# Algebra for Calculus: A Guided Inquiry

**Author(s):**
The POGIL Project
,
Catherine
Bénéteau
,
Zdenka
Guadarrama
,
Jill
E. Guerra
,
Laurie
Lenz
,
Andrei
Straumanis

**Edition:
**
1

**Copyright:
**
2022

**Pages:
**
242

**Edition:
**
1

**Copyright:
**
2022

**Pages:
**
244

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These guided activities were written because much research has shown that more learning takes place when the student is actively engaged and when ideas and concepts are developed by the student, rather than being presented by an *authority* - a textbook or an instructor. The activities presented are structured so that information is presented to the reader in some form (and equation, table, graph, figure, written prose, etc.) followed by a series of *Construct-Your-Understanding Questions *that lead the student to the development of a particular concept or idea. Learning follows the scientific process as much as possible throughout. Students are often asked to construct a concept based on the model that has been developed up to that point, and then further data or information is provided to help refine the concept. In this way, students simultaneously learn course content and key process skills that constitute mathematical and scientific thought and exploration.

**If you are interested in having instructor resources please reach out to ****POGILKHrep@kendallhunt.com****.**

Kendall Hunt is excited to partner with The POGIL Project to publish materials in a variety of disciplines that are designed for use in active learning, student-centered classrooms.

POGIL is an acronym for Process Oriented Guided Inquiry Learning. Because POGIL is a student-centered instructional approach, in a typical POGIL classroom or laboratory, students work in small teams with the instructor acting as a facilitator. The student teams use specially designed activities that generally follow a learning cycle paradigm. These activities are designed to have three key characteristics:

- They are designed for use with self-managed teams that employ the instructor as a facilitator of learning rather than a source of information.
- They guide students through an exploration to construct understanding.
- They use discipline content to facilitate the development of important process skills, including higher-level thinking and the ability to learn and to apply knowledge in new contexts.

For more information, please visit www.pogil.org

**Introduction to Functions**

F1 Introduction to Function sand Function Notation

F2 Graphing of Functions

F3 Combinations of Functions

F4a Vertical and Horizontal Shifts

F4B Stretching and Reflecting

F5 Compositions of Functions

F6 Inverse Functions

**Polynomial Functions**

P1 Linear Functions

P2A Exploring Linear Functions

P2B Finding Equations of Lines

P2C Parallel and Perpendicular Lines

P3 Quadratic Functions

P4A Standard and Vertex Form of a Quadratic Function

P4B Completing the Square

P4C Roots of Quadratic Functions

P5 Monomial Functions

P6 Polynomial Functions

P7 Graphing Polynomial Functions

**Rational Functions**

R1 Rational Functions 1

R2 Rational Functions 2

**Exponential Functions**

E1 Introduction to Exponential Functions

E2 Exponential Functions 2

E3 Graphing Exponential Functions

**Logarithmic Functions**

L1 Logarithmic Functions 1

L2 Logarithmic Functions 2

**Systems of Equations**

S1 Linear Systems

S2 Nonlinear Systems of Equations

**The POGIL Project**

Kendall Hunt is excited to partner with The POGIL Project to publish materials in a variety of disciplines that are designed for use in active learning, student-centered classrooms.

POGIL is an acronym for Process Oriented Guided Inquiry Learning. Because POGIL is a student-centered instructional approach, in a typical POGIL classroom or laboratory, students work in small teams with the instructor acting as a facilitator. The student teams use specially designed activities that generally follow a learning cycle paradigm. These activities are designed to have three key characteristics:

- They are designed for use with self-managed teams that employ the instructor as a facilitator of learning rather than a source of information.
- They guide students through an exploration to construct understanding.
- They use discipline content to facilitate the development of important process skills, including higher-level thinking and the ability to learn and to apply knowledge in new contexts.

For more information, please visit www.pogil.org

**Catherine Bénéteau**

Catherine Bénéteau is an associate professor in mathematics and statistics at the University of South Florida. She was educated in Canada at McGill University where she earned her bachelor's and master's degrees in mathematics. She obtained her Ph.D. in 1999 at the University at Albany, under the supervision of Boris Korenblum. Her main research interests are in complex function theory and mathematics education.

**Zdenka Guadarrama**

Zdenka Guadarrama is an associate professor and chair of the department of mathematics at Rockhurst University. She is passionate about mathematics education and outreach, with her work currently focusing on mathematics curriculum development through inquiry, and the intersections of mathematics with other fields, particularly the arts.

**Jill E. Guerra**

Jill E. Guerra is a preceptor of mathematics at Harvard University. She earned her B.S. from the University of Buffalo and her Ph.D. from the University of Arkansas.

**Laurie Lenz**

Laurie Lenz is currently a professor of mathematics at Marymount University. She has done research in the field of combinatorial group theory, a blend of group theory and topology. She is currently studying college algebra and calculus reform, the use of technology in the classroom, and research and assessment of teaching methodologies. She earned her B.S., M.A., and Ph.D. from the State University of New York Albany.

**Andrei Straumanis**

Andrei Straumanis has a B.A. in Chemistry from Oberlin College and a Ph.D. in organic chemistry from Stanford University. During a three-year NSF-supported post-doctoral fellowship in SMET education, Dr. Straumanis developed and tested materials for guided inquiry organic chemistry. Since 1997, he has given numerous talks and workshops on active learning in organic chemistry and the use of guided inquiry in large classrooms.

These guided activities were written because much research has shown that more learning takes place when the student is actively engaged and when ideas and concepts are developed by the student, rather than being presented by an *authority* - a textbook or an instructor. The activities presented are structured so that information is presented to the reader in some form (and equation, table, graph, figure, written prose, etc.) followed by a series of *Construct-Your-Understanding Questions *that lead the student to the development of a particular concept or idea. Learning follows the scientific process as much as possible throughout. Students are often asked to construct a concept based on the model that has been developed up to that point, and then further data or information is provided to help refine the concept. In this way, students simultaneously learn course content and key process skills that constitute mathematical and scientific thought and exploration.

**If you are interested in having instructor resources please reach out to ****POGILKHrep@kendallhunt.com****.**

Kendall Hunt is excited to partner with The POGIL Project to publish materials in a variety of disciplines that are designed for use in active learning, student-centered classrooms.

POGIL is an acronym for Process Oriented Guided Inquiry Learning. Because POGIL is a student-centered instructional approach, in a typical POGIL classroom or laboratory, students work in small teams with the instructor acting as a facilitator. The student teams use specially designed activities that generally follow a learning cycle paradigm. These activities are designed to have three key characteristics:

- They are designed for use with self-managed teams that employ the instructor as a facilitator of learning rather than a source of information.
- They guide students through an exploration to construct understanding.
- They use discipline content to facilitate the development of important process skills, including higher-level thinking and the ability to learn and to apply knowledge in new contexts.

For more information, please visit www.pogil.org

**Introduction to Functions**

F1 Introduction to Function sand Function Notation

F2 Graphing of Functions

F3 Combinations of Functions

F4a Vertical and Horizontal Shifts

F4B Stretching and Reflecting

F5 Compositions of Functions

F6 Inverse Functions

**Polynomial Functions**

P1 Linear Functions

P2A Exploring Linear Functions

P2B Finding Equations of Lines

P2C Parallel and Perpendicular Lines

P3 Quadratic Functions

P4A Standard and Vertex Form of a Quadratic Function

P4B Completing the Square

P4C Roots of Quadratic Functions

P5 Monomial Functions

P6 Polynomial Functions

P7 Graphing Polynomial Functions

**Rational Functions**

R1 Rational Functions 1

R2 Rational Functions 2

**Exponential Functions**

E1 Introduction to Exponential Functions

E2 Exponential Functions 2

E3 Graphing Exponential Functions

**Logarithmic Functions**

L1 Logarithmic Functions 1

L2 Logarithmic Functions 2

**Systems of Equations**

S1 Linear Systems

S2 Nonlinear Systems of Equations

**The POGIL Project**

- They guide students through an exploration to construct understanding.

For more information, please visit www.pogil.org

**Catherine Bénéteau**

Catherine Bénéteau is an associate professor in mathematics and statistics at the University of South Florida. She was educated in Canada at McGill University where she earned her bachelor's and master's degrees in mathematics. She obtained her Ph.D. in 1999 at the University at Albany, under the supervision of Boris Korenblum. Her main research interests are in complex function theory and mathematics education.

**Zdenka Guadarrama**

Zdenka Guadarrama is an associate professor and chair of the department of mathematics at Rockhurst University. She is passionate about mathematics education and outreach, with her work currently focusing on mathematics curriculum development through inquiry, and the intersections of mathematics with other fields, particularly the arts.

**Jill E. Guerra**

Jill E. Guerra is a preceptor of mathematics at Harvard University. She earned her B.S. from the University of Buffalo and her Ph.D. from the University of Arkansas.

**Laurie Lenz**

Laurie Lenz is currently a professor of mathematics at Marymount University. She has done research in the field of combinatorial group theory, a blend of group theory and topology. She is currently studying college algebra and calculus reform, the use of technology in the classroom, and research and assessment of teaching methodologies. She earned her B.S., M.A., and Ph.D. from the State University of New York Albany.

**Andrei Straumanis**

Andrei Straumanis has a B.A. in Chemistry from Oberlin College and a Ph.D. in organic chemistry from Stanford University. During a three-year NSF-supported post-doctoral fellowship in SMET education, Dr. Straumanis developed and tested materials for guided inquiry organic chemistry. Since 1997, he has given numerous talks and workshops on active learning in organic chemistry and the use of guided inquiry in large classrooms.