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