This week we will examine the concept of a function, a fundamental concept underlying all of modern mathematics. You’re undoubtedly already familiar with functions in an intuitive sense: a function is something which, given

an input, produces an output. But you’ve probably never seen the formal definition of a function as it relates to set theory, which is what we’ll look at this week.

# 259 Results

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 aspects of the task and its potential use.

- Subject:
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 08/06/2015

8th Grade Regular Math: Course Scope & Sequence.

- Subject:
- Mathematics
- Material Type:
- Full Course
- Provider:
- Liberty Public Schools
- Date Added:
- 08/15/2017

APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- APEX: Affordable Print and Electronic TeXtbooks
- Author:
- Brian Heinold
- Dimplekumar Chalishajar
- Gregory Hartman
- Troy Siemers
- Date Added:
- 01/01/2014

The problem presents a context where a quadratic function arises. Careful analysis, including graphing, of the function is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 05/01/2012

The problem statement describes a changing algae population as reported by the Maryland Department of Natural Resources. In part (a), students are expected to build an exponential function modeling algae concentration from the description given of the relationship between concentrations in cells/ml and days of rapid growth (F-LE.2).

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 05/01/2012

A work in progress, CK-12's Algebra I Second Edition is a clear presentation of algebra for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations.

- Subject:
- Algebra
- Functions
- Material Type:
- Textbook
- Provider:
- CK-12 Foundation
- Provider Set:
- CK-12 FlexBook
- Author:
- Andrew
- Annamaria
- Anne
- Eve
- Farbizio
- Gloag
- Rawley
- Date Added:
- 12/03/2010

CK-12 Foundation's Basic Algebra FlexBook is an introduction to the algebraic topics of functions, equations, and graphs for middle-school and high-school students.

- Subject:
- Algebra
- Functions
- Material Type:
- Textbook
- Provider:
- CK-12 Foundation
- Provider Set:
- CK-12 FlexBook
- Author:
- Farbizio, Annamaria
- Gloag, Andrew
- Gloag, Anne
- Kramer, Melissa
- Date Added:
- 09/21/2010

CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.

- Subject:
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Lesson Plan
- Textbook
- Provider:
- CK-12 Foundation
- Provider Set:
- CK-12 FlexBook
- Author:
- Mary Cavanagh, Carol Findell, Carole Greenes
- Date Added:
- 10/04/2011

Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers. This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions. Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra. Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.

- Subject:
- Algebra
- Material Type:
- Module
- Provider:
- New York State Education Department
- Provider Set:
- EngageNY
- Date Added:
- 05/14/2013

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.

- Subject:
- Algebra
- Material Type:
- Module
- Provider:
- New York State Education Department
- Provider Set:
- EngageNY
- Date Added:
- 09/16/2014

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.

- Subject:
- Algebra
- Material Type:
- Module
- Provider:
- New York State Education Department
- Provider Set:
- EngageNY
- Date Added:
- 09/17/2013

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.

- Subject:
- Algebra
- Material Type:
- Module
- Provider:
- New York State Education Department
- Provider Set:
- EngageNY
- Date Added:
- 09/17/2013

Students compare real-time Earth and Mars measurements for temperature, wind speed, humidity and atmospheric pressure by accessing Internet-data resources from NASA.

- Subject:
- Physical Science
- Astronomy
- Material Type:
- Activity/Lab
- Assessment
- Lesson Plan
- Provider:
- Montana State University
- Provider Set:
- NASA/MSU Center for Educational Resources (CERES)
- Date Added:
- 02/16/2011

In this video segment from Cyberchase, Matt tries for a second time to arrange tables and chairs to accommodate 20 workers.

- Subject:
- Mathematics
- Algebra
- Functions
- Material Type:
- Lecture
- Provider:
- PBS LearningMedia
- Provider Set:
- PBS Learning Media: Multimedia Resources for the Classroom and Professional Development
- Author:
- U.S. Department of Education
- WNET
- Date Added:
- 09/23/2008

Students learn more about assistive devices, specifically biomedical engineering applied to computer engineering concepts, with an engineering challenge to create an automatic floor cleaner computer program. Following the steps of the design process, they design computer programs and test them by programming a simulated robot vacuum cleaner (a LEGO® robot) to move in designated patterns. Successful programs meet all the design requirements.

- Subject:
- Engineering
- Health, Medicine and Nursing
- Material Type:
- Activity/Lab
- Provider:
- TeachEngineering
- Provider Set:
- TeachEngineering
- Author:
- Jared R. Quinn
- Kristen Billiar
- Terri Camesano
- Date Added:
- 09/18/2014

In this real world problem students solve questions based on the relationship between production costs and price.

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 05/01/2012

This task provides a real world context for interpreting and solving exponential equations. There are two solutions provided for part (a). The first solution demonstrates how to deduce the conclusion by thinking in terms of the functions and their rates of change. The second approach illustrates a rigorous algebraic demonstration that the two populations can never be equal.

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 05/01/2012

This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 05/01/2012

This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 05/01/2012

This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 05/01/2012

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 05/01/2012

This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.

- Subject:
- Functions
- Material Type:
- Textbook
- Provider:
- Virginia Commonwealth University
- Author:
- Richard Hammack
- Date Added:
- 01/01/2009

This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

- Subject:
- Mathematics
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 05/01/2012

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

- Subject:
- Mathematics
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 08/20/2012

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.

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 08/15/2012

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

- Subject:
- Mathematics
- Functions
- Material Type:
- Activity/Lab
- Provider:
- Illustrative Mathematics
- Provider Set:
- Illustrative Mathematics
- Author:
- Illustrative Mathematics
- Date Added:
- 08/26/2013

This course provides an introduction to applied concepts in Calculus that are relevant to the managerial, life, and social sciences. Students should have a firm grasp of the concept of functions to succeed in this course. Topics covered include derivatives of basic functions and how they can be used to optimize quantities such as profit and revenues, as well as integrals of basic functions and how they can be used to describe the total change in a quantity over time.

- Subject:
- Calculus
- Material Type:
- Full Course
- Textbook
- Provider:
- Lumen Learning
- Provider Set:
- Candela Courseware
- Date Added:
- 03/31/2016

Full course of Algebra 1 is presented online by Georgia Virtual Learning. Audio, video, text, games and activities are included to engage ninth grade students in learning.

- Subject:
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Full Course
- Reading
- Provider:
- Georgia Department of Education
- Provider Set:
- Georgia Virtual Learning
- Date Added:
- 08/02/2013

The student will learn the mechanics of editing and compiling a simple program written in C++ beginning with a discussion of the essential elements of C++ programming: variables, loops, expressions, functions, and string class. Next, the student will cover the basics of object-oriented programming: classes, inheritance, templates, exceptions, and file manipulation. The student will then review function and class templates and the classes that perform output and input of characters to/from files. This course will also cover the topics of namespaces, exception handling, and preprocessor directives. In the last part of the course, the student will learn some slightly more sophisticated programming techniques that deal with data structures such as linked lists and binary trees. Upon successful completion of this course, students will be able to: Compile and execute code written in C++ language; Work with the elementary data types and conditional and iteration structures; Define and use functions, pointers, arrays, struct, unions, and enumerations; Write C++ using principles of object-oriented programming; Write templates and manipulate the files; Code and use namespaces, exceptions, and preprocessor instructions; Write a code that represents linked lists and binary trees; Translate simple word problems into C++ language. (Computer Science 107)

- Subject:
- Computer Science
- Material Type:
- Full Course
- Provider:
- The Saylor Foundation
- Date Added:
- 11/16/2011

One of the most magnificent structures in the computer science world is the function. Functions (sometimes called procedures) are mini programs that you can use over and over inside of your bigger program. This lesson will help students intuitively understand why combining chunks of code into functions can be such a helpful practice.

- Subject:
- Computer Science
- Material Type:
- Lesson Plan
- Provider:
- Code.org
- Provider Set:
- CS Fundamentals 2019-2020
- Date Added:
- 09/10/2019

Students will begin to understand how functions can be helpful in this fun and interactive Minecraft adventure!

- Subject:
- Computer Science
- Material Type:
- Lesson Plan
- Provider:
- Code.org
- Provider Set:
- CS Fundamentals 2019-2020
- Date Added:
- 09/10/2019

Students have practiced creating impressive designs in Artist and navigating mazes in Bee, but today they will use functions to harvest crops in Harvester. This lesson will push students to use functions in the new ways by combining them with `while` loops and `if / else` statements.

- Subject:
- Computer Science
- Material Type:
- Lesson Plan
- Provider:
- Code.org
- Provider Set:
- CS Fundamentals 2019-2020
- Date Added:
- 09/10/2019

Students will be introduced to using functions with the Artist. Magnificent images will be created and modified. For more complicated patterns, students will learn about nesting functions by calling one function from inside another.

- Subject:
- Computer Science
- Material Type:
- Lesson Plan
- Provider:
- Code.org
- Provider Set:
- CS Fundamentals 2019-2020
- Date Added:
- 09/10/2019

Students will begin to understand how functions can be helpful in this fun and interactive Minecraft adventure!

- Subject:
- Computer Science
- Material Type:
- Lesson Plan
- Provider:
- Code.org
- Provider Set:
- CS Fundamentals 2019-2020
- Date Added:
- 09/10/2019

Students have practiced creating impressive designs in Artist and navigating mazes in Bee, but today they will use functions to harvest crops in Harvester. This lesson will push students to use functions in the new ways by combining them with `while` loops and `if / else` statements.

- Subject:
- Computer Science
- Material Type:
- Lesson Plan
- Provider:
- Code.org
- Provider Set:
- CS Fundamentals 2019-2020
- Date Added:
- 09/10/2019

Students will be introduced to using functions on Code.org. Magnificent images will be created and modified with functions in Artist. For more complicated patterns, students will learn about nesting functions by calling one function from inside another.

- Subject:
- Computer Science
- Material Type:
- Lesson Plan
- Provider:
- Code.org
- Provider Set:
- CS Fundamentals 2019-2020
- Date Added:
- 09/10/2019

This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

- Subject:
- Health, Medicine and Nursing
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Lesson Plan
- Provider:
- National Association of State Directors of Career Technical Education Consortium
- Provider Set:
- Career Technical Education
- Date Added:
- 07/27/2012

This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

- Subject:
- Health, Medicine and Nursing
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Lesson Plan
- Provider:
- National Association of State Directors of Career Technical Education Consortium
- Provider Set:
- Career Technical Education
- Date Added:
- 07/26/2012

The CUNY HSE Curriculum Framework provides direction, structure and materials for teaching math, science and social studies (integrated with reading and writing) in the new era of HSE instruction. The complete framework is available for free download.

The framework was written by the CUNY Adult Literacy PD Team to respond to the challenges facing high school equivalency (HSE) teachers and their students. It is a guide for planning your instruction – including topic recommendations, model lessons, guiding questions, readings, and problems. The framework prioritizes depth over breadth. It does not address all of the content that might potentially be included on an HSE exam, but instead models a focused and coherent study of high priority topics within each content area.

As teachers in adult literacy and HSE education, our work has always been demanding. Now that our students face a new and more challenging HSE test, the demands on teachers are even greater. Teaching students to read, write and do math at the HSE level is no longer enough. Students need specific, deep and coherent content knowledge, as well as the capacity to apply this content knowledge to analysis and problem solving.

As the demands on our students and teachers are increasing, it is important that we don’t lose sight of one of our greatest strengths — our practice of starting from where students are and our serious respect for their learning processes. As a student of ours once said, “You can’t make a plant grow by pulling on it, you only make it rootless.”

The Social Studies section integrates reading and writing through a focus on U.S. history, with extensions to civics, economics and geography. This section has a curriculum map, 12 unit descriptions, six model lesson plans and additional resources.

The Science section provides an introduction to matter and basic chemistry with extensions to science/math connections. This section includes a curriculum map with 23 topic descriptions and key questions, and three complete inquiry-based model lesson plans.

The Math section focuses on problem-solving in functions and algebra. It integrates problem-solving strategies, productive struggle, perseverance and mathematical discussion into content learning. This section includes a curriculum map, model lessons, rich engaging math problems, samples of student work, powerful routines for math classrooms, classroom videos, and more.

- Subject:
- U.S. History
- Mathematics
- Physical Science
- Material Type:
- Activity/Lab
- Assessment
- Lesson Plan
- Primary Source
- Reading
- Teaching/Learning Strategy
- Provider:
- City University of New York
- Author:
- Eric Appleton
- Kate Brandt
- Mark Trushkowsky
- Rebecca Leece
- Tyler Holzer
- Date Added:
- 08/21/2017