A set of links to Algebra and Trigonometry GeoGebra applets hosted on GeoGebraTube.
How to interpret absolute value notation and solve equations that include absolute values. Examples are linear equations, but the same approach works with non-linear equations.
What are “like terms” in algebra, why can they be combined, and how should they be combined? Both an intuitive and an algebraic approach are described, with examples.
Fractions whose numerator and denominator share a common factor can be simplified. See why this is the case, with multiple examples to demonstrate the process.
Math problems often include negative differences. Familiarity with ways of manipulating them will help to both avoid common errors and recognize equivalent expressions.
Explanation of why a negative sign can be placed, or moved to, in front of a fraction, in front of its numerator, or in front of its denominator, without changing the value of the fraction.
How to recognize, create, and describe a geometric sequence (also called a geometric progression) using closed and recursive definitions. Formulas for calculating the Nth term, the sum of the first N terms, and the sum of an infinite number of terms are derived. Also describes approaches to solving problems based on Geometric Sequences and Series.
How to recognize, create, and describe an arithmetic sequence (also called an arithmetic progression) using closed and recursive definitions. Formulas for calculating the Nth term, and the sum of the first N terms are derived. Also describes approaches to solving problems based on arithmetic sequences and series.
Introduction to definitions that are a combination of various functions or relations, each over a specific domain. Such definitions are called piecewise functions or relations. Shows how a piecewise definition can define a “smiley face” .
A system of linear equations consists of multiple linear equations. You can think of this as multiple lines graphed on one coordinate plane. Three situations can arise when looking at such a graph. Either:1) No point(s) are shared by all lines shown2) There is one point that all lines cross through3) The lines lie on top…… Continue reading Linear Systems: Why Does Linear Combination Work (Graphically)?
I have started a separate blog devoted to helping students learn to find mistakes in worked problems (their own, or someone else’s). If this is of interest, check it out: http://mathmistakes.wordpress.com/ 7/17/11 Update: There can be great value in work that contains mistakes. Learning to catch your own mistakes is a critical life skill, as is…… Continue reading Where’s the mistake?
This post begins a series intended to help introduce or re-introduce some of the core concepts of Algebra. It is often very helpful to re-visit these concepts with students who may have memorized their way through previous math courses without slowing down to contemplate some of the concepts behind Algebra. Numbers Numbers are used in…… Continue reading Algebra Intro 1: Numbers and Variables
Mathematical thinking probably started with addition. Someone may have combined two piles of bricks, and wondered how many were in the single large pile. Addition is the mathematical term that describes “joining quantities together”. Properties of Addition Looking at the patterns that can occur when quantities are joined together, you might have noticed that it does…… Continue reading Algebra Intro 2: Addition
Once addition has been explored a bit, it leads pretty naturally to a new question: if there are three bricks in a pile, how many bricks do I need to add to it so that there will be five in the pile? Our addition problems were all phrased using a pattern like number + number…… Continue reading Algebra Intro 3: Subtraction
Negative Numbers Negative numbers are something new and interesting to think about. What do they mean? They arose from changing the order in which we subtracted two numbers. While we usually think of a “difference” by starting our thought process with the larger number, when we fail to do that and try to “take away”…… Continue reading Algebra Intro 4: Negative Numbers, Zero, Absolute Values, and Opposites