Algebra Connections
Beginning Algebra Skills


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Algebra Connections, created by to support a Beginning Algebra class, presents fundamental concepts of algebra and suggests links to review skills.   The ideas ws to give students organized notes and resources to take with them when the took Intermediate Algebra. 

The files posted here are in downloadable, printable, pdf format (created in an older verion of Acrobat that did not supporting hyperlinks) and gif screencaputes for online viewing (again, not supporting hyperlinks). 

Please click  HERE for direct links to the many Web resources are recommended in each issue of Algebra Connections.  To see all of the "newsletters" in sequence, CLICK HERE.

Algebra Connections

Divisibility Rules.  Recognizing when a number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, and 10 without a calculator is important -- it prepares us to work with fractions, common denominators, lowest common multiples, and factoring.  There are patterns in numbers.  (Click HERE for printable, .pdf version)

Main Factors of Factoring.  In many ways, algebra is all about taking numbers and expressions apart and then putting them back together in simpler forms.   Multiplication tells us that 2*3=6.  Factor is the reverse -- 2 factors of 9 are 2 and 3.  (Click HERE for printable, .pdf  version)

Decimals and Percents.  These math skills are critical to student success in most ALL academic classes at UW-W.  Our text has a Review Chapter the reinforces these skills, but I wanted to give my students a little bit more.  (Click HERE for printable, .pdf version)

Percents.  Here is a more detailed review of an important concept, percentages.  Rate, base, and percentage are reviewed along with some examples of practical applications.  (Click HERE for printable, .pdf version)

Fractions 101  Working with fractions is an important part of many classes -- it is also the foundation of many algebraic concepts.  Here are the basics.  (Click HERE for printable, .pdf version)

Different Views, Same Concepts:  LCM & LCD.  Sometimes, looking alternative perspectives is the best way to learn,  Here are two ways to look at the same concept -- lowest common multiple and lowest common denominator.  (Click HERE for printable, .pdf version)

Fractions:  Operations  Adding, subtracting, multiplying, and dividing fractions all represent important skills.  Here's a quick review along with more Web resources to review these concepts.  (Click HERE for printable, .pdf version)

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Properties of Real Numbers.  Here is a review of different types of number sets, properties of real numbers, and the order of operations.  Does MS Excel understand the order of operations?  Let's find out!  (Click HERE for printable, .pdf version)

Negative Numbers.  This handout reviews properties of negative numbers and rules of addition, subtraction, multiplication, and division.  There are also some suggested Websites for additional help. (Click HERE for printable, .pdf version)

Simplifying Expressions.  Combining like terms is the basis of much of algebra.  Here is a short review, with examples.  It includes online resources to practice problems, an equation calculator, and a combining like terms calculator.  (Click HERE for printable, .pdf version)

Formulas.  Here are some geometric and other common formulas used to solve a variety of problems.  (Click HERE for printable, .pdf version)

Problem Solving.  Polya's strategy for solving problems is useful in virtually any context.  This handout reviews how we can apply it to typical math and algebra problems.  Many examples of translating words to numbers are presented.  (Click HERE for printable, .pdf version)

Solving Linear Equations in 1 Variable.  This handout reviews the basics of linear equations and the properties of algebra that are used to solve them.  Several online resources are included.  (Click HERE for printable, .pdf version)

Solving Inequalities.  Working with expressions that are greater than, less than, equal to or greater than, or less than or greater than is the foundation of higher-level math courses.  This handout compares and contrasts equations and inequalities and suggests some helpful Web resources.  (Click HERE for printable, .pdf version)

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Exponents.  This handout reviews exponent rules and provides Web resources for students for further study and practice.  (Click HERE for printable, .pdf version)

Scientific Notation.  Once we understand exponents, we should apply that understanding to scientific notation.  This handout reviews that concept and procedures.  Does MS Excel understand Scientific Notation?  Let's find out.  (Click HERE for printable, .pdf version)

Polynomials.  The basics of polynomials and the different types are covered here.  There are many online resources to direct students for additional information, reviews, and interactive tutorials.  (Click HERE for printable, .pdf version)

Multiplying Polynomials.  This handout reviews the basics of multiplying different types of polynomials.  Building and understanding of these concepts provides a solid foundation for much of the rest of this class.  (Click HERE for printable, .pdf version)

Dividing Polynomials.  This is an important unit that ties polynomial basics, working with exponents, and operations with polynomials together.  We start with the simplest case, dividing a polynomial by a monomial -- its really just a review of fractions and simplifying terms.  Then, we look at long division, which sometimes called synthetic division.  (Click HERE for printable, .pdf version)

GCF & Factoring Polynomials.  Anytime we factor an expression, we start by looking for greatest common factors.  Then, we look for ways to rewrite it as a product.  (Click HERE for printable, .pdf version)

Factoring Polynomials.  The reverse of multiplying polynomials is to write them as products, factoring.  This is an important skill, it prepares us for working with quadratics and rational expressions.   (Click HERE for printable, .pdf version)

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Factoring Trinomials in the Form x2+bx+c.  Starting with the simplest case, let's look at the patterns that help us write trinomials as a product.  (Click HERE for printable, .pdf version)

Factoring Trinomials in the Form ax2+bx+c.  Now that we can factor trinomials that have a lead coefficient of 1 (x2+bx+c), lets look at how these patterns help us when working with polynomials with a lead coefficient other than 1.  (Click HERE for printable, .pdf version)

Solving Quadratic Equations by Factoring.  In many ways, everything we have done up to this point is to prepare us to look at mathematical expression of relationships.  Quadratic equations can be used to model many "real-word" problems.  Let's look at one way to solve quadratic equations.  (Click HERE for printable, .pdf version)

Rational Expressions.  If we understand polynomials, rational expressions are not really new.  A rational number is one that can be written as a quotient.  Rational expressions are quotients of polynomials.  (Click HERE for printable, .pdf version)

Multiplying & Dividing Rational Expressions.   Here is where we start to tie everything together -- factoring the numerators and denominators (polynomials) of rational expressions allows us to cancel common factors, just like when we are working with simple fractions.  (Click HERE for printable, .pdf version)

Adding & Subtracting Rational Expressions.  This is really a review of LCD, factoring polynomials, and canceling common factors.  Students that master this unit are well on their way for success in Algebra 41 and any other higher-level math class they choose to take.  (Click HERE for printable, .pdf version)

Graphing.  Here is a simple review of rectangular coordinate systems and graphing linear equations.  (Click HERE for printable, .pdf version)

Lines, Equations, and Inequalities.  Many believe that modeling and predicting with functions is the single most important concept in mathematics.  This edition of Algebra Connections reviews graphing and working with linear equations and inequalities.  (Click HERE for printable, .pdf version)

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Skill Building Links

These are the Web sites that Algebra Connections directs readers to for further study, practice, and information.  Topics include: 

bulletMain Factors of Factoring
bulletDecimals & Percents
bulletWorking With Fractions
bulletProperties of Real Numbers
bulletNegative Numbers
bulletCombining Like Terms & Simplifying Expressions
bulletProblem Solving & Story Problems
bulletLinear Equalities in 1 Variable
bulletLinear Inequalities
bulletScientific Notation
bulletAdding & Subtracting Polynomials
bulletMultiplying & Dividing Polynomials
bulletFactoring Polynomials
bulletFactoring Trinomials
bulletSolving Quadratic Equations by Factoring
bulletRational Expressions
bulletMultiplying & Dividing Rational Expression
bulletAdding & Subtracting Rational Expressions
bulletGraphing Linear Equations & Inequalities

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Skill Review Certificates

The "achievement awards" review fundamental algebra skills in a bright and visual way.  The make good "reference tools" when doing homework or studying.  Some tell me they can visualize theses colorful handouts when they take quizzes and tests.  These printable, downloadable files are all .pdf's -- you will need Acrobat Reader to view them.

Exponent Expert.  Working with exponents is a fundamental skill.  Let's make sure we all feel comfortable, confident, and can accurately work with them. 

Polynomial Ph.D.  The sum of terms raised to exponents are important "building blocks" to many algebraic concepts.  Let's review the basics.

Strategic Factorer.  When we work with numbers and fractions, factoring is a key skill.  It is also the key to working with polynomials.

Really Good at Rational Expressions.  When we write fractions that contain polynomials in the numerator and denominator, they are called rational expressions.  Here's a simple review.

Fully Competent:  Complex Fractions.  Not all fractions have simple numerators and denominators.  When we have fractions made up of fractions, they are called complex fractions.  Sound complex?  Don't worry, here are some suggestions to make them easy to work with.  

Linear Equations.  Let's look at how we can model and predict with mathematical statements and draw those statements as graphs.

Systems of Linear Equations.  Many phenomena can be models with linear equations.  A system of equations contains more than 1; a solution to the system has to also be a solution to each equation.  Let's review how it works. 

Rockin' at Radicals.   Let's review how to work with radicals and roots.  

Quintessential Quadratics.  Obviously, we cannot represent everything with a linear equations, equations without variables.  Quadratic equations are important forms that are used to model many situations. 

Parabolas.  Often we have to write equations for lines that curve.  The graph of a quadratic equation is a special type of curved line called a parabola.  These equations have exponents, hence the curve.  Let's look at how this works using quadratic equations.

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