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.

Reflection #6: Reading Comprehension Strategies

    

    I really agree with a statement from the Daniels and Zemelman chapter, that “if a student can’t read the material, he can’t get anything out of it or get any better at comprehending it” (p. 240).  There are so many reading strategies offered throughout this book, but I believe that this is the most important point.  If a student is struggling to read or comprehend a text, something must change.  The student needs a new opportunity to succeed at reading.  It is important to find the right reading strategy to use with this student, as well as to encourage them to keep making the effort to read or comprehend texts.  Students generally do not all like the same style of literature, so providing students with options of what they want to read can add some self-motivation for students when reading.

 I really enjoyed this week's readings because they offered comprehensive reading strategies that can be applied to any subject area, including mathematics.  The Bean, Baldwin, and Readence chapter mentioned several of these strategies.  I particularly enjoyed the polar opposite strategy because there is no right or wrong answer, as long as students justify their answer.  This seems to fit very well into the new common core state standards, which encourage students to justify their answers.  Although there are usually right and wrong answers in mathematics, I believe that by supporting the reasoning of their solution, students will determine the right answer to a problem.  We are always stressing for our students to be able to explain how they got their solutions. 

Reflection #5: Purposeful Reading Comprehension Strategies

     I was really inspired by the scenario in Tovani's Chapter 5 with Molly and her high school English class.  In this example, teaching the book became more and more difficult for Molly because she was becoming an expert reader.  Tovani explains that "this is a common problem for teachers.  Many of us become experts on our content" (Tovani, p. 54).  I have also noticed this problem when teaching mathematics.  Sometimes the content I am presenting seems so simple; however, I forget that I am teaching students who are seeing the material for the first time.  It is sometimes difficult to put myself in my students' shoes.  The main point from this chapter was that students' should have a clear purpose when reading.  In mathematics, students must also have a clear purpose when reading word problems, or even reading equations to be solved.  Teaching students to identify this purpose can be challenging.  The instructional focus guide helped me see how to plan a lesson involving reading with a clear purpose in mind.  We are actually going to have a day next week dedicating to solely teaching students how to do word problems.  I believe that planning this lesson would be a perfect opportunity to use the instructional focus guide.