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  • Functions
8.F Introducing Functions
Conditions of Use:
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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
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
02/16/2018
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A-Rei Springboard Dive
Conditions of Use:
No Strings Attached
A-Rei Springboard Dive
Rating

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
MoreLess
Algae Blooms
Conditions of Use:
No Strings Attached
Algae Blooms
Rating

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
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Algebra 1 (2nd Student's Edition)
Conditions of Use:
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Algebra 1 (2nd Student's Edition)
Rating

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
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Algebra 1 Quadratic Functions: Vertex Form
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Algebra 1 Quadratic Functions: Vertex Form
Rating

Understanding characteristics of quadratic functions and connections between various representations, tables, graphs and equations, are developed in this unit. The symmetry of the function values can be found in the table, the graph and the equation. The graphical form shows common characteristics of quadratic functions including maximum or minimum values, symmetric shapes (parabolas), location of the y-intercept, and the ability to determine roots of the function. Quadratic functions can be written in a variety of formats: polynomial form f (x) = ax2 + bx + c, factored form f (x) = a (x -p ) (x - q), and vertex form f (x) = a (x - h) 2 + k. This unit focusses on the vertex form. The impact of changing the parameters a, h, and k will be explored and understood.

Subject:
Mathematics
Functions
Material Type:
Unit of Study
Provider:
Michigan Virtual
Author:
Kathleen Ilaoro
Date Added:
04/17/2017
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Algebra - Basic (Student's Edition)
Conditions of Use:
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Algebra - Basic (Student's Edition)
Rating

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
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Bacteria Populations
Conditions of Use:
No Strings Attached
Bacteria Populations
Rating

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
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Baseball Cards
Conditions of Use:
No Strings Attached
Baseball Cards
Rating

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
MoreLess
Basketball Rebounds
Conditions of Use:
No Strings Attached
Basketball Rebounds
Rating

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
MoreLess
Battery Charging
Conditions of Use:
No Strings Attached
Battery Charging
Rating

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
MoreLess
Bike Race
Conditions of Use:
No Strings Attached
Bike Race
Rating

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
MoreLess
Braking Distance
Conditions of Use:
No Strings Attached
Braking Distance
Rating

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
MoreLess
Building a Quadratic Function From F(X)=X2
Conditions of Use:
No Strings Attached
Building a Quadratic Function From F(X)=X2
Rating

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
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Calculus (Student's Edition)
Conditions of Use:
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Calculus (Student's Edition)
Rating

CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.

Subject:
Calculus
Functions
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Date Added:
10/06/2009
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Calculus - TI Activities (Student's Edition)
Conditions of Use:
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Calculus - TI Activities (Student's Edition)
Rating

CK-12's Texas Instrument Calculus Student Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.

Subject:
Calculus
Functions
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Jordan, Lori
Date Added:
12/15/2010
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Calculus - TI Activities (Teacher's Edition)
Conditions of Use:
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Calculus - TI Activities (Teacher's Edition)
Rating

CK-12's Texas Instruments Calculus Teacher's Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.

Subject:
Calculus
Functions
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Jordan, Lori
Date Added:
12/17/2010
MoreLess