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#2: Functions and Relations
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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.

Subject:
Functions
Mathematics
Material Type:
Reading
Author:
Brent Yorgey
Date Added:
10/14/2020
8.F  Introducing Functions
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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
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/06/2015
A-Rei Springboard Dive
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CC BY
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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:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Algae Blooms
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CC BY
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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:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Algebra - Basic (Student's Edition)
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CC BY-NC-SA
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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
Mathematics
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
Arrangement 2
Read the Fine Print
Educational Use
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In this video segment from Cyberchase, Matt tries for a second time to arrange tables and chairs to accommodate 20 workers.

Subject:
Algebra
Functions
Mathematics
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
Bacteria Populations
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CC BY
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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:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Baseball Cards
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CC BY
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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:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Basketball Rebounds
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CC BY
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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:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Battery Charging
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CC BY
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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:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Bike Race
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CC BY
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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:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Book of Proof
Only Sharing Permitted
CC BY-ND
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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
Mathematics
Material Type:
Textbook
Provider:
Virginia Commonwealth University
Author:
Richard Hammack
Date Added:
01/01/2009
Braking Distance
Unrestricted Use
CC BY
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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:
Algebra
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
CCGPS Algebra 1
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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
Mathematics
Material Type:
Activity/Lab
Full Course
Reading
Provider:
Georgia Department of Education
Provider Set:
Georgia Virtual Learning
Date Added:
08/02/2013
CTE Health Sciences: Medication Dosage
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CC BY-NC-SA
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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:
Algebra
Applied Science
Functions
Health, Medicine and Nursing
Mathematics
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
CTE Health Sciences: Spread of Disease
Conditional Remix & Share Permitted
CC BY-NC-SA
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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:
Algebra
Applied Science
Functions
Health, Medicine and Nursing
Mathematics
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