Text Set Collection #2: General Resources for Working with Polynomials

 General Resources for Working with Polynomials

Books

CK-12 Algebra I, Second Edition, Volume 2 of 2

CK-12 Foundation (Author)

Age: 9th grade & up

CK-12's Algebra I Second Edition is a clear presentation of algebra for the high school student.  Volume 2 covers everything from Solving Systems of Equations to Geometry Connections.  I chose this text book because it gives easy to follow instructions and support to high school students on the topic of simplifying or solving polynomials.

Shortcut Algebra I: A Quick and Easy Way to Increase your Algebra I 

Knowledge and Test Scores

Andrew Marx (Co-Author), Kaplan (Co-Author)

Age: 9th grade & up

Shortcut Algebra I contains coverage and review for algebra concepts, as well as strategies that students can use to apply to their homework and tests.  I chose this book because it is a great resource to help students in Algebra I, especially when it comes to sometimes challenging topics such as solving polynomial equations.

Beginning Algebra

Roy David Gustafson (Co-Author), Peter D. Frisk (Co-Author)

Ages: 8th grade & up

Beginning Algebra is a textbook that is unparalleled in its ability to engage students in mathematics and prepare them for higher-level courses.  This book covers essential Algebra I topics such as solving polynomial equations.  I chose this book because it is easy to understand and is filled with relevant applications to help engage students in algebra.

Algebra I is Easy! So Easy

Nathaniel Max Rock (Author)

Ages: 8th grade & up

Algebra I is Easy! So Easy, is a resources that takes readers through each of the Algebra I standards so that they learn what is required to master Algebra.  I particularly like this resource because it offers several problems on polynomials-an essential topic in Algebra I.  This resource gives teachers resources to differentiate instruction on a unit on polynomials, as well as giving students extra problems to practice solving polynomials.

Algebra for College Students

Peter D. Frisk

Ages: College

Algebra for College Students provides clear, no-nonsense explanations that will help students learn difficult concepts with ease. This is a great resource on polynomials for advanced high school students or college algebra students.  I chose this book as a resource for high school teachers to use for differentiating instruction with advanced algebra students.  Having higher-level students work form this book can provide these students with the challenge they need, while the rest of the class focuses on the regular classroom text.

Websites

• Multiplying Polynomials

http://www.purplemath.com/modules/polymult.htm

Age: 8th grade & up

This website walks students through the step-by-step process of multiplying polynomials, a topic covered in Algebra I.  I chose this website because it is a great resource for students to use to learn the process of multiplying polynomials.

• Multiplying and Dividing Polynomials

http://www.mathplanet.com/education/algebra-2/polynomials-and-radical-expressions/polynomials

Age: 8th grade & up

This is a great resource for helping students learn to multiply and divide polynomials.  This website not only shows an example of both multiplying and dividing polynomials, but also includes a short video explaining how this process works.

• Substituting Numbers into Polynomials

http://www.coolmath.com/crunchers/algebra-problems-polynomials-substituting.htm

Age: 8th grade & up

This is a great resource for students learning how to substitute numbers into polynomials.  This website walks students through step-by-step examples of how to solve systems of equations in this way, as well as allowing students to practice solving these systems of equations on their own.

• Adding and Subtracting Polynomials

http://www.brightstorm.com/math/algebra/polynomials-2/adding-and-subtracting-polynomials/

Age: 8th grade & up

This website includes a short video explaining how to add or subtract polynomials.  I especially liked this resource because it explains to students the concept of combining like terms to simplify your final answer.  This is an important factor to keep in mind when adding or subtracting polynomials.

• Simplifying Polynomials

https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/polynomial_basics/v/simply-a-polynomial

Age: 8th grade & up

This video walks students through the step-by-step process of simplifying polynomials.  I specifically chose this website because I have used KhanAcademy before and I know first-hand that this is a great resource for students and teachers.  I would recommend this website to my own students struggling with simplifying polynomials.

Applications

• Factor Polynomials

https://itunes.apple.com/us/app/factor-polynomials/id555358722?mt=8

Age: 8th grade & up

The Factor Polynomials application is designed for both the iPhone and iPad and costs $0.99.  I chose this application because it can help students with everything from a binomial to an 8th degree polynomial.  This application solves and factors polynomials, and even gives complex solutions!  It is a great resource for students to use when checking their work.

• Polynomials Math

https://play.google.com/store/apps/details?id=an.Poly

Age: 9th grade & up

Polynomials Math is a free android application that can help students factor, divide, graph, or solve polynomials.  I chose this application because it is a great tool for both high school and college algebra students.  This application can even be used to construct polynomial rings, which is an essential skill in algebraic geometry (college-level mathematics).  

• Polynomial Calculator

https://play.google.com/store/apps/details?id=an.PolynomCalPro&hl=en

Age: 8th grade & up

The Polynomial Calculator is a free android application that allows students to add, subtract, multiply, or divide polynomials.  I chose this application because it is a great resource for algebra students in both high school and college.  This is a great tool for students to use to check their work when working with polynomials.

• Polynomials

https://itunes.apple.com/us/app/polynomials/id513725299?mt=8

Age: 8th grade & up

The Polynomials application is a free iTunes application that is designed to help beginning algebra students learn how to add, subtract, multiply, and divide polynomials.  I chose this application because it includes detailed videos to help explain all the concepts needed to be successful with polynomials for beginning algebra students.  

• Polynomials Even and Odd Functions

https://itunes.apple.com/us/app/polynomials-even-odd-functions/id293668394?mt=8

Age: 10th grade & up

The Polynomials Even and Odd Functions is an iTunes application that costs $0.99.  This is a powerful resource designed to help students determine algebraically whether a polynomial function is even, odd, both, or neither.  I chose this application because determining whether a polynomial function is even, odd, both, or neither is an essential skill in Algebra II.  Students could use this application as a tool to check their solutions to certain problems.

Reflection #10: Technology & Learning

     This weeks readings focused on technology in the classroom.  I really liked the SAND (Search, Analyze, Note Details) strategy mentioned in BBR Chapter 10.  When using the internet for research in the classroom, it is so important that students know the appropriate websites to use.  As this chapter explains, "the potential for students to retrieve and believe misinformation on the Internet is high" (Bean, Baldwin & Readence, 2012, p. 181).  I can still remember being taught to check the credibility of a website when I was in high school.  This is an important skill that I now take for granted.  I am not sure if I will ever need to teach my students this skill, as a mathematics teacher; but I will be prepared to teach students how to find the right websites if the situation arises.
     I also found the Bauerlein & Howe program, "The Millennials: The Dumbest Generation or the Next Great Generation" to be intriguing.  Although this generation is very tech savvy, they do not seem to know as much without this technology.  I know working with my own Algebra I students, they are completely dependent on their calculators.  Anything the calculator says has got to be the correct answer, in my students' opinions.  They do not stop to think about whether or not their answer makes sense.  I know when I was in school, we had to memorize all of our basic arithmetic.   I do not believe students are held to this standard today.  In fact, I recently had a student need to use a calculator to do 10-10.  That completely blew my mind.  Technology is great but the human brain is the most valuable tool.  After watching this video and hearing both sides, I am still not very optimistic about our next generation.  Being an educator, I hate to say that I am not optimistic about this generation.  This is just based on my own experience with these kids.

Web Resource Review #2: Algebra vs. the Cockroaches

For my second web resource review, I would like to mention the site for the game Algebra vs. the Cockroaches.  This is a wonderful resource for Algebra I teachers.  I recently played this game with my classes and it was a huge success.  The game starts with one roach running along a line on the coordinate plane.  The object of the game is to kill the roach(es) by identifying the equation of the line that the roach(es) are running along.  As time goes by, the roaches multiply (all running along the same line).  If you get more than 15 roaches on the line, the game is over and the cockroaches win.  I played this game with high school freshman.  At first they thought that the game was lame and cheesy.  However, by the end of the game, they were really into it and wanted to play again.  I would highly recommend this site to any Algebra I teacher.  It assesses the skills of identifying the slope from a graph, identifying the y-intercept from a graph, and writing an equation in slope-intercept form.  These are all essential skills of Algebra I.  This is also a game that students can play at home, on their own, to practice these skills.

Reflection #9: Motivating Students to Read

     The Pitcher et al. article discussed the challenge of motivating young adolescents to read.  Adolescents can sometimes have the perception that reading is something that is primarily done in the classroom.  However, reading is a skill that most adults use every day, whether we realize it or not.   Reading has become a skill that is too often taken for granted.  I liked the questions that were asked in this study.  These questions helped students recognize that they actually are reading even when they are simply surfing the web or texting a friend.

     In addition, this article mentions the role that technology plays in students’ daily lives and how reading factors into this role.  Today, most students even in the poorest of areas have some access to technology-whether it be a cell phone, television, computer, or iPad.  As teachers, we can motivate students to read through such technologies.  I know in my classroom we currently have a class set of iPads for our students to use.  I have seen firsthand how students can engage in programs on the iPad without even realizing that they are doing math!!  If using technology can engage students in math, I fully believe that it can do the same for reading.

Text Set Collection #1: General Resources for Solving Systems of Equations

General Resources for Solving Systems of Equations

Books

Elementary Algebra with Early Systems of Equations

Tom Carson (Co-Author), Ellyn Gillespie (Co-Author)

Age: 9th grade & up

This is a textbook designed to build student confidence and understanding in basic mathematical skills, including solving systems of equations.  I chose this book because I like that the author purposefully uses user-friendly text to help struggling students understand mathematics better.

College Algebra, 7th Edition

Jerome E. Kaufmann (Co-Author), Karen L. Schwitters (Co-Author)

Age: Undergraduate College & up, teachers

This is a great resource on solving systems of equations for advanced high school students or college algebra students.  I chose this book as a resource for high school teachers to use for differentiating instruction.  Having higher-level students work from this book can challenge these students, while the rest of the class focuses on the on-grade-level text.

Intermediate Algebra: Student Support Edition

Ron Larson (Co-Author), Robert P. Hostetler (Co-Author)

Age: 8th grade & up

This book is designed to further the mathematical development of struggling math students.  The process of solving systems of equations is also included in this resource.  I chose this book because I was impressed by the level of support and guidance it provides struggling math students.  

An Introduction to the History of Algebra: Solving Equations from Mesopotamian Times to the Renaissance

Jacques Sesiano (Author)

Age: Teachers

This book explains the history of solving equations from the Mesopotamian times to the Renaissance.  I thought that this would be a great resource for teachers to use when trying to find a hook for the lesson or trying to find a way to make the lesson meaningful to students.

61 Cooperative Learning Activities in Algebra 1

Robert H. Jenkins (Author)

Age: Teachers

Cooperative Learning Activities are always in high demand in mathematics classrooms.  This book contains several cooperative learning activities on Algebra 1 topics, including solving systems of equations.  I chose this book because it is a wonderful resource for teachers to use in the classroom, especially with the new Common Core State Standards.

Websites

• Solving Systems of Equations by Elimination

http://www.purplemath.com/modules/systlin5.htm

Age: Grades 8 & up

This website walks students through the step-by-step process of solving systems of equations by the elimination method.  I chose this website because it is a great resource for students to use and to follow along to solve systems of equations.

• Solving Systems of Equations by Elimination

https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/fast-systems-of-equations/v/solving-systems-of-equations-by-elimination

Age: Grades 8 & up

This video walks students through the step-by-step process of solving systems of linear equations by the elimination method.  I specifically chose this website because I have used khanacademy before and I know first-hand that this is a great resource.  I would recommend this link to my own students struggling with this topic.

• Solving Systems of Equations by Graphing

http://www.mathplanet.com/education/pre-algebra/graphing-and-functions/solve-systems-of-equations-by-graphing

Age: Grades 8 & up

This is a great resource for helping students learn to solve systems of linear equations by graphing.  This website not only shows an example of solving systems of equations by graphing, but also includes a short video explaining how this process works.

• Solving Systems of Equations by Substitution

http://www.brightstorm.com/math/algebra/solving-systems-of-equations/solving-systems-of-equations-using-substitution/

Age: Grades 8 & up

This website includes a short video explaining how to solve systems of equations by using the substitution method.  I especially liked this resource because it explains to students the concept of substitution.  For example, in the video she explains that 4 quarters are equal to 1 dollar.  So you could substitute one for the other and still have the same amount of money.

• Solving Systems of Equations by Substitution

http://www.coolmath.com/algebra/12-2x2-systems-of-equations/02-solving-by-substitution-01.htm

Age: Grades 8 & up

This is a great resource for students learning how to solve systems of equations by the substitution method.  This website walks students through step-by-step examples of how to solve systems of equations in this way, as well as allowing students to practice solving these systems of equations on their own.

Applications

• Linear Equation System Solver

https://play.google.com/store/apps/details?id=an.LinearX&hl=en

Age: Grades 8 & up

This is an Android application for solving systems of linear equations.  For students that have compatible devices, this is a free resource that can calculate and solve systems of linear equations.  This application can work for more than 4 variables and 4 equations.

• Math Helper: Systems of Equations

https://itunes.apple.com/us/app/math-helper-systems-equations/id507309865?mt=8

Age: Grades 8 & up

Math Helper is an iTunes application that can be downloaded for $1.99 to help with solving systems of equations.  Although this application can only be used for up to three equations, it does give complete step-by-step work for the entire solution.

• Equation System Solver

https://play.google.com/store/apps/details?id=com.roaddogs.android.math.equationsystem&hl=en

Age: Grades 8 & up

Equation System Solver is a free Android application that can be used to solve up to 5 linear equations and 1 quadratic equation.  I am very impressed that this application could solve a system of equations that involves a quadratic equation.

• Solving a System of 2 Equations in 2 Unknowns

https://itunes.apple.com/us/app/solving-system-2-equations/id655012614?mt=8

Age: Grades 8 & up

Solving a System of 2 Equations in 2 Unknowns is a free iTunes applications that allows students to practice methods for solving systems of equations.  This is a great resource for kids looking for extra homework or for another way to study for upcoming quizzes and tests.

• Algebra Explained c. 6 Systems of Equations

https://itunes.apple.com/us/app/algebra-explained-c.-6-systems/id584624285?mt=8

Age: Grades 9 & up

Algebra Explained c. 6 Systems of Equations is an iTunes application that costs $3.99.  This application can provide students with videos and step-by-step instructions and examples for solving systems of linear equations.  It is almost like having your own personal algebra tutor at home.  I would recommend this resource to any of my algebra students.

Reflection #8: Vocabulary Instruction Continued...

    This week's readings continued to discuss vocabulary instruction strategies.  The Bromley article was full of strategies for teaching new vocabulary words to students.  I especially liked the example from Table 1 for "The most frequently appearing and most commonly taught prefixes, roots, and suffixes."  I remember using a similar strategy when I took Latin in High School and College, and it was very successful for me.  I believe that something similar could also help my students in mathematics.  For example, the word "binomial" contains the prefix "bi," meaning two, and a binomial has two terms.  Math can be a difficult subject to grasp, but by understanding such key vocabulary, students will have a better shot at being successful in mathematics.  

      The Baumann & Graves article defined several types of academic vocabulary and described strategies for identifying important vocabulary to teach.  My favorite part of this article was the description of the importance of symbols.  Baumann & Graves go on to explain that “mathematics is laden with symbols, which involve another type of academic vocabulary “(p. 11).  Symbols are such a huge part of mathematics.  As a result, it is crucial that students learn the meanings of these symbols, just as they would for key academic vocabulary words.

Reflection #7: Vocabulary Instruction

 

    This week’s readings were on vocabulary knowledge and reading comprehension.  I particularly liked the Tierney & Readance article which mentioned strategies to help students learn vocabulary.  My favorite strategy was Levin’s Keyword Method.  This method is “a mnemonic strategy that helps students to learn new information by associating it with interactive visual images for later recall” (Tierney & Readance, p. 324).  I believe that of all of the strategies mentioned in this article, this would be the best for math students.  Mathematics can be such a vague and abstract subject for students to understand.  However, the Levin’s Keyword Method would allow students to visualize and remember key mathematical vocabulary.  If students can recognize mathematical vocabulary in this way, they will be more likely to succeed in mathematics.  I have noticed in my classroom that most students who struggle with math also struggle with mathematical vocabulary.

     I also really liked the idea of using a personal glossary in the classroom.  Once students learn vocabulary in mathematics, it is essential that they remember that vocabulary for future mathematics lessons.  Math is a subject that builds upon itself and understanding the vocabulary is a crucial part of understanding mathematics.  By keeping a personal glossary, students can refer back to it to remember key vocabulary words and to help students keep track of these vocabulary words.