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.

# 213 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

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

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 Common Core Collection
- Teachers' Domain
- Author:
- U.S. Department of Education
- WNET
- Date Added:
- 09/23/2008

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

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