human effects on environment in Biology.

This lesson has students create, compare, and solve linear, quadratic, exponential, and cubic functions based on a primary source from Weather Underground about the melting of the polar ice caps. If the formatting is an issue, contact me at rob.leichner@gmail.com for a Google drive link to the lesson plan.

Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.

Context based exponential growth and decay questions.

(This is used as a test of OER)

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.

The lesson uses a Desmos Activity entitled Guess My Rule. Students will give an input to a "machine" and the machine will give an output. Students will then be asked to determine a rule that the machine uses to produce an output from the given input. The goal of this activity is to develop the definition of a function using examples and nonexamples.

In the middle grades, students have lots of experience analyzing and comparing linear functions using graphs, tables, symbolic expressions, and verbal descriptions. In this task, students may choose a representation that suits them and then reason from within that representation.

The purpose of this task is to introduce students to exponential growth. While the context presents a classic example of exponential growth, it approaches it from a non-standard point of view. Instead of giving a starting value and asking for subsequent values, it gives an end value and asks about what happened in the past. The simple first question can generate a surprisingly lively discussion as students often think that the algae will grow linearly.

Desmos activities are interactive, math based activities that can be altered to fit your needs.  This particular Desmos activity works through inverses of linear equations for Secondary Math III students.

This lesson unit is intended to help teachers assess how well students are able to: make sense of a real life situation and decide what math to apply to the problem; understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model; represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams; and interpret the results and communicate their reasoning clearly.

This lesson unit is intended to help teachers assess how well students understand conditional probability, and, in particular, to help teachers identify and assist students who have the following difficulties: representing events as a subset of a sample space using tables and tree diagrams; and understanding when conditional probabilities are equal for particular and general situations.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

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.