I created my "newsletter" Algebra
Connections to give students
the organized notes that I talk about in class. Click here
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basic math/algebra skills each week - FREE!
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 at 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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About Algebra Connections
I want students to succeed and I
work hard to do what I can to support their studies. I have
created these "newsletters: to review fundamental algebraic
concepts and procedures and to suggest online resources that might be
useful in developing mastery of algebraic skills. Click HERE
to see the comprehensive set of skill
building links that my students use when they want online
help.
At UW-Whitewater, students rent their books from the textbook rental
center (paid for by student fees). While this save students large
amounts of money, it does mean that they are not building collections of
resources to help them in higher level classes. While students do
take their mastery of Beginning Algebra with them to their next math
class, I want to give them a little more.
Students tell me that Algebra Connections provides them with
short, easy-to-read reviews of important concepts. Developmental
Education classes are designed to provide a foundation for higher lever
courses at UW-W. The "core curriculum" of my algebra
class is all here, along with suggestions for online resources that
support each area we have reviewed.
I also give these handouts to students in the summer camps and
college transition programs I work with. Many students learn best
when the "see the bigger picture (global learners). Not only
does Algebra Connections accommodate different learning styles,
but they allow students to get a "head-start" on the course
while developing a better self-understanding of their learning
needs.
Perhaps most import of all, I hope that Algebra Connections
shows students that I care about them and want to see them achieve their
goals at UW-Whitewater.
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