(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 los grados 6 y 7, los estudiantes trabajaron con datos que involucraban una sola variable. El módulo 6 presenta a los estudiantes a bivariando datos. Los estudiantes se introducen a una función como una regla que asigna exactamente un valor a cada entrada. En este módulo, los estudiantes usan su comprensión de las funciones para modelar las posibles relaciones de datos bivariados. Este módulo es importante para establecer una base para los estudiantes que trabajan en álgebra en el grado 9.

English Description:
In Grades 6 and 7, students worked with data involving a single variable.  Module 6 introduces students to bivariate data.  Students are introduced to a function as a rule that assigns exactly one value to each input.  In this module, students use their understanding of functions to model the possible relationships of bivariate data.  This module is important in setting a foundation for students’ work in algebra in Grade 9.

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

This shows how Newton's method (also known as Newton-Raphson) is used to find a root of a function. You can show/hide various parts of the construction, and edit the particular function being considered.

The following notes and practice problems are ancillary materials for OpenStax Calculus Volume 1. Topics include:

Limit of a Function
Continuity
Derivatives
Differentiation

This supplemental resource provides problems and activities related to Numerical and Algebraic Operations & Analytical Thinking in Middle School Mathematics.

The primary purpose of this task is to illustrate that the domain of a function is a property of the function in a specific context and not a property of the formula that represents the function. Similarly, the range of a function arises from the domain by applying the function rule to the input values in the domain. A second purpose would be to illicit and clarify a common misconception, that the domain and range are properties of the formula that represent a function.

Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.

This collection of worksheets, homework assignments, and study skills exercises was created through a Round 14 Textbook Transformation Grant. The worksheets supplement the following topics as covered in OpenStax Precalculus: Functions, domain and range, rates of change, inverse functions, exponential functions, logarithmic functions, exponential growth modeling, angles, sine and cosine, right triangles, sum identities, and difference identities. Study skills exercises include growth mindset and metacognition activities.

Watch this music video to help you learn about PEMDAS (Please Excuse My Dear Aunt Sally). Does this sound familiar? If not, this is an excellent device to memorize the algebraic order of operations. This video is produced by Mr. Davis Productions and plays music by Odyssey Sound Lab.

This task assumes students have an understanding of the relationship between functions and equations. Using this knowledge, the students are prompted to try to solve equations in order to find the inverse of a function given in equation form: when no such solution is possible, this means that the function does not have an inverse.

The purpose of this task is to investigate the meaning of the definition of function in a real-world context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.

This supplemental resource provides problems and activities related to Patterns, Relationships and Functions in Middle School Mathematics.

This task requires students to use functions to calculate how to best benefit from a pizza promotion.

This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.

During this activity students will learn how to estimate population size using two techniques, density extrapolation and the mark-recapture method.

In this task students construct and compare linear and exponential functions and find where the two functions intersect. One purpose of this task is to demonstrate that exponential functions grow faster than linear functions even if the linear function has a higher initial value and even if we increase the slope of the line. This task could be used as an introduction to this idea.

Students follow the steps of the engineering design process while learning more about assistive devices and biomedical engineering applied to basic structural engineering concepts. Their engineering challenge is to design, build and test small-scale portable wheelchair ramp prototypes for fictional clients. They identify suitable materials and demonstrate two methods of representing design solutions (scale drawings and simple models or classroom prototypes). Students test the ramp prototypes using a weighted bucket; successful prototypes meet all the student-generated design requirements, including support of a predetermined weight.

In this lesson, through various examples and activities, exponential growth and polynomial growth are compared to develop an insight about how quickly the number can grow or decay in exponentials. A basic knowledge of scientific notation, plotting graphs and finding intersection of two functions is assumed.

This OER course using a new textbook is based a section of MAT103 Pre-Calculus. It is a preparatory course for Calculus. It builds upon the intermediate level of Algebra and makes intensive use of technology to conceptualize functions and methods of function manipulation with emphasis on quantitative change. All course content written by Fahmil Shah. Added to OER Commons by Victoria Vidal.

Mathematics is the language of Science, Engineering and Technology. Calculus is an elementary Mathematical course in any Science and Engineering Bachelor. Pre-university Calculus will prepare you for the Introductory Calculus courses by revising four important mathematical subjects that are assumed to be mastered by beginning Bachelor students:

functions,
equations,
differentiation,
integration.

Preuniversity Calculus has been awarded with the Award for Open Education Excellence in the Open MOOC category in 2016.