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

This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

After watching the video and lecture notes, students are evaluated for their understanding on the concepts with a quiz and activity

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 Remote Learning Plan was created by Jennifer Gier in collaboration with Tyler Cronin and Craig Hicks as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for Grades 7-12 math students. Students will learn to perform compositions of functions algebraically. This Remote Learning Plan addresses the following NDE Standard: 11.2.2m.It is expected that this Remote Learning Plan will take students 90 minutes to complete.Here is the direct link to the Google Slide: https://docs.google.com/presentation/d/1SUxq2GPuTMEjAU54d5_b8NehjR0ArSFAP6MV119p2OU/edit?usp=sharing 

Learn how to graph the inverse of a series of discrete and continuous. Also learn how to determine whether the inverse of a function is also a function.

The point of the lesson is for students to be able to distinguish between situations that can be modeled with linear functions and with exponential functions. • Prove that linear functions grow by equal differences over equal intervals, and exponential functions grow by equal factors over equal intervals. • Recognize linear situations. • Recognize exponential situations.

In this seminar you will learn how to identify, simplify and solve rational equations and functions.  You will understand how to use rational equations to solve real-world problems.StandardsCCSI: HS: Algebra: HSA-SSE.A. Interpret the structure of expressions.CCSI: HS: Algebra: HSA-SSE.B. Write expressions in equivalent forms to solve problems.

This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations in order to find the explicit equation of the line through two points (when that line is not vertical).

This problem complements the problem ``Do two points always determine a linear function?''

Modeling, Functions, and Graphs covers the content of a typical college algebra course with an emphasis on functions and modeling; when combined with a trigonometry text or supplement, this text can be used in a precalculus course.

The text employs a variety of applications to motivate mathematical thinking. Each chapter opens with a problem of historical or contemporary significance highlighting the material in the chapter, and includes by an Investigation that previews the skills to be introduced. These Investigations can be used in class as guided explorations or as projects for small groups. We have also provided a set of more challenging Projects at the end of each chapter.

This half-semester course studies basic continuous control theory as well as representation of functions in the complex frequency domain. It covers generalized functions, unit impulse response, and convolution. Also covered are the Laplace transform, system (or transfer) functions, and the pole diagram. Examples from mechanical and electrical engineering are provided.
Go to OCW’s Open Learning Library site for 18.031: System Functions and the Laplace Transform. The site is free to use, just like all OCW sites. You have the option to sign up and enroll in the course if you want to track your progress, or you can view and use all the materials without enrolling.

After watching the video and lecture notes, students are evaluated for their understanding on the concepts with a quiz and activity

This is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral theorem.

A lesson plan outlining the teaching of linear functions at a Grade 8-9 level.

This Remote Learning Plan was created by Elizabeth Hock in collaboration with Craig Hicks and Tyler Cronin as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for 9-12 mathematics students. Students will use technology to graph and describe functions. This Remote Learning Plan addresses the following NDE Standard: MA 11.2.1 Algebraic Relationships: Students will demonstrate, represent, and show relationships with functions. It is expected that this Remote Learning Plan will take students 100 minutes to complete. Here is the direct link to the Google Doc: https://docs.google.com/presentation/d/1DsoE018GEbWmtkv2GaeH6WCvdnx_LpxfQ7t0xxnbBtU/view

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.